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<!DOCTYPE html> <html xmlns:mml=http://www.w3.org/1998/Math/MathML style lang=en><!--
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url: https://www.degruyter.com/document/doi/10.1515/phys-2023-0110/html
saved date: Mon Jun 10 2024 00:31:19 GMT-0400 (EDT)
--><meta charset=utf-8>
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<title>The reciprocal linear effect, a new optical effect of the Sagnac type</title>
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)format("woff2")}@media 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<meta name=description content="The Sagnac effect can be demonstrated with light propagating either along a circular contour or, as done by Wang et al ., back and forth along a linear contour. In the linear Sagnac effect, the emitter–receiver device is in motion relative to the contour where light propagates. In the reciprocal linear Sagnac effect (RLSE), the device is stationary and the contour is in motion. When the contour changes direction of motion, some special features of the linear Sagnac effect are not fully reciprocal to the RLSE, which foresees variations of the first order in v ⁄ c v/c in the round-trip time taken by a light signal to cover the contour. The RLSE can be tested with present technology and, if confirmed experimentally, it might have interesting technological applications. Presently, it can be important for testing light-speed invariance, simultaneity, and the relativity principle.">
<meta property=og:url content=https://www.degruyter.com/document/doi/10.1515/phys-2023-0110/html><meta property=og:site_name content="De Gruyter"><meta property=og:title content="The reciprocal linear effect, a new optical effect of the Sagnac type"><meta property=og:type content=article><meta property=og:locale content=en><meta property=og:image content=https://www.degruyter.com/document/cover/journal_key/PHYS/product><meta property=og:image:type content=image/jpeg><meta property=og:description content="The Sagnac effect can be demonstrated with light propagating either along a circular contour or, as done by Wang et al ., back and forth along a linear contour. In the linear Sagnac effect, the emitter–receiver device is in motion relative to the contour where light propagates. In the reciprocal linear Sagnac effect (RLSE), the device is stationary and the contour is in motion. When the contour changes direction of motion, some special features of the linear Sagnac effect are not fully reciprocal to the RLSE, which foresees variations of the first order in v ⁄ c v/c in the round-trip time taken by a light signal to cover the contour. The RLSE can be tested with present technology and, if confirmed experimentally, it might have interesting technological applications. Presently, it can be important for testing light-speed invariance, simultaneity, and the relativity principle."><meta property=og:locale:alternate content=de><meta property=article:author content="Gianfranco Spavieri"><meta property=article:author content="Espen Gaarder Haug"><meta property=article:tag content="light propagation"><meta property=article:tag content="Sagnac effect"><meta property=article:tag content="one-way speed of light"><meta property=article:tag content="relative simultaneity"><meta property=article:tag content="Lorentz invariance"><meta property=article:published_time content=2023-01-01><meta property=article:section content="Open Physics">
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<script type=application/ld+json>{"author":[{"@type":"Person","name":"Gianfranco Spavieri"},{"@type":"Person","name":"Espen Gaarder Haug"}],"editor":[],"audience":null,"datePublished":"2023-01-01","headline":"","keywords":"keyword,keyword,keyword,keyword,keyword","isAccessibleForFree":true,"publisher":{"@type":"Organization","name":"De Gruyter Open Access"},"@context":"https://schema.org","@type":"Article","name":"The reciprocal linear effect, a new optical effect of the Sagnac type","image":"https://www.degruyter.com/document/cover/journal_key/PHYS/thumbnail","url":"https://doi.org/10.1515/phys-2023-0110"}</script>
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<h1>The reciprocal linear effect, a new optical effect of the Sagnac type</h1>
<ul class="contributors list-unstyled mb-2">
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<span class=metadataAndContributorsFont><span class=contributor>
<span class="displayName linkAnimation">Gianfranco Spavieri</span>
<contributor-popdown name="Gianfranco Spavieri" position=1 email affiliations="Centro de Fiiisica Fundamental, Universidad de Los Andes, Mérida, 5101, Venezuela" class=sf-hidden>
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<span class="displayName linkAnimation">Espen Gaarder Haug</span>
<contributor-popdown name="Espen Gaarder Haug" position=2 email=espenhaug@mac.com affiliations="Norwegian University of Life Sciences, Christian Magnus Falsensvei 18, 1433 As, Norway" class=sf-hidden>
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<div class=subTitleInfoProductPage>From the journal <a class="ga_parent ga_parent_journal" href=https://www.degruyter.com/journal/key/phys/html>Open Physics</a></div>
<div class=doi><a href=https://doi.org/10.1515/phys-2023-0110 class="linkWithoutStyle subTitleInfoProductPage ga_doi" target=_blank>https://doi.org/10.1515/phys-2023-0110</a></div>
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<div class="__db_score __db_score_normal">1</div>
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<div class="d-none analyticsHolder sf-hidden" data-subjects=PY|PY-01|PY-07|PY-18 data-publishercode=DG_OA data-license=open-access data-publisher="De Gruyter Open Access" data-contentname="The reciprocal linear effect, a new optical effect of the Sagnac type" data-doi=10.1515/phys-2023-0110 data-parentidentifier=PHYS data-parentname="Open Physics" data-languages=en></div>
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<div xmlns:dgdoi=http://degruyter.com/resources/doi-from-crossref xmlns:dgpm=http://degruyter.com/resources/fetched-pubmed-id class=contentWrapper><div class=article lang=en><div class=abstract>
<h2 class=subheading>Abstract</h2>
<p>The Sagnac effect can be demonstrated with light propagating either along a circular contour or, as done by Wang <em>et al</em>., back and forth along a linear contour. In the linear Sagnac effect, the emitter–receiver device is in motion relative to the contour where light propagates. In the reciprocal linear Sagnac effect (RLSE), the device is stationary and the contour is in motion. When the contour changes direction of motion, some special features of the linear Sagnac effect are not fully reciprocal to the RLSE, which foresees variations of the first order in <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-1><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2>v</span><span class=MJXp-mo id=MJXp-Span-3 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4>c</span></span></span><span id=MathJax-Element-1-Frame class="mjx-chtml MathJax_CHTML MJXc-processed sf-hidden" tabindex=0 style=font-size:127%></span>
</span>
</span> in the round-trip time taken by a light signal to cover the contour. The RLSE can be tested with present technology and, if confirmed experimentally, it might have interesting technological applications. Presently, it can be important for testing light-speed invariance, simultaneity, and the relativity principle.</p>
</div><div class="keywords mb-3">Keywords: <a href="https://www.degruyter.com/search?query=keywordValues%3A%28%22light%20propagation%22%29%20AND%20journalKey%3A%28%22PHYS%22%29&amp;documentVisibility=all&amp;documentTypeFacet=article" class=ga_keyword>light propagation</a>; <a href="https://www.degruyter.com/search?query=keywordValues%3A%28%22Sagnac%20effect%22%29%20AND%20journalKey%3A%28%22PHYS%22%29&amp;documentVisibility=all&amp;documentTypeFacet=article" class=ga_keyword>Sagnac effect</a>; <a href="https://www.degruyter.com/search?query=keywordValues%3A%28%22one-way%20speed%20of%20light%22%29%20AND%20journalKey%3A%28%22PHYS%22%29&amp;documentVisibility=all&amp;documentTypeFacet=article" class=ga_keyword>one-way speed of light</a>; <a href="https://www.degruyter.com/search?query=keywordValues%3A%28%22relative%20simultaneity%22%29%20AND%20journalKey%3A%28%22PHYS%22%29&amp;documentVisibility=all&amp;documentTypeFacet=article" class=ga_keyword>relative simultaneity</a>; <a href="https://www.degruyter.com/search?query=keywordValues%3A%28%22Lorentz%20invariance%22%29%20AND%20journalKey%3A%28%22PHYS%22%29&amp;documentVisibility=all&amp;documentTypeFacet=article" class=ga_keyword>Lorentz invariance</a></div><div class=body>
<section id=j_phys-2023-0110_s_001>
<h2 class=subheading>1 Introduction</h2>
<p>The experiment related to the circular Sagnac effect [<a href=#j_phys-2023-0110_ref_001 class="link link-bibr" data-bs-target=j_phys-2023-0110_ref_001 data-bs-toggle=tooltip title="[1] Sagnac G. Regarding the proof for the existence of a luminiferous ether using a rotating interferometer experiment. C R Acad Sci. 1913;157:708–10. Search in Google Scholar">1</a>], shown in <a href=#j_phys-2023-0110_fig_001 class="link link-fig" data-bs-target=j_phys-2023-0110_fig_001>Figure 1</a>(a), was performed in 1913, and the one corresponding to the linear effect, shown in <a href=#j_phys-2023-0110_fig_001 class="link link-fig" data-bs-target=j_phys-2023-0110_fig_001>Figure 1</a>(b), was accomplished by Wang <em>et al</em>. [<a href=#j_phys-2023-0110_ref_002 class="link link-bibr" data-bs-target=j_phys-2023-0110_ref_002 data-bs-toggle=tooltip title="[2] Wang R, Zhengb Y, Yao A, Langley D. Modified Sagnac experiment for measuring travel-time difference between counter-propagating light beams in a uniformly moving fiber. Phys Lett A. 2003;312:7–10. Wang R, Zheng Y, Yao A. Generalized Sagnac effect. Phys Rev Lett. 2004;93(14):143901.10.1016/S0375-9601(03)00575-9Search in Google Scholar">2</a>] in 2003. In both effects, the measuring device <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-5><span class=MJXp-msup id=MJXp-Span-6><span class=MJXp-mrow id=MJXp-Span-7 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-8>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-9 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-10>*</span></span></span></span></span><span id=MathJax-Element-2-Frame class="mjx-chtml MathJax_CHTML MJXc-processed sf-hidden" tabindex=0 style=font-size:127%></span>
</span>
</span> (emitter–receiver clock or interferometer) is in motion relative to a stationary contour, and <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-11><span class=MJXp-msup id=MJXp-Span-12><span class=MJXp-mrow id=MJXp-Span-13 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-14>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-15 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-16>*</span></span></span></span></span><span id=MathJax-Element-3-Frame class="mjx-chtml MathJax_CHTML MJXc-processed sf-hidden" tabindex=0 style=font-size:127%></span>
</span>
</span> measures the difference <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-17><span class=MJXp-mi id=MJXp-Span-18>Δ</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-19>T</span></span></span><span id=MathJax-Element-4-Frame class="mjx-chtml MathJax_CHTML MJXc-processed sf-hidden" tabindex=0 style=font-size:127%></span>
</span>
</span> of the round-trip times of two light signals counterpropagating around the contour. Following Post [<a href=#j_phys-2023-0110_ref_003 class="link link-bibr" data-bs-target=j_phys-2023-0110_ref_003 data-bs-toggle=tooltip title="[3] Post EJ. Sagnac effect. Rev Mod Phys. 1967;39(2):475–93. 10.1103/RevModPhys.39.475Search in Google Scholar">3</a>], <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-20><span class=MJXp-mi id=MJXp-Span-21>Δ</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-22>T</span></span></span><span id=MathJax-Element-5-Frame class="mjx-chtml MathJax_CHTML MJXc-processed sf-hidden" tabindex=0 style=font-size:127%></span>
</span>
</span> is given by, <div class=formula id=j_phys-2023-0110_eq_001>
<span class=label>(1)</span>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class="MJXp-math MJXp-display" id=MJXp-Span-23><span class=MJXp-mtable id=MJXp-Span-24><span><span class=MJXp-mtr id=MJXp-Span-25 style=vertical-align:baseline><span class=MJXp-mtd id=MJXp-Span-26 style=text-align:center><span class=MJXp-mi id=MJXp-Span-27>Δ</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-28>T</span></span><span class=MJXp-mtd id=MJXp-Span-29 style=padding-left:0.33em;text-align:center><span class=MJXp-mo id=MJXp-Span-30 style=margin-left:0.333em;margin-right:0.333em>=</span></span><span class=MJXp-mtd id=MJXp-Span-31 style=padding-left:0.33em;text-align:center><span class=MJXp-msub id=MJXp-Span-32><span class=MJXp-mrow id=MJXp-Span-33 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-34>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-35 style=vertical-align:-0.4em><span class=MJXp-mo id=MJXp-Span-36>⇐</span></span></span><span class=MJXp-mo id=MJXp-Span-37 style=margin-left:0.267em;margin-right:0.267em>−</span><span class=MJXp-msub id=MJXp-Span-38><span class=MJXp-mrow id=MJXp-Span-39 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-40>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-41 style=vertical-align:-0.4em><span class=MJXp-mo id=MJXp-Span-42>⇒</span></span></span></span></span><span class=MJXp-mtr id=MJXp-Span-43 style=vertical-align:baseline><span class=MJXp-mtd id=MJXp-Span-44 style=padding-top:0.431em;text-align:center></span><span class=MJXp-mtd id=MJXp-Span-45 style=padding-left:0.33em;padding-top:0.431em;text-align:center><span class=MJXp-mo id=MJXp-Span-46 style=margin-left:0.333em;margin-right:0.333em>=</span></span><span class=MJXp-mtd id=MJXp-Span-47 style=padding-left:0.33em;padding-top:0.431em;text-align:center><span class=MJXp-mfrac id=MJXp-Span-48 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-49><span class=MJXp-mn id=MJXp-Span-50>2</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-51>L</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-52><span class="MJXp-mi MJXp-italic" id=MJXp-Span-53>γ</span><span class=MJXp-mrow id=MJXp-Span-54><span class=MJXp-mo id=MJXp-Span-55 style=margin-left:0em;margin-right:0em>(</span><span class=MJXp-mrow id=MJXp-Span-56><span class="MJXp-mi MJXp-italic" id=MJXp-Span-57>c</span><span class=MJXp-mo id=MJXp-Span-58 style=margin-left:0.267em;margin-right:0.267em>−</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-59>v</span></span><span class=MJXp-mo id=MJXp-Span-60 style=margin-left:0em;margin-right:0em>)</span></span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-61 style=margin-left:0.267em;margin-right:0.267em>−</span><span class=MJXp-mfrac id=MJXp-Span-62 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-63><span class=MJXp-mn id=MJXp-Span-64>2</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-65>L</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-66><span class="MJXp-mi MJXp-italic" id=MJXp-Span-67>γ</span><span class=MJXp-mrow id=MJXp-Span-68><span class=MJXp-mo id=MJXp-Span-69 style=margin-left:0em;margin-right:0em>(</span><span class=MJXp-mrow id=MJXp-Span-70><span class="MJXp-mi MJXp-italic" id=MJXp-Span-71>c</span><span class=MJXp-mo id=MJXp-Span-72 style=margin-left:0.267em;margin-right:0.267em>+</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-73>v</span></span><span class=MJXp-mo id=MJXp-Span-74 style=margin-left:0em;margin-right:0em>)</span></span></span></span></span></span></span></span></span></span><span class=MJXp-mtr id=MJXp-Span-75 style=vertical-align:baseline><span class=MJXp-mtd id=MJXp-Span-76 style=padding-top:0.431em;text-align:center></span><span class=MJXp-mtd id=MJXp-Span-77 style=padding-left:0.33em;padding-top:0.431em;text-align:center><span class=MJXp-mo id=MJXp-Span-78 style=margin-left:0.333em;margin-right:0.333em>=</span></span><span class=MJXp-mtd id=MJXp-Span-79 style=padding-left:0.33em;padding-top:0.431em;text-align:center><span class=MJXp-mfrac id=MJXp-Span-80 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-81><span class=MJXp-mn id=MJXp-Span-82>4</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-83>γ</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-84>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-85>L</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-86><span class=MJXp-msup id=MJXp-Span-87><span class=MJXp-mrow id=MJXp-Span-88 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-89>c</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-90 style=vertical-align:0.5em><span class=MJXp-mn id=MJXp-Span-91>2</span></span></span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-92 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-mfrac id=MJXp-Span-93 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-94><span class=MJXp-mn id=MJXp-Span-95>2</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-96>γ</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-97>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-98>P</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-99><span class=MJXp-msup id=MJXp-Span-100><span class=MJXp-mrow id=MJXp-Span-101 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-102>c</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-103 style=vertical-align:0.5em><span class=MJXp-mn id=MJXp-Span-104>2</span></span></span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-105 style=margin-left:0em;margin-right:0.222em>,</span></span></span></span></span></span></span><span class="mjx-chtml MJXc-display MJXc-processed sf-hidden" style=text-align:center></span>
</span>
</div><p> where <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-106><span class=MJXp-msub id=MJXp-Span-107><span class=MJXp-mrow id=MJXp-Span-108 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-109>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-110 style=vertical-align:-0.4em><span class=MJXp-mo id=MJXp-Span-111>⇐</span></span></span></span></span><span id=MathJax-Element-7-Frame class="mjx-chtml MathJax_CHTML MJXc-processed sf-hidden" tabindex=0 style=font-size:127%></span>
</span>
</span> and <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-112><span class=MJXp-msub id=MJXp-Span-113><span class=MJXp-mrow id=MJXp-Span-114 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-115>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-116 style=vertical-align:-0.4em><span class=MJXp-mo id=MJXp-Span-117>⇒</span></span></span></span></span><span id=MathJax-Element-8-Frame class="mjx-chtml MathJax_CHTML MJXc-processed sf-hidden" tabindex=0 style=font-size:127%></span>
</span>
</span> represent the round-trip time of the co- and counter-moving light signals (or photons) along the contour of perimeter <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-118><span class="MJXp-mi MJXp-italic" id=MJXp-Span-119>P</span><span class=MJXp-mo id=MJXp-Span-120 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-mn id=MJXp-Span-121>2</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-122>π</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-123>r</span></span></span><span id=MathJax-Element-9-Frame class="mjx-chtml MathJax_CHTML MJXc-processed sf-hidden" tabindex=0 style=font-size:127%></span>
</span>
</span> or <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-124><span class=MJXp-mn id=MJXp-Span-125>2</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-126>L</span></span></span><span id=MathJax-Element-10-Frame class="mjx-chtml MathJax_CHTML MJXc-processed sf-hidden" tabindex=0 style=font-size:127%></span>
</span>
</span> in the circular and linear effects, respectively. For the circular Sagnac effect, with <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-127><span class="MJXp-mi MJXp-italic" id=MJXp-Span-128>v</span><span class=MJXp-mo id=MJXp-Span-129 style=margin-left:0.333em;margin-right:0.333em>=</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-130>ω</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-131>r</span></span></span><span id=MathJax-Element-11-Frame class="mjx-chtml MathJax_CHTML MJXc-processed sf-hidden" tabindex=0 style=font-size:127%></span>
</span>
</span>, result (<a href=#j_phys-2023-0110_eq_001 class="link link-disp-formula" data-bs-target=j_phys-2023-0110_eq_001>1</a>) is usually expressed [<a href=#j_phys-2023-0110_ref_003 class="link link-bibr" data-bs-target=j_phys-2023-0110_ref_003 data-bs-toggle=tooltip title="[3] Post EJ. Sagnac effect. Rev Mod Phys. 1967;39(2):475–93. 10.1103/RevModPhys.39.475Search in Google Scholar">3</a>] as <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-132><span class=MJXp-mi id=MJXp-Span-133>Δ</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-134>T</span><span class=MJXp-mo id=MJXp-Span-135 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-mn id=MJXp-Span-136>4</span><span class="MJXp-mi MJXp-bold MJXp-italic" id=MJXp-Span-137>ω</span><span class=MJXp-mo id=MJXp-Span-138 style=margin-left:0.267em;margin-right:0.267em>⋅</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-139>A</span><span class=MJXp-mo id=MJXp-Span-140 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class=MJXp-msup id=MJXp-Span-141><span class=MJXp-mrow id=MJXp-Span-142 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-143>c</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-144 style=vertical-align:0.5em><span class=MJXp-mn id=MJXp-Span-145>2</span></span></span></span></span><span id=MathJax-Element-12-Frame class="mjx-chtml MathJax_CHTML MJXc-processed sf-hidden" tabindex=0 style=font-size:127%></span>
</span>
</span>, where <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-146><span class="MJXp-mi MJXp-italic" id=MJXp-Span-147>A</span></span></span><span id=MathJax-Element-13-Frame class="mjx-chtml MathJax_CHTML MJXc-processed sf-hidden" tabindex=0 style=font-size:127%></span>
</span>
</span> is the area enclosed by the light path.</p>
<div class=figure-wrapper id=j_phys-2023-0110_fig_001><div class="figure w-100"><div class=graphic><img loading=lazy 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" alt="Figure 1
(a) In the circular Sagnac effect, two counter-propagating photons are emitted from the device
C
*
{{\rm{C}}}^{* }
and travel along the circumference of the rotating platform (only a single photon is shown).
C
*
{{\rm{C}}}^{* }
measures the difference
Δ
T
\Delta T
of the arrival times after a round trip. (b) In the linear Sagnac effect, the counter-propagating photons travel in an optical fiber that may slide frictionless around the two pulleys A and B. The segment AC* of length
D
D
represents the initial position of device
C
*
{{\rm{C}}}^{* }
relative to A, the left end point of the contour. If AC*
=
=
D
>
2
v
L
⁄
c
=
(
v
⁄
c
)
P
D\gt 2vL/c=\left(v/c)P
, the counter-moving photon performs a round trip and gets back to
C
*
{{\rm{C}}}^{* }
when this is still moving on the contour lower section.
"></div><div class="figure-description mb-3"><div class="figure-label h3"><span class=label>Figure 1</span></div><div class="figure-caption mb-2"><span class=caption><p>(a) In the circular Sagnac effect, two counter-propagating photons are emitted from the device <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-148><span class=MJXp-msup id=MJXp-Span-149><span class=MJXp-mrow id=MJXp-Span-150 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-151>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-152 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-153>*</span></span></span></span></span><span id=MathJax-Element-14-Frame class="mjx-chtml MathJax_CHTML MJXc-processed sf-hidden" tabindex=0 style=font-size:129%></span>
</span>
</span> and travel along the circumference of the rotating platform (only a single photon is shown). <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-154><span class=MJXp-msup id=MJXp-Span-155><span class=MJXp-mrow id=MJXp-Span-156 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-157>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-158 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-159>*</span></span></span></span></span><span id=MathJax-Element-15-Frame class="mjx-chtml MathJax_CHTML MJXc-processed sf-hidden" tabindex=0 style=font-size:129%></span>
</span>
</span> measures the difference <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-160><span class=MJXp-mi id=MJXp-Span-161>Δ</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-162>T</span></span></span><span id=MathJax-Element-16-Frame class="mjx-chtml MathJax_CHTML MJXc-processed sf-hidden" tabindex=0 style=font-size:129%></span>
</span>
</span> of the arrival times after a round trip. (b) In the linear Sagnac effect, the counter-propagating photons travel in an optical fiber that may slide frictionless around the two pulleys A and B. The segment AC* of length <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-163><span class="MJXp-mi MJXp-italic" id=MJXp-Span-164>D</span></span></span><span id=MathJax-Element-17-Frame class="mjx-chtml MathJax_CHTML MJXc-processed sf-hidden" tabindex=0 style=font-size:129%></span>
</span>
</span> represents the initial position of device <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-165><span class=MJXp-msup id=MJXp-Span-166><span class=MJXp-mrow id=MJXp-Span-167 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-168>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-169 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-170>*</span></span></span></span></span><span id=MathJax-Element-18-Frame class="mjx-chtml MathJax_CHTML MJXc-processed sf-hidden" tabindex=0 style=font-size:129%></span>
</span>
</span> relative to A, the left end point of the contour. If AC* <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-171><span class=MJXp-mo id=MJXp-Span-172 style=margin-left:0.333em;margin-right:0.333em>=</span></span></span><span id=MathJax-Element-19-Frame class="mjx-chtml MathJax_CHTML MJXc-processed sf-hidden" tabindex=0 style=font-size:129%></span>
</span>
</span>
<span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-173><span class="MJXp-mi MJXp-italic" id=MJXp-Span-174>D</span><span class=MJXp-mo id=MJXp-Span-175 style=margin-left:0.333em;margin-right:0.333em>&gt;</span><span class=MJXp-mn id=MJXp-Span-176>2</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-177>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-178>L</span><span class=MJXp-mo id=MJXp-Span-179 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-180>c</span><span class=MJXp-mo id=MJXp-Span-181 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-mrow id=MJXp-Span-182><span class=MJXp-mo id=MJXp-Span-183 style=margin-left:0em;margin-right:0em>(</span><span class=MJXp-mrow id=MJXp-Span-184><span class="MJXp-mi MJXp-italic" id=MJXp-Span-185>v</span><span class=MJXp-mo id=MJXp-Span-186 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-187>c</span></span><span class=MJXp-mo id=MJXp-Span-188 style=margin-left:0em;margin-right:0em>)</span></span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-189>P</span></span></span><span id=MathJax-Element-20-Frame class="mjx-chtml MathJax_CHTML MJXc-processed sf-hidden" tabindex=0 style=font-size:129%></span>
</span>
</span>, the counter-moving photon performs a round trip and gets back to <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-190><span class=MJXp-msup id=MJXp-Span-191><span class=MJXp-mrow id=MJXp-Span-192 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-193>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-194 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-195>*</span></span></span></span></span><span id=MathJax-Element-21-Frame class="mjx-chtml MathJax_CHTML MJXc-processed sf-hidden" tabindex=0 style=font-size:129%></span>
</span>
</span> when this is still moving on the contour lower section.</p></span></div></div></div></div>
<p>In the linear Sagnac effect of <a href=#j_phys-2023-0110_fig_001 class="link link-fig" data-bs-target=j_phys-2023-0110_fig_001>Figure 1</a>(b), the arm AB of the contour is stationary and the measuring device <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-196><span class=MJXp-msup id=MJXp-Span-197><span class=MJXp-mrow id=MJXp-Span-198 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-199>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-200 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-201>*</span></span></span></span></span><span id=MathJax-Element-22-Frame class="mjx-chtml MathJax_CHTML MJXc-processed sf-hidden" tabindex=0 style=font-size:127%></span>
</span>
</span> is moving clockwise with uniform speed <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-202><span class="MJXp-mi MJXp-italic" id=MJXp-Span-203>v</span></span></span><span id=MathJax-Element-23-Frame class="mjx-chtml MathJax_CHTML MJXc-processed sf-hidden" tabindex=0 style=font-size:127%></span>
</span>
</span> along the contour, going from the lower to the upper section of the contour and vice versa. While sliding around the pulley of radius <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-204><span class="MJXp-mi MJXp-italic" id=MJXp-Span-205>R</span></span></span><span id=MathJax-Element-24-Frame class="mjx-chtml MathJax_CHTML MJXc-processed sf-hidden" tabindex=0 style=font-size:127%></span>
</span>
</span> during the short time <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-206><span class="MJXp-mi MJXp-italic" id=MJXp-Span-207>η</span></span></span><span id=MathJax-Element-25-Frame class="mjx-chtml MathJax_CHTML MJXc-processed sf-hidden" tabindex=0 style=font-size:127%></span>
</span>
</span>, the device <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-208><span class=MJXp-msup id=MJXp-Span-209><span class=MJXp-mrow id=MJXp-Span-210 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-211>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-212 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-213>*</span></span></span></span></span><span id=MathJax-Element-26-Frame class="mjx-chtml MathJax_CHTML MJXc-processed sf-hidden" tabindex=0 style=font-size:127%></span>
</span>
</span> changes the direction of motion at the pulley A (or B). Locally, the speed <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-214><span class="MJXp-mi MJXp-italic" id=MJXp-Span-215>v</span></span></span><span id=MathJax-Element-27-Frame class="mjx-chtml MathJax_CHTML MJXc-processed sf-hidden" tabindex=0 style=font-size:127%></span>
</span>
</span> of <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-216><span class=MJXp-msup id=MJXp-Span-217><span class=MJXp-mrow id=MJXp-Span-218 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-219>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-220 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-221>*</span></span></span></span></span><span id=MathJax-Element-28-Frame class="mjx-chtml MathJax_CHTML MJXc-processed sf-hidden" tabindex=0 style=font-size:127%></span>
</span>
</span> relative to the contour is always constant. In the linear experiment performed by Wang <em>et al</em>. [<a href=#j_phys-2023-0110_ref_002 class="link link-bibr" data-bs-target=j_phys-2023-0110_ref_002 data-bs-toggle=tooltip title="[2] Wang R, Zhengb Y, Yao A, Langley D. Modified Sagnac experiment for measuring travel-time difference between counter-propagating light beams in a uniformly moving fiber. Phys Lett A. 2003;312:7–10. Wang R, Zheng Y, Yao A. Generalized Sagnac effect. Phys Rev Lett. 2004;93(14):143901.10.1016/S0375-9601(03)00575-9Search in Google Scholar">2</a>], the device <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-222><span class=MJXp-msup id=MJXp-Span-223><span class=MJXp-mrow id=MJXp-Span-224 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-225>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-226 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-227>*</span></span></span></span></span><span id=MathJax-Element-29-Frame class="mjx-chtml MathJax_CHTML MJXc-processed sf-hidden" tabindex=0 style=font-size:127%></span>
</span>
</span> is always in uniform rectilinear motion on the lower contour section during the round-trip time <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-228><span class="MJXp-mi MJXp-italic" id=MJXp-Span-229>T</span><span class=MJXp-mo id=MJXp-Span-230 style=margin-left:0.333em;margin-right:0.333em>≃</span><span class=MJXp-msub id=MJXp-Span-231><span class=MJXp-mrow id=MJXp-Span-232 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-233>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-234 style=vertical-align:-0.4em><span class=MJXp-mo id=MJXp-Span-235>⇐</span></span></span><span class=MJXp-mo id=MJXp-Span-236 style=margin-left:0.333em;margin-right:0.333em>≃</span><span class=MJXp-msub id=MJXp-Span-237><span class=MJXp-mrow id=MJXp-Span-238 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-239>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-240 style=vertical-align:-0.4em><span class=MJXp-mo id=MJXp-Span-241>⇒</span></span></span></span></span><span id=MathJax-Element-30-Frame class="mjx-chtml MathJax_CHTML MJXc-processed sf-hidden" tabindex=0 style=font-size:127%></span>
</span>
</span>. Therefore, in this experiment, <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-242><span class=MJXp-msup id=MJXp-Span-243><span class=MJXp-mrow id=MJXp-Span-244 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-245>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-246 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-247>*</span></span></span></span></span><span id=MathJax-Element-31-Frame class="mjx-chtml MathJax_CHTML MJXc-processed sf-hidden" tabindex=0 style=font-size:127%></span>
</span>
</span> does not turn around the pulleys A or B. However, since the relative speed <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-248><span class="MJXp-mi MJXp-italic" id=MJXp-Span-249>v</span></span></span><span id=MathJax-Element-32-Frame class="mjx-chtml MathJax_CHTML MJXc-processed sf-hidden" tabindex=0 style=font-size:127%></span>
</span>
</span> between <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-250><span class=MJXp-msup id=MJXp-Span-251><span class=MJXp-mrow id=MJXp-Span-252 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-253>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-254 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-255>*</span></span></span></span></span><span id=MathJax-Element-33-Frame class="mjx-chtml MathJax_CHTML MJXc-processed sf-hidden" tabindex=0 style=font-size:127%></span>
</span>
</span> and the contour is constant, there is no reason to suppose that the result differs from the theoretical prediction (<a href=#j_phys-2023-0110_eq_001 class="link link-disp-formula" data-bs-target=j_phys-2023-0110_eq_001>1</a>) if <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-256><span class=MJXp-msup id=MJXp-Span-257><span class=MJXp-mrow id=MJXp-Span-258 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-259>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-260 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-261>*</span></span></span></span></span><span id=MathJax-Element-34-Frame class="mjx-chtml MathJax_CHTML MJXc-processed sf-hidden" tabindex=0 style=font-size:127%></span>
</span>
</span> turns around the pulley during the round-trip time <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-262><span class="MJXp-mi MJXp-italic" id=MJXp-Span-263>T</span></span></span><span id=MathJax-Element-35-Frame class="mjx-chtml MathJax_CHTML MJXc-processed sf-hidden" tabindex=0 style=font-size:127%></span>
</span>
</span>.</p>
<p>In Section 2, we consider the reciprocal linear Sagnac effect (RLSE), shown in <a href=#j_phys-2023-0110_fig_002 class="link link-fig" data-bs-target=j_phys-2023-0110_fig_002>Figure 2</a>, where the device <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-264><span class=MJXp-msup id=MJXp-Span-265><span class=MJXp-mrow id=MJXp-Span-266 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-267>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-268 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-269>*</span></span></span></span></span><span id=MathJax-Element-36-Frame class="mjx-chtml MathJax_CHTML MJXc-processed sf-hidden" tabindex=0 style=font-size:127%></span>
</span>
</span> is stationary and the contour is in relative motion. We find that, for counter-propagating light signals, the same observable <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-270><span class=MJXp-mi id=MJXp-Span-271>Δ</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-272>T</span></span></span><span id=MathJax-Element-37-Frame class="mjx-chtml MathJax_CHTML MJXc-processed sf-hidden" tabindex=0 style=font-size:127%></span>
</span>
</span> in (<a href=#j_phys-2023-0110_eq_001 class="link link-disp-formula" data-bs-target=j_phys-2023-0110_eq_001>1</a>) is foreseen in the RLSE and, thus, with regard to <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-273><span class=MJXp-mi id=MJXp-Span-274>Δ</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-275>T</span></span></span><span id=MathJax-Element-38-Frame class="mjx-chtml MathJax_CHTML MJXc-processed sf-hidden" tabindex=0 style=font-size:127%></span>
</span>
</span>, the RLSE is reciprocal to the linear Sagnac effect.</p>
<div class=figure-wrapper id=j_phys-2023-0110_fig_002><div class="figure w-100"><div class=graphic><img loading=lazy 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V2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2Kv/9Ls2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2Kv/9Ps2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2Kv/9Ts2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2Kv/9Xs2Ksd1Hzdb2fmew8trA8t3fIZTKtOMaDl8T/8BirIQaiuKpD5v8zjyzp8OoPbmeB544ZiG4+mshp6v+VxxVPI3EkauDUMAQfYiuKr8VdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVaxVJNP84eX9S1SfSbC8We/tufqwBWBHA8X4swCPxb+VsVTsGoB8cVbxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KpN5u1e40Xy1qOqWqq1xawmSNX3XlUL8VPnirCNJ1z82tU0qHV7RdNntp0LxRcXV2AqpH2tviGKso8j+cR5ns7j1rc2mo2Mno3luTXi38yn/K4tirKMVdirsVdirsVdirsVdirsVf/W7KxoCcVeO3fmS1tfzU1TUZle7ksYFstPs4BzllmcD4I1/wAhvU5YqybQvzHubrXI9D1rSJdJvLkVtTIao1AW4t7so+HFVf8AN70z5C1Av4wlP9b1E/hirJPL0jS6HYSuau9vET/wIxVMsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVSbzbrUeieXr/UWI5QwsYwTxq7DjGg/ymbFXkUWlXHk9fKvm1lJmvXI1Rv2SLg80Lfyt6T4q90RldFdTyVgCrDuD3xVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVYx+ZP/KC61/zDn/iS4qwnyv551bSvKNhbWnli9uvRiIhuY1rC4qW5/ByYLy+1iqZfk82nyWmpXwuhLq19cGXULWhUwmrGNOL0Lfaf48Vel4q7FXYq7FXYq7FXYq7FXYq//9fsU0ywoXb7Kgk036CuKvLPyo0u3vb/AFrzZIoe4uLyWK1Zh9lC3qSMP9bkq4qiPM5j1L80vLtjbktLYo09xIu5VSGZVf8A4H/h8VRH5zXLPodjo8JH1jU7uOJU7lR+0B/L6hTFWf2FuLWygtlFBDGkYH+qoXFURirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdiryv83dRuLq50jy7ZwS3Us8n1u5tYByd44z+7AH0M2Kofzbr+sa95cudIPlDUIE4AwSFfgjMe6u237C4qy78steOteULKSQ1uLUfVZ/9aIDj/ySKYqy7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYqxj8yP+UF1r/mHP/ElxVIvIvm/yvZeTtLtr3VbWG4hhIkgeVQ60ZtuPX4sVS3yTImr/mPrev6WhGjel6RnC0WWRuH2QadeH/CYq9WxV2KuxV2KuxV2KuxV2KuxV//Q6xrNtdXel3dtZusdzNE8cUjdFZhxqaYq8/0nyF548s2SQeX9Yi4SqPrVtOnJFl6NLbVHwjj/ADYqyDyh5JOgz3eqaldfpDXr8/6Renb4aikcdd96LyxVILBT5w/Ml9TQh9F8uAwwMfiWS4b7TJ/qt8X/ADzxV6YBQUxVvFXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FWG6d5Qv087ah5o1CWOX1I/QsIkqGRKcfjr8H2MVZeU+Dj12pTtirDvJ3lDUPLetaxIsqPpOoS+tbxVPNGqWPw9P2+H+wxVmmKuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxVRu7S3vLaS1uolmt5lKyROAysD2ZTiqRjyF5PD8/0Palu9YwRsKfZ+ziqdW9jbW0YhgiSKEbLGihVFP5VHwjFURirsVdirsVdirsVdirsVdir/9Hs2KuxVQvLb61ay2xdoxMjRmRDR1DDiWRv2X3xVA+XfL9h5e01NOsFIhQszM55O7N9qR2/mbFU1xV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxVomm5xVwIO4NRjat4q7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FWqg98VbxV2KuxV2KuxV//9Ls2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxVD3l/aWVu9zcyrFCn2mY/h/rYQCeSaYPe/mpZIxFlZvcpWnORhGCPFdnzK/Kypu8G0L/ytiVdhpQAHb1qf8y8RpJHkkYC7/lbU3/VqH/I7/r3hGkkjwWv+VtTf9Wof8jv+veP5OSfALf8Aytqb/q1D/kd/17x/JyXwC7/lbU3/AFah/wAjv+veP5SS+AXf8ram/wCrUP8Akd/17x/KSXwC7/lbU3/VqH/I7/r3j+UkvgF3/K2pv+rUP+R3/XvH8pJfALv+VtTf9Wof8jv+veP5SS+AXf8AK2pv+rUP+R3/AF7x/KSXwC7/AJW1N/1ah/yO/wCveP5SS+AXf8ram/6tQ/5Hf9e8fykl8Au/5W1N/wBWof8AI7/r3j+UkvgF3/K2pv8Aq1D/AJHf9e8fykl8Au/5W1N/1ah/yO/694/lJL4Bd/ytqb/q1D/kd/17x/KSXwC7/lbU3/VqH/I7/r3j+UkvgF3/ACtqb/q1D/kd/wBe8fykl8Au/wCVtTf9Wof8jv8Ar3j+UkvgF3/K2pv+rUP+R3/XvH8pJfALv+VtTf8AVqH/ACO/694/lJL4Bd/ytqb/AKtQ/wCR3/XvH8pJfALv+VtTf9Wof8jv+veP5SS+AXf8ram/6tQ/5Hf9e8fykl8Au/5W1N/1ah/yO/694/lJL4Bd/wAram/6tQ/5Hf8AXvH8pJfALv8AlbU3/VqH/I7/AK94/lJL4Bd/ytqb/q1D/kd/17x/KSXwC7/lbU3/AFah/wAjv+veP5SS+AXf8ram/wCrUP8Akd/17x/KSXwC7/lbU3/VqH/I7/r3j+UkvgF3/K2pv+rUP+R3/XvH8pJfALv+VtTf9Wof8jv+veP5SS+AXf8AK2pv+rUP+R3/AF7x/KSXwC7/AJW1N/1ah/yO/wCveP5SS+AXf8ram/6tQ/5Hf9e8fykl8Au/5W1N/wBWof8AI7/r3j+UkvgF3/K2pv8Aq1D/AJHf9e8fykl8Au/5W1N/1ah/yO/694/lJL4Bd/ytqb/q1D/kd/17x/KSXwC7/lbU3/VqH/I7/r3j+UkvgF3/ACtqb/q1D/kd/wBe8fykl8Au/wCVtTf9Wof8jv8Ar3j+UkvgF3/K2pv+rUP+R3/XvH8pJfALv+VtTf8AVqH/ACO/694/lJL4Bd/ytqb/AKtQ/wCR3/XvH8pJfALv+VtTf9Wof8jv+veP5SS+AXf8ram/6tQ/5Hf9e8fykl8Au/5W1N/1ah/yO/694/lJL4Bd/wAram/6tQ/5Hf8AXvH8pJfALv8AlbU3/VqH/I7/AK94/lJL4Bd/ytqb/q1D/kd/17x/KSXwC7/lbU3/AFah/wAjv+veP5SS+AXf8ram/wCrUP8Akd/17x/KSXwC7/lbU3/VqH/I7/r3j+UkvgF3/K2pv+rUP+R3/XvH8pJfALv+VtTf9Wof8jv+veP5SS+AXf8AK2pv+rUP+R3/AF7x/KSXwC7/AJW1N/1ah/yO/wCveP5SS+AXf8ram/6tQ/5Hf9e8fykl8Au/5W1N/wBWof8AI7/r3j+UkvgF3/K2pv8Aq1D/AJHf9e8fykl8Au/5W1N/1ah/yO/694/lJL4BaP5tTf8AVrA9/W/694jRyR4KJs/zXtWb/TbF4UrTnE3q0+YITIy0sgpwlnGn6lZ6lbLc2colhb9odj/Kw/ZbMeUSDu0kUisih2KqVzPFbwSTzOI4o1LvIeiqBVmxV5P5X/M99Q87XVrdShNKv29LTgekTL/ctuP+PwfE+KvW1O3v3xVdirsVdirsVf/T7NirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirRFRkZCwryj8zNSeTU4tMVj9Xt1DSIvUu/xKzf7DNto8VQ4nKxBI9C8r6lrqytatGqRERtLISFLH4x9jll2XNHGOGTZq5xw0B6uJOf+VY66ASbi2AH+VId/+AzFGrEOXJq8eMRf0xdH+WGvyLyFxbAeHJ/+aMJ1tbBAzQ/yf92u/wCVWeYP+Wm1/wCCf/mjI/nSz/MO/wCVWeYP+Wm1/wCCf/mjCdcSx8Z3/KrPMH/LTa/8E/8AzRg/OFPjO/5VZ5g/5abX/gn/AOaMfzhXxnf8qs8wf8tNr/wT/wDNGP5wr4zv+VWeYP8Alptf+Cf/AJox/OFfGd/yqzzB/wAtNr/wT/8ANGP5wr4zv+VWeYP+Wm1/4J/+aMfzhXxnf8qs8wf8tNr/AME//NGP5wr4zv8AlVnmD/lptf8Agn/5ox/OFfGd/wAqs8wf8tNr/wAE/wDzRj+cK+M7/lVnmD/lptf+Cf8A5ox/OFfGd/yqzzB/y02v/BP/AM0Y/nCvjO/5VZ5g/wCWm1/4J/8AmjH84V8Z3/KrPMH/AC02v/BP/wA0Y/nCvjO/5VZ5g/5abX/gn/5ox/OFfGd/yqzzB/y02v8AwT/80Y/nCvjO/wCVWeYP+Wm1/wCCf/mjH84V8Z3/ACqzzB/y02v/AAT/APNGP5wr4zv+VWeYP+Wm1/4J/wDmjH84V8Z3/KrPMH/LTa/8E/8AzRj+cK+M7/lVnmD/AJabX/gn/wCaMfzhXxnf8qs8wf8ALTa/8E//ADRj+cK+M7/lVnmD/lptf+Cf/mjH84V8Z3/KrPMH/LTa/wDBP/zRj+cK+M7/AJVZ5g/5abX/AIJ/+aMfzhXxnf8AKrPMH/LTa/8ABP8A80Y/nCvjO/5VZ5g/5abX/gn/AOaMfzhXxnf8qs8wf8tNr/wT/wDNGP5wr4zv+VWeYP8Alptf+Cf/AJox/OFfGd/yqzzB/wAtNr/wT/8ANGP5wr4zv+VWeYP+Wm1/4J/+aMfzhXxnf8qs8wf8tNr/AME//NGP5wr4zv8AlVnmD/lptf8Agn/5ox/OFfGd/wAqs8wf8tNr/wAE/wDzRj+cK+M7/lVnmD/lptf+Cf8A5ox/OFfGd/yqzzB/y02v/BP/AM0Y/nCvjO/5VZ5g/wCWm1/4J/8AmjH84V8Z3/KrPMH/AC02v/BP/wA0Y/nCvjO/5VZ5g/5abX/gn/5ox/OFfGd/yqzzB/y02v8AwT/80Y/nCvjO/wCVWeYP+Wm1/wCCf/mjH84V8Z3/ACqzzB/y02v/AAT/APNGP5wr4zv+VWeYP+Wm1/4J/wDmjH84V8Z3/KrPMH/LTa/8E/8AzRj+cK+M7/lVnmD/AJabX/gn/wCaMfzhXxnf8qs8wf8ALTa/8E//ADRj+cK+M7/lVnmD/lptf+Cf/mjH84V8Z3/KrPMH/LTa/wDBP/zRj+cK+M7/AJVZ5g/5abX/AIJ/+aMfzhXxnf8AKrPMH/LTa/8ABP8A80Y/nCvjO/5VZ5g/5abX/gn/AOaMfzhXxnf8qs8wf8tNr/wT/wDNGP5wr4zv+VWeYP8Alptf+Cf/AJox/OFfGd/yqzzB/wAtNr/wT/8ANGP5wr4zv+VWeYP+Wm1/4J/+aMfzhXxnf8qs8wf8tNr/AME//NGP5wr4zv8AlVnmD/lptf8Agn/5ox/OFfGd/wAqs8wf8tNr/wAE/wDzRj+cK+M7/lVnmD/lptf+Cf8A5ox/OFfGd/yqzzB/y02v/BP/AM0Y/nCvjNH8rteAqbm2p/rSf80YjWFHi3slGveU9W0KKO4ujHJE7emrxk0505ps/H/LzJw6gyLOOqkfSEy/LnVJrbXBp4ctBeK37vsJFHqep/wIZMp1cDza8kR1eucwAM1u7iykIrqjFk8t/OTzY0FrH5ZsDW8vwPrPHqIifhgH/Fk7YoBt4vDp2oi4uYoo2W5sFaacdHjELDmf9aN2xS+jPy281r5l8vpNK3+5C2pDeL3LAfDMP8mZf+SnPFWX4q7FXYq7FX//1OzYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYqtY9MrmapXjP5hH/na7yvQJDX/AIDN3inw4LdhpxYSzTdW1wafLpulP6EDyGae5U0k5UVOPP8A1f8AfeazLjya6fF9MYfj+BOonp9FDjynxc/+pQn+8/5V5EQdP1aNjINWlWT/AH5zZBX241bMr+TahUDx5HX4/avDLaWLLPi/meEyPyz58v7a8g0jXhzWUhLa9NNwdhzZevx/DybNeIyjtP0zcw48WSHiYRKOGX+e9KjJI3Pxd6dMnTgSFFUyIKabw2mnY2tOxtadja07G1p2NrTsbWnY2tOxtadja07G1p2NrTsbWnY2tOxtadja07G1p2NrTsbWnY2tOxtadja07G1p2NrTsbWnY2tOxtadja07G1p2NrTsbWnY2tOxtadja07G1p2NrTsbWnY2tOxtadja07G1p2NrTsbWnY2tOxtadja07G1p2NrTsbWnY2tOxtadja07G1p2NrTsbWnY2tOxtadja07G1ppumJKhhP5n/wDKPReH1pP+ItmbpJATtytCYgkl5B+kL+PUFTTZjbXEPImZTxarLxc/8A2W63UxATp9PLVZiIq8F95lspDdWmqTidSC1ZCQ1Ozqft5roaqEnZansOdcX/FPXfy/84f4k05vrYCaraN6dyqgqCD/AHciL/l4ZC+ToTLhlwFL7b8t3fz1L5nv7tbm29T1raD4uYkGyerX93xh/Y45GqZEUwzyBFFP+amtQyrzhlF+jKejK0gDLihm3kn8urryv5g1C+S8D6bcoUgsxyqAWDJ6pb4f3K/CnHFWfKwYch0OKrsVdirsVf/V7NirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdiq3j4nI8O+6l4r+ZJI8z3tD+xD/xDMrNIjT7O87JgCfV6lujxLDYxKAeTL6hbxJGbvTREYAR/mvmvaupnlzmcvUIz4P9IjORJCn4j2B6Zf4IG4Ph/wBVwpTP1D91H/a0r1+2B05nK/vImBRl7cu+artPCDHiB9T1fs3rSJSw/wB7HN6MUMn+R/qfzHrfli+lvdA065f7c1urMfenH/jXNTAVHd2eXFRkP4optFXckk7dMls1Ql6a/iVKYGTqYq6mKupirqYq6mKupirqYq6mKupirqYq6mKupirqYq6mKupirqYq6mKupirqYq6mKupirqYq6mKupirqYq6mKupirqYq6mKupirqYq6mKupirqYq6mKupirqYq6mKupirqYq6mKupirqYq6mKupirqYq6mKupirqYq6mKupirqYq6mKupirqYq6mKupirqYq0w+HBSbYT+Zv/KPx77fWo/1Pmbpq4j/VbdJH1mP854zZyeleTxvszE8SfDMTtPCTRHc7rsHJHHllA/VxJgz8FZnNFA3J2zT48cpSsDhetkY4wTKXHGTL/wAnbaeS91a/UUtSFhjfty5eof8AhM3kgOAD+J8zzADNI/wvW41UIOPTtlEQQKJ4kXbxD8uiT+besDsTe1/5GjJK9zxVrFW8VdirsVf/1uzYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXiv5ixl/NN8vikNP+AzOji49OXcaHLwBA6HqEP1f6vcECSIUR2qFK/81LlvZ2t4/SfRKLzPtD2NmxT8TGJZNLP+ZH/fpqOTLvVVXYsRsPuzYZsO/EZel5UjHEihxzn/AAJbdNPql1Do+nfvZZXG69gD8bn/ACI/ttyzRa7PxHhx/wB2992FoZaKMtTqBwZ5x/dYp/u5/wDEPZNMs0sbG2tIyONvGEAHQ07rlB2i1Z5HJM5P56OQ1J2wjkgcrX4q7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq03Q4oLCfzPp/h6Kn/LUn/EXzK0ouR/quZpD6iT/ADXmWl+X4Nf1e2sXlMDzclEy9RwHNvh9xmfq6ERf81ruUQZj6+NlNt+Tjm4P13VzLa1qkSRsshHg/JmGYGLUARqnH1Jy5I83pGkaNY6RYQ2OnxCK2i6CtanuzE/abMOcblbHhIABTEAAUGSZvDvy5/8AJuax877/AJPDFXueKuxV2KuxV2Kv/9fs2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KtYq8c/MWF080zM+wnjjaM9iEXi3/AA2bfRz9HD/C5eI7ITQ7fyndWM8OtXH1K7Eomtp6mpjKhPT4gP8ADzXlmJrsJnK4jwv+E/u2/FqJ4z/q8P8AU8/73GqDQfL4kq/mtfRPWMQyVp8yf+Ncw448tUZZK/rST+ZHFxeDpf8AlVBleg3X5d6HGRbaijyyCksz8ize2yfCMlHEYiqaNXnyZyOL+BPF87+UFFP0nGfmH/5oxljkRVONwSXDz35SH/Szj+5/+aMRjkByRwFv/HnlL/q5xfc//NOHgl3LwSd/jzyl/wBXOL7n/wCaceCXcvBJ3+PPKX/Vzi+5/wDmnHgl3LwSd/jzyl/1c4vuf/mnHgl3LwSd/jzyl/1c4vuf/mnHgl3LwSd/jzyl/wBXOL7n/wCaceCXcvBJ3+PPKX/Vzi+5/wDmnHgl3LwSd/jzyl/1c4vuf/mnHgl3LwSd/jzyl/1c4vuf/mnHgl3LwSd/jzyl/wBXOL7n/wCaceCXcvBJ3+PPKX/Vzi+5/wDmnHgl3LwSd/jzyl/1c4vuf/mnHgl3LwSd/jzyl/1c4vuf/mnHgl3LwSd/jzyl/wBXOL7n/wCaceCXcvBJ3+PPKX/Vzi+5/wDmnHgl3LwSd/jzyl/1c4vuf/mnHgl3LwSd/jzyl/1c4vuf/mnHgl3LwSd/jzyl/wBXOL7n/wCaceCXcvBJ3+PPKX/Vzi+5/wDmnHgl3LwSd/jzyl/1c4vuf/mnHgl3LwSd/jzyl/1c4vuf/mnHgl3LwSd/jzyl/wBXOL7n/wCaceCXcvBJ3+PPKX/Vzi+5/wDmnHgl3LwSd/jzyl/1c4vuf/mnHgl3LwSd/jzyl/1c4vuf/mnHgl3LwSd/jzyl/wBXOL7n/wCaceCXcvBJ3+PPKX/Vzi+5/wDmnHgl3LwSd/jzyl/1c4vuf/mnHgl3LwSd/jzyl/1c4vuf/mnHgl3LwSd/jzyl/wBXOL7n/wCaceCXcvBJ3+PPKX/Vzi+5/wDmnHgl3LwSd/jzyl/1c4vuf/mnHgl3LwSd/jzyl/1c4vuf/mnHgl3LwSd/jzyl/wBXOL7n/wCaceCXcvBJ3+PPKX/Vzi+5/wDmnHgl3LwSd/jzyl/1c4vuf/mnHgl3LwSd/jzyl/1c4vuf/mnHgl3LwSd/jzyl/wBXOL7n/wCaceCXcvBJ3+PPKX/Vzi+5/wDmnHgl3LwSd/jzyl/1c4vuf/mnHgl3LwSd/jzyl/1c4vuf/mnHgl3LwSd/jzyl/wBXOL7n/wCaceCXcvBJ3+PPKX/Vzi+5/wDmnHgl3LwSd/jzyl/1c4vuf/mnHgl3LwSd/jzyl/1c4vuf/mnHgl3LwSd/jzyl/wBXOL7n/wCaceCXcvBJ3+PPKX/Vzi+5/wDmnHgl3LwSd/jzyl/1c4vuf/mnHgl3LwSd/jzyl/1c4vuf/mnHgl3LwSd/jzyl/wBXOL7n/wCaceCXcvBJ3+PPKX/Vzi+5/wDmnHgl3LwSd/jzyl/1c4vuf/mnHgl3LwSd/jzyl/1c4vuf/mnHgl3LwSd/jzyl/wBXOL7n/wCaceCXcvBJ3+PPKX/Vzi+5/wDmnHgl3LwSd/jzyl/1c4vuf/mnHgl3LwSd/jzyl/1c4vuf/mnHgl3LwSd/jzyl/wBXOL7n/wCaceCXcvBJ3+PPKX/Vzi+5/wDmnHgl3LwSabz35SKkHU4/uf8A5ox8OXcg4yxTz55l0XU9Kt7LTbtbiVp1lbiD8KIDWvLj+065maSMuNyMYN2kPkGJ382WbIpKx82dh4cHVn/4L4cv7QGwXKbe0LGo375qXFiKFLiK4CLS7oMQKV4p+X1jfQ/mrq1xLbSxwsb3jKyMqGsoIo7Lx+L9nCr2zFXYq7FXYq7FX//Q7NirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVYt508qHXLVZICEvYN4mP7Q6+mT2zIw5eFthOnlt1oGuWjmKaxnHGoBiT1F61bdKtxrmxjqI9XI4woDTNVqWFhcAnc0hk/wCNlyZzwXjDv0Vqf/LBcj5Qyf8ANOQ8eKfEDv0Vqn/LDc/8iZP+acfHivih36K1T/lhuf8AkTJ/zTj48V8UO/RWqf8ALDc/8iZP+acfHivih36K1T/lhuf+RMn/ADTj48V8UO/RWqf8sNz/AMiZP+acfHivih36K1T/AJYbn/kTJ/zTj48V8UO/RWqf8sNz/wAiZP8AmnHx4r4od+itU/5Ybn/kTJ/zTj48V8UO/RWqf8sNz/yJk/5px8eK+KHforVP+WG5/wCRMn/NOPjxXxQ79Fap/wAsNz/yJk/5px8eK+KHforVP+WG5/5Eyf8ANOPjxXxQ79Fap/yw3P8AyJk/5px8eK+KHforVP8Alhuf+RMn/NOPjxXxQ79Fap/yw3P/ACJk/wCacfHivih36K1T/lhuf+RMn/NOPjxXxQ79Fap/yw3P/ImT/mnHx4r4od+itU/5Ybn/AJEyf804+PFfFDv0Vqn/ACw3P/ImT/mnHx4r4od+itU/5Ybn/kTJ/wA04+PFfFDv0Vqn/LDc/wDImT/mnHx4r4od+itU/wCWG5/5Eyf804+PFfFDv0Vqn/LDc/8AImT/AJpx8eK+KHforVP+WG5/5Eyf804+PFfFDv0Vqn/LDc/8iZP+acfHivih36K1T/lhuf8AkTJ/zTj48V8UO/RWqf8ALDc/8iZP+acfHivih36K1T/lhuf+RMn/ADTj48V8UO/RWqf8sNz/AMiZP+acfHivih36K1T/AJYbn/kTJ/zTj48V8UO/RWqf8sNz/wAiZP8AmnHx4r4od+itU/5Ybn/kTJ/zTj48V8UO/RWqf8sNz/yJk/5px8eK+KHforVP+WG5/wCRMn/NOPjxXxQ79Fap/wAsNz/yJk/5px8eK+KHforVP+WG5/5Eyf8ANOPjxXxQ79Fap/yw3P8AyJk/5px8eK+KHforVP8Alhuf+RMn/NOPjxXxQ79Fap/yw3P/ACJk/wCacfHivih36K1T/lhuf+RMn/NOPjxXxQ79Fap/yw3P/ImT/mnHx4r4od+itU/5Ybn/AJEyf804+PFfFDv0Vqn/ACw3P/ImT/mnHx4r4od+itU/5Ybn/kTJ/wA04+PFfFDv0Vqn/LDc/wDImT/mnHx4r4od+itU/wCWG5/5Eyf804+PFfFDv0Vqn/LDc/8AImT/AJpx8eK+KHforVP+WG5/5Eyf804+PFfFDv0Vqn/LDc/8iZP+acfHivih36K1T/lhuf8AkTJ/zTj48V8UO/RWqf8ALDc/8iZP+acfHivih36K1T/lhuf+RMn/ADTj48V8UO/RWqf8sNz/AMiZP+acfHivih36K1T/AJYbn/kTJ/zTj48V8UO/RWqf8sNz/wAiZP8AmnHx4r4od+itU/5Ybn/kTJ/zTj48V8UO/RWqf8sNz/yJk/5px8eK+KHforVP+WG5/wCRMn/NOPjxXxQ79Fap/wAsNz/yJk/5px8eK+KHforVP+WG5/5Eyf8ANOPjxXxQ79Fap/yw3P8AyJk/5px8eK+KHforVP8Alhuf+RUn/NOPjxQcgKpb6Frdy5jg0+Yu2xLxlB/wUnH9rAM8RuEcQem+SvKL6Gj3d0VN9OoTiNwidSgP7Xx/Fmv1Wo4y48zbMMx2tvFWj74qtJjAFTttQ70xVcGBJFdx1GKt4q7FXYq7FX//0ezYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FXYq7FWsVdxGKupirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdirsVdiriARQ9MVa4jFW6DFW8VdiqE1O+j0/T7m+kFY7eNpGHjxFaYq8y8q+V7nzxZN5l1/ULkC7eQWdrbyGJIo1YqtOP2sVZ55V0G70GxksJ76S/hWQm1km+2kRG0JarcuDYqnmKuxV2KuxV/9Ls2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KuxV2KsQ/MzzDqfl3y22o6Y6x3Qmjj5Oode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 alt="Figure 2
In the RLSE, the emitter–receiver
C
*
{{\rm{C}}}^{* }
is stationary and the contour of length
≃
2
L
=
P
\simeq 2L=P
is moving with a relative speed
v
v
. (a) The device
C
*
{{\rm{C}}}^{* }
emits a photon that travels on the contour lower section from the position
AC
*
=
D
<
2
v
L
⁄
c
2
{\rm{AC}}* =D\lt 2vL/{c}^{2}
. (b) When point A reaches
C
*
{{\rm{C}}}^{* }
, the contour changes direction of motion while sliding in the perpendicular direction at speed
v
v
on
C
*
{{\rm{C}}}^{* }
for a short negligible time interval
η
\eta
. (c) After the contour has resumed its motion in the horizontal direction, after a round-trip,
C
*
{{\rm{C}}}^{* }
receives the returning photon on the contour upper section.
"></div><div class="figure-description mb-3"><div class="figure-label h3"><span class=label>Figure 2</span></div><div class="figure-caption mb-2"><span class=caption><p>In the RLSE, the emitter–receiver <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-276><span class=MJXp-msup id=MJXp-Span-277><span class=MJXp-mrow id=MJXp-Span-278 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-279>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-280 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-281>*</span></span></span></span></span><span id=MathJax-Element-39-Frame class="mjx-chtml MathJax_CHTML MJXc-processed sf-hidden" tabindex=0 style=font-size:129%></span>
</span>
</span> is stationary and the contour of length <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-282><span class=MJXp-mo id=MJXp-Span-283 style=margin-left:0.333em;margin-right:0.333em>≃</span><span class=MJXp-mn id=MJXp-Span-284>2</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-285>L</span><span class=MJXp-mo id=MJXp-Span-286 style=margin-left:0.333em;margin-right:0.333em>=</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-287>P</span></span></span><span id=MathJax-Element-40-Frame class="mjx-chtml MathJax_CHTML MJXc-processed sf-hidden" tabindex=0 style=font-size:129%></span>
</span>
</span> is moving with a relative speed <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-288><span class="MJXp-mi MJXp-italic" id=MJXp-Span-289>v</span></span></span><span id=MathJax-Element-41-Frame class="mjx-chtml MathJax_CHTML MJXc-processed sf-hidden" tabindex=0 style=font-size:129%></span>
</span>
</span>. (a) The device <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-290><span class=MJXp-msup id=MJXp-Span-291><span class=MJXp-mrow id=MJXp-Span-292 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-293>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-294 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-295>*</span></span></span></span></span><span id=MathJax-Element-42-Frame class="mjx-chtml MathJax_CHTML MJXc-processed sf-hidden" tabindex=0 style=font-size:129%></span>
</span>
</span> emits a photon that travels on the contour lower section from the position <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-296><span class=MJXp-mi id=MJXp-Span-297>AC</span><span class=MJXp-mo id=MJXp-Span-298 style=margin-left:0.222em;margin-right:0.222em>*</span><span class=MJXp-mo id=MJXp-Span-299 style=margin-left:0.333em;margin-right:0.333em>=</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-300>D</span><span class=MJXp-mo id=MJXp-Span-301 style=margin-left:0.333em;margin-right:0.333em>&lt;</span><span class=MJXp-mn id=MJXp-Span-302>2</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-303>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-304>L</span><span class=MJXp-mo id=MJXp-Span-305 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class=MJXp-msup id=MJXp-Span-306><span class=MJXp-mrow id=MJXp-Span-307 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-308>c</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-309 style=vertical-align:0.5em><span class=MJXp-mn id=MJXp-Span-310>2</span></span></span></span></span><span id=MathJax-Element-43-Frame class="mjx-chtml MathJax_CHTML MJXc-processed sf-hidden" tabindex=0 style=font-size:129%></span>
</span>
</span>. (b) When point A reaches <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-311><span class=MJXp-msup id=MJXp-Span-312><span class=MJXp-mrow id=MJXp-Span-313 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-314>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-315 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-316>*</span></span></span></span></span><span id=MathJax-Element-44-Frame class="mjx-chtml MathJax_CHTML MJXc-processed sf-hidden" tabindex=0 style=font-size:129%></span>
</span>
</span>, the contour changes direction of motion while sliding in the perpendicular direction at speed <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-317><span class="MJXp-mi MJXp-italic" id=MJXp-Span-318>v</span></span></span><span id=MathJax-Element-45-Frame class="mjx-chtml MathJax_CHTML MJXc-processed sf-hidden" tabindex=0 style=font-size:129%></span>
</span>
</span> on <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-319><span class=MJXp-msup id=MJXp-Span-320><span class=MJXp-mrow id=MJXp-Span-321 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-322>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-323 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-324>*</span></span></span></span></span><span id=MathJax-Element-46-Frame class="mjx-chtml MathJax_CHTML MJXc-processed sf-hidden" tabindex=0 style=font-size:129%></span>
</span>
</span> for a short negligible time interval <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-325><span class="MJXp-mi MJXp-italic" id=MJXp-Span-326>η</span></span></span><span id=MathJax-Element-47-Frame class="mjx-chtml MathJax_CHTML MJXc-processed sf-hidden" tabindex=0 style=font-size:129%></span>
</span>
</span>. (c) After the contour has resumed its motion in the horizontal direction, after a round-trip, <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-327><span class=MJXp-msup id=MJXp-Span-328><span class=MJXp-mrow id=MJXp-Span-329 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-330>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-331 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-332>*</span></span></span></span></span><span id=MathJax-Element-48-Frame class="mjx-chtml MathJax_CHTML MJXc-processed sf-hidden" tabindex=0 style=font-size:129%></span>
</span>
</span> receives the returning photon on the contour upper section.</p></span></div></div></div></div>
<p>Nevertheless, within the context of standard special relativity based on light speed invariance, there are observable features of the linear Sagnac effect that are not reciprocal to those of the RLSE. In fact, when in the interval <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-333><span class=MJXp-msub id=MJXp-Span-334><span class=MJXp-mrow id=MJXp-Span-335 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-336>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-337 style=vertical-align:-0.4em><span class=MJXp-mo id=MJXp-Span-338>⇒</span></span></span></span></span><span id=MathJax-Element-49-Frame class="mjx-chtml MathJax_CHTML MJXc-processed sf-hidden" tabindex=0 style=font-size:127%></span>
</span>
</span> (or <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-339><span class=MJXp-msub id=MJXp-Span-340><span class=MJXp-mrow id=MJXp-Span-341 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-342>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-343 style=vertical-align:-0.4em><span class=MJXp-mo id=MJXp-Span-344>⇐</span></span></span></span></span><span id=MathJax-Element-50-Frame class="mjx-chtml MathJax_CHTML MJXc-processed sf-hidden" tabindex=0 style=font-size:127%></span>
</span>
</span>) the device <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-345><span class=MJXp-msup id=MJXp-Span-346><span class=MJXp-mrow id=MJXp-Span-347 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-348>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-349 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-350>*</span></span></span></span></span><span id=MathJax-Element-51-Frame class="mjx-chtml MathJax_CHTML MJXc-processed sf-hidden" tabindex=0 style=font-size:127%></span>
</span>
</span> turns around the pulley in the linear Sagnac effect of <a href=#j_phys-2023-0110_fig_001 class="link link-fig" data-bs-target=j_phys-2023-0110_fig_001>Figure 1</a>(b), for the corresponding RLSE of <a href=#j_phys-2023-0110_fig_002 class="link link-fig" data-bs-target=j_phys-2023-0110_fig_002>Figure 2</a>, the Lorentz transformations (LTs) foresee variations in the first order in <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-351><span class="MJXp-mi MJXp-italic" id=MJXp-Span-352>v</span><span class=MJXp-mo id=MJXp-Span-353 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-354>c</span></span></span><span id=MathJax-Element-52-Frame class="mjx-chtml MathJax_CHTML MJXc-processed sf-hidden" tabindex=0 style=font-size:127%></span>
</span>
</span> for the interval <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-355><span class=MJXp-msub id=MJXp-Span-356><span class=MJXp-mrow id=MJXp-Span-357 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-358>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-359 style=vertical-align:-0.4em><span class=MJXp-mo id=MJXp-Span-360>⇒</span></span></span></span></span><span id=MathJax-Element-53-Frame class="mjx-chtml MathJax_CHTML MJXc-processed sf-hidden" tabindex=0 style=font-size:127%></span>
</span>
</span> (or <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-361><span class=MJXp-msub id=MJXp-Span-362><span class=MJXp-mrow id=MJXp-Span-363 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-364>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-365 style=vertical-align:-0.4em><span class=MJXp-mo id=MJXp-Span-366>⇐</span></span></span></span></span><span id=MathJax-Element-54-Frame class="mjx-chtml MathJax_CHTML MJXc-processed sf-hidden" tabindex=0 style=font-size:127%></span>
</span>
</span>), which differ from that given by Eq. (<a href=#j_phys-2023-0110_eq_001 class="link link-disp-formula" data-bs-target=j_phys-2023-0110_eq_001>1</a>). Thus, if experimentally confirmed, the RLSE represents a new optical effect, which differs from the standard Sagnac effect.</p>
<p>In Section 3, we describe a realistic experiment, feasible with present technology, which can measure the mentioned variations related to the velocity <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-367><span class="MJXp-mi MJXp-italic" id=MJXp-Span-368>v</span></span></span><span id=MathJax-Element-55-Frame class="mjx-chtml MathJax_CHTML MJXc-processed sf-hidden" tabindex=0 style=font-size:127%></span>
</span>
</span>.</p>
<p>There are no problems in interpreting the circular and linear Sagnac effect in the inertial frame of reference <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-369><span class=MJXp-msub id=MJXp-Span-370><span class=MJXp-mrow id=MJXp-Span-371 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-372>S</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-373 style=vertical-align:-0.4em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-374>c</span></span></span></span></span><span id=MathJax-Element-56-Frame class="mjx-chtml MathJax_CHTML MJXc-processed sf-hidden" tabindex=0 style=font-size:127%></span>
</span>
</span> of the stationary contour where the speed of light is assumed to be <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-375><span class="MJXp-mi MJXp-italic" id=MJXp-Span-376>c</span></span></span><span id=MathJax-Element-57-Frame class="mjx-chtml MathJax_CHTML MJXc-processed sf-hidden" tabindex=0 style=font-size:127%></span>
</span>
</span>, while different interpretations of the Sagnac effects are given [<a href=#j_phys-2023-0110_ref_004 class="link link-bibr" data-bs-target=j_phys-2023-0110_ref_004 data-bs-toggle=tooltip title="[4] Lee C. Simultaneity in cylindrical spacetime. Am J Phys. 2020;88:131. 10.1119/10.0000002Search in Google Scholar">4</a>–<a href=#j_phys-2023-0110_ref_012 class="link link-bibr" data-bs-target=j_phys-2023-0110_ref_012 data-bs-toggle=tooltip title="[12] Field JH. The Sagnac effect and transformations of relative velocities between inertial frames. Fund J Modern Phys. 2017;10(1):1–30. Search in Google Scholar">12</a>] in the frame <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-377><span class=MJXp-msub id=MJXp-Span-378><span class=MJXp-mrow id=MJXp-Span-379 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-380>S</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-381 style=vertical-align:-0.4em><span class=MJXp-msup id=MJXp-Span-382><span class=MJXp-mrow id=MJXp-Span-383 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-384>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-385 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-386>*</span></span></span></span></span></span></span><span id=MathJax-Element-58-Frame class="mjx-chtml MathJax_CHTML MJXc-processed sf-hidden" tabindex=0 style=font-size:127%></span>
</span>
</span> comoving with the device <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-387><span class=MJXp-msup id=MJXp-Span-388><span class=MJXp-mrow id=MJXp-Span-389 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-390>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-391 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-392>*</span></span></span></span></span><span id=MathJax-Element-59-Frame class="mjx-chtml MathJax_CHTML MJXc-processed sf-hidden" tabindex=0 style=font-size:127%></span>
</span>
</span>.</p>
<p>Some of the calculations that support our results are presented in the Appendix. Moreover, in the Appendix, we discuss some of the interpretations of the Sagnac effects in the wider scenario of relativistic theories [<a href=#j_phys-2023-0110_ref_004 class="link link-bibr" data-bs-target=j_phys-2023-0110_ref_004 data-bs-toggle=tooltip title="[4] Lee C. Simultaneity in cylindrical spacetime. Am J Phys. 2020;88:131. 10.1119/10.0000002Search in Google Scholar">4</a>–<a href=#j_phys-2023-0110_ref_013 class="link link-bibr" data-bs-target=j_phys-2023-0110_ref_013 data-bs-toggle=tooltip title="[13] Mansouri R, Sexl RU. A test theory of special relativity: I. Simultaneity and clock synchronization. Gen Rel Grav. 1977;8:497, 515, 809. 10.1007/BF00762634Search in Google Scholar">13</a>], involving tests on simultaneity confirming that relative and absolute simultaneity are not physically equivalent. In this scenario, we show how the RLSE can be used as a test of light speed invariance.</p>
</section>
<section id=j_phys-2023-0110_s_002>
<h2 class=subheading>2 The reciprocal linear Sagnac effect</h2>
<p>In the RLSE of <a href=#j_phys-2023-0110_fig_002 class="link link-fig" data-bs-target=j_phys-2023-0110_fig_002>Figure 2</a>, the measuring device <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-393><span class=MJXp-msup id=MJXp-Span-394><span class=MJXp-mrow id=MJXp-Span-395 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-396>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-397 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-398>*</span></span></span></span></span><span id=MathJax-Element-60-Frame class="mjx-chtml MathJax_CHTML MJXc-processed sf-hidden" tabindex=0 style=font-size:127%></span>
</span>
</span> (clock or interferometer) is stationary, while the whole contour is moving back and forth with uniform speed <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-399><span class="MJXp-mi MJXp-italic" id=MJXp-Span-400>v</span></span></span><span id=MathJax-Element-61-Frame class="mjx-chtml MathJax_CHTML MJXc-processed sf-hidden" tabindex=0 style=font-size:127%></span>
</span>
</span> relative to <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-401><span class=MJXp-msup id=MJXp-Span-402><span class=MJXp-mrow id=MJXp-Span-403 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-404>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-405 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-406>*</span></span></span></span></span><span id=MathJax-Element-62-Frame class="mjx-chtml MathJax_CHTML MJXc-processed sf-hidden" tabindex=0 style=font-size:127%></span>
</span>
</span>. Ideally, the motion of the contour should be such that, locally, the relative speed between the contour and <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-407><span class=MJXp-msup id=MJXp-Span-408><span class=MJXp-mrow id=MJXp-Span-409 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-410>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-411 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-412>*</span></span></span></span></span><span id=MathJax-Element-63-Frame class="mjx-chtml MathJax_CHTML MJXc-processed sf-hidden" tabindex=0 style=font-size:127%></span>
</span>
</span> would always be <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-413><span class="MJXp-mi MJXp-italic" id=MJXp-Span-414>v</span></span></span><span id=MathJax-Element-64-Frame class="mjx-chtml MathJax_CHTML MJXc-processed sf-hidden" tabindex=0 style=font-size:127%></span>
</span>
</span>. In <a href=#j_phys-2023-0110_fig_002 class="link link-fig" data-bs-target=j_phys-2023-0110_fig_002>Figure 2</a>(a), the contour is moving with uniform motion relative to <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-415><span class=MJXp-msup id=MJXp-Span-416><span class=MJXp-mrow id=MJXp-Span-417 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-418>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-419 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-420>*</span></span></span></span></span><span id=MathJax-Element-65-Frame class="mjx-chtml MathJax_CHTML MJXc-processed sf-hidden" tabindex=0 style=font-size:127%></span>
</span>
</span>, which stays on the contour lower section until pulley A (not shown) reaches <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-421><span class=MJXp-msup id=MJXp-Span-422><span class=MJXp-mrow id=MJXp-Span-423 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-424>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-425 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-426>*</span></span></span></span></span><span id=MathJax-Element-66-Frame class="mjx-chtml MathJax_CHTML MJXc-processed sf-hidden" tabindex=0 style=font-size:127%></span>
</span>
</span>. At this moment, since <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-427><span class=MJXp-msup id=MJXp-Span-428><span class=MJXp-mrow id=MJXp-Span-429 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-430>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-431 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-432>*</span></span></span></span></span><span id=MathJax-Element-67-Frame class="mjx-chtml MathJax_CHTML MJXc-processed sf-hidden" tabindex=0 style=font-size:127%></span>
</span>
</span> is stationary, the contour has to move slightly in the direction perpendicular to AB during the short time <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-433><span class="MJXp-mi MJXp-italic" id=MJXp-Span-434>η</span></span></span><span id=MathJax-Element-68-Frame class="mjx-chtml MathJax_CHTML MJXc-processed sf-hidden" tabindex=0 style=font-size:127%></span>
</span>
</span> when sliding around <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-435><span class=MJXp-msup id=MJXp-Span-436><span class=MJXp-mrow id=MJXp-Span-437 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-438>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-439 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-440>*</span></span></span></span></span><span id=MathJax-Element-69-Frame class="mjx-chtml MathJax_CHTML MJXc-processed sf-hidden" tabindex=0 style=font-size:127%></span>
</span>
</span> at A, as shown in <a href=#j_phys-2023-0110_fig_002 class="link link-fig" data-bs-target=j_phys-2023-0110_fig_002>Figure 2</a>(b). After changing direction of motion, the contour is moving relative to <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-441><span class=MJXp-msup id=MJXp-Span-442><span class=MJXp-mrow id=MJXp-Span-443 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-444>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-445 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-446>*</span></span></span></span></span><span id=MathJax-Element-70-Frame class="mjx-chtml MathJax_CHTML MJXc-processed sf-hidden" tabindex=0 style=font-size:127%></span>
</span>
</span>, now on the upper section as shown in <a href=#j_phys-2023-0110_fig_002 class="link link-fig" data-bs-target=j_phys-2023-0110_fig_002>Figure 2</a>(c).</p>
<p>If the pulleys have diameter <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-447><span class=MJXp-mn id=MJXp-Span-448>2</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-449>R</span></span></span><span id=MathJax-Element-71-Frame class="mjx-chtml MathJax_CHTML MJXc-processed sf-hidden" tabindex=0 style=font-size:127%></span>
</span>
</span>, the motion in the perpendicular direction <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-450><span class=MJXp-mn id=MJXp-Span-451>2</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-452>H</span><span class=MJXp-mo id=MJXp-Span-453 style=margin-left:0.333em;margin-right:0.333em>≃</span><span class=MJXp-mn id=MJXp-Span-454>2</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-455>R</span></span></span><span id=MathJax-Element-72-Frame class="mjx-chtml MathJax_CHTML MJXc-processed sf-hidden" tabindex=0 style=font-size:127%></span>
</span>
</span> takes place during the finite time interval <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-456><span class="MJXp-mi MJXp-italic" id=MJXp-Span-457>η</span><span class=MJXp-mo id=MJXp-Span-458 style=margin-left:0.333em;margin-right:0.333em>≃</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-459>π</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-460>R</span><span class=MJXp-mo id=MJXp-Span-461 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-462>v</span></span></span><span id=MathJax-Element-73-Frame class="mjx-chtml MathJax_CHTML MJXc-processed sf-hidden" tabindex=0 style=font-size:127%></span>
</span>
</span> when the contour is accelerating and changing its direction of motion relative to <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-463><span class=MJXp-msup id=MJXp-Span-464><span class=MJXp-mrow id=MJXp-Span-465 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-466>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-467 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-468>*</span></span></span></span></span><span id=MathJax-Element-74-Frame class="mjx-chtml MathJax_CHTML MJXc-processed sf-hidden" tabindex=0 style=font-size:127%></span>
</span>
</span>. However, for the purpose of simplifying calculations, we omit the process taking place during the negligible short finite interval <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-469><span class="MJXp-mi MJXp-italic" id=MJXp-Span-470>η</span></span></span><span id=MathJax-Element-75-Frame class="mjx-chtml MathJax_CHTML MJXc-processed sf-hidden" tabindex=0 style=font-size:127%></span>
</span>
</span> by assuming that the round-trip time <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-471><span class="MJXp-mi MJXp-italic" id=MJXp-Span-472>T</span></span></span><span id=MathJax-Element-76-Frame class="mjx-chtml MathJax_CHTML MJXc-processed sf-hidden" tabindex=0 style=font-size:127%></span>
</span>
</span> is much greater than <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-473><span class="MJXp-mi MJXp-italic" id=MJXp-Span-474>η</span></span></span><span id=MathJax-Element-77-Frame class="mjx-chtml MathJax_CHTML MJXc-processed sf-hidden" tabindex=0 style=font-size:127%></span>
</span>
</span> (<span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-475><span class="MJXp-mi MJXp-italic" id=MJXp-Span-476>T</span><span class=MJXp-mo id=MJXp-Span-477 style=margin-left:0.333em;margin-right:0.333em>≫</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-478>η</span></span></span><span id=MathJax-Element-78-Frame class="mjx-chtml MathJax_CHTML MJXc-processed sf-hidden" tabindex=0 style=font-size:127%></span>
</span>
</span> and <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-479><span class="MJXp-mi MJXp-italic" id=MJXp-Span-480>L</span><span class=MJXp-mo id=MJXp-Span-481 style=margin-left:0.333em;margin-right:0.333em>≫</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-482>η</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-483>v</span><span class=MJXp-mo id=MJXp-Span-484 style=margin-left:0.333em;margin-right:0.333em>≃</span><span class=MJXp-mn id=MJXp-Span-485>2</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-486>H</span><span class=MJXp-mo id=MJXp-Span-487 style=margin-left:0.333em;margin-right:0.333em>≃</span><span class=MJXp-mn id=MJXp-Span-488>2</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-489>R</span></span></span><span id=MathJax-Element-79-Frame class="mjx-chtml MathJax_CHTML MJXc-processed sf-hidden" tabindex=0 style=font-size:127%></span>
</span>
</span>, while <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-490><span class=MJXp-mrow id=MJXp-Span-491><span class=MJXp-mo id=MJXp-Span-492 style=margin-left:0em;margin-right:0em>(</span><span class=MJXp-mrow id=MJXp-Span-493><span class="MJXp-mi MJXp-italic" id=MJXp-Span-494>v</span><span class=MJXp-mo id=MJXp-Span-495 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-496>c</span></span><span class=MJXp-mo id=MJXp-Span-497 style=margin-left:0em;margin-right:0em>)</span></span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-498>L</span><span class=MJXp-mo id=MJXp-Span-499 style=margin-left:0.333em;margin-right:0.333em>≫</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-500>η</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-501>c</span></span></span><span id=MathJax-Element-80-Frame class="mjx-chtml MathJax_CHTML MJXc-processed sf-hidden" tabindex=0 style=font-size:127%></span>
</span>
</span>). Thus, in the following, we consider the simple ideal case of a linear contour moving back and forth in the direction AB at the uniform speed <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-502><span class="MJXp-mi MJXp-italic" id=MJXp-Span-503>v</span></span></span><span id=MathJax-Element-81-Frame class="mjx-chtml MathJax_CHTML MJXc-processed sf-hidden" tabindex=0 style=font-size:127%></span>
</span>
</span> relative to <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-504><span class=MJXp-msup id=MJXp-Span-505><span class=MJXp-mrow id=MJXp-Span-506 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-507>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-508 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-509>*</span></span></span></span></span><span id=MathJax-Element-82-Frame class="mjx-chtml MathJax_CHTML MJXc-processed sf-hidden" tabindex=0 style=font-size:127%></span>
</span>
</span>. However, in the Appendix, we consider also the more realistic case of a rectangular contour where <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-510><span class="MJXp-mi MJXp-italic" id=MJXp-Span-511>η</span></span></span><span id=MathJax-Element-83-Frame class="mjx-chtml MathJax_CHTML MJXc-processed sf-hidden" tabindex=0 style=font-size:127%></span>
</span>
</span> is not negligible and the motion perpendicular to AB is taken into account.</p>
<p>Denoting by <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-512><span class="MJXp-mi MJXp-italic" id=MJXp-Span-513>P</span><span class=MJXp-mo id=MJXp-Span-514 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-mn id=MJXp-Span-515>2</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-516>L</span></span></span><span id=MathJax-Element-84-Frame class="mjx-chtml MathJax_CHTML MJXc-processed sf-hidden" tabindex=0 style=font-size:127%></span>
</span>
</span> the perimeter of the contour, assuming the light speed to be <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-517><span class="MJXp-mi MJXp-italic" id=MJXp-Span-518>c</span></span></span><span id=MathJax-Element-85-Frame class="mjx-chtml MathJax_CHTML MJXc-processed sf-hidden" tabindex=0 style=font-size:127%></span>
</span>
</span> and using the LT, we find the following results valid for the RLSE:</p>
<p>
<strong>(a)</strong>
<span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-519><span class=MJXp-msup id=MJXp-Span-520><span class=MJXp-mrow id=MJXp-Span-521 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-522>AC</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-523 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-524>*</span></span></span><span class=MJXp-mo id=MJXp-Span-525 style=margin-left:0.333em;margin-right:0.333em>=</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-526>D</span><span class=MJXp-mo id=MJXp-Span-527 style=margin-left:0.333em;margin-right:0.333em>&gt;</span><span class=MJXp-mn id=MJXp-Span-528>2</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-529>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-530>L</span><span class=MJXp-mo id=MJXp-Span-531 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-532>c</span><span class=MJXp-mo id=MJXp-Span-533 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-mrow id=MJXp-Span-534><span class=MJXp-mo id=MJXp-Span-535 style=margin-left:0em;margin-right:0em>(</span><span class=MJXp-mrow id=MJXp-Span-536><span class="MJXp-mi MJXp-italic" id=MJXp-Span-537>v</span><span class=MJXp-mo id=MJXp-Span-538 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-539>c</span></span><span class=MJXp-mo id=MJXp-Span-540 style=margin-left:0em;margin-right:0em>)</span></span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-541>P</span></span></span><span id=MathJax-Element-86-Frame class="mjx-chtml MathJax_CHTML MJXc-processed sf-hidden" tabindex=0 style=font-size:127%></span>
</span>
</span>. <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-542><span class=MJXp-msup id=MJXp-Span-543><span class=MJXp-mrow id=MJXp-Span-544 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-545>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-546 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-547>*</span></span></span></span></span><span id=MathJax-Element-87-Frame class="mjx-chtml MathJax_CHTML MJXc-processed sf-hidden" tabindex=0 style=font-size:127%></span>
</span>
</span>
<strong>remains always on one of the sections of the contour in the interval</strong>
<span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-548><span class="MJXp-mi MJXp-italic" id=MJXp-Span-549>T</span></span></span><span id=MathJax-Element-88-Frame class="mjx-chtml MathJax_CHTML MJXc-processed sf-hidden" tabindex=0 style=font-size:127%></span>
</span>
</span>.</p>
<p>The segment <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-550><span class=MJXp-msup id=MJXp-Span-551><span class=MJXp-mrow id=MJXp-Span-552 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-553>AC</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-554 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-555>*</span></span></span></span></span><span id=MathJax-Element-89-Frame class="mjx-chtml MathJax_CHTML MJXc-processed sf-hidden" tabindex=0 style=font-size:127%></span>
</span>
</span> of length <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-556><span class="MJXp-mi MJXp-italic" id=MJXp-Span-557>D</span></span></span><span id=MathJax-Element-90-Frame class="mjx-chtml MathJax_CHTML MJXc-processed sf-hidden" tabindex=0 style=font-size:127%></span>
</span>
</span> represents the initial position of device <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-558><span class=MJXp-msup id=MJXp-Span-559><span class=MJXp-mrow id=MJXp-Span-560 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-561>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-562 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-563>*</span></span></span></span></span><span id=MathJax-Element-91-Frame class="mjx-chtml MathJax_CHTML MJXc-processed sf-hidden" tabindex=0 style=font-size:127%></span>
</span>
</span> relative to A, the left end point of the contour. For light counter-propagation (photon moving counter-clockwise) starting from the device <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-564><span class=MJXp-msup id=MJXp-Span-565><span class=MJXp-mrow id=MJXp-Span-566 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-567>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-568 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-569>*</span></span></span></span></span><span id=MathJax-Element-92-Frame class="mjx-chtml MathJax_CHTML MJXc-processed sf-hidden" tabindex=0 style=font-size:127%></span>
</span>
</span>, when <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-570><span class="MJXp-mi MJXp-italic" id=MJXp-Span-571>D</span><span class=MJXp-mo id=MJXp-Span-572 style=margin-left:0.333em;margin-right:0.333em>&gt;</span><span class=MJXp-mn id=MJXp-Span-573>2</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-574>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-575>L</span><span class=MJXp-mo id=MJXp-Span-576 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class=MJXp-msup id=MJXp-Span-577><span class=MJXp-mrow id=MJXp-Span-578 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-579>c</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-580 style=vertical-align:0.5em><span class=MJXp-mn id=MJXp-Span-581>2</span></span></span></span></span><span id=MathJax-Element-93-Frame class="mjx-chtml MathJax_CHTML MJXc-processed sf-hidden" tabindex=0 style=font-size:127%></span>
</span>
</span> the description of the RLSE is reciprocal to that shown in (<a href=#j_phys-2023-0110_fig_001 class="link link-fig" data-bs-target=j_phys-2023-0110_fig_001>Figure 1</a>(b)), where <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-582><span class=MJXp-msup id=MJXp-Span-583><span class=MJXp-mrow id=MJXp-Span-584 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-585>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-586 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-587>*</span></span></span></span></span><span id=MathJax-Element-94-Frame class="mjx-chtml MathJax_CHTML MJXc-processed sf-hidden" tabindex=0 style=font-size:127%></span>
</span>
</span> remains always on the lower section of the contour, while the photon performs a round trip in the interval <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-588><span class=MJXp-msub id=MJXp-Span-589><span class=MJXp-mrow id=MJXp-Span-590 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-591>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-592 style=vertical-align:-0.4em><span class=MJXp-mo id=MJXp-Span-593>⇒</span></span></span></span></span><span id=MathJax-Element-95-Frame class="mjx-chtml MathJax_CHTML MJXc-processed sf-hidden" tabindex=0 style=font-size:127%></span>
</span>
</span> and gets back to <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-594><span class=MJXp-msup id=MJXp-Span-595><span class=MJXp-mrow id=MJXp-Span-596 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-597>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-598 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-599>*</span></span></span></span></span><span id=MathJax-Element-96-Frame class="mjx-chtml MathJax_CHTML MJXc-processed sf-hidden" tabindex=0 style=font-size:127%></span>
</span>
</span>. The Lorentz-contracted moving contour has length <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-600><span class="MJXp-mi MJXp-italic" id=MJXp-Span-601>L</span><span class=MJXp-mo id=MJXp-Span-602 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-603>γ</span></span></span><span id=MathJax-Element-97-Frame class="mjx-chtml MathJax_CHTML MJXc-processed sf-hidden" tabindex=0 style=font-size:127%></span>
</span>
</span> and the round-trip times for counter-, <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-604><span class=MJXp-msub id=MJXp-Span-605><span class=MJXp-mrow id=MJXp-Span-606 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-607>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-608 style=vertical-align:-0.4em><span class=MJXp-mo id=MJXp-Span-609>⇒</span></span></span></span></span><span id=MathJax-Element-98-Frame class="mjx-chtml MathJax_CHTML MJXc-processed sf-hidden" tabindex=0 style=font-size:127%></span>
</span>
</span>, and co-propagation, <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-610><span class=MJXp-msub id=MJXp-Span-611><span class=MJXp-mrow id=MJXp-Span-612 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-613>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-614 style=vertical-align:-0.4em><span class=MJXp-mo id=MJXp-Span-615>⇐</span></span></span></span></span><span id=MathJax-Element-99-Frame class="mjx-chtml MathJax_CHTML MJXc-processed sf-hidden" tabindex=0 style=font-size:127%></span>
</span>
</span>, have the expected values, <div class=formula id=j_phys-2023-0110_eq_002>
<span class=label>(2)</span>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class="MJXp-math MJXp-display" id=MJXp-Span-616><span class=MJXp-mtable id=MJXp-Span-617><span><span class=MJXp-mtr id=MJXp-Span-618 style=vertical-align:baseline><span class=MJXp-mtd id=MJXp-Span-619 style=text-align:center><span class=MJXp-msub id=MJXp-Span-620><span class=MJXp-mrow id=MJXp-Span-621 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-622>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-623 style=vertical-align:-0.4em><span class=MJXp-mo id=MJXp-Span-624>⇒</span></span></span></span><span class=MJXp-mtd id=MJXp-Span-625 style=padding-left:0.33em;text-align:center><span class=MJXp-mo id=MJXp-Span-626 style=margin-left:0.333em;margin-right:0.333em>=</span></span><span class=MJXp-mtd id=MJXp-Span-627 style=padding-left:0.33em;text-align:center><span class=MJXp-mfrac id=MJXp-Span-628 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-629><span class=MJXp-mn id=MJXp-Span-630>2</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-631>L</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-632><span class="MJXp-mi MJXp-italic" id=MJXp-Span-633>γ</span><span class=MJXp-mrow id=MJXp-Span-634><span class=MJXp-mo id=MJXp-Span-635 style=margin-left:0em;margin-right:0em>(</span><span class=MJXp-mrow id=MJXp-Span-636><span class="MJXp-mi MJXp-italic" id=MJXp-Span-637>c</span><span class=MJXp-mo id=MJXp-Span-638 style=margin-left:0.267em;margin-right:0.267em>+</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-639>v</span></span><span class=MJXp-mo id=MJXp-Span-640 style=margin-left:0em;margin-right:0em>)</span></span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-641 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-mfrac id=MJXp-Span-642 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-643><span class=MJXp-mn id=MJXp-Span-644>2</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-645>γ</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-646>L</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-647><span class="MJXp-mi MJXp-italic" id=MJXp-Span-648>c</span></span></span></span></span></span></span><span class=MJXp-mfenced id=MJXp-Span-649><span class=MJXp-mo id=MJXp-Span-650 style=margin-left:0em;margin-right:0em;vertical-align:-0.5em><span style=font-size:3em;margin-left:-0.13em class="MJXp-right MJXp-scale5">(</span></span><span class=MJXp-mrow id=MJXp-Span-651><span class=MJXp-mn id=MJXp-Span-652>1</span><span class=MJXp-mo id=MJXp-Span-653 style=margin-left:0.267em;margin-right:0.267em>−</span><span class=MJXp-mfrac id=MJXp-Span-654 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-655><span class="MJXp-mi MJXp-italic" id=MJXp-Span-656>v</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-657><span class="MJXp-mi MJXp-italic" id=MJXp-Span-658>c</span></span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-659 style=margin-left:0em;margin-right:0em;vertical-align:-0.5em><span style=font-size:3em;margin-left:-0.13em class="MJXp-right MJXp-scale5">)</span></span></span></span></span><span class=MJXp-mtr id=MJXp-Span-660 style=vertical-align:baseline><span class=MJXp-mtd id=MJXp-Span-661 style=padding-top:0.431em;text-align:center><span class=MJXp-msub id=MJXp-Span-662><span class=MJXp-mrow id=MJXp-Span-663 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-664>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-665 style=vertical-align:-0.4em><span class=MJXp-mo id=MJXp-Span-666>⇐</span></span></span></span><span class=MJXp-mtd id=MJXp-Span-667 style=padding-left:0.33em;padding-top:0.431em;text-align:center><span class=MJXp-mo id=MJXp-Span-668 style=margin-left:0.333em;margin-right:0.333em>=</span></span><span class=MJXp-mtd id=MJXp-Span-669 style=padding-left:0.33em;padding-top:0.431em;text-align:center><span class=MJXp-mfrac id=MJXp-Span-670 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-671><span class=MJXp-mn id=MJXp-Span-672>2</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-673>L</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-674><span class="MJXp-mi MJXp-italic" id=MJXp-Span-675>γ</span><span class=MJXp-mrow id=MJXp-Span-676><span class=MJXp-mo id=MJXp-Span-677 style=margin-left:0em;margin-right:0em>(</span><span class=MJXp-mrow id=MJXp-Span-678><span class="MJXp-mi MJXp-italic" id=MJXp-Span-679>c</span><span class=MJXp-mo id=MJXp-Span-680 style=margin-left:0.267em;margin-right:0.267em>−</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-681>v</span></span><span class=MJXp-mo id=MJXp-Span-682 style=margin-left:0em;margin-right:0em>)</span></span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-683 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-mfrac id=MJXp-Span-684 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-685><span class=MJXp-mn id=MJXp-Span-686>2</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-687>γ</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-688>L</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-689><span class="MJXp-mi MJXp-italic" id=MJXp-Span-690>c</span></span></span></span></span></span></span><span class=MJXp-mfenced id=MJXp-Span-691><span class=MJXp-mo id=MJXp-Span-692 style=margin-left:0em;margin-right:0em;vertical-align:-0.5em><span style=font-size:3em;margin-left:-0.13em class="MJXp-right MJXp-scale5">(</span></span><span class=MJXp-mrow id=MJXp-Span-693><span class=MJXp-mn id=MJXp-Span-694>1</span><span class=MJXp-mo id=MJXp-Span-695 style=margin-left:0.267em;margin-right:0.267em>+</span><span class=MJXp-mfrac id=MJXp-Span-696 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-697><span class="MJXp-mi MJXp-italic" id=MJXp-Span-698>v</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-699><span class="MJXp-mi MJXp-italic" id=MJXp-Span-700>c</span></span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-701 style=margin-left:0em;margin-right:0em;vertical-align:-0.5em><span style=font-size:3em;margin-left:-0.13em class="MJXp-right MJXp-scale5">)</span></span></span></span></span><span class=MJXp-mtr id=MJXp-Span-702 style=vertical-align:baseline><span class=MJXp-mtd id=MJXp-Span-703 style=padding-top:0.431em;text-align:center><span class=MJXp-mi id=MJXp-Span-704>Δ</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-705>T</span></span><span class=MJXp-mtd id=MJXp-Span-706 style=padding-left:0.33em;padding-top:0.431em;text-align:center><span class=MJXp-mo id=MJXp-Span-707 style=margin-left:0.333em;margin-right:0.333em>=</span></span><span class=MJXp-mtd id=MJXp-Span-708 style=padding-left:0.33em;padding-top:0.431em;text-align:center><span class=MJXp-msub id=MJXp-Span-709><span class=MJXp-mrow id=MJXp-Span-710 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-711>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-712 style=vertical-align:-0.4em><span class=MJXp-mo id=MJXp-Span-713>⇐</span></span></span><span class=MJXp-mo id=MJXp-Span-714 style=margin-left:0.267em;margin-right:0.267em>−</span><span class=MJXp-msub id=MJXp-Span-715><span class=MJXp-mrow id=MJXp-Span-716 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-717>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-718 style=vertical-align:-0.4em><span class=MJXp-mo id=MJXp-Span-719>⇒</span></span></span><span class=MJXp-mo id=MJXp-Span-720 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-mfrac id=MJXp-Span-721 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-722><span class=MJXp-mn id=MJXp-Span-723>4</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-724>γ</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-725>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-726>L</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-727><span class=MJXp-msup id=MJXp-Span-728><span class=MJXp-mrow id=MJXp-Span-729 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-730>c</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-731 style=vertical-align:0.5em><span class=MJXp-mn id=MJXp-Span-732>2</span></span></span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-733 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-mfrac id=MJXp-Span-734 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-735><span class=MJXp-mn id=MJXp-Span-736>4</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-737>γ</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-738>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-739>L</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-740><span class=MJXp-msup id=MJXp-Span-741><span class=MJXp-mrow id=MJXp-Span-742 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-743>c</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-744 style=vertical-align:0.5em><span class=MJXp-mn id=MJXp-Span-745>2</span></span></span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-746 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-mfrac id=MJXp-Span-747 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-748><span class=MJXp-mn id=MJXp-Span-749>2</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-750>γ</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-751>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-752>P</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-753><span class=MJXp-msup id=MJXp-Span-754><span class=MJXp-mrow id=MJXp-Span-755 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-756>c</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-757 style=vertical-align:0.5em><span class=MJXp-mn id=MJXp-Span-758>2</span></span></span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-759 style=margin-left:0em;margin-right:0.222em>,</span></span></span></span></span></span></span><span class="mjx-chtml MJXc-display MJXc-processed sf-hidden" style=text-align:center></span>
</span>
</div><p> where in Eq. (<a href=#j_phys-2023-0110_eq_002 class="link link-disp-formula" data-bs-target=j_phys-2023-0110_eq_002>2</a>), <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-760><span class=MJXp-msub id=MJXp-Span-761><span class=MJXp-mrow id=MJXp-Span-762 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-763>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-764 style=vertical-align:-0.4em><span class=MJXp-mo id=MJXp-Span-765>⇐</span></span></span></span></span><span id=MathJax-Element-101-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>, <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-766><span class=MJXp-msub id=MJXp-Span-767><span class=MJXp-mrow id=MJXp-Span-768 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-769>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-770 style=vertical-align:-0.4em><span class=MJXp-mo id=MJXp-Span-771>⇒</span></span></span></span></span><span id=MathJax-Element-102-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>, and <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-772><span class=MJXp-mi id=MJXp-Span-773>Δ</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-774>T</span></span></span><span id=MathJax-Element-103-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> are the same as given in Eq. (<a href=#j_phys-2023-0110_eq_001 class="link link-disp-formula" data-bs-target=j_phys-2023-0110_eq_001>1</a>). In some cases, we may approximate the results to the first order in <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-775><span class="MJXp-mi MJXp-italic" id=MJXp-Span-776>v</span><span class=MJXp-mo id=MJXp-Span-777 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-778>c</span></span></span><span id=MathJax-Element-104-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> to simplify calculations. In Appendix (A.3), we calculate the round-trip interval <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-779><span class=MJXp-msub id=MJXp-Span-780><span class=MJXp-mrow id=MJXp-Span-781 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-782>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-783 style=vertical-align:-0.4em><span class=MJXp-mo id=MJXp-Span-784>⇒</span></span></span></span></span><span id=MathJax-Element-105-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> for the counter-propagating photon emitted by <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-785><span class=MJXp-msup id=MJXp-Span-786><span class=MJXp-mrow id=MJXp-Span-787 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-788>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-789 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-790>*</span></span></span></span></span><span id=MathJax-Element-106-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> from the distance <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-791><span class=MJXp-msup id=MJXp-Span-792><span class=MJXp-mrow id=MJXp-Span-793 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-794>AC</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-795 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-796>*</span></span></span><span class=MJXp-mo id=MJXp-Span-797 style=margin-left:0.333em;margin-right:0.333em>=</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-798>D</span><span class=MJXp-mo id=MJXp-Span-799 style=margin-left:0.333em;margin-right:0.333em>&gt;</span><span class=MJXp-mn id=MJXp-Span-800>2</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-801>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-802>L</span><span class=MJXp-mo id=MJXp-Span-803 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-804>c</span></span></span><span id=MathJax-Element-107-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>, and show in (<a href=#j_phys-2023-0110_eq_037 class="link link-disp-formula" data-bs-target=j_phys-2023-0110_eq_037>A15</a>) that <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-805><span class=MJXp-msub id=MJXp-Span-806><span class=MJXp-mrow id=MJXp-Span-807 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-808>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-809 style=vertical-align:-0.4em><span class=MJXp-mo id=MJXp-Span-810>⇒</span></span></span></span></span><span id=MathJax-Element-108-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> is independent of <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-811><span class="MJXp-mi MJXp-italic" id=MJXp-Span-812>D</span></span></span><span id=MathJax-Element-109-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> when <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-813><span class=MJXp-msup id=MJXp-Span-814><span class=MJXp-mrow id=MJXp-Span-815 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-816>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-817 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-818>*</span></span></span></span></span><span id=MathJax-Element-110-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> stays on the same track (lower contour section, in this case) during the interval <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-819><span class=MJXp-msub id=MJXp-Span-820><span class=MJXp-mrow id=MJXp-Span-821 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-822>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-823 style=vertical-align:-0.4em><span class=MJXp-mo id=MJXp-Span-824>⇒</span></span></span></span></span><span id=MathJax-Element-111-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>.</p>
<p>In this case (<span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-825><span class="MJXp-mi MJXp-italic" id=MJXp-Span-826>D</span><span class=MJXp-mo id=MJXp-Span-827 style=margin-left:0.333em;margin-right:0.333em>&gt;</span><span class=MJXp-mn id=MJXp-Span-828>2</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-829>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-830>L</span><span class=MJXp-mo id=MJXp-Span-831 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-832>c</span></span></span><span id=MathJax-Element-112-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>), the RLSE foresees results that are the same as those of the standard linear Sagnac effect. Moreover, the symmetry is such that <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-833><span class=MJXp-msub id=MJXp-Span-834><span class=MJXp-mrow id=MJXp-Span-835 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-836>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-837 style=vertical-align:-0.4em><span class=MJXp-mo id=MJXp-Span-838>⇐</span></span></span></span></span><span id=MathJax-Element-113-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> is the same as <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-839><span class=MJXp-msub id=MJXp-Span-840><span class=MJXp-mrow id=MJXp-Span-841 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-842>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-843 style=vertical-align:-0.4em><span class=MJXp-mo id=MJXp-Span-844>⇒</span></span></span></span></span><span id=MathJax-Element-114-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> by changing <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-845><span class="MJXp-mi MJXp-italic" id=MJXp-Span-846>v</span></span></span><span id=MathJax-Element-115-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> to <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-847><span class=MJXp-mo id=MJXp-Span-848 style=margin-left:0em;margin-right:0.111em>−</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-849>v</span></span></span><span id=MathJax-Element-116-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>. It follows that, for <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-850><span class=MJXp-msup id=MJXp-Span-851><span class=MJXp-mrow id=MJXp-Span-852 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-853>AC</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-854 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-855>*</span></span></span><span class=MJXp-mo id=MJXp-Span-856 style=margin-left:0.333em;margin-right:0.333em>=</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-857>D</span><span class=MJXp-mo id=MJXp-Span-858 style=margin-left:0.333em;margin-right:0.333em>&gt;</span><span class=MJXp-mn id=MJXp-Span-859>2</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-860>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-861>L</span><span class=MJXp-mo id=MJXp-Span-862 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-863>c</span></span></span><span id=MathJax-Element-117-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>, results (<a href=#j_phys-2023-0110_eq_002 class="link link-disp-formula" data-bs-target=j_phys-2023-0110_eq_002>2</a>) for the RLSE are equivalent to results (<a href=#j_phys-2023-0110_eq_001 class="link link-disp-formula" data-bs-target=j_phys-2023-0110_eq_001>1</a>) of the standard Sagnac effect. In fact, in agreement with the principle of relativity, provided that <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-864><span class=MJXp-msup id=MJXp-Span-865><span class=MJXp-mrow id=MJXp-Span-866 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-867>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-868 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-869>*</span></span></span></span></span><span id=MathJax-Element-118-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> and the contour are in uniform relative motion in the interval <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-870><span class=MJXp-msub id=MJXp-Span-871><span class=MJXp-mrow id=MJXp-Span-872 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-873>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-874 style=vertical-align:-0.4em><span class=MJXp-mo id=MJXp-Span-875>⇒</span></span></span></span></span><span id=MathJax-Element-119-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>, the two effects are the same when observed either from the rest frame of the contour or the device <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-876><span class=MJXp-msup id=MJXp-Span-877><span class=MJXp-mrow id=MJXp-Span-878 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-879>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-880 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-881>*</span></span></span></span></span><span id=MathJax-Element-120-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>.</p>
<p>
<strong>(b)</strong>
<span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-882><span class=MJXp-msup id=MJXp-Span-883><span class=MJXp-mrow id=MJXp-Span-884 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-885>AC</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-886 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-887>*</span></span></span><span class=MJXp-mo id=MJXp-Span-888 style=margin-left:0.333em;margin-right:0.333em>=</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-889>D</span><span class=MJXp-mo id=MJXp-Span-890 style=margin-left:0.333em;margin-right:0.333em>&lt;</span><span class=MJXp-mn id=MJXp-Span-891>2</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-892>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-893>L</span><span class=MJXp-mo id=MJXp-Span-894 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-895>c</span></span></span><span id=MathJax-Element-121-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>. <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-896><span class=MJXp-msup id=MJXp-Span-897><span class=MJXp-mrow id=MJXp-Span-898 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-899>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-900 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-901>*</span></span></span></span></span><span id=MathJax-Element-122-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>
<strong>and the contour change their direction of relative motion in the interval</strong>
<span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-902><span class="MJXp-mi MJXp-italic" id=MJXp-Span-903>T</span></span></span><span id=MathJax-Element-123-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>.</p>
<p>In this case, for light counter-propagation, the successive positions of the contour relative to <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-904><span class=MJXp-msup id=MJXp-Span-905><span class=MJXp-mrow id=MJXp-Span-906 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-907>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-908 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-909>*</span></span></span></span></span><span id=MathJax-Element-124-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> are shown in <a href=#j_phys-2023-0110_fig_002 class="link link-fig" data-bs-target=j_phys-2023-0110_fig_002>Figure 2</a>, indicating that <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-910><span class=MJXp-msup id=MJXp-Span-911><span class=MJXp-mrow id=MJXp-Span-912 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-913>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-914 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-915>*</span></span></span></span></span><span id=MathJax-Element-125-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> and the contour change their direction of relative motion during the round-trip time.</p>
<p>
<strong>Special case</strong>
<span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-916><span class="MJXp-mi MJXp-italic" id=MJXp-Span-917>D</span><span class=MJXp-mo id=MJXp-Span-918 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-msub id=MJXp-Span-919><span class=MJXp-mrow id=MJXp-Span-920 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-921>D</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-922 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-923>0</span></span></span><span class=MJXp-mo id=MJXp-Span-924 style=margin-left:0.333em;margin-right:0.333em>=</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-925>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-926>L</span><span class=MJXp-mo id=MJXp-Span-927 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-928>c</span></span></span><span id=MathJax-Element-126-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>. Starting from <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-929><span class=MJXp-msub id=MJXp-Span-930><span class=MJXp-mrow id=MJXp-Span-931 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-932>D</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-933 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-934>0</span></span></span><span class=MJXp-mo id=MJXp-Span-935 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-936>γ</span></span></span><span id=MathJax-Element-127-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> (where the factor <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-937><span class="MJXp-mi MJXp-italic" id=MJXp-Span-938>γ</span></span></span><span id=MathJax-Element-128-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> takes into account the length contraction of the moving contour) on the lower section of the contour, the photon travels at speed <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-939><span class="MJXp-mi MJXp-italic" id=MJXp-Span-940>c</span></span></span><span id=MathJax-Element-129-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> toward the moving point B that, at time <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-941><span class="MJXp-mi MJXp-italic" id=MJXp-Span-942>t</span></span></span><span id=MathJax-Element-130-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>, is at the distance <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-943><span class="MJXp-mi MJXp-italic" id=MJXp-Span-944>L</span><span class=MJXp-mo id=MJXp-Span-945 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-946>γ</span><span class=MJXp-mo id=MJXp-Span-947 style=margin-left:0.267em;margin-right:0.267em>−</span><span class=MJXp-msub id=MJXp-Span-948><span class=MJXp-mrow id=MJXp-Span-949 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-950>D</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-951 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-952>0</span></span></span><span class=MJXp-mo id=MJXp-Span-953 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-954>γ</span><span class=MJXp-mo id=MJXp-Span-955 style=margin-left:0.267em;margin-right:0.267em>+</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-956>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-957>t</span><span class=MJXp-mo id=MJXp-Span-958 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-mrow id=MJXp-Span-959><span class=MJXp-mo id=MJXp-Span-960 style=margin-left:0em;margin-right:0em>(</span><span class=MJXp-mrow id=MJXp-Span-961><span class="MJXp-mi MJXp-italic" id=MJXp-Span-962>L</span><span class=MJXp-mo id=MJXp-Span-963 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-964>γ</span></span><span class=MJXp-mo id=MJXp-Span-965 style=margin-left:0em;margin-right:0em>)</span></span><span class=MJXp-mrow id=MJXp-Span-966><span class=MJXp-mo id=MJXp-Span-967 style=margin-left:0em;margin-right:0em>(</span><span class=MJXp-mrow id=MJXp-Span-968><span class=MJXp-mn id=MJXp-Span-969>1</span><span class=MJXp-mo id=MJXp-Span-970 style=margin-left:0.267em;margin-right:0.267em>−</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-971>v</span><span class=MJXp-mo id=MJXp-Span-972 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-973>c</span></span><span class=MJXp-mo id=MJXp-Span-974 style=margin-left:0em;margin-right:0em>)</span></span><span class=MJXp-mo id=MJXp-Span-975 style=margin-left:0.267em;margin-right:0.267em>+</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-976>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-977>t</span></span></span><span id=MathJax-Element-131-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>. Then, the signal reaches point B when <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-978><span class="MJXp-mi MJXp-italic" id=MJXp-Span-979>c</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-980>t</span><span class=MJXp-mo id=MJXp-Span-981 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-mrow id=MJXp-Span-982><span class=MJXp-mo id=MJXp-Span-983 style=margin-left:0em;margin-right:0em>(</span><span class=MJXp-mrow id=MJXp-Span-984><span class="MJXp-mi MJXp-italic" id=MJXp-Span-985>L</span><span class=MJXp-mo id=MJXp-Span-986 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-987>γ</span></span><span class=MJXp-mo id=MJXp-Span-988 style=margin-left:0em;margin-right:0em>)</span></span><span class=MJXp-mrow id=MJXp-Span-989><span class=MJXp-mo id=MJXp-Span-990 style=margin-left:0em;margin-right:0em>(</span><span class=MJXp-mrow id=MJXp-Span-991><span class=MJXp-mn id=MJXp-Span-992>1</span><span class=MJXp-mo id=MJXp-Span-993 style=margin-left:0.267em;margin-right:0.267em>−</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-994>v</span><span class=MJXp-mo id=MJXp-Span-995 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-996>c</span></span><span class=MJXp-mo id=MJXp-Span-997 style=margin-left:0em;margin-right:0em>)</span></span><span class=MJXp-mo id=MJXp-Span-998 style=margin-left:0.267em;margin-right:0.267em>+</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-999>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1000>t</span></span></span><span id=MathJax-Element-132-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>, <em>i.e.</em>, after the time interval <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-1001><span class=MJXp-msub id=MJXp-Span-1002><span class=MJXp-mrow id=MJXp-Span-1003 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1004>t</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-1005 style=vertical-align:-0.4em><span class=MJXp-mi id=MJXp-Span-1006>out</span></span></span><span class=MJXp-mo id=MJXp-Span-1007 style=margin-left:0.333em;margin-right:0.333em>=</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1008>L</span><span class=MJXp-mo id=MJXp-Span-1009 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class=MJXp-mrow id=MJXp-Span-1010><span class=MJXp-mo id=MJXp-Span-1011 style=margin-left:0em;margin-right:0em>(</span><span class=MJXp-mrow id=MJXp-Span-1012><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1013>γ</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1014>c</span></span><span class=MJXp-mo id=MJXp-Span-1015 style=margin-left:0em;margin-right:0em>)</span></span></span></span><span id=MathJax-Element-133-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>. Moreover, since point A is moving toward <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-1016><span class=MJXp-msup id=MJXp-Span-1017><span class=MJXp-mrow id=MJXp-Span-1018 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-1019>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-1020 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-1021>*</span></span></span></span></span><span id=MathJax-Element-134-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> at speed <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-1022><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1023>v</span></span></span><span id=MathJax-Element-135-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> from the initial distance <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-1024><span class=MJXp-msup id=MJXp-Span-1025><span class=MJXp-mrow id=MJXp-Span-1026 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-1027>AC</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-1028 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-1029>*</span></span></span><span class=MJXp-mo id=MJXp-Span-1030 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-msub id=MJXp-Span-1031><span class=MJXp-mrow id=MJXp-Span-1032 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1033>D</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-1034 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-1035>0</span></span></span></span></span><span id=MathJax-Element-136-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>, point A reaches <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-1036><span class=MJXp-msup id=MJXp-Span-1037><span class=MJXp-mrow id=MJXp-Span-1038 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-1039>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-1040 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-1041>*</span></span></span></span></span><span id=MathJax-Element-137-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> when <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-1042><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1043>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1044>t</span><span class=MJXp-mo id=MJXp-Span-1045 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-msub id=MJXp-Span-1046><span class=MJXp-mrow id=MJXp-Span-1047 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1048>D</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-1049 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-1050>0</span></span></span><span class=MJXp-mo id=MJXp-Span-1051 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1052>γ</span><span class=MJXp-mo id=MJXp-Span-1053 style=margin-left:0.333em;margin-right:0.333em>=</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1054>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1055>L</span><span class=MJXp-mo id=MJXp-Span-1056 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class=MJXp-mrow id=MJXp-Span-1057><span class=MJXp-mo id=MJXp-Span-1058 style=margin-left:0em;margin-right:0em>(</span><span class=MJXp-mrow id=MJXp-Span-1059><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1060>γ</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1061>c</span></span><span class=MJXp-mo id=MJXp-Span-1062 style=margin-left:0em;margin-right:0em>)</span></span></span></span><span id=MathJax-Element-138-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>, <em>i.e.</em>, at <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-1063><span class=MJXp-msub id=MJXp-Span-1064><span class=MJXp-mrow id=MJXp-Span-1065 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1066>t</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-1067 style=vertical-align:-0.4em><span class=MJXp-mi id=MJXp-Span-1068>out</span></span></span><span class=MJXp-mo id=MJXp-Span-1069 style=margin-left:0.333em;margin-right:0.333em>=</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1070>L</span><span class=MJXp-mo id=MJXp-Span-1071 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class=MJXp-mrow id=MJXp-Span-1072><span class=MJXp-mo id=MJXp-Span-1073 style=margin-left:0em;margin-right:0em>(</span><span class=MJXp-mrow id=MJXp-Span-1074><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1075>γ</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1076>c</span></span><span class=MJXp-mo id=MJXp-Span-1077 style=margin-left:0em;margin-right:0em>)</span></span></span></span><span id=MathJax-Element-139-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>. Hence, the two events “photon at B” and “A at the position of <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-1078><span class=MJXp-msup id=MJXp-Span-1079><span class=MJXp-mrow id=MJXp-Span-1080 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-1081>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-1082 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-1083>*</span></span></span></span></span><span id=MathJax-Element-140-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>” are simultaneous in the reference frame <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-1084><span class=MJXp-msub id=MJXp-Span-1085><span class=MJXp-mrow id=MJXp-Span-1086 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1087>S</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-1088 style=vertical-align:-0.4em><span class=MJXp-msup id=MJXp-Span-1089><span class=MJXp-mrow id=MJXp-Span-1090 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-1091>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-1092 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-1093>*</span></span></span></span></span></span></span><span id=MathJax-Element-141-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> where <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-1094><span class=MJXp-msup id=MJXp-Span-1095><span class=MJXp-mrow id=MJXp-Span-1096 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-1097>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-1098 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-1099>*</span></span></span></span></span><span id=MathJax-Element-142-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> is at rest, as shown in <a href=#j_phys-2023-0110_fig_002 class="link link-fig" data-bs-target=j_phys-2023-0110_fig_002>Figure 2</a>(b). The return time interval of the photon from B to <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-1100><span class=MJXp-msup id=MJXp-Span-1101><span class=MJXp-mrow id=MJXp-Span-1102 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-1103>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-1104 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-1105>*</span></span></span></span></span><span id=MathJax-Element-143-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> on the contour upper section is obviously <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-1106><span class=MJXp-msub id=MJXp-Span-1107><span class=MJXp-mrow id=MJXp-Span-1108 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1109>t</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-1110 style=vertical-align:-0.4em><span class=MJXp-mi id=MJXp-Span-1111>ret</span></span></span><span class=MJXp-mo id=MJXp-Span-1112 style=margin-left:0.333em;margin-right:0.333em>=</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1113>L</span><span class=MJXp-mo id=MJXp-Span-1114 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class=MJXp-mrow id=MJXp-Span-1115><span class=MJXp-mo id=MJXp-Span-1116 style=margin-left:0em;margin-right:0em>(</span><span class=MJXp-mrow id=MJXp-Span-1117><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1118>γ</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1119>c</span></span><span class=MJXp-mo id=MJXp-Span-1120 style=margin-left:0em;margin-right:0em>)</span></span></span></span><span id=MathJax-Element-144-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>, the return interval <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-1121><span class=MJXp-msub id=MJXp-Span-1122><span class=MJXp-mrow id=MJXp-Span-1123 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1124>t</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-1125 style=vertical-align:-0.4em><span class=MJXp-mi id=MJXp-Span-1126>ret</span></span></span></span></span><span id=MathJax-Element-145-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> being independent of the motion of the contour. Then, in the RLSE of <a href=#j_phys-2023-0110_fig_002 class="link link-fig" data-bs-target=j_phys-2023-0110_fig_002>Figure 2</a>(b), the return interval <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-1127><span class=MJXp-msub id=MJXp-Span-1128><span class=MJXp-mrow id=MJXp-Span-1129 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1130>t</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-1131 style=vertical-align:-0.4em><span class=MJXp-mi id=MJXp-Span-1132>ret</span></span></span></span></span><span id=MathJax-Element-146-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> is the same regardless of whether the contour keeps moving to the right or starts moving to the left of the stationary <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-1133><span class=MJXp-msup id=MJXp-Span-1134><span class=MJXp-mrow id=MJXp-Span-1135 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-1136>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-1137 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-1138>*</span></span></span></span></span><span id=MathJax-Element-147-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>.</p>
<p>Working out the calculations also for the co-propagating signal, for <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-1139><span class=MJXp-msub id=MJXp-Span-1140><span class=MJXp-mrow id=MJXp-Span-1141 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1142>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-1143 style=vertical-align:-0.4em><span class=MJXp-mo id=MJXp-Span-1144>⇐</span></span></span></span></span><span id=MathJax-Element-148-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>, we find the exact result (<a href=#j_phys-2023-0110_eq_045 class="link link-disp-formula" data-bs-target=j_phys-2023-0110_eq_045>A18</a>) of Appendix (A.3). Then, <div class=formula id=j_phys-2023-0110_eq_003>
<span class=label>(3)</span>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class="MJXp-math MJXp-display" id=MJXp-Span-1145><span class=MJXp-mtable id=MJXp-Span-1146><span><span class=MJXp-mtr id=MJXp-Span-1147 style=vertical-align:baseline><span class=MJXp-mtd id=MJXp-Span-1148 style=text-align:center><span class=MJXp-msub id=MJXp-Span-1149><span class=MJXp-mrow id=MJXp-Span-1150 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1151>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-1152 style=vertical-align:-0.4em><span class=MJXp-mo id=MJXp-Span-1153>⇐</span></span></span></span><span class=MJXp-mtd id=MJXp-Span-1154 style=padding-left:0.33em;text-align:center><span class=MJXp-mo id=MJXp-Span-1155 style=margin-left:0.333em;margin-right:0.333em>=</span></span><span class=MJXp-mtd id=MJXp-Span-1156 style=padding-left:0.33em;text-align:center><span class=MJXp-mfrac id=MJXp-Span-1157 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-1158><span class=MJXp-mn id=MJXp-Span-1159>2</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1160>L</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-1161><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1162>γ</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1163>c</span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-1164 style=margin-left:0.267em;margin-right:0.267em>+</span><span class=MJXp-mfrac id=MJXp-Span-1165 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-1166><span class=MJXp-mn id=MJXp-Span-1167>4</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1168>γ</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1169>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1170>L</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-1171><span class=MJXp-msup id=MJXp-Span-1172><span class=MJXp-mrow id=MJXp-Span-1173 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1174>c</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-1175 style=vertical-align:0.5em><span class=MJXp-mn id=MJXp-Span-1176>2</span></span></span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-1177 style=margin-left:0em;margin-right:0.222em>,</span><span class=MJXp-mspace id=MJXp-Span-1178 style=width:1em;height:0em></span><span class=MJXp-msub id=MJXp-Span-1179><span class=MJXp-mrow id=MJXp-Span-1180 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1181>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-1182 style=vertical-align:-0.4em><span class=MJXp-mo id=MJXp-Span-1183>⇒</span></span></span><span class=MJXp-mo id=MJXp-Span-1184 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-mfrac id=MJXp-Span-1185 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-1186><span class=MJXp-mn id=MJXp-Span-1187>2</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1188>L</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-1189><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1190>γ</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1191>c</span></span></span></span></span></span></span></span></span><span class=MJXp-mtr id=MJXp-Span-1192 style=vertical-align:baseline><span class=MJXp-mtd id=MJXp-Span-1193 style=padding-top:0.431em;text-align:center><span class=MJXp-mi id=MJXp-Span-1194>Δ</span><span class=MJXp-msub id=MJXp-Span-1195><span class=MJXp-mrow id=MJXp-Span-1196 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1197>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-1198 style=vertical-align:-0.4em><span class=MJXp-mi id=MJXp-Span-1199>RLSE</span></span></span></span><span class=MJXp-mtd id=MJXp-Span-1200 style=padding-left:0.33em;padding-top:0.431em;text-align:center><span class=MJXp-mo id=MJXp-Span-1201 style=margin-left:0.333em;margin-right:0.333em>=</span></span><span class=MJXp-mtd id=MJXp-Span-1202 style=padding-left:0.33em;padding-top:0.431em;text-align:center><span class=MJXp-msub id=MJXp-Span-1203><span class=MJXp-mrow id=MJXp-Span-1204 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1205>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-1206 style=vertical-align:-0.4em><span class=MJXp-mo id=MJXp-Span-1207>⇐</span></span></span><span class=MJXp-mo id=MJXp-Span-1208 style=margin-left:0.267em;margin-right:0.267em>−</span><span class=MJXp-msub id=MJXp-Span-1209><span class=MJXp-mrow id=MJXp-Span-1210 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1211>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-1212 style=vertical-align:-0.4em><span class=MJXp-mo id=MJXp-Span-1213>⇒</span></span></span><span class=MJXp-mo id=MJXp-Span-1214 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-mfrac id=MJXp-Span-1215 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-1216><span class=MJXp-mn id=MJXp-Span-1217>4</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1218>γ</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1219>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1220>L</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-1221><span class=MJXp-msup id=MJXp-Span-1222><span class=MJXp-mrow id=MJXp-Span-1223 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1224>c</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-1225 style=vertical-align:0.5em><span class=MJXp-mn id=MJXp-Span-1226>2</span></span></span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-1227 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-mfrac id=MJXp-Span-1228 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-1229><span class=MJXp-mn id=MJXp-Span-1230>2</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1231>γ</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1232>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1233>P</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-1234><span class=MJXp-msup id=MJXp-Span-1235><span class=MJXp-mrow id=MJXp-Span-1236 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1237>c</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-1238 style=vertical-align:0.5em><span class=MJXp-mn id=MJXp-Span-1239>2</span></span></span></span></span></span></span></span></span></span></span><span class=MJXp-mtr id=MJXp-Span-1240 style=vertical-align:baseline><span class=MJXp-mtd id=MJXp-Span-1241 style=padding-top:0.431em;text-align:center></span><span class=MJXp-mtd id=MJXp-Span-1242 style=padding-left:0.33em;padding-top:0.431em;text-align:center><span class=MJXp-mo id=MJXp-Span-1243 style=margin-left:0.333em;margin-right:0.333em>=</span></span><span class=MJXp-mtd id=MJXp-Span-1244 style=padding-left:0.33em;padding-top:0.431em;text-align:center><span class=MJXp-mi id=MJXp-Span-1245>Δ</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1246>T</span><span class=MJXp-mo id=MJXp-Span-1247 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-mi id=MJXp-Span-1248>invariant</span><span class=MJXp-mo id=MJXp-Span-1249 style=margin-left:0em;margin-right:0.222em>.</span></span></span></span></span></span></span><span class="mjx-chtml MJXc-display MJXc-processing sf-hidden"></span>
</span>
</div><p>
</p>
<p>We see that, in the special case considered earlier where <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-1250><span class=MJXp-msup id=MJXp-Span-1251><span class=MJXp-mrow id=MJXp-Span-1252 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-1253>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-1254 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-1255>*</span></span></span></span></span><span id=MathJax-Element-150-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> is initially on the lower and then on the upper section of the moving contour, the round-trip time <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-1256><span class=MJXp-msub id=MJXp-Span-1257><span class=MJXp-mrow id=MJXp-Span-1258 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1259>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-1260 style=vertical-align:-0.4em><span class=MJXp-mo id=MJXp-Span-1261>⇒</span></span></span></span></span><span id=MathJax-Element-151-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> in Eq. (<a href=#j_phys-2023-0110_eq_003 class="link link-disp-formula" data-bs-target=j_phys-2023-0110_eq_003>3</a>) is greater than the corresponding value in Eq. (<a href=#j_phys-2023-0110_eq_002 class="link link-disp-formula" data-bs-target=j_phys-2023-0110_eq_002>2</a>). However, also the round-trip time <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-1262><span class=MJXp-msub id=MJXp-Span-1263><span class=MJXp-mrow id=MJXp-Span-1264 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1265>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-1266 style=vertical-align:-0.4em><span class=MJXp-mo id=MJXp-Span-1267>⇐</span></span></span></span></span><span id=MathJax-Element-152-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> turns out to be greater than the corresponding value in (<a href=#j_phys-2023-0110_eq_002 class="link link-disp-formula" data-bs-target=j_phys-2023-0110_eq_002>2</a>). Then, for counter-propagating light signals, the difference <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-1268><span class=MJXp-mi id=MJXp-Span-1269>Δ</span><span class=MJXp-msub id=MJXp-Span-1270><span class=MJXp-mrow id=MJXp-Span-1271 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1272>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-1273 style=vertical-align:-0.4em><span class=MJXp-mi id=MJXp-Span-1274>RLSE</span></span></span></span></span><span id=MathJax-Element-153-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> in Eq. (<a href=#j_phys-2023-0110_eq_003 class="link link-disp-formula" data-bs-target=j_phys-2023-0110_eq_003>3</a>) is still the same as in Eq. (<a href=#j_phys-2023-0110_eq_002 class="link link-disp-formula" data-bs-target=j_phys-2023-0110_eq_002>2</a>) and, as far as <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-1275><span class=MJXp-mi id=MJXp-Span-1276>Δ</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1277>T</span></span></span><span id=MathJax-Element-154-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> is concerned, <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-1278><span class=MJXp-mi id=MJXp-Span-1279>Δ</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1280>T</span><span class=MJXp-mo id=MJXp-Span-1281 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-mi id=MJXp-Span-1282>Δ</span><span class=MJXp-msub id=MJXp-Span-1283><span class=MJXp-mrow id=MJXp-Span-1284 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1285>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-1286 style=vertical-align:-0.4em><span class=MJXp-mi id=MJXp-Span-1287>RLSE</span></span></span><span class=MJXp-mo id=MJXp-Span-1288 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-mi id=MJXp-Span-1289>invariant</span></span></span><span id=MathJax-Element-155-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> and the RLSE is equivalent to the standard linear Sagnac effect.</p>
<p>
<strong>Special features of the RLSE.</strong> The important interesting feature of the RLSE is that in Eq. (<a href=#j_phys-2023-0110_eq_003 class="link link-disp-formula" data-bs-target=j_phys-2023-0110_eq_003>3</a>) the round-trip time <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-1290><span class=MJXp-msub id=MJXp-Span-1291><span class=MJXp-mrow id=MJXp-Span-1292 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1293>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-1294 style=vertical-align:-0.4em><span class=MJXp-mo id=MJXp-Span-1295>⇒</span></span></span></span></span><span id=MathJax-Element-156-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> of a single photon (<em>i.e.</em>, the counter-propagating one) differs from the corresponding <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-1296><span class=MJXp-msub id=MJXp-Span-1297><span class=MJXp-mrow id=MJXp-Span-1298 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1299>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-1300 style=vertical-align:-0.4em><span class=MJXp-mo id=MJXp-Span-1301>⇒</span></span></span></span></span><span id=MathJax-Element-157-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> in Eq. (<a href=#j_phys-2023-0110_eq_002 class="link link-disp-formula" data-bs-target=j_phys-2023-0110_eq_002>2</a>). The difference persists as long as <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-1302><span class=MJXp-mn id=MJXp-Span-1303>0</span><span class=MJXp-mo id=MJXp-Span-1304 style=margin-left:0.333em;margin-right:0.333em>&lt;</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1305>D</span><span class=MJXp-mo id=MJXp-Span-1306 style=margin-left:0.333em;margin-right:0.333em>&lt;</span><span class=MJXp-mn id=MJXp-Span-1307>2</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1308>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1309>L</span><span class=MJXp-mo id=MJXp-Span-1310 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1311>c</span></span></span><span id=MathJax-Element-158-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> and <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-1312><span class=MJXp-msup id=MJXp-Span-1313><span class=MJXp-mrow id=MJXp-Span-1314 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-1315>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-1316 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-1317>*</span></span></span></span></span><span id=MathJax-Element-159-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> moves from the lower to the upper section during the round-trip time <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-1318><span class=MJXp-msub id=MJXp-Span-1319><span class=MJXp-mrow id=MJXp-Span-1320 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1321>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-1322 style=vertical-align:-0.4em><span class=MJXp-mo id=MJXp-Span-1323>⇒</span></span></span></span></span><span id=MathJax-Element-160-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>. Then, the function <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-1324><span class=MJXp-msub id=MJXp-Span-1325><span class=MJXp-mrow id=MJXp-Span-1326 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1327>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-1328 style=vertical-align:-0.4em><span class=MJXp-mo id=MJXp-Span-1329>⇒</span></span></span><span class=MJXp-mo id=MJXp-Span-1330 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-msub id=MJXp-Span-1331><span class=MJXp-mrow id=MJXp-Span-1332 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1333>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-1334 style=vertical-align:-0.4em><span class=MJXp-mo id=MJXp-Span-1335>⇒</span></span></span><span class=MJXp-mrow id=MJXp-Span-1336><span class=MJXp-mo id=MJXp-Span-1337 style=margin-left:0em;margin-right:0em>(</span><span class=MJXp-mrow id=MJXp-Span-1338><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1339>D</span></span><span class=MJXp-mo id=MJXp-Span-1340 style=margin-left:0em;margin-right:0em>)</span></span></span></span><span id=MathJax-Element-161-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> varies from the minimum value given in Eq. (<a href=#j_phys-2023-0110_eq_002 class="link link-disp-formula" data-bs-target=j_phys-2023-0110_eq_002>2</a>) (for <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-1341><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1342>D</span><span class=MJXp-mo id=MJXp-Span-1343 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-mn id=MJXp-Span-1344>0</span></span></span><span id=MathJax-Element-162-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> or <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-1345><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1346>D</span><span class=MJXp-mo id=MJXp-Span-1347 style=margin-left:0.333em;margin-right:0.333em>&gt;</span><span class=MJXp-mn id=MJXp-Span-1348>2</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1349>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1350>L</span><span class=MJXp-mo id=MJXp-Span-1351 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1352>c</span></span></span><span id=MathJax-Element-163-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>) to the maximum one given in Eq. (<a href=#j_phys-2023-0110_eq_003 class="link link-disp-formula" data-bs-target=j_phys-2023-0110_eq_003>3</a>) (for <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-1353><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1354>D</span><span class=MJXp-mo id=MJXp-Span-1355 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-msub id=MJXp-Span-1356><span class=MJXp-mrow id=MJXp-Span-1357 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1358>D</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-1359 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-1360>0</span></span></span><span class=MJXp-mo id=MJXp-Span-1361 style=margin-left:0.333em;margin-right:0.333em>=</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1362>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1363>L</span><span class=MJXp-mo id=MJXp-Span-1364 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1365>c</span></span></span><span id=MathJax-Element-164-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>). We must stress that <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-1366><span class=MJXp-msub id=MJXp-Span-1367><span class=MJXp-mrow id=MJXp-Span-1368 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1369>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-1370 style=vertical-align:-0.4em><span class=MJXp-mo id=MJXp-Span-1371>⇒</span></span></span></span></span><span id=MathJax-Element-165-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> is an observable measurable by clock <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-1372><span class=MJXp-msup id=MJXp-Span-1373><span class=MJXp-mrow id=MJXp-Span-1374 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-1375>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-1376 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-1377>*</span></span></span></span></span><span id=MathJax-Element-166-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> and, for the standard linear Sagnac effect, the theory foresees <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-1378><span class=MJXp-msub id=MJXp-Span-1379><span class=MJXp-mrow id=MJXp-Span-1380 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1381>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-1382 style=vertical-align:-0.4em><span class=MJXp-mo id=MJXp-Span-1383>⇒</span></span></span><span class=MJXp-mo id=MJXp-Span-1384 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-mn id=MJXp-Span-1385>2</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1386>L</span><span class=MJXp-mo id=MJXp-Span-1387 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1388>γ</span><span class=MJXp-mrow id=MJXp-Span-1389><span class=MJXp-mo id=MJXp-Span-1390 style=margin-left:0em;margin-right:0em>(</span><span class=MJXp-mrow id=MJXp-Span-1391><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1392>c</span><span class=MJXp-mo id=MJXp-Span-1393 style=margin-left:0.267em;margin-right:0.267em>+</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1394>v</span></span><span class=MJXp-mo id=MJXp-Span-1395 style=margin-left:0em;margin-right:0em>)</span></span></span></span><span id=MathJax-Element-167-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>, independent of the value of <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-1396><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1397>D</span></span></span><span id=MathJax-Element-168-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>. Analogous considerations can be made for <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-1398><span class=MJXp-msub id=MJXp-Span-1399><span class=MJXp-mrow id=MJXp-Span-1400 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1401>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-1402 style=vertical-align:-0.4em><span class=MJXp-mo id=MJXp-Span-1403>⇐</span></span></span></span></span><span id=MathJax-Element-169-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>.</p>
<p>Thus, results (<a href=#j_phys-2023-0110_eq_002 class="link link-disp-formula" data-bs-target=j_phys-2023-0110_eq_002>2</a>) and (<a href=#j_phys-2023-0110_eq_003 class="link link-disp-formula" data-bs-target=j_phys-2023-0110_eq_003>3</a>) indicate that there are special features of the RLSE not equivalent to those of the standard Sagnac effect. In case (b), when velocity variations are involved and <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-1404><span class=MJXp-msup id=MJXp-Span-1405><span class=MJXp-mrow id=MJXp-Span-1406 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-1407>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-1408 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-1409>*</span></span></span></span></span><span id=MathJax-Element-170-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> and the contour change their direction of relative motion in the interval <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-1410><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1411>T</span></span></span><span id=MathJax-Element-171-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>, the differences indicate that the relativity principle does not hold. The differences between the two effects are interpreted below in the context of special relativity and the LT, showing that can be linked to relative simultaneity.</p>
<p>Since the standard RLSE, where <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-1412><span class=MJXp-mi id=MJXp-Span-1413>Δ</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1414>T</span><span class=MJXp-mo id=MJXp-Span-1415 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-msub id=MJXp-Span-1416><span class=MJXp-mrow id=MJXp-Span-1417 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1418>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-1419 style=vertical-align:-0.4em><span class=MJXp-mo id=MJXp-Span-1420>⇐</span></span></span><span class=MJXp-mo id=MJXp-Span-1421 style=margin-left:0.267em;margin-right:0.267em>−</span><span class=MJXp-msub id=MJXp-Span-1422><span class=MJXp-mrow id=MJXp-Span-1423 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1424>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-1425 style=vertical-align:-0.4em><span class=MJXp-mo id=MJXp-Span-1426>⇒</span></span></span></span></span><span id=MathJax-Element-172-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> is measured, is equivalent to the standard linear Sagnac effect, the usual approach based on measuring <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-1427><span class=MJXp-mi id=MJXp-Span-1428>Δ</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1429>T</span><span class=MJXp-mo id=MJXp-Span-1430 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-mi id=MJXp-Span-1431>Δ</span><span class=MJXp-msub id=MJXp-Span-1432><span class=MJXp-mrow id=MJXp-Span-1433 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1434>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-1435 style=vertical-align:-0.4em><span class=MJXp-mi id=MJXp-Span-1436>RLSE</span></span></span><span class=MJXp-mo id=MJXp-Span-1437 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-mi id=MJXp-Span-1438>invariant</span></span></span><span id=MathJax-Element-173-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> does not reveal the special features of the RLSE. Then, for the purpose of pointing out these special features foreseen by the LT, we consider below the special reciprocal linear Sagnac effect (S-RLSE), and show how the S-RLSE can be tested and represents an optical effect with properties that differ from those of the standard linear Sagnac effect.</p>
<p>
<strong>Testing the S-RLSE with an experiment</strong>
</p>
<p>We pointed out that the round-trip <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-1439><span class=MJXp-msub id=MJXp-Span-1440><span class=MJXp-mrow id=MJXp-Span-1441 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1442>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-1443 style=vertical-align:-0.4em><span class=MJXp-mo id=MJXp-Span-1444>⇒</span></span></span></span></span><span id=MathJax-Element-174-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> of the counter-propagating signal is an observable that can be measured by the single clock <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-1445><span class=MJXp-msup id=MJXp-Span-1446><span class=MJXp-mrow id=MJXp-Span-1447 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-1448>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-1449 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-1450>*</span></span></span></span></span><span id=MathJax-Element-175-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>. Therefore, the special features of the RLSE can be revealed with this type of measurements. In general, for precise measurements, we need to compare the observable <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-1451><span class=MJXp-msub id=MJXp-Span-1452><span class=MJXp-mrow id=MJXp-Span-1453 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1454>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-1455 style=vertical-align:-0.4em><span class=MJXp-mo id=MJXp-Span-1456>⇒</span></span></span></span></span><span id=MathJax-Element-176-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> with the corresponding observable <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-1457><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1458>T</span></span></span><span id=MathJax-Element-177-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>* of a signal on a different light path. In the case of the S-RLSE, for the optical light path of the co-propagating photon, we choose a contour with the same perimeter <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-1459><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1460>P</span><span class=MJXp-mo id=MJXp-Span-1461 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-mn id=MJXp-Span-1462>2</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1463>L</span></span></span><span id=MathJax-Element-178-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>, but stationary in the device frame <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-1464><span class=MJXp-msub id=MJXp-Span-1465><span class=MJXp-mrow id=MJXp-Span-1466 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1467>S</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-1468 style=vertical-align:-0.4em><span class=MJXp-msup id=MJXp-Span-1469><span class=MJXp-mrow id=MJXp-Span-1470 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-1471>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-1472 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-1473>*</span></span></span></span></span></span></span><span id=MathJax-Element-179-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>.</p>
<p>Hence, the main difference between the RLSE and the S-RLSE is that in the RLSE, we have <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-1474><span class=MJXp-msup id=MJXp-Span-1475><span class=MJXp-mrow id=MJXp-Span-1476 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1477>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-1478 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-1479>*</span></span></span><span class=MJXp-mo id=MJXp-Span-1480 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-msub id=MJXp-Span-1481><span class=MJXp-mrow id=MJXp-Span-1482 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1483>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-1484 style=vertical-align:-0.4em><span class=MJXp-mo id=MJXp-Span-1485>⇐</span></span></span></span></span><span id=MathJax-Element-180-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>, while in the S-RLSE, the round-trip time interval of the co-propagating signal is now <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-1486><span class=MJXp-msup id=MJXp-Span-1487><span class=MJXp-mrow id=MJXp-Span-1488 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1489>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-1490 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-1491>*</span></span></span><span class=MJXp-mo id=MJXp-Span-1492 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-mn id=MJXp-Span-1493>2</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1494>L</span><span class=MJXp-mo id=MJXp-Span-1495 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1496>c</span></span></span><span id=MathJax-Element-181-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>. With our choice, by means of (<a href=#j_phys-2023-0110_eq_001 class="link link-disp-formula" data-bs-target=j_phys-2023-0110_eq_001>1</a>), for the standard Sagnac effect, we have <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-1497><span class=MJXp-mi id=MJXp-Span-1498>Δ</span><span class=MJXp-msubsup id=MJXp-Span-1499><span class=MJXp-mrow id=MJXp-Span-1500 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1501>T</span></span><span class=MJXp-script-box style=height:1.86em;vertical-align:-0.64em><span class=MJXp-script><span><span style=margin-bottom:-0.25em><span class=MJXp-mrow id=MJXp-Span-1504><span class=MJXp-mo id=MJXp-Span-1505>*</span></span></span></span></span><span class=MJXp-script><span><span style=margin-top:-0.85em><span class=MJXp-mrow id=MJXp-Span-1502><span class=MJXp-mi id=MJXp-Span-1503>Sagnac</span></span></span></span></span></span></span></span></span><span id=MathJax-Element-182-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> = <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-1506><span class=MJXp-msup id=MJXp-Span-1507><span class=MJXp-mrow id=MJXp-Span-1508 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1509>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-1510 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-1511>*</span></span></span><span class=MJXp-mo id=MJXp-Span-1512 style=margin-left:0.267em;margin-right:0.267em>−</span><span class=MJXp-msub id=MJXp-Span-1513><span class=MJXp-mrow id=MJXp-Span-1514 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1515>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-1516 style=vertical-align:-0.4em><span class=MJXp-mo id=MJXp-Span-1517>⇒</span></span></span></span></span><span id=MathJax-Element-183-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> = <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-1518><span class=MJXp-mn id=MJXp-Span-1519>2</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1520>L</span><span class=MJXp-mo id=MJXp-Span-1521 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1522>c</span><span class=MJXp-mo id=MJXp-Span-1523 style=margin-left:0.267em;margin-right:0.267em>−</span><span class=MJXp-mn id=MJXp-Span-1524>2</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1525>γ</span><span class=MJXp-mrow id=MJXp-Span-1526><span class=MJXp-mo id=MJXp-Span-1527 style=margin-left:0em;margin-right:0em>(</span><span class=MJXp-mrow id=MJXp-Span-1528><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1529>L</span><span class=MJXp-mo id=MJXp-Span-1530 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1531>c</span></span><span class=MJXp-mo id=MJXp-Span-1532 style=margin-left:0em;margin-right:0em>)</span></span><span class=MJXp-mrow id=MJXp-Span-1533><span class=MJXp-mo id=MJXp-Span-1534 style=margin-left:0em;margin-right:0em>(</span><span class=MJXp-mrow id=MJXp-Span-1535><span class=MJXp-mn id=MJXp-Span-1536>1</span><span class=MJXp-mo id=MJXp-Span-1537 style=margin-left:0.267em;margin-right:0.267em>+</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1538>v</span><span class=MJXp-mo id=MJXp-Span-1539 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1540>c</span></span><span class=MJXp-mo id=MJXp-Span-1541 style=margin-left:0em;margin-right:0em>)</span></span><span class=MJXp-mo id=MJXp-Span-1542 style=margin-left:0.333em;margin-right:0.333em>≃</span><span class=MJXp-msubsup id=MJXp-Span-1543><span class=MJXp-mrow id=MJXp-Span-1544 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-1545>Δ</span></span><span class=MJXp-script-box style=height:1.86em;vertical-align:-0.64em><span class=MJXp-script><span><span style=margin-bottom:-0.25em><span class=MJXp-mrow id=MJXp-Span-1548><span class=MJXp-mo id=MJXp-Span-1549>∗</span></span></span></span></span><span class=MJXp-script><span><span style=margin-top:-0.85em><span class=MJXp-mrow id=MJXp-Span-1546><span class=MJXp-mi id=MJXp-Span-1547>Sagn</span></span></span></span></span></span></span></span></span><span id=MathJax-Element-184-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> = <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-1550><span class=MJXp-mn id=MJXp-Span-1551>2</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1552>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1553>L</span><span class=MJXp-mo id=MJXp-Span-1554 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class=MJXp-msup id=MJXp-Span-1555><span class=MJXp-mrow id=MJXp-Span-1556 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1557>c</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-1558 style=vertical-align:0.5em><span class=MJXp-mn id=MJXp-Span-1559>2</span></span></span></span></span><span id=MathJax-Element-185-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> constant and independent of <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-1560><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1561>D</span></span></span><span id=MathJax-Element-186-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>. Instead, for the S-RLSE, we have <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-1562><span class=MJXp-mi id=MJXp-Span-1563>Δ</span><span class=MJXp-msup id=MJXp-Span-1564><span class=MJXp-mrow id=MJXp-Span-1565 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1566>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-1567 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-1568>*</span></span></span><span class=MJXp-mo id=MJXp-Span-1569 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-mi id=MJXp-Span-1570>Δ</span><span class=MJXp-msup id=MJXp-Span-1571><span class=MJXp-mrow id=MJXp-Span-1572 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1573>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-1574 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-1575>*</span></span></span><span class=MJXp-mrow id=MJXp-Span-1576><span class=MJXp-mo id=MJXp-Span-1577 style=margin-left:0em;margin-right:0em>(</span><span class=MJXp-mrow id=MJXp-Span-1578><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1579>D</span></span><span class=MJXp-mo id=MJXp-Span-1580 style=margin-left:0em;margin-right:0em>)</span></span><span class=MJXp-mo id=MJXp-Span-1581 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-msup id=MJXp-Span-1582><span class=MJXp-mrow id=MJXp-Span-1583 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1584>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-1585 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-1586>*</span></span></span><span class=MJXp-mo id=MJXp-Span-1587 style=margin-left:0.267em;margin-right:0.267em>−</span><span class=MJXp-msub id=MJXp-Span-1588><span class=MJXp-mrow id=MJXp-Span-1589 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1590>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-1591 style=vertical-align:-0.4em><span class=MJXp-mo id=MJXp-Span-1592>⇒</span></span></span><span class=MJXp-mo id=MJXp-Span-1593 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-msup id=MJXp-Span-1594><span class=MJXp-mrow id=MJXp-Span-1595 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1596>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-1597 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-1598>*</span></span></span><span class=MJXp-mo id=MJXp-Span-1599 style=margin-left:0.267em;margin-right:0.267em>−</span><span class=MJXp-msub id=MJXp-Span-1600><span class=MJXp-mrow id=MJXp-Span-1601 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1602>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-1603 style=vertical-align:-0.4em><span class=MJXp-mo id=MJXp-Span-1604>⇒</span></span></span><span class=MJXp-mrow id=MJXp-Span-1605><span class=MJXp-mo id=MJXp-Span-1606 style=margin-left:0em;margin-right:0em>(</span><span class=MJXp-mrow id=MJXp-Span-1607><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1608>D</span></span><span class=MJXp-mo id=MJXp-Span-1609 style=margin-left:0em;margin-right:0em>)</span></span></span></span><span id=MathJax-Element-187-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> dependent on <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-1610><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1611>D</span></span></span><span id=MathJax-Element-188-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>.</p>
<p>With the help of (<a href=#j_phys-2023-0110_eq_002 class="link link-disp-formula" data-bs-target=j_phys-2023-0110_eq_002>2</a>) and (<a href=#j_phys-2023-0110_eq_003 class="link link-disp-formula" data-bs-target=j_phys-2023-0110_eq_003>3</a>), we find, <div class=formula id=j_phys-2023-0110_eq_004>
<span class=label>(4)</span>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class="MJXp-math MJXp-display" id=MJXp-Span-1619><span class=MJXp-mtable id=MJXp-Span-1620><span><span class=MJXp-mtr id=MJXp-Span-1621 style=vertical-align:baseline><span class=MJXp-mtd id=MJXp-Span-1622 style=text-align:center><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1623>D</span></span><span class=MJXp-mtd id=MJXp-Span-1624 style=padding-left:0.33em;text-align:center><span class=MJXp-mo id=MJXp-Span-1625 style=margin-left:0.333em;margin-right:0.333em>≳</span></span><span class=MJXp-mtd id=MJXp-Span-1626 style=padding-left:0.33em;text-align:center><span class=MJXp-mfrac id=MJXp-Span-1627 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-1628><span class=MJXp-mn id=MJXp-Span-1629>2</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1630>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1631>L</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-1632><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1633>c</span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-1634 style=margin-left:0.333em;margin-right:0.333em>⇒</span></span></span><span class=MJXp-mtr id=MJXp-Span-1635 style=vertical-align:baseline><span class=MJXp-mtd id=MJXp-Span-1636 style=padding-top:0.431em;text-align:center><span class=MJXp-mi id=MJXp-Span-1637>Δ</span><span class=MJXp-msup id=MJXp-Span-1638><span class=MJXp-mrow id=MJXp-Span-1639 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1640>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-1641 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-1642>*</span></span></span><span class=MJXp-mrow id=MJXp-Span-1643><span class=MJXp-mo id=MJXp-Span-1644 style=margin-left:0em;margin-right:0em>(</span><span class=MJXp-mrow id=MJXp-Span-1645><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1646>D</span></span><span class=MJXp-mo id=MJXp-Span-1647 style=margin-left:0em;margin-right:0em>)</span></span></span><span class=MJXp-mtd id=MJXp-Span-1648 style=padding-left:0.33em;padding-top:0.431em;text-align:center><span class=MJXp-mo id=MJXp-Span-1649 style=margin-left:0.333em;margin-right:0.333em>=</span></span><span class=MJXp-mtd id=MJXp-Span-1650 style=padding-left:0.33em;padding-top:0.431em;text-align:center><span class=MJXp-msup id=MJXp-Span-1651><span class=MJXp-mrow id=MJXp-Span-1652 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1653>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-1654 style=vertical-align:0.5em><span class="MJXp-mstyle MJXp-script" id=MJXp-Span-1655><span class=MJXp-mspace id=MJXp-Span-1656 style=width:0.1em;height:0em></span><span class=MJXp-mtext id=MJXp-Span-1657>*</span><span class=MJXp-mspace id=MJXp-Span-1658 style=width:0.1em;height:0em></span></span></span></span><span class=MJXp-mo id=MJXp-Span-1659 style=margin-left:0.267em;margin-right:0.267em>−</span><span class=MJXp-msub id=MJXp-Span-1660><span class=MJXp-mrow id=MJXp-Span-1661 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1662>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-1663 style=vertical-align:-0.4em><span class=MJXp-mo id=MJXp-Span-1664>⇒</span></span></span><span class=MJXp-mo id=MJXp-Span-1665 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-mfrac id=MJXp-Span-1666 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-1667><span class=MJXp-mn id=MJXp-Span-1668>2</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1669>L</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-1670><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1671>c</span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-1672 style=margin-left:0.267em;margin-right:0.267em>−</span><span class=MJXp-mfrac id=MJXp-Span-1673 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-1674><span class=MJXp-mn id=MJXp-Span-1675>2</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1676>γ</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1677>L</span><span class=MJXp-mrow id=MJXp-Span-1678><span class=MJXp-mo id=MJXp-Span-1679 style=margin-left:0em;margin-right:0em>(</span><span class=MJXp-mrow id=MJXp-Span-1680><span class=MJXp-mn id=MJXp-Span-1681>1</span><span class=MJXp-mo id=MJXp-Span-1682 style=margin-left:0.267em;margin-right:0.267em>−</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1683>v</span><span class=MJXp-mo id=MJXp-Span-1684 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1685>c</span></span><span class=MJXp-mo id=MJXp-Span-1686 style=margin-left:0em;margin-right:0em>)</span></span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-1687><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1688>c</span></span></span></span></span></span></span></span></span><span class=MJXp-mtr id=MJXp-Span-1689 style=vertical-align:baseline><span class=MJXp-mtd id=MJXp-Span-1690 style=padding-top:0.431em;text-align:center></span><span class=MJXp-mtd id=MJXp-Span-1691 style=padding-left:0.33em;padding-top:0.431em;text-align:center><span class=MJXp-mo id=MJXp-Span-1692 style=margin-left:0.333em;margin-right:0.333em>≃</span></span><span class=MJXp-mtd id=MJXp-Span-1693 style=padding-left:0.33em;padding-top:0.431em;text-align:center><span class=MJXp-mfrac id=MJXp-Span-1694 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-1695><span class=MJXp-mn id=MJXp-Span-1696>2</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1697>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1698>L</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-1699><span class=MJXp-msup id=MJXp-Span-1700><span class=MJXp-mrow id=MJXp-Span-1701 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1702>c</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-1703 style=vertical-align:0.5em><span class=MJXp-mn id=MJXp-Span-1704>2</span></span></span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-1705 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-mi id=MJXp-Span-1706>Δ</span><span class=MJXp-msubsup id=MJXp-Span-1707><span class=MJXp-mrow id=MJXp-Span-1708 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1709>T</span></span><span class=MJXp-script-box style=height:1.86em;vertical-align:-0.64em><span class=MJXp-script><span><span style=margin-bottom:-0.25em><span class=MJXp-mrow id=MJXp-Span-1712><span class="MJXp-mstyle MJXp-script" id=MJXp-Span-1713><span class=MJXp-mspace id=MJXp-Span-1714 style=width:0.1em;height:0em></span><span class=MJXp-mtext id=MJXp-Span-1715>*</span><span class=MJXp-mspace id=MJXp-Span-1716 style=width:0.1em;height:0em></span></span></span></span></span></span><span class=MJXp-script><span><span style=margin-top:-0.85em><span class=MJXp-mrow id=MJXp-Span-1710><span class=MJXp-mi id=MJXp-Span-1711>Sagnac</span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-1717 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-msubsup id=MJXp-Span-1718><span class=MJXp-mrow id=MJXp-Span-1719 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-1720>Δ</span></span><span class=MJXp-script-box style=height:1.86em;vertical-align:-0.64em><span class=MJXp-script><span><span style=margin-bottom:-0.25em><span class=MJXp-mrow id=MJXp-Span-1723><span class=MJXp-mo id=MJXp-Span-1724>∗</span></span></span></span></span><span class=MJXp-script><span><span style=margin-top:-0.85em><span class=MJXp-mrow id=MJXp-Span-1721><span class=MJXp-mi id=MJXp-Span-1722>Sagn</span></span></span></span></span></span></span></span></span><span class=MJXp-mtr id=MJXp-Span-1725 style=vertical-align:baseline><span class=MJXp-mtd id=MJXp-Span-1726 style=padding-top:0.431em;text-align:center><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1727>D</span></span><span class=MJXp-mtd id=MJXp-Span-1728 style=padding-left:0.33em;padding-top:0.431em;text-align:center><span class=MJXp-mo id=MJXp-Span-1729 style=margin-left:0.333em;margin-right:0.333em>=</span></span><span class=MJXp-mtd id=MJXp-Span-1730 style=padding-left:0.33em;padding-top:0.431em;text-align:center><span class=MJXp-msub id=MJXp-Span-1731><span class=MJXp-mrow id=MJXp-Span-1732 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1733>D</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-1734 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-1735>0</span></span></span><span class=MJXp-mo id=MJXp-Span-1736 style=margin-left:0.333em;margin-right:0.333em>≃</span><span class=MJXp-mfrac id=MJXp-Span-1737 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-1738><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1739>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1740>L</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-1741><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1742>c</span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-1743 style=margin-left:0.333em;margin-right:0.333em>≲</span><span class=MJXp-mfrac id=MJXp-Span-1744 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-1745><span class=MJXp-mn id=MJXp-Span-1746>2</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1747>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1748>L</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-1749><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1750>c</span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-1751 style=margin-left:0.333em;margin-right:0.333em>⇒</span></span></span><span class=MJXp-mtr id=MJXp-Span-1752 style=vertical-align:baseline><span class=MJXp-mtd id=MJXp-Span-1753 style=padding-top:0.431em;text-align:center><span class=MJXp-mi id=MJXp-Span-1754>Δ</span><span class=MJXp-msup id=MJXp-Span-1755><span class=MJXp-mrow id=MJXp-Span-1756 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1757>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-1758 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-1759>*</span></span></span><span class=MJXp-mrow id=MJXp-Span-1760><span class=MJXp-mo id=MJXp-Span-1761 style=margin-left:0em;margin-right:0em;vertical-align:-0.244em><span style=font-size:1.978em;margin-left:-0.05em class="MJXp-right MJXp-scale7">(</span></span><span class=MJXp-mrow id=MJXp-Span-1762><span class=MJXp-msub id=MJXp-Span-1763><span class=MJXp-mrow id=MJXp-Span-1764 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1765>D</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-1766 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-1767>0</span></span></span></span><span class=MJXp-mo id=MJXp-Span-1768 style=margin-left:0em;margin-right:0em;vertical-align:-0.244em><span style=font-size:1.978em;margin-left:-0.05em class="MJXp-right MJXp-scale7">)</span></span></span></span><span class=MJXp-mtd id=MJXp-Span-1769 style=padding-left:0.33em;padding-top:0.431em;text-align:center><span class=MJXp-mo id=MJXp-Span-1770 style=margin-left:0.333em;margin-right:0.333em>=</span></span><span class=MJXp-mtd id=MJXp-Span-1771 style=padding-left:0.33em;padding-top:0.431em;text-align:center><span class=MJXp-msup id=MJXp-Span-1772><span class=MJXp-mrow id=MJXp-Span-1773 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1774>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-1775 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-1776>*</span></span></span><span class=MJXp-mo id=MJXp-Span-1777 style=margin-left:0.267em;margin-right:0.267em>−</span><span class=MJXp-msub id=MJXp-Span-1778><span class=MJXp-mrow id=MJXp-Span-1779 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1780>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-1781 style=vertical-align:-0.4em><span class=MJXp-mo id=MJXp-Span-1782>⇒</span></span></span><span class=MJXp-mrow id=MJXp-Span-1783><span class=MJXp-mo id=MJXp-Span-1784 style=margin-left:0em;margin-right:0em;vertical-align:-0.244em><span style=font-size:1.978em;margin-left:-0.05em class="MJXp-right MJXp-scale7">(</span></span><span class=MJXp-mrow id=MJXp-Span-1785><span class=MJXp-msub id=MJXp-Span-1786><span class=MJXp-mrow id=MJXp-Span-1787 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1788>D</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-1789 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-1790>0</span></span></span></span><span class=MJXp-mo id=MJXp-Span-1791 style=margin-left:0em;margin-right:0em;vertical-align:-0.244em><span style=font-size:1.978em;margin-left:-0.05em class="MJXp-right MJXp-scale7">)</span></span></span><span class=MJXp-mo id=MJXp-Span-1792 style=margin-left:0.333em;margin-right:0.333em>≃</span><span class=MJXp-mfrac id=MJXp-Span-1793 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-1794><span class=MJXp-mn id=MJXp-Span-1795>2</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1796>L</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-1797><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1798>c</span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-1799 style=margin-left:0.267em;margin-right:0.267em>−</span><span class=MJXp-mfrac id=MJXp-Span-1800 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-1801><span class=MJXp-mn id=MJXp-Span-1802>2</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1803>L</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-1804><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1805>c</span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-1806 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-mn id=MJXp-Span-1807>0</span><span class=MJXp-mo id=MJXp-Span-1808 style=margin-left:0em;margin-right:0.222em>.</span></span></span></span></span></span></span><span class="mjx-chtml MJXc-display MJXc-processing sf-hidden"></span>
</span>
</div><p>
</p>
<p>According to results (<a href=#j_phys-2023-0110_eq_004 class="link link-disp-formula" data-bs-target=j_phys-2023-0110_eq_004>4</a>), the function <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-1809><span class=MJXp-mi id=MJXp-Span-1810>Δ</span><span class=MJXp-msup id=MJXp-Span-1811><span class=MJXp-mrow id=MJXp-Span-1812 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1813>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-1814 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-1815>*</span></span></span><span class=MJXp-mrow id=MJXp-Span-1816><span class=MJXp-mo id=MJXp-Span-1817 style=margin-left:0em;margin-right:0em>(</span><span class=MJXp-mrow id=MJXp-Span-1818><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1819>D</span></span><span class=MJXp-mo id=MJXp-Span-1820 style=margin-left:0em;margin-right:0em>)</span></span></span></span><span id=MathJax-Element-190-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> is constant for <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-1821><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1822>D</span><span class=MJXp-mo id=MJXp-Span-1823 style=margin-left:0.333em;margin-right:0.333em>≳</span><span class=MJXp-mn id=MJXp-Span-1824>2</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1825>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1826>L</span><span class=MJXp-mo id=MJXp-Span-1827 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1828>c</span></span></span><span id=MathJax-Element-191-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> and given by <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-1829><span class=MJXp-mn id=MJXp-Span-1830>2</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1831>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1832>L</span><span class=MJXp-mo id=MJXp-Span-1833 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class=MJXp-msup id=MJXp-Span-1834><span class=MJXp-mrow id=MJXp-Span-1835 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1836>c</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-1837 style=vertical-align:0.5em><span class=MJXp-mn id=MJXp-Span-1838>2</span></span></span><span class=MJXp-mo id=MJXp-Span-1839 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-msubsup id=MJXp-Span-1840><span class=MJXp-mrow id=MJXp-Span-1841 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-1842>Δ</span></span><span class=MJXp-script-box style=height:1.86em;vertical-align:-0.64em><span class=MJXp-script><span><span style=margin-bottom:-0.25em><span class=MJXp-mrow id=MJXp-Span-1845><span class=MJXp-mo id=MJXp-Span-1846>∗</span></span></span></span></span><span class=MJXp-script><span><span style=margin-top:-0.85em><span class=MJXp-mrow id=MJXp-Span-1843><span class=MJXp-mi id=MJXp-Span-1844>Sagn</span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-1847 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-mi id=MJXp-Span-1848>Δ</span><span class=MJXp-msubsup id=MJXp-Span-1849><span class=MJXp-mrow id=MJXp-Span-1850 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1851>T</span></span><span class=MJXp-script-box style=height:1.86em;vertical-align:-0.64em><span class=MJXp-script><span><span style=margin-bottom:-0.25em><span class=MJXp-mrow id=MJXp-Span-1854><span class=MJXp-mo id=MJXp-Span-1855>*</span></span></span></span></span><span class=MJXp-script><span><span style=margin-top:-0.85em><span class=MJXp-mrow id=MJXp-Span-1852><span class=MJXp-mi id=MJXp-Span-1853>Sagnac</span></span></span></span></span></span></span></span></span><span id=MathJax-Element-192-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>, which is the same for the RLSE and the linear Sagnac effect. However, for <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-1856><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1857>D</span><span class=MJXp-mo id=MJXp-Span-1858 style=margin-left:0.333em;margin-right:0.333em>≲</span><span class=MJXp-mn id=MJXp-Span-1859>2</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1860>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1861>L</span><span class=MJXp-mo id=MJXp-Span-1862 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1863>c</span></span></span><span id=MathJax-Element-193-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>, the function <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-1864><span class=MJXp-mi id=MJXp-Span-1865>Δ</span><span class=MJXp-msup id=MJXp-Span-1866><span class=MJXp-mrow id=MJXp-Span-1867 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1868>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-1869 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-1870>*</span></span></span><span class=MJXp-mrow id=MJXp-Span-1871><span class=MJXp-mo id=MJXp-Span-1872 style=margin-left:0em;margin-right:0em>(</span><span class=MJXp-mrow id=MJXp-Span-1873><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1874>D</span></span><span class=MJXp-mo id=MJXp-Span-1875 style=margin-left:0em;margin-right:0em>)</span></span></span></span><span id=MathJax-Element-194-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> varies from the maximum values <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-1876><span class=MJXp-mn id=MJXp-Span-1877>2</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1878>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1879>L</span><span class=MJXp-mo id=MJXp-Span-1880 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class=MJXp-msup id=MJXp-Span-1881><span class=MJXp-mrow id=MJXp-Span-1882 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1883>c</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-1884 style=vertical-align:0.5em><span class=MJXp-mn id=MJXp-Span-1885>2</span></span></span></span></span><span id=MathJax-Element-195-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> (<span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-1886><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1887>D</span><span class=MJXp-mo id=MJXp-Span-1888 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-mn id=MJXp-Span-1889>0</span></span></span><span id=MathJax-Element-196-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> and <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-1890><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1891>D</span><span class=MJXp-mo id=MJXp-Span-1892 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-mn id=MJXp-Span-1893>2</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1894>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1895>L</span><span class=MJXp-mo id=MJXp-Span-1896 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1897>c</span></span></span><span id=MathJax-Element-197-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>) to zero (<span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-1898><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1899>D</span><span class=MJXp-mo id=MJXp-Span-1900 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-msub id=MJXp-Span-1901><span class=MJXp-mrow id=MJXp-Span-1902 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1903>D</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-1904 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-1905>0</span></span></span><span class=MJXp-mo id=MJXp-Span-1906 style=margin-left:0.333em;margin-right:0.333em>=</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1907>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1908>L</span><span class=MJXp-mo id=MJXp-Span-1909 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1910>c</span></span></span><span id=MathJax-Element-198-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>), as shown in <a href=#j_phys-2023-0110_fig_004 class="link link-fig" data-bs-target=j_phys-2023-0110_fig_004>Figure 4</a>. Analogous results, given in the following section and in the Appendix, are obtained when light propagates in a medium of refractive index <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-1911><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1912>n</span></span></span><span id=MathJax-Element-199-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>.</p>
<p>Thus, by assuming light speed invariance and the LT, the S-RLSE foresees the variant <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-1913><span class=MJXp-mi id=MJXp-Span-1914>Δ</span><span class=MJXp-msup id=MJXp-Span-1915><span class=MJXp-mrow id=MJXp-Span-1916 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1917>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-1918 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-1919>*</span></span></span><span class=MJXp-mrow id=MJXp-Span-1920><span class=MJXp-mo id=MJXp-Span-1921 style=margin-left:0em;margin-right:0em>(</span><span class=MJXp-mrow id=MJXp-Span-1922><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1923>D</span></span><span class=MJXp-mo id=MJXp-Span-1924 style=margin-left:0em;margin-right:0em>)</span></span></span></span><span id=MathJax-Element-200-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> of (<a href=#j_phys-2023-0110_eq_004 class="link link-disp-formula" data-bs-target=j_phys-2023-0110_eq_004>4</a>) that can be observed. The variant special feature of (<a href=#j_phys-2023-0110_eq_004 class="link link-disp-formula" data-bs-target=j_phys-2023-0110_eq_004>4</a>) is discussed in the Appendix within the wider scenario of relativistic theories. To fully understand the difference between the <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-1925><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1926>D</span></span></span><span id=MathJax-Element-201-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>-dependent S-RLSE results (<a href=#j_phys-2023-0110_eq_004 class="link link-disp-formula" data-bs-target=j_phys-2023-0110_eq_004>4</a>) and the <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-1927><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1928>D</span></span></span><span id=MathJax-Element-202-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>-independent results of the linear Sagnac effect in Eq. (<a href=#j_phys-2023-0110_eq_002 class="link link-disp-formula" data-bs-target=j_phys-2023-0110_eq_002>2</a>) and in Eq. (<a href=#j_phys-2023-0110_eq_001 class="link link-disp-formula" data-bs-target=j_phys-2023-0110_eq_001>1</a>), we consider the following corresponding interpretations.</p>
<section id=j_phys-2023-0110_s_002_s_001>
<h3 class=subheading>2.1 Interpreting the RLSE and the linear Sagnac effect using the LTs</h3>
<p>In the linear Sagnac effect and in the RLSE, the measurements are made by device <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-1929><span class=MJXp-msup id=MJXp-Span-1930><span class=MJXp-mrow id=MJXp-Span-1931 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-1932>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-1933 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-1934>*</span></span></span></span></span><span id=MathJax-Element-203-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>. Why are the round-trip time intervals of the propagating signals different in the two effects? Let us, then, consider an observer comoving with clock <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-1935><span class=MJXp-msup id=MJXp-Span-1936><span class=MJXp-mrow id=MJXp-Span-1937 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-1938>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-1939 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-1940>*</span></span></span></span></span><span id=MathJax-Element-204-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> (let us call it “observer <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-1941><span class=MJXp-msup id=MJXp-Span-1942><span class=MJXp-mrow id=MJXp-Span-1943 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-1944>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-1945 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-1946>*</span></span></span></span></span><span id=MathJax-Element-205-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>” or simply “<span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-1947><span class=MJXp-msup id=MJXp-Span-1948><span class=MJXp-mrow id=MJXp-Span-1949 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-1950>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-1951 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-1952>*</span></span></span></span></span><span id=MathJax-Element-206-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>”) and check first what happens in the linear Sagnac effect of <a href=#j_phys-2023-0110_fig_001 class="link link-fig" data-bs-target=j_phys-2023-0110_fig_001>Figure 1</a>(b) when <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-1953><span class=MJXp-msup id=MJXp-Span-1954><span class=MJXp-mrow id=MJXp-Span-1955 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-1956>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-1957 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-1958>*</span></span></span></span></span><span id=MathJax-Element-207-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> is near point A and, during the round-trip interval <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-1959><span class=MJXp-msub id=MJXp-Span-1960><span class=MJXp-mrow id=MJXp-Span-1961 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1962>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-1963 style=vertical-align:-0.4em><span class=MJXp-mo id=MJXp-Span-1964>⇒</span></span></span></span></span><span id=MathJax-Element-208-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>, changes the direction of motion in the negligible time interval <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-1965><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1966>η</span></span></span><span id=MathJax-Element-209-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> moving from the lower to the upper section of the contour. While on the lower section, <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-1967><span class=MJXp-msup id=MJXp-Span-1968><span class=MJXp-mrow id=MJXp-Span-1969 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-1970>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-1971 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-1972>*</span></span></span></span></span><span id=MathJax-Element-210-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> is comoving with the inertial frame <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-1979><span class=MJXp-msup id=MJXp-Span-1980><span class=MJXp-mrow id=MJXp-Span-1981 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1982>S</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-1983 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-1984>″</span></span></span></span></span><span id=MathJax-Element-211-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> and with the inertial frame <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-1985><span class=MJXp-msup id=MJXp-Span-1986><span class=MJXp-mrow id=MJXp-Span-1987 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-1988>S</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-1989 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-1990>′</span></span></span></span></span><span id=MathJax-Element-212-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> when on the upper section.</p>
<p>If the counter-propagating photon is emitted by <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-1991><span class=MJXp-msup id=MJXp-Span-1992><span class=MJXp-mrow id=MJXp-Span-1993 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-1994>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-1995 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-1996>*</span></span></span></span></span><span id=MathJax-Element-213-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> at <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-1997><span class=MJXp-msup id=MJXp-Span-1998><span class=MJXp-mrow id=MJXp-Span-1999 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-2000>AC</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-2001 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-2002>*</span></span></span><span class=MJXp-mo id=MJXp-Span-2003 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-msub id=MJXp-Span-2004><span class=MJXp-mrow id=MJXp-Span-2005 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2006>D</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-2007 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-2008>0</span></span></span><span class=MJXp-mo id=MJXp-Span-2009 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-mrow id=MJXp-Span-2010><span class=MJXp-mo id=MJXp-Span-2011 style=margin-left:0em;margin-right:0em>(</span><span class=MJXp-mrow id=MJXp-Span-2012><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2013>v</span><span class=MJXp-mo id=MJXp-Span-2014 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2015>c</span></span><span class=MJXp-mo id=MJXp-Span-2016 style=margin-left:0em;margin-right:0em>)</span></span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2017>L</span></span></span><span id=MathJax-Element-214-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> when in the lower section frame <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-2018><span class=MJXp-msup id=MJXp-Span-2019><span class=MJXp-mrow id=MJXp-Span-2020 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2021>S</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-2022 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-2023>″</span></span></span></span></span><span id=MathJax-Element-215-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>, <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-2024><span class=MJXp-msup id=MJXp-Span-2025><span class=MJXp-mrow id=MJXp-Span-2026 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-2027>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-2028 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-2029>*</span></span></span></span></span><span id=MathJax-Element-216-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> reaches A when, simultaneously, the photon reaches point B, as shown in <a href=#j_phys-2023-0110_fig_003 class="link link-fig" data-bs-target=j_phys-2023-0110_fig_003>Figure 3</a>. Then, for the relative position of photon and <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-2030><span class=MJXp-msup id=MJXp-Span-2031><span class=MJXp-mrow id=MJXp-Span-2032 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-2033>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-2034 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-2035>*</span></span></span></span></span><span id=MathJax-Element-217-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>, the situation is the same as that in the RLSE of <a href=#j_phys-2023-0110_fig_002 class="link link-fig" data-bs-target=j_phys-2023-0110_fig_002>Figure 2</a>(b).</p>
<div class=figure-wrapper id=j_phys-2023-0110_fig_003><div class="figure w-100"><div class=graphic><img loading=lazy 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" alt="Figure 3
Effect of relative simultaneity observed by
C
*
{{\rm{C}}}^{* }
in the linear Sagnac effect. The two events “
C
*
{{\rm{C}}}^{* }
at A” and “photon at B” are simultaneous on frame
S
″
{S}^{^{\prime\prime} }
comoving with
C
*
{{\rm{C}}}^{* }
when on the contour lower section. After turning around the pulley in the negligible time interval
η
\eta
and changing velocity,
C
*
{{\rm{C}}}^{* }
starts comoving with frame
S
′
{S}^{^{\prime} }
on the upper section at
t
′
=
t
″
=
0
{t}^{^{\prime} }={t}^{^{\prime\prime} }=0
. However, due to relative simultaneity between
S
′
{S}^{^{\prime} }
and
S
″
{S}^{^{\prime\prime} }
, for observer
C
*
{{\rm{C}}}^{* }
on
S
′
{S}^{^{\prime} }
, the photon is no longer at B but is at K already.
"></div><div class="figure-description mb-3"><div class="figure-label h3"><span class=label>Figure 3</span></div><div class="figure-caption mb-2"><span class=caption><p>Effect of relative simultaneity observed by <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-2036><span class=MJXp-msup id=MJXp-Span-2037><span class=MJXp-mrow id=MJXp-Span-2038 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-2039>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-2040 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-2041>*</span></span></span></span></span><span id=MathJax-Element-218-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> in the linear Sagnac effect. The two events “<span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-2042><span class=MJXp-msup id=MJXp-Span-2043><span class=MJXp-mrow id=MJXp-Span-2044 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-2045>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-2046 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-2047>*</span></span></span></span></span><span id=MathJax-Element-219-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> at A” and “photon at B” are simultaneous on frame <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-2048><span class=MJXp-msup id=MJXp-Span-2049><span class=MJXp-mrow id=MJXp-Span-2050 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2051>S</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-2052 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-2053>″</span></span></span></span></span><span id=MathJax-Element-220-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> comoving with <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-2054><span class=MJXp-msup id=MJXp-Span-2055><span class=MJXp-mrow id=MJXp-Span-2056 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-2057>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-2058 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-2059>*</span></span></span></span></span><span id=MathJax-Element-221-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> when on the contour lower section. After turning around the pulley in the negligible time interval <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-2060><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2061>η</span></span></span><span id=MathJax-Element-222-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> and changing velocity, <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-2062><span class=MJXp-msup id=MJXp-Span-2063><span class=MJXp-mrow id=MJXp-Span-2064 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-2065>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-2066 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-2067>*</span></span></span></span></span><span id=MathJax-Element-223-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> starts comoving with frame <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-2068><span class=MJXp-msup id=MJXp-Span-2069><span class=MJXp-mrow id=MJXp-Span-2070 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2071>S</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-2072 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-2073>′</span></span></span></span></span><span id=MathJax-Element-224-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> on the upper section at <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-2074><span class=MJXp-msup id=MJXp-Span-2075><span class=MJXp-mrow id=MJXp-Span-2076 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2077>t</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-2078 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-2079>′</span></span></span><span class=MJXp-mo id=MJXp-Span-2080 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-msup id=MJXp-Span-2081><span class=MJXp-mrow id=MJXp-Span-2082 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2083>t</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-2084 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-2085>″</span></span></span><span class=MJXp-mo id=MJXp-Span-2086 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-mn id=MJXp-Span-2087>0</span></span></span><span id=MathJax-Element-225-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>. However, due to relative simultaneity between <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-2088><span class=MJXp-msup id=MJXp-Span-2089><span class=MJXp-mrow id=MJXp-Span-2090 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2091>S</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-2092 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-2093>′</span></span></span></span></span><span id=MathJax-Element-226-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> and <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-2094><span class=MJXp-msup id=MJXp-Span-2095><span class=MJXp-mrow id=MJXp-Span-2096 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2097>S</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-2098 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-2099>″</span></span></span></span></span><span id=MathJax-Element-227-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>, for observer <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-2100><span class=MJXp-msup id=MJXp-Span-2101><span class=MJXp-mrow id=MJXp-Span-2102 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-2103>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-2104 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-2105>*</span></span></span></span></span><span id=MathJax-Element-228-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> on <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-2106><span class=MJXp-msup id=MJXp-Span-2107><span class=MJXp-mrow id=MJXp-Span-2108 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2109>S</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-2110 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-2111>′</span></span></span></span></span><span id=MathJax-Element-229-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>, the photon is no longer at B but is at K already.</p></span></div></div></div></div>
<p>However, when (after reaching A and turning around the pulley) <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-2112><span class=MJXp-msup id=MJXp-Span-2113><span class=MJXp-mrow id=MJXp-Span-2114 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-2115>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-2116 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-2117>*</span></span></span></span></span><span id=MathJax-Element-230-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> starts comoving with frame <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-2118><span class=MJXp-msup id=MJXp-Span-2119><span class=MJXp-mrow id=MJXp-Span-2120 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2121>S</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-2122 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-2123>′</span></span></span></span></span><span id=MathJax-Element-231-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> on the upper section, we can see in <a href=#j_phys-2023-0110_fig_003 class="link link-fig" data-bs-target=j_phys-2023-0110_fig_003>Figure 3</a> that now the position of the photon is not at B, but at K, being AK <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-2124><span class=MJXp-mo id=MJXp-Span-2125 style=margin-left:0.333em;margin-right:0.333em>≃</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2126>L</span><span class=MJXp-mrow id=MJXp-Span-2127><span class=MJXp-mo id=MJXp-Span-2128 style=margin-left:0em;margin-right:0em>(</span><span class=MJXp-mrow id=MJXp-Span-2129><span class=MJXp-mn id=MJXp-Span-2130>1</span><span class=MJXp-mo id=MJXp-Span-2131 style=margin-left:0.267em;margin-right:0.267em>−</span><span class=MJXp-mn id=MJXp-Span-2132>2</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2133>v</span><span class=MJXp-mo id=MJXp-Span-2134 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2135>c</span></span><span class=MJXp-mo id=MJXp-Span-2136 style=margin-left:0em;margin-right:0em>)</span></span><span class=MJXp-mo id=MJXp-Span-2137 style=margin-left:0.333em;margin-right:0.333em>&lt;</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2138>L</span></span></span><span id=MathJax-Element-232-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> and, thus, the situation differs from that of <a href=#j_phys-2023-0110_fig_002 class="link link-fig" data-bs-target=j_phys-2023-0110_fig_002>Figure 2</a>(b) of the RLSE.</p>
<p>The difference is due to the fact that, in the linear Sagnac effect, the mechanism of relative simultaneity takes place when <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-2139><span class=MJXp-msup id=MJXp-Span-2140><span class=MJXp-mrow id=MJXp-Span-2141 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-2142>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-2143 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-2144>*</span></span></span></span></span><span id=MathJax-Element-233-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> changes velocity by moving from frame <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-2145><span class=MJXp-msup id=MJXp-Span-2146><span class=MJXp-mrow id=MJXp-Span-2147 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2148>S</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-2149 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-2150>″</span></span></span></span></span><span id=MathJax-Element-234-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> on the lower section to the frame <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-2151><span class=MJXp-msup id=MJXp-Span-2152><span class=MJXp-mrow id=MJXp-Span-2153 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2154>S</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-2155 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-2156>′</span></span></span></span></span><span id=MathJax-Element-235-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> on the upper section [<a href=#j_phys-2023-0110_ref_007 class="link link-bibr" data-bs-target=j_phys-2023-0110_ref_007 data-bs-toggle=tooltip title="[7] Spavieri G, Gillies GT, GaarderHaug E, Sanchez A. Light propagation and local speed in the linear Sagnac effect. J Modern Optics. 2019;66(21):2131–41. 10.1080/09500340.2019.1695005. Spavieri G, Gillies GT, Gaarder Haug E. The Sagnac effect and the role of simultaneity in relativity theory. J Mod Opt. 2021. doi: 10.1080/09500340.2021.1887384. Spavieri G. On measuring the one-way speed of light. Eur Phys J D. 2012;66:76. doi: 10.1140/epjd/e2012-20524-8; Spavieri G. Light propagation on a moving closed contour and the role of simultaneity in special relativity. Eur J Appl Phys. 2021;3:4:48. doi :10.24018/ejphysics.2021.3.4.99; Spavieri G, Gaarder Haug E. Testing light speed invariance by measuring the one-way light speed on earth. Physics Open 2022;12:100113. doi: 10.1016/j.physo.2022.100113. Search in Google Scholar">7</a>]. The two events, “<span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-2157><span class=MJXp-msup id=MJXp-Span-2158><span class=MJXp-mrow id=MJXp-Span-2159 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-2160>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-2161 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-2162>*</span></span></span></span></span><span id=MathJax-Element-236-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> at A” and “photon at B,” are simultaneous for observer <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-2163><span class=MJXp-msup id=MJXp-Span-2164><span class=MJXp-mrow id=MJXp-Span-2165 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-2166>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-2167 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-2168>*</span></span></span></span></span><span id=MathJax-Element-237-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> on frame <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-2169><span class=MJXp-msup id=MJXp-Span-2170><span class=MJXp-mrow id=MJXp-Span-2171 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2172>S</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-2173 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-2174>″</span></span></span></span></span><span id=MathJax-Element-238-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> in the lower section, but no longer simultaneous for <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-2175><span class=MJXp-msup id=MJXp-Span-2176><span class=MJXp-mrow id=MJXp-Span-2177 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-2178>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-2179 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-2180>*</span></span></span></span></span><span id=MathJax-Element-239-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> on frame <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-2181><span class=MJXp-msup id=MJXp-Span-2182><span class=MJXp-mrow id=MJXp-Span-2183 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2184>S</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-2185 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-2186>′</span></span></span></span></span><span id=MathJax-Element-240-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> in the upper section because <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-2187><span class=MJXp-msup id=MJXp-Span-2188><span class=MJXp-mrow id=MJXp-Span-2189 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2190>S</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-2191 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-2192>′</span></span></span></span></span><span id=MathJax-Element-241-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> is in motion with speed <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-2193><span class=MJXp-mo id=MJXp-Span-2194 style=margin-left:0.333em;margin-right:0.333em>≃</span><span class=MJXp-mn id=MJXp-Span-2195>2</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2196>v</span></span></span><span id=MathJax-Element-242-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> relative to <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-2197><span class=MJXp-msup id=MJXp-Span-2198><span class=MJXp-mrow id=MJXp-Span-2199 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2200>S</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-2201 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-2202>″</span></span></span></span></span><span id=MathJax-Element-243-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>.</p>
<p>As shown in <a href=#j_phys-2023-0110_fig_003 class="link link-fig" data-bs-target=j_phys-2023-0110_fig_003>Figure 3</a>, in the linear Sagnac effect, clock <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-2203><span class=MJXp-msup id=MJXp-Span-2204><span class=MJXp-mrow id=MJXp-Span-2205 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-2206>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-2207 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-2208>*</span></span></span></span></span><span id=MathJax-Element-244-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> is reached by the photon returning on the upper section after the proper time interval <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-2209><span class=MJXp-msub id=MJXp-Span-2210><span class=MJXp-mrow id=MJXp-Span-2211 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2212>τ</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-2213 style=vertical-align:-0.4em><span class=MJXp-mi id=MJXp-Span-2214>ret</span></span></span><span class=MJXp-mo id=MJXp-Span-2215 style=margin-left:0.333em;margin-right:0.333em>≃</span><span class=MJXp-mrow id=MJXp-Span-2216><span class=MJXp-mo id=MJXp-Span-2217 style=margin-left:0em;margin-right:0em>(</span><span class=MJXp-mrow id=MJXp-Span-2218><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2219>L</span><span class=MJXp-mo id=MJXp-Span-2220 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2221>c</span></span><span class=MJXp-mo id=MJXp-Span-2222 style=margin-left:0em;margin-right:0em>)</span></span><span class=MJXp-mrow id=MJXp-Span-2223><span class=MJXp-mo id=MJXp-Span-2224 style=margin-left:0em;margin-right:0em>(</span><span class=MJXp-mrow id=MJXp-Span-2225><span class=MJXp-mn id=MJXp-Span-2226>1</span><span class=MJXp-mo id=MJXp-Span-2227 style=margin-left:0.267em;margin-right:0.267em>−</span><span class=MJXp-mn id=MJXp-Span-2228>2</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2229>v</span><span class=MJXp-mo id=MJXp-Span-2230 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2231>c</span></span><span class=MJXp-mo id=MJXp-Span-2232 style=margin-left:0em;margin-right:0em>)</span></span></span></span><span id=MathJax-Element-245-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> and the round-trip time interval is, as expected, <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-2233><span class=MJXp-msub id=MJXp-Span-2234><span class=MJXp-mrow id=MJXp-Span-2235 style=margin-right:0.05em><span class=MJXp-mrow id=MJXp-Span-2236><span class=MJXp-mo id=MJXp-Span-2237 style=margin-left:0em;margin-right:0em;vertical-align:-0.244em><span style=font-size:1.978em;margin-left:-0.05em class="MJXp-right MJXp-scale7">(</span></span><span class=MJXp-mrow id=MJXp-Span-2238><span class=MJXp-msub id=MJXp-Span-2239><span class=MJXp-mrow id=MJXp-Span-2240 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2241>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-2242 style=vertical-align:-0.4em><span class=MJXp-mo id=MJXp-Span-2243>⇒</span></span></span></span><span class=MJXp-mo id=MJXp-Span-2244 style=margin-left:0em;margin-right:0em;vertical-align:-0.244em><span style=font-size:1.978em;margin-left:-0.05em class="MJXp-right MJXp-scale7">)</span></span></span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-2245 style=vertical-align:-0.74em><span class=MJXp-mi id=MJXp-Span-2246>Sagnac</span></span></span><span class=MJXp-mo id=MJXp-Span-2247 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-msub id=MJXp-Span-2248><span class=MJXp-mrow id=MJXp-Span-2249 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2250>τ</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-2251 style=vertical-align:-0.4em><span class=MJXp-mi id=MJXp-Span-2252>out</span></span></span><span class=MJXp-mo id=MJXp-Span-2253 style=margin-left:0.267em;margin-right:0.267em>+</span><span class=MJXp-msub id=MJXp-Span-2254><span class=MJXp-mrow id=MJXp-Span-2255 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2256>τ</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-2257 style=vertical-align:-0.4em><span class=MJXp-mi id=MJXp-Span-2258>ret</span></span></span><span class=MJXp-mo id=MJXp-Span-2259 style=margin-left:0.333em;margin-right:0.333em>≃</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2260>L</span><span class=MJXp-mo id=MJXp-Span-2261 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2262>c</span><span class=MJXp-mo id=MJXp-Span-2263 style=margin-left:0.267em;margin-right:0.267em>+</span><span class=MJXp-mrow id=MJXp-Span-2264><span class=MJXp-mo id=MJXp-Span-2265 style=margin-left:0em;margin-right:0em>(</span><span class=MJXp-mrow id=MJXp-Span-2266><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2267>L</span><span class=MJXp-mo id=MJXp-Span-2268 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2269>c</span></span><span class=MJXp-mo id=MJXp-Span-2270 style=margin-left:0em;margin-right:0em>)</span></span><span class=MJXp-mrow id=MJXp-Span-2271><span class=MJXp-mo id=MJXp-Span-2272 style=margin-left:0em;margin-right:0em>(</span><span class=MJXp-mrow id=MJXp-Span-2273><span class=MJXp-mn id=MJXp-Span-2274>1</span><span class=MJXp-mo id=MJXp-Span-2275 style=margin-left:0.267em;margin-right:0.267em>−</span><span class=MJXp-mn id=MJXp-Span-2276>2</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2277>v</span><span class=MJXp-mo id=MJXp-Span-2278 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2279>c</span></span><span class=MJXp-mo id=MJXp-Span-2280 style=margin-left:0em;margin-right:0em>)</span></span><span class=MJXp-mo id=MJXp-Span-2281 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-mn id=MJXp-Span-2282>2</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2283>L</span><span class=MJXp-mo id=MJXp-Span-2284 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class=MJXp-mrow id=MJXp-Span-2285><span class=MJXp-mo id=MJXp-Span-2286 style=margin-left:0em;margin-right:0em>(</span><span class=MJXp-mrow id=MJXp-Span-2287><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2288>c</span><span class=MJXp-mo id=MJXp-Span-2289 style=margin-left:0.267em;margin-right:0.267em>+</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2290>v</span></span><span class=MJXp-mo id=MJXp-Span-2291 style=margin-left:0em;margin-right:0em>)</span></span></span></span><span id=MathJax-Element-246-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>. In this case, relative to <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-2292><span class=MJXp-msup id=MJXp-Span-2293><span class=MJXp-mrow id=MJXp-Span-2294 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-2295>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-2296 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-2297>*</span></span></span></span></span><span id=MathJax-Element-247-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>, in the return trip, the photon covers at speed <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-2298><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2299>c</span></span></span><span id=MathJax-Element-248-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> the shorter distance <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-2300><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2301>L</span><span class=MJXp-mrow id=MJXp-Span-2302><span class=MJXp-mo id=MJXp-Span-2303 style=margin-left:0em;margin-right:0em>(</span><span class=MJXp-mrow id=MJXp-Span-2304><span class=MJXp-mn id=MJXp-Span-2305>1</span><span class=MJXp-mo id=MJXp-Span-2306 style=margin-left:0.267em;margin-right:0.267em>−</span><span class=MJXp-mn id=MJXp-Span-2307>2</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2308>v</span><span class=MJXp-mo id=MJXp-Span-2309 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2310>c</span></span><span class=MJXp-mo id=MJXp-Span-2311 style=margin-left:0em;margin-right:0em>)</span></span></span></span><span id=MathJax-Element-249-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> only.</p>
<p>However, in the case of the RLSE (<a href=#j_phys-2023-0110_fig_002 class="link link-fig" data-bs-target=j_phys-2023-0110_fig_002>Figure 2</a>(b)), <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-2312><span class=MJXp-msup id=MJXp-Span-2313><span class=MJXp-mrow id=MJXp-Span-2314 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-2315>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-2316 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-2317>*</span></span></span></span></span><span id=MathJax-Element-250-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> is stationary and, since the mechanism of relative simultaneity does not apply, in the return trip, the photon covers at speed <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-2318><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2319>c</span></span></span><span id=MathJax-Element-251-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> the full distance <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-2320><span class=MJXp-mo id=MJXp-Span-2321 style=margin-left:0.333em;margin-right:0.333em>≃</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2322>L</span></span></span><span id=MathJax-Element-252-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> in the time interval <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-2323><span class=MJXp-msub id=MJXp-Span-2324><span class=MJXp-mrow id=MJXp-Span-2325 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2326>t</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-2327 style=vertical-align:-0.4em><span class=MJXp-mi id=MJXp-Span-2328>ret</span></span></span><span class=MJXp-mo id=MJXp-Span-2329 style=margin-left:0.333em;margin-right:0.333em>=</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2330>L</span><span class=MJXp-mo id=MJXp-Span-2331 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class=MJXp-mrow id=MJXp-Span-2332><span class=MJXp-mo id=MJXp-Span-2333 style=margin-left:0em;margin-right:0em>(</span><span class=MJXp-mrow id=MJXp-Span-2334><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2335>γ</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2336>c</span></span><span class=MJXp-mo id=MJXp-Span-2337 style=margin-left:0em;margin-right:0em>)</span></span><span class=MJXp-mo id=MJXp-Span-2338 style=margin-left:0.333em;margin-right:0.333em>≃</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2339>L</span><span class=MJXp-mo id=MJXp-Span-2340 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2341>c</span></span></span><span id=MathJax-Element-253-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>. Thus, for the special case <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-2342><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2343>D</span><span class=MJXp-mo id=MJXp-Span-2344 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-msub id=MJXp-Span-2345><span class=MJXp-mrow id=MJXp-Span-2346 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2347>D</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-2348 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-2349>0</span></span></span><span class=MJXp-mo id=MJXp-Span-2350 style=margin-left:0.333em;margin-right:0.333em>=</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2351>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2352>L</span><span class=MJXp-mo id=MJXp-Span-2353 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class=MJXp-msup id=MJXp-Span-2354><span class=MJXp-mrow id=MJXp-Span-2355 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2356>c</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-2357 style=vertical-align:0.5em><span class=MJXp-mn id=MJXp-Span-2358>2</span></span></span></span></span><span id=MathJax-Element-254-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>, in the RLSE, the round-trip time is <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-2359><span class=MJXp-msub id=MJXp-Span-2360><span class=MJXp-mrow id=MJXp-Span-2361 style=margin-right:0.05em><span class=MJXp-mrow id=MJXp-Span-2362><span class=MJXp-mo id=MJXp-Span-2363 style=margin-left:0em;margin-right:0em;vertical-align:-0.244em><span style=font-size:1.978em;margin-left:-0.05em class="MJXp-right MJXp-scale7">(</span></span><span class=MJXp-mrow id=MJXp-Span-2364><span class=MJXp-msub id=MJXp-Span-2365><span class=MJXp-mrow id=MJXp-Span-2366 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2367>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-2368 style=vertical-align:-0.4em><span class=MJXp-mo id=MJXp-Span-2369>⇒</span></span></span></span><span class=MJXp-mo id=MJXp-Span-2370 style=margin-left:0em;margin-right:0em;vertical-align:-0.244em><span style=font-size:1.978em;margin-left:-0.05em class="MJXp-right MJXp-scale7">)</span></span></span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-2371 style=vertical-align:-0.74em><span class=MJXp-mi id=MJXp-Span-2372>RLSE</span></span></span><span class=MJXp-mo id=MJXp-Span-2373 style=margin-left:0.333em;margin-right:0.333em>≃</span><span class=MJXp-mn id=MJXp-Span-2374>2</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2375>L</span><span class=MJXp-mo id=MJXp-Span-2376 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2377>c</span></span></span><span id=MathJax-Element-255-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>, which is greater than the corresponding one <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-2378><span class=MJXp-msub id=MJXp-Span-2379><span class=MJXp-mrow id=MJXp-Span-2380 style=margin-right:0.05em><span class=MJXp-mrow id=MJXp-Span-2381><span class=MJXp-mo id=MJXp-Span-2382 style=margin-left:0em;margin-right:0em;vertical-align:-0.244em><span style=font-size:1.978em;margin-left:-0.05em class="MJXp-right MJXp-scale7">(</span></span><span class=MJXp-mrow id=MJXp-Span-2383><span class=MJXp-msub id=MJXp-Span-2384><span class=MJXp-mrow id=MJXp-Span-2385 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2386>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-2387 style=vertical-align:-0.4em><span class=MJXp-mo id=MJXp-Span-2388>⇒</span></span></span></span><span class=MJXp-mo id=MJXp-Span-2389 style=margin-left:0em;margin-right:0em;vertical-align:-0.244em><span style=font-size:1.978em;margin-left:-0.05em class="MJXp-right MJXp-scale7">)</span></span></span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-2390 style=vertical-align:-0.74em><span class=MJXp-mi id=MJXp-Span-2391>Sagnac</span></span></span><span class=MJXp-mo id=MJXp-Span-2392 style=margin-left:0.333em;margin-right:0.333em>≃</span><span class=MJXp-mn id=MJXp-Span-2393>2</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2394>L</span><span class=MJXp-mo id=MJXp-Span-2395 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class=MJXp-mrow id=MJXp-Span-2396><span class=MJXp-mo id=MJXp-Span-2397 style=margin-left:0em;margin-right:0em>(</span><span class=MJXp-mrow id=MJXp-Span-2398><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2399>c</span><span class=MJXp-mo id=MJXp-Span-2400 style=margin-left:0.267em;margin-right:0.267em>+</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2401>v</span></span><span class=MJXp-mo id=MJXp-Span-2402 style=margin-left:0em;margin-right:0em>)</span></span></span></span><span id=MathJax-Element-256-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> of the linear Sagnac effect.</p>
<p>As shown in ref. [<a href=#j_phys-2023-0110_ref_007 class="link link-bibr" data-bs-target=j_phys-2023-0110_ref_007 data-bs-toggle=tooltip title="[7] Spavieri G, Gillies GT, GaarderHaug E, Sanchez A. Light propagation and local speed in the linear Sagnac effect. J Modern Optics. 2019;66(21):2131–41. 10.1080/09500340.2019.1695005. Spavieri G, Gillies GT, Gaarder Haug E. The Sagnac effect and the role of simultaneity in relativity theory. J Mod Opt. 2021. doi: 10.1080/09500340.2021.1887384. Spavieri G. On measuring the one-way speed of light. Eur Phys J D. 2012;66:76. doi: 10.1140/epjd/e2012-20524-8; Spavieri G. Light propagation on a moving closed contour and the role of simultaneity in special relativity. Eur J Appl Phys. 2021;3:4:48. doi :10.24018/ejphysics.2021.3.4.99; Spavieri G, Gaarder Haug E. Testing light speed invariance by measuring the one-way light speed on earth. Physics Open 2022;12:100113. doi: 10.1016/j.physo.2022.100113. Search in Google Scholar">7</a>], in the case of the linear Sagnac effect, the “time gap” <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-2403><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2404>δ</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2405>t</span><span class=MJXp-mo id=MJXp-Span-2406 style=margin-left:0.333em;margin-right:0.333em>≃</span><span class=MJXp-mn id=MJXp-Span-2407>2</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2408>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2409>L</span><span class=MJXp-mo id=MJXp-Span-2410 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class=MJXp-msup id=MJXp-Span-2411><span class=MJXp-mrow id=MJXp-Span-2412 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2413>c</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-2414 style=vertical-align:0.5em><span class=MJXp-mn id=MJXp-Span-2415>2</span></span></span></span></span><span id=MathJax-Element-257-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>, due to relative simultaneity between <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-2416><span class=MJXp-msup id=MJXp-Span-2417><span class=MJXp-mrow id=MJXp-Span-2418 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2419>S</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-2420 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-2421>′</span></span></span></span></span><span id=MathJax-Element-258-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> and <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-2422><span class=MJXp-msup id=MJXp-Span-2423><span class=MJXp-mrow id=MJXp-Span-2424 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2425>S</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-2426 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-2427>″</span></span></span></span></span><span id=MathJax-Element-259-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>, corresponds to the length difference <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-2428><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2429>c</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2430>δ</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2431>t</span><span class=MJXp-mo id=MJXp-Span-2432 style=margin-left:0.333em;margin-right:0.333em>≃</span><span class=MJXp-mn id=MJXp-Span-2433>2</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2434>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2435>L</span><span class=MJXp-mo id=MJXp-Span-2436 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2437>c</span></span></span><span id=MathJax-Element-260-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> not covered by the photon when <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-2438><span class=MJXp-msup id=MJXp-Span-2439><span class=MJXp-mrow id=MJXp-Span-2440 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-2441>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-2442 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-2443>*</span></span></span></span></span><span id=MathJax-Element-261-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> is on the upper section. Therefore, we find that <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-2444><span class=MJXp-msub id=MJXp-Span-2445><span class=MJXp-mrow id=MJXp-Span-2446 style=margin-right:0.05em><span class=MJXp-mrow id=MJXp-Span-2447><span class=MJXp-mo id=MJXp-Span-2448 style=margin-left:0em;margin-right:0em;vertical-align:-0.244em><span style=font-size:1.978em;margin-left:-0.05em class="MJXp-right MJXp-scale7">(</span></span><span class=MJXp-mrow id=MJXp-Span-2449><span class=MJXp-msub id=MJXp-Span-2450><span class=MJXp-mrow id=MJXp-Span-2451 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2452>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-2453 style=vertical-align:-0.4em><span class=MJXp-mo id=MJXp-Span-2454>⇒</span></span></span></span><span class=MJXp-mo id=MJXp-Span-2455 style=margin-left:0em;margin-right:0em;vertical-align:-0.244em><span style=font-size:1.978em;margin-left:-0.05em class="MJXp-right MJXp-scale7">)</span></span></span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-2456 style=vertical-align:-0.74em><span class=MJXp-mi id=MJXp-Span-2457>RLSE</span></span></span><span class=MJXp-mo id=MJXp-Span-2458 style=margin-left:0.333em;margin-right:0.333em>≃</span><span class=MJXp-msub id=MJXp-Span-2459><span class=MJXp-mrow id=MJXp-Span-2460 style=margin-right:0.05em><span class=MJXp-mrow id=MJXp-Span-2461><span class=MJXp-mo id=MJXp-Span-2462 style=margin-left:0em;margin-right:0em;vertical-align:-0.244em><span style=font-size:1.978em;margin-left:-0.05em class="MJXp-right MJXp-scale7">(</span></span><span class=MJXp-mrow id=MJXp-Span-2463><span class=MJXp-msub id=MJXp-Span-2464><span class=MJXp-mrow id=MJXp-Span-2465 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2466>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-2467 style=vertical-align:-0.4em><span class=MJXp-mo id=MJXp-Span-2468>⇒</span></span></span></span><span class=MJXp-mo id=MJXp-Span-2469 style=margin-left:0em;margin-right:0em;vertical-align:-0.244em><span style=font-size:1.978em;margin-left:-0.05em class="MJXp-right MJXp-scale7">)</span></span></span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-2470 style=vertical-align:-0.74em><span class=MJXp-mi id=MJXp-Span-2471>Sagnac</span></span></span><span class=MJXp-mo id=MJXp-Span-2472 style=margin-left:0.267em;margin-right:0.267em>+</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2473>δ</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2474>t</span></span></span><span id=MathJax-Element-262-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>, showing that the difference can be related to relative simultaneity.</p>
<p>In general, in the linear Sagnac effect, the round-trip time <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-2475><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2476>T</span></span></span><span id=MathJax-Element-263-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> of light signals is independent of <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-2477><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2478>D</span></span></span><span id=MathJax-Element-264-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> and the stationary contour shape, while in the RLSE, the round-trip time <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-2479><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2480>T</span></span></span><span id=MathJax-Element-265-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> depends on <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-2481><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2482>D</span></span></span><span id=MathJax-Element-266-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> and on the shape of the moving contour. Then, the RLSE represents an optical effect not fully equivalent to the linear Sagnac effect.</p>
</section>
</section>
<section id=j_phys-2023-0110_s_003>
<h2 class=subheading>3 Experiment testing the S-RLSE</h2>
<p>Here, we discuss the results obtained for the rectangular contour of <a href=#j_phys-2023-0110_fig_004 class="link link-fig" data-bs-target=j_phys-2023-0110_fig_004>Figure 4</a> (shown also in <a href=#j_phys-2023-0110_fig_005 class="link link-fig" data-bs-target=j_phys-2023-0110_fig_005>Figure A1</a> of the Appendix) of sizes <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-2483><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2484>L</span></span></span><span id=MathJax-Element-267-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> and <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-2485><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2486>H</span></span></span><span id=MathJax-Element-268-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>. With <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-2487><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2488>H</span><span class=MJXp-mo id=MJXp-Span-2489 style=margin-left:0.333em;margin-right:0.333em>≃</span><span class=MJXp-mn id=MJXp-Span-2490>2</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2491>R</span></span></span><span id=MathJax-Element-269-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>, where <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-2492><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2493>R</span></span></span><span id=MathJax-Element-270-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> is the radius of the pulley in the linear Sagnac effect, the shape of this contour represents more realistically the RLSE.</p>
<div class=figure-wrapper id=j_phys-2023-0110_fig_004><div class="figure w-100"><div class=graphic><img loading=lazy 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 alt="Figure 4
Time difference
Δ
T
*
(
D
)
\Delta {T}^{* }\left(D)
for the counter-moving photon in the S-RLSE. For the Sagnac effect,
Δ
T
\Delta T
*
=
v
P
⁄
c
2
=vP/{c}^{2}
is constant and represented by the dotted line. For the S-RLSE, starting from right to left with
C
*
{{\rm{C}}}^{* }
on the contour lower section
L
L
from the position
D
>
2
v
L
⁄
c
2
D\gt 2vL/{c}^{2}
, we have
Δ
T
*
=
v
P
⁄
c
2
\Delta {T}^{* }=vP/{c}^{2}
until
D
≃
2
v
L
⁄
c
D\simeq 2vL/c
. When
D
<
2
v
L
⁄
c
D\lt 2vL/c
and until
D
=
D
0
=
v
L
⁄
c
D={D}_{0}=vL/c
,
Δ
T
*
(
D
)
\Delta {T}^{* }\left(D)
decreases up to
v
L
⁄
c
2
vL/{c}^{2}
. Then,
Δ
T
\Delta T
* increases and reaches again the value
v
P
⁄
c
2
vP/{c}^{2}
at
D
=
0
D=0
and afterwards when
C
*
{{\rm{C}}}^{* }
is on the left side
H
H
of the moving contour. The broken line refers to the S-RLSE of Figure 2, where
P
=
2
L
P=2L
and the dip is
2
v
L
⁄
c
2
2vL/{c}^{2}
with
Δ
T
*
=
0
\Delta {T}^{* }=0
at
D
=
D
0
D={D}_{0}
.
"></div><div class="figure-description mb-3"><div class="figure-label h3"><span class=label>Figure 4</span></div><div class="figure-caption mb-2"><span class=caption><p>Time difference <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-2494><span class=MJXp-mi id=MJXp-Span-2495>Δ</span><span class=MJXp-msup id=MJXp-Span-2496><span class=MJXp-mrow id=MJXp-Span-2497 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2498>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-2499 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-2500>*</span></span></span><span class=MJXp-mrow id=MJXp-Span-2501><span class=MJXp-mo id=MJXp-Span-2502 style=margin-left:0em;margin-right:0em>(</span><span class=MJXp-mrow id=MJXp-Span-2503><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2504>D</span></span><span class=MJXp-mo id=MJXp-Span-2505 style=margin-left:0em;margin-right:0em>)</span></span></span></span><span id=MathJax-Element-271-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> for the counter-moving photon in the S-RLSE. For the Sagnac effect, <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-2506><span class=MJXp-mi id=MJXp-Span-2507>Δ</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2508>T</span></span></span><span id=MathJax-Element-272-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>* <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-2509><span class=MJXp-mo id=MJXp-Span-2510 style=margin-left:0.333em;margin-right:0.333em>=</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2511>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2512>P</span><span class=MJXp-mo id=MJXp-Span-2513 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class=MJXp-msup id=MJXp-Span-2514><span class=MJXp-mrow id=MJXp-Span-2515 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2516>c</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-2517 style=vertical-align:0.5em><span class=MJXp-mn id=MJXp-Span-2518>2</span></span></span></span></span><span id=MathJax-Element-273-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> is constant and represented by the dotted line. For the S-RLSE, starting from right to left with <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-2519><span class=MJXp-msup id=MJXp-Span-2520><span class=MJXp-mrow id=MJXp-Span-2521 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-2522>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-2523 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-2524>*</span></span></span></span></span><span id=MathJax-Element-274-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> on the contour lower section <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-2525><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2526>L</span></span></span><span id=MathJax-Element-275-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> from the position <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-2527><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2528>D</span><span class=MJXp-mo id=MJXp-Span-2529 style=margin-left:0.333em;margin-right:0.333em>&gt;</span><span class=MJXp-mn id=MJXp-Span-2530>2</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2531>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2532>L</span><span class=MJXp-mo id=MJXp-Span-2533 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class=MJXp-msup id=MJXp-Span-2534><span class=MJXp-mrow id=MJXp-Span-2535 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2536>c</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-2537 style=vertical-align:0.5em><span class=MJXp-mn id=MJXp-Span-2538>2</span></span></span></span></span><span id=MathJax-Element-276-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>, we have <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-2539><span class=MJXp-mi id=MJXp-Span-2540>Δ</span><span class=MJXp-msup id=MJXp-Span-2541><span class=MJXp-mrow id=MJXp-Span-2542 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2543>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-2544 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-2545>*</span></span></span><span class=MJXp-mo id=MJXp-Span-2546 style=margin-left:0.333em;margin-right:0.333em>=</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2547>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2548>P</span><span class=MJXp-mo id=MJXp-Span-2549 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class=MJXp-msup id=MJXp-Span-2550><span class=MJXp-mrow id=MJXp-Span-2551 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2552>c</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-2553 style=vertical-align:0.5em><span class=MJXp-mn id=MJXp-Span-2554>2</span></span></span></span></span><span id=MathJax-Element-277-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> until <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-2555><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2556>D</span><span class=MJXp-mo id=MJXp-Span-2557 style=margin-left:0.333em;margin-right:0.333em>≃</span><span class=MJXp-mn id=MJXp-Span-2558>2</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2559>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2560>L</span><span class=MJXp-mo id=MJXp-Span-2561 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2562>c</span></span></span><span id=MathJax-Element-278-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>. When <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-2563><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2564>D</span><span class=MJXp-mo id=MJXp-Span-2565 style=margin-left:0.333em;margin-right:0.333em>&lt;</span><span class=MJXp-mn id=MJXp-Span-2566>2</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2567>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2568>L</span><span class=MJXp-mo id=MJXp-Span-2569 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2570>c</span></span></span><span id=MathJax-Element-279-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> and until <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-2571><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2572>D</span><span class=MJXp-mo id=MJXp-Span-2573 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-msub id=MJXp-Span-2574><span class=MJXp-mrow id=MJXp-Span-2575 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2576>D</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-2577 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-2578>0</span></span></span><span class=MJXp-mo id=MJXp-Span-2579 style=margin-left:0.333em;margin-right:0.333em>=</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2580>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2581>L</span><span class=MJXp-mo id=MJXp-Span-2582 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2583>c</span></span></span><span id=MathJax-Element-280-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>, <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-2584><span class=MJXp-mi id=MJXp-Span-2585>Δ</span><span class=MJXp-msup id=MJXp-Span-2586><span class=MJXp-mrow id=MJXp-Span-2587 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2588>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-2589 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-2590>*</span></span></span><span class=MJXp-mrow id=MJXp-Span-2591><span class=MJXp-mo id=MJXp-Span-2592 style=margin-left:0em;margin-right:0em>(</span><span class=MJXp-mrow id=MJXp-Span-2593><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2594>D</span></span><span class=MJXp-mo id=MJXp-Span-2595 style=margin-left:0em;margin-right:0em>)</span></span></span></span><span id=MathJax-Element-281-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> decreases up to <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-2596><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2597>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2598>L</span><span class=MJXp-mo id=MJXp-Span-2599 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class=MJXp-msup id=MJXp-Span-2600><span class=MJXp-mrow id=MJXp-Span-2601 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2602>c</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-2603 style=vertical-align:0.5em><span class=MJXp-mn id=MJXp-Span-2604>2</span></span></span></span></span><span id=MathJax-Element-282-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>. Then, <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-2605><span class=MJXp-mi id=MJXp-Span-2606>Δ</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2607>T</span></span></span><span id=MathJax-Element-283-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>* increases and reaches again the value <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-2608><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2609>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2610>P</span><span class=MJXp-mo id=MJXp-Span-2611 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class=MJXp-msup id=MJXp-Span-2612><span class=MJXp-mrow id=MJXp-Span-2613 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2614>c</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-2615 style=vertical-align:0.5em><span class=MJXp-mn id=MJXp-Span-2616>2</span></span></span></span></span><span id=MathJax-Element-284-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> at <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-2617><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2618>D</span><span class=MJXp-mo id=MJXp-Span-2619 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-mn id=MJXp-Span-2620>0</span></span></span><span id=MathJax-Element-285-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> and afterwards when <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-2621><span class=MJXp-msup id=MJXp-Span-2622><span class=MJXp-mrow id=MJXp-Span-2623 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-2624>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-2625 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-2626>*</span></span></span></span></span><span id=MathJax-Element-286-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> is on the left side <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-2627><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2628>H</span></span></span><span id=MathJax-Element-287-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> of the moving contour. The broken line refers to the S-RLSE of <a href=#j_phys-2023-0110_fig_002 class="link link-fig" data-bs-target=j_phys-2023-0110_fig_002>Figure 2</a>, where <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-2629><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2630>P</span><span class=MJXp-mo id=MJXp-Span-2631 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-mn id=MJXp-Span-2632>2</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2633>L</span></span></span><span id=MathJax-Element-288-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> and the dip is <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-2634><span class=MJXp-mn id=MJXp-Span-2635>2</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2636>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2637>L</span><span class=MJXp-mo id=MJXp-Span-2638 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class=MJXp-msup id=MJXp-Span-2639><span class=MJXp-mrow id=MJXp-Span-2640 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2641>c</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-2642 style=vertical-align:0.5em><span class=MJXp-mn id=MJXp-Span-2643>2</span></span></span></span></span><span id=MathJax-Element-289-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> with <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-2644><span class=MJXp-mi id=MJXp-Span-2645>Δ</span><span class=MJXp-msup id=MJXp-Span-2646><span class=MJXp-mrow id=MJXp-Span-2647 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2648>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-2649 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-2650>*</span></span></span><span class=MJXp-mo id=MJXp-Span-2651 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-mn id=MJXp-Span-2652>0</span></span></span><span id=MathJax-Element-290-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> at <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-2653><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2654>D</span><span class=MJXp-mo id=MJXp-Span-2655 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-msub id=MJXp-Span-2656><span class=MJXp-mrow id=MJXp-Span-2657 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2658>D</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-2659 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-2660>0</span></span></span></span></span><span id=MathJax-Element-291-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>.</p></span></div></div></div></div>
<p>For the rectangular contour of <a href=#j_phys-2023-0110_fig_005 class="link link-fig" data-bs-target=j_phys-2023-0110_fig_005>Figure A1</a>, we assume that the contour slides continuously at the local speed <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-2661><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2662>v</span></span></span><span id=MathJax-Element-292-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> relative to <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-2663><span class=MJXp-msup id=MJXp-Span-2664><span class=MJXp-mrow id=MJXp-Span-2665 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-2666>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-2667 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-2668>*</span></span></span></span></span><span id=MathJax-Element-293-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>. This is a mechanical difficulty that, in principle, can be surmounted, although it increases the cost of the experiment in comparison to the standard Sagnac experiments. Actually, for the experiment, the rectangular contour can move relative to <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-2669><span class=MJXp-msup id=MJXp-Span-2670><span class=MJXp-mrow id=MJXp-Span-2671 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-2672>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-2673 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-2674>*</span></span></span></span></span><span id=MathJax-Element-294-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> for a short distance, starting with <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-2675><span class=MJXp-msup id=MJXp-Span-2676><span class=MJXp-mrow id=MJXp-Span-2677 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-2678>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-2679 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-2680>*</span></span></span></span></span><span id=MathJax-Element-295-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> on the lower section <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-2681><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2682>L</span></span></span><span id=MathJax-Element-296-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> and ending on the left side <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-2683><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2684>H</span></span></span><span id=MathJax-Element-297-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>, as shown in <a href=#j_phys-2023-0110_fig_005 class="link link-fig" data-bs-target=j_phys-2023-0110_fig_005>Figure A1</a>. For the size of the contour to be manageable, it is convenient to have light propagating in an optical fiber with a high refractive index <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-2685><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2686>n</span></span></span><span id=MathJax-Element-298-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>. In this case, the round-trip time is increased to <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-2687><span class=MJXp-msub id=MJXp-Span-2688><span class=MJXp-mrow id=MJXp-Span-2689 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2690>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-2691 style=vertical-align:-0.4em><span class=MJXp-mo id=MJXp-Span-2692>⇒</span></span></span><span class=MJXp-mo id=MJXp-Span-2693 style=margin-left:0.333em;margin-right:0.333em>≃</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2694>n</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2695>P</span><span class=MJXp-mo id=MJXp-Span-2696 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2697>c</span></span></span><span id=MathJax-Element-299-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>.</p>
<p>In the case of light propagation in a medium, we have to distinguish the case when the medium is locally at rest along the contour from the case when the medium is locally at rest with <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-2698><span class=MJXp-msup id=MJXp-Span-2699><span class=MJXp-mrow id=MJXp-Span-2700 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-2701>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-2702 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-2703>*</span></span></span></span></span><span id=MathJax-Element-300-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> and sliding along the contour. The speed of light in the moving medium is obtained from the standard relativistic velocity transformations. The results using the LT, derived in the Appendix (neglecting dispersion), are shown schematically below.</p>
<p>S-RLSE with medium locally at rest with the contour <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-2704><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2705>P</span><span class=MJXp-mo id=MJXp-Span-2706 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-mn id=MJXp-Span-2707>2</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2708>L</span><span class=MJXp-mo id=MJXp-Span-2709 style=margin-left:0.267em;margin-right:0.267em>+</span><span class=MJXp-mn id=MJXp-Span-2710>2</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2711>H</span></span></span><span id=MathJax-Element-301-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>
<div class=formula id=j_phys-2023-0110_eq_005>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class="MJXp-math MJXp-display" id=MJXp-Span-2712><span class=MJXp-mtable id=MJXp-Span-2713><span><span class=MJXp-mtr id=MJXp-Span-2714 style=vertical-align:baseline><span class=MJXp-mtd id=MJXp-Span-2715 style=text-align:center><span class=MJXp-msup id=MJXp-Span-2716><span class=MJXp-mrow id=MJXp-Span-2717 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2718>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-2719 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-2720>*</span></span></span><span class=MJXp-mo id=MJXp-Span-2721 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-mfrac id=MJXp-Span-2722 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-2723><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2724>n</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2725>P</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-2726><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2727>c</span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-2728 style=margin-left:0em;margin-right:0.222em>,</span><span class=MJXp-mspace id=MJXp-Span-2729 style=width:1em;height:0em></span><span class=MJXp-mi id=MJXp-Span-2730>Δ</span><span class=MJXp-msup id=MJXp-Span-2731><span class=MJXp-mrow id=MJXp-Span-2732 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2733>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-2734 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-2735>*</span></span></span><span class=MJXp-mo id=MJXp-Span-2736 style=margin-left:0.333em;margin-right:0.333em>≃</span><span class=MJXp-msup id=MJXp-Span-2737><span class=MJXp-mrow id=MJXp-Span-2738 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2739>n</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-2740 style=vertical-align:0.5em><span class=MJXp-mn id=MJXp-Span-2741>2</span></span></span><span class=MJXp-mfrac id=MJXp-Span-2742 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-2743><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2744>v</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-2745><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2746>c</span></span></span></span></span></span></span><span class=MJXp-mfrac id=MJXp-Span-2747 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-2748><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2749>P</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-2750><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2751>c</span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-2752 style=margin-left:0em;margin-right:0.222em>,</span><span class=MJXp-mspace id=MJXp-Span-2753 style=width:1em;height:0em></span><span class=MJXp-mstyle id=MJXp-Span-2754><span class=MJXp-mspace id=MJXp-Span-2755 style=width:0.1em;height:0em></span><span class=MJXp-mtext id=MJXp-Span-2756>independent of</span><span class=MJXp-mspace id=MJXp-Span-2757 style=width:0.1em;height:0em></span></span><span class=MJXp-mspace id=MJXp-Span-2758 style=width:0.33em;height:0em></span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2759>D</span></span></span></span></span></span></span><span class="mjx-chtml MJXc-display MJXc-processing sf-hidden"></span>
</span>
</div><p>
<div class=formula id=j_phys-2023-0110_eq_006>
<span class=label>(5)</span>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class="MJXp-math MJXp-display" id=MJXp-Span-2760><span class=MJXp-mtable id=MJXp-Span-2761><span><span class=MJXp-mtr id=MJXp-Span-2762 style=vertical-align:baseline><span class=MJXp-mtd id=MJXp-Span-2763 style=text-align:center><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2764>D</span></span><span class=MJXp-mtd id=MJXp-Span-2765 style=padding-left:0.33em;text-align:center><span class=MJXp-mo id=MJXp-Span-2766 style=margin-left:0.333em;margin-right:0.333em>=</span></span><span class=MJXp-mtd id=MJXp-Span-2767 style=padding-left:0.33em;text-align:center><span class=MJXp-msub id=MJXp-Span-2768><span class=MJXp-mrow id=MJXp-Span-2769 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2770>D</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-2771 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-2772>0</span></span></span><span class=MJXp-mo id=MJXp-Span-2773 style=margin-left:0.333em;margin-right:0.333em>≃</span><span class=MJXp-mfrac id=MJXp-Span-2774 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-2775><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2776>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2777>n</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2778>L</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-2779><span class=MJXp-msup id=MJXp-Span-2780><span class=MJXp-mrow id=MJXp-Span-2781 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2782>c</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-2783 style=vertical-align:0.5em><span class=MJXp-mn id=MJXp-Span-2784>2</span></span></span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-2785 style=margin-left:0em;margin-right:0.222em>,</span><span class=MJXp-mspace id=MJXp-Span-2786 style=width:1em;height:0em></span><span class=MJXp-msub id=MJXp-Span-2787><span class=MJXp-mrow id=MJXp-Span-2788 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2789>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-2790 style=vertical-align:-0.4em><span class=MJXp-mo id=MJXp-Span-2791>⇒</span></span></span><span class=MJXp-mo id=MJXp-Span-2792 style=margin-left:0.333em;margin-right:0.333em>≃</span><span class=MJXp-mfrac id=MJXp-Span-2793 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-2794><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2795>n</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2796>P</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-2797><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2798>c</span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-2799 style=margin-left:0.267em;margin-right:0.267em>−</span><span class=MJXp-msup id=MJXp-Span-2800><span class=MJXp-mrow id=MJXp-Span-2801 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2802>n</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-2803 style=vertical-align:0.5em><span class=MJXp-mn id=MJXp-Span-2804>2</span></span></span><span class=MJXp-mfrac id=MJXp-Span-2805 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-2806><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2807>v</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-2808><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2809>c</span></span></span></span></span></span></span><span class=MJXp-mfrac id=MJXp-Span-2810 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-2811><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2812>P</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-2813><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2814>c</span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-2815 style=margin-left:0.267em;margin-right:0.267em>+</span><span class=MJXp-mfrac id=MJXp-Span-2816 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-2817><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2818>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2819>L</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-2820><span class=MJXp-msup id=MJXp-Span-2821><span class=MJXp-mrow id=MJXp-Span-2822 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2823>c</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-2824 style=vertical-align:0.5em><span class=MJXp-mn id=MJXp-Span-2825>2</span></span></span></span></span></span></span></span></span></span></span><span class=MJXp-mtr id=MJXp-Span-2826 style=vertical-align:baseline><span class=MJXp-mtd id=MJXp-Span-2827 style=padding-top:0.431em;text-align:center><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2828>D</span></span><span class=MJXp-mtd id=MJXp-Span-2829 style=padding-left:0.33em;padding-top:0.431em;text-align:center><span class=MJXp-mo id=MJXp-Span-2830 style=margin-left:0.333em;margin-right:0.333em>=</span></span><span class=MJXp-mtd id=MJXp-Span-2831 style=padding-left:0.33em;padding-top:0.431em;text-align:center><span class=MJXp-msub id=MJXp-Span-2832><span class=MJXp-mrow id=MJXp-Span-2833 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2834>D</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-2835 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-2836>0</span></span></span><span class=MJXp-mo id=MJXp-Span-2837 style=margin-left:0.333em;margin-right:0.333em>≃</span><span class=MJXp-mfrac id=MJXp-Span-2838 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-2839><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2840>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2841>n</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2842>L</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-2843><span class=MJXp-msup id=MJXp-Span-2844><span class=MJXp-mrow id=MJXp-Span-2845 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2846>c</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-2847 style=vertical-align:0.5em><span class=MJXp-mn id=MJXp-Span-2848>2</span></span></span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-2849 style=margin-left:0em;margin-right:0.222em>,</span><span class=MJXp-mspace id=MJXp-Span-2850 style=width:1em;height:0em></span><span class=MJXp-mi id=MJXp-Span-2851>Δ</span><span class=MJXp-msup id=MJXp-Span-2852><span class=MJXp-mrow id=MJXp-Span-2853 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2854>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-2855 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-2856>*</span></span></span><span class=MJXp-mrow id=MJXp-Span-2857><span class=MJXp-mo id=MJXp-Span-2858 style=margin-left:0em;margin-right:0em;vertical-align:-0.244em><span style=font-size:1.978em;margin-left:-0.05em class="MJXp-right MJXp-scale7">(</span></span><span class=MJXp-mrow id=MJXp-Span-2859><span class=MJXp-msub id=MJXp-Span-2860><span class=MJXp-mrow id=MJXp-Span-2861 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2862>D</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-2863 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-2864>0</span></span></span></span><span class=MJXp-mo id=MJXp-Span-2865 style=margin-left:0em;margin-right:0em;vertical-align:-0.244em><span style=font-size:1.978em;margin-left:-0.05em class="MJXp-right MJXp-scale7">)</span></span></span><span class=MJXp-mo id=MJXp-Span-2866 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-msup id=MJXp-Span-2867><span class=MJXp-mrow id=MJXp-Span-2868 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2869>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-2870 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-2871>*</span></span></span><span class=MJXp-mo id=MJXp-Span-2872 style=margin-left:0.267em;margin-right:0.267em>−</span><span class=MJXp-msub id=MJXp-Span-2873><span class=MJXp-mrow id=MJXp-Span-2874 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2875>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-2876 style=vertical-align:-0.4em><span class=MJXp-mo id=MJXp-Span-2877>⇒</span></span></span><span class=MJXp-mo id=MJXp-Span-2878 style=margin-left:0.333em;margin-right:0.333em>≃</span><span class=MJXp-msubsup id=MJXp-Span-2879><span class=MJXp-mrow id=MJXp-Span-2880 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-2881>Δ</span></span><span class=MJXp-script-box style=height:1.86em;vertical-align:-0.64em><span class=MJXp-script><span><span style=margin-bottom:-0.25em><span class=MJXp-mrow id=MJXp-Span-2884><span class=MJXp-mo id=MJXp-Span-2885>∗</span></span></span></span></span><span class=MJXp-script><span><span style=margin-top:-0.85em><span class=MJXp-mrow id=MJXp-Span-2882><span class=MJXp-mi id=MJXp-Span-2883>Sagn</span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-2886 style=margin-left:0.267em;margin-right:0.267em>−</span><span class=MJXp-mfrac id=MJXp-Span-2887 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-2888><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2889>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2890>L</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-2891><span class=MJXp-msup id=MJXp-Span-2892><span class=MJXp-mrow id=MJXp-Span-2893 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2894>c</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-2895 style=vertical-align:0.5em><span class=MJXp-mn id=MJXp-Span-2896>2</span></span></span></span></span></span></span></span></span></span></span><span class=MJXp-mtr id=MJXp-Span-2897 style=vertical-align:baseline><span class=MJXp-mtd id=MJXp-Span-2898 style=padding-top:0.431em;text-align:center><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2899>D</span></span><span class=MJXp-mtd id=MJXp-Span-2900 style=padding-left:0.33em;padding-top:0.431em;text-align:center><span class=MJXp-mo id=MJXp-Span-2901 style=margin-left:0.333em;margin-right:0.333em>&gt;</span></span><span class=MJXp-mtd id=MJXp-Span-2902 style=padding-left:0.33em;padding-top:0.431em;text-align:center><span class=MJXp-mfrac id=MJXp-Span-2903 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-2904><span class=MJXp-mn id=MJXp-Span-2905>2</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2906>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2907>n</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2908>L</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-2909><span class=MJXp-msup id=MJXp-Span-2910><span class=MJXp-mrow id=MJXp-Span-2911 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2912>c</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-2913 style=vertical-align:0.5em><span class=MJXp-mn id=MJXp-Span-2914>2</span></span></span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-2915 style=margin-left:0em;margin-right:0.222em>,</span><span class=MJXp-mspace id=MJXp-Span-2916 style=width:1em;height:0em></span><span class=MJXp-msub id=MJXp-Span-2917><span class=MJXp-mrow id=MJXp-Span-2918 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2919>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-2920 style=vertical-align:-0.4em><span class=MJXp-mo id=MJXp-Span-2921>⇒</span></span></span><span class=MJXp-mo id=MJXp-Span-2922 style=margin-left:0.333em;margin-right:0.333em>≃</span><span class=MJXp-mfrac id=MJXp-Span-2923 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-2924><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2925>n</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2926>P</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-2927><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2928>c</span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-2929 style=margin-left:0.267em;margin-right:0.267em>−</span><span class=MJXp-msup id=MJXp-Span-2930><span class=MJXp-mrow id=MJXp-Span-2931 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2932>n</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-2933 style=vertical-align:0.5em><span class=MJXp-mn id=MJXp-Span-2934>2</span></span></span><span class=MJXp-mfrac id=MJXp-Span-2935 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-2936><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2937>v</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-2938><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2939>c</span></span></span></span></span></span></span><span class=MJXp-mfrac id=MJXp-Span-2940 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-2941><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2942>P</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-2943><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2944>c</span></span></span></span></span></span></span></span></span><span class=MJXp-mtr id=MJXp-Span-2945 style=vertical-align:baseline><span class=MJXp-mtd id=MJXp-Span-2946 style=padding-top:0.431em;text-align:center><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2947>D</span></span><span class=MJXp-mtd id=MJXp-Span-2948 style=padding-left:0.33em;padding-top:0.431em;text-align:center><span class=MJXp-mo id=MJXp-Span-2949 style=margin-left:0.333em;margin-right:0.333em>&gt;</span></span><span class=MJXp-mtd id=MJXp-Span-2950 style=padding-left:0.33em;padding-top:0.431em;text-align:center><span class=MJXp-mfrac id=MJXp-Span-2951 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-2952><span class=MJXp-mn id=MJXp-Span-2953>2</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2954>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2955>n</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2956>L</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-2957><span class=MJXp-msup id=MJXp-Span-2958><span class=MJXp-mrow id=MJXp-Span-2959 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2960>c</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-2961 style=vertical-align:0.5em><span class=MJXp-mn id=MJXp-Span-2962>2</span></span></span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-2963 style=margin-left:0em;margin-right:0.222em>,</span><span class=MJXp-mspace id=MJXp-Span-2964 style=width:1em;height:0em></span><span class=MJXp-mi id=MJXp-Span-2965>Δ</span><span class=MJXp-msup id=MJXp-Span-2966><span class=MJXp-mrow id=MJXp-Span-2967 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2968>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-2969 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-2970>*</span></span></span><span class=MJXp-mrow id=MJXp-Span-2971><span class=MJXp-mo id=MJXp-Span-2972 style=margin-left:0em;margin-right:0em>(</span><span class=MJXp-mrow id=MJXp-Span-2973><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2974>D</span></span><span class=MJXp-mo id=MJXp-Span-2975 style=margin-left:0em;margin-right:0em>)</span></span><span class=MJXp-mo id=MJXp-Span-2976 style=margin-left:0.333em;margin-right:0.333em>=</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2977>T</span><span class=MJXp-mstyle id=MJXp-Span-2978><span class=MJXp-mspace id=MJXp-Span-2979 style=width:0.1em;height:0em></span><span class=MJXp-mtext id=MJXp-Span-2980>*</span><span class=MJXp-mspace id=MJXp-Span-2981 style=width:0.1em;height:0em></span></span><span class=MJXp-mo id=MJXp-Span-2982 style=margin-left:0.267em;margin-right:0.267em>−</span><span class=MJXp-msub id=MJXp-Span-2983><span class=MJXp-mrow id=MJXp-Span-2984 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-2985>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-2986 style=vertical-align:-0.4em><span class=MJXp-mo id=MJXp-Span-2987>⇒</span></span></span><span class=MJXp-mo id=MJXp-Span-2988 style=margin-left:0.333em;margin-right:0.333em>≃</span><span class=MJXp-msubsup id=MJXp-Span-2989><span class=MJXp-mrow id=MJXp-Span-2990 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-2991>Δ</span></span><span class=MJXp-script-box style=height:1.86em;vertical-align:-0.64em><span class=MJXp-script><span><span style=margin-bottom:-0.25em><span class=MJXp-mrow id=MJXp-Span-2994><span class=MJXp-mo id=MJXp-Span-2995>∗</span></span></span></span></span><span class=MJXp-script><span><span style=margin-top:-0.85em><span class=MJXp-mrow id=MJXp-Span-2992><span class=MJXp-mi id=MJXp-Span-2993>Sagn</span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-2996 style=margin-left:0em;margin-right:0.222em>.</span></span></span></span></span></span></span><span class="mjx-chtml MJXc-display MJXc-processing sf-hidden"></span>
</span>
</div><p>
</p>
<p>
<span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-2997><span class=MJXp-mtable id=MJXp-Span-2998><span><span class=MJXp-mtr id=MJXp-Span-2999 style=vertical-align:baseline><span class=MJXp-mtd id=MJXp-Span-3000 style=text-align:center><span class=MJXp-mstyle id=MJXp-Span-3001><span class=MJXp-mspace id=MJXp-Span-3002 style=width:0.1em;height:0em></span><span class=MJXp-mtext id=MJXp-Span-3003>S-RLSE with medium locally</span><span class=MJXp-mspace id=MJXp-Span-3004 style=width:0.1em;height:0em></span></span></span></span><span class=MJXp-mtr id=MJXp-Span-3005 style=vertical-align:baseline><span class=MJXp-mtd id=MJXp-Span-3006 style=padding-top:0.431em;text-align:center><span class=MJXp-mstyle id=MJXp-Span-3007><span class=MJXp-mspace id=MJXp-Span-3008 style=width:0.1em;height:0em></span><span class=MJXp-mtext id=MJXp-Span-3009>at rest with</span><span class=MJXp-mspace id=MJXp-Span-3010 style=width:0.1em;height:0em></span></span><span class=MJXp-mspace id=MJXp-Span-3011 style=width:0.33em;height:0em></span><span class=MJXp-msup id=MJXp-Span-3012><span class=MJXp-mrow id=MJXp-Span-3013 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-3014>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-3015 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-3016>*</span></span></span><span class=MJXp-mo id=MJXp-Span-3017 style=margin-left:0em;margin-right:0.222em>,</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3018>P</span><span class=MJXp-mo id=MJXp-Span-3019 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-mn id=MJXp-Span-3020>2</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3021>L</span><span class=MJXp-mo id=MJXp-Span-3022 style=margin-left:0.267em;margin-right:0.267em>+</span><span class=MJXp-mn id=MJXp-Span-3023>2</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3024>H</span></span></span></span></span></span></span><span id=MathJax-Element-304-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>
<div class=formula id=j_phys-2023-0110_eq_007>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class="MJXp-math MJXp-display" id=MJXp-Span-3025><span class=MJXp-msup id=MJXp-Span-3026><span class=MJXp-mrow id=MJXp-Span-3027 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3028>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-3029 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-3030>*</span></span></span><span class=MJXp-mo id=MJXp-Span-3031 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-mfrac id=MJXp-Span-3032 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-3033><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3034>n</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3035>P</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-3036><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3037>c</span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-3038 style=margin-left:0em;margin-right:0.222em>,</span><span class=MJXp-mspace id=MJXp-Span-3039 style=width:1em;height:0em></span><span class=MJXp-msubsup id=MJXp-Span-3040><span class=MJXp-mrow id=MJXp-Span-3041 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-3042>Δ</span></span><span class=MJXp-script-box style=height:1.86em;vertical-align:-0.64em><span class=MJXp-script><span><span style=margin-bottom:-0.25em><span class=MJXp-mrow id=MJXp-Span-3045><span class=MJXp-mo id=MJXp-Span-3046>∗</span></span></span></span></span><span class=MJXp-script><span><span style=margin-top:-0.85em><span class=MJXp-mrow id=MJXp-Span-3043><span class=MJXp-mi id=MJXp-Span-3044>Sagn</span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-3047 style=margin-left:0.333em;margin-right:0.333em>≃</span><span class=MJXp-mfrac id=MJXp-Span-3048 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-3049><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3050>v</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-3051><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3052>c</span></span></span></span></span></span></span><span class=MJXp-mfrac id=MJXp-Span-3053 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-3054><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3055>P</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-3056><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3057>c</span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-3058 style=margin-left:0em;margin-right:0.222em>,</span><span class=MJXp-mspace id=MJXp-Span-3059 style=width:1em;height:0em></span><span class=MJXp-mstyle id=MJXp-Span-3060><span class=MJXp-mspace id=MJXp-Span-3061 style=width:0.1em;height:0em></span><span class=MJXp-mtext id=MJXp-Span-3062>independent of</span><span class=MJXp-mspace id=MJXp-Span-3063 style=width:0.1em;height:0em></span></span><span class=MJXp-mspace id=MJXp-Span-3064 style=width:0.33em;height:0em></span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3065>D</span></span></span><span class="mjx-chtml MJXc-display MJXc-processing sf-hidden"></span>
</span>
</div><p>
<div class=formula id=j_phys-2023-0110_eq_008>
<span class=label>(6)</span>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class="MJXp-math MJXp-display" id=MJXp-Span-3066><span class=MJXp-mtable id=MJXp-Span-3067><span><span class=MJXp-mtr id=MJXp-Span-3068 style=vertical-align:baseline><span class=MJXp-mtd id=MJXp-Span-3069 style=text-align:center><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3070>D</span></span><span class=MJXp-mtd id=MJXp-Span-3071 style=padding-left:0.33em;text-align:center><span class=MJXp-mo id=MJXp-Span-3072 style=margin-left:0.333em;margin-right:0.333em>=</span></span><span class=MJXp-mtd id=MJXp-Span-3073 style=padding-left:0.33em;text-align:center><span class=MJXp-msub id=MJXp-Span-3074><span class=MJXp-mrow id=MJXp-Span-3075 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3076>D</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-3077 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-3078>0</span></span></span><span class=MJXp-mo id=MJXp-Span-3079 style=margin-left:0.333em;margin-right:0.333em>≃</span><span class=MJXp-mfrac id=MJXp-Span-3080 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-3081><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3082>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3083>n</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3084>L</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-3085><span class=MJXp-msup id=MJXp-Span-3086><span class=MJXp-mrow id=MJXp-Span-3087 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3088>c</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-3089 style=vertical-align:0.5em><span class=MJXp-mn id=MJXp-Span-3090>2</span></span></span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-3091 style=margin-left:0em;margin-right:0.222em>,</span><span class=MJXp-mspace id=MJXp-Span-3092 style=width:1em;height:0em></span><span class=MJXp-msub id=MJXp-Span-3093><span class=MJXp-mrow id=MJXp-Span-3094 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3095>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-3096 style=vertical-align:-0.4em><span class=MJXp-mo id=MJXp-Span-3097>⇒</span></span></span><span class=MJXp-mo id=MJXp-Span-3098 style=margin-left:0.333em;margin-right:0.333em>≃</span><span class=MJXp-mfrac id=MJXp-Span-3099 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-3100><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3101>n</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3102>P</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-3103><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3104>c</span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-3105 style=margin-left:0.267em;margin-right:0.267em>−</span><span class=MJXp-mfrac id=MJXp-Span-3106 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-3107><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3108>v</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-3109><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3110>c</span></span></span></span></span></span></span><span class=MJXp-mfrac id=MJXp-Span-3111 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-3112><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3113>P</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-3114><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3115>c</span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-3116 style=margin-left:0.267em;margin-right:0.267em>+</span><span class=MJXp-mfrac id=MJXp-Span-3117 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-3118><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3119>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3120>L</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-3121><span class=MJXp-msup id=MJXp-Span-3122><span class=MJXp-mrow id=MJXp-Span-3123 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3124>c</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-3125 style=vertical-align:0.5em><span class=MJXp-mn id=MJXp-Span-3126>2</span></span></span></span></span></span></span></span></span></span></span><span class=MJXp-mtr id=MJXp-Span-3127 style=vertical-align:baseline><span class=MJXp-mtd id=MJXp-Span-3128 style=padding-top:0.431em;text-align:center><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3129>D</span></span><span class=MJXp-mtd id=MJXp-Span-3130 style=padding-left:0.33em;padding-top:0.431em;text-align:center><span class=MJXp-mo id=MJXp-Span-3131 style=margin-left:0.333em;margin-right:0.333em>=</span></span><span class=MJXp-mtd id=MJXp-Span-3132 style=padding-left:0.33em;padding-top:0.431em;text-align:center><span class=MJXp-msub id=MJXp-Span-3133><span class=MJXp-mrow id=MJXp-Span-3134 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3135>D</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-3136 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-3137>0</span></span></span><span class=MJXp-mo id=MJXp-Span-3138 style=margin-left:0.333em;margin-right:0.333em>≃</span><span class=MJXp-mfrac id=MJXp-Span-3139 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-3140><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3141>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3142>n</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3143>L</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-3144><span class=MJXp-msup id=MJXp-Span-3145><span class=MJXp-mrow id=MJXp-Span-3146 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3147>c</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-3148 style=vertical-align:0.5em><span class=MJXp-mn id=MJXp-Span-3149>2</span></span></span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-3150 style=margin-left:0em;margin-right:0.222em>,</span><span class=MJXp-mspace id=MJXp-Span-3151 style=width:1em;height:0em></span><span class=MJXp-mi id=MJXp-Span-3152>Δ</span><span class=MJXp-msup id=MJXp-Span-3153><span class=MJXp-mrow id=MJXp-Span-3154 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3155>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-3156 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-3157>*</span></span></span><span class=MJXp-mrow id=MJXp-Span-3158><span class=MJXp-mo id=MJXp-Span-3159 style=margin-left:0em;margin-right:0em;vertical-align:-0.244em><span style=font-size:1.978em;margin-left:-0.05em class="MJXp-right MJXp-scale7">(</span></span><span class=MJXp-mrow id=MJXp-Span-3160><span class=MJXp-msub id=MJXp-Span-3161><span class=MJXp-mrow id=MJXp-Span-3162 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3163>D</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-3164 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-3165>0</span></span></span></span><span class=MJXp-mo id=MJXp-Span-3166 style=margin-left:0em;margin-right:0em;vertical-align:-0.244em><span style=font-size:1.978em;margin-left:-0.05em class="MJXp-right MJXp-scale7">)</span></span></span><span class=MJXp-mo id=MJXp-Span-3167 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-msup id=MJXp-Span-3168><span class=MJXp-mrow id=MJXp-Span-3169 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3170>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-3171 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-3172>*</span></span></span><span class=MJXp-mo id=MJXp-Span-3173 style=margin-left:0.267em;margin-right:0.267em>−</span><span class=MJXp-msub id=MJXp-Span-3174><span class=MJXp-mrow id=MJXp-Span-3175 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3176>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-3177 style=vertical-align:-0.4em><span class=MJXp-mo id=MJXp-Span-3178>⇒</span></span></span><span class=MJXp-mo id=MJXp-Span-3179 style=margin-left:0.333em;margin-right:0.333em>≃</span><span class=MJXp-msubsup id=MJXp-Span-3180><span class=MJXp-mrow id=MJXp-Span-3181 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-3182>Δ</span></span><span class=MJXp-script-box style=height:1.86em;vertical-align:-0.64em><span class=MJXp-script><span><span style=margin-bottom:-0.25em><span class=MJXp-mrow id=MJXp-Span-3185><span class=MJXp-mo id=MJXp-Span-3186>∗</span></span></span></span></span><span class=MJXp-script><span><span style=margin-top:-0.85em><span class=MJXp-mrow id=MJXp-Span-3183><span class=MJXp-mi id=MJXp-Span-3184>Sagn</span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-3187 style=margin-left:0.267em;margin-right:0.267em>−</span><span class=MJXp-mfrac id=MJXp-Span-3188 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-3189><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3190>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3191>L</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-3192><span class=MJXp-msup id=MJXp-Span-3193><span class=MJXp-mrow id=MJXp-Span-3194 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3195>c</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-3196 style=vertical-align:0.5em><span class=MJXp-mn id=MJXp-Span-3197>2</span></span></span></span></span></span></span></span></span></span></span><span class=MJXp-mtr id=MJXp-Span-3198 style=vertical-align:baseline><span class=MJXp-mtd id=MJXp-Span-3199 style=padding-top:0.431em;text-align:center><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3200>D</span></span><span class=MJXp-mtd id=MJXp-Span-3201 style=padding-left:0.33em;padding-top:0.431em;text-align:center><span class=MJXp-mo id=MJXp-Span-3202 style=margin-left:0.333em;margin-right:0.333em>&gt;</span></span><span class=MJXp-mtd id=MJXp-Span-3203 style=padding-left:0.33em;padding-top:0.431em;text-align:center><span class=MJXp-mfrac id=MJXp-Span-3204 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-3205><span class=MJXp-mn id=MJXp-Span-3206>2</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3207>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3208>n</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3209>L</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-3210><span class=MJXp-msup id=MJXp-Span-3211><span class=MJXp-mrow id=MJXp-Span-3212 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3213>c</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-3214 style=vertical-align:0.5em><span class=MJXp-mn id=MJXp-Span-3215>2</span></span></span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-3216 style=margin-left:0em;margin-right:0.222em>,</span><span class=MJXp-mspace id=MJXp-Span-3217 style=width:1em;height:0em></span><span class=MJXp-msub id=MJXp-Span-3218><span class=MJXp-mrow id=MJXp-Span-3219 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3220>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-3221 style=vertical-align:-0.4em><span class=MJXp-mo id=MJXp-Span-3222>⇒</span></span></span><span class=MJXp-mo id=MJXp-Span-3223 style=margin-left:0.333em;margin-right:0.333em>≃</span><span class=MJXp-mfrac id=MJXp-Span-3224 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-3225><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3226>n</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3227>P</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-3228><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3229>c</span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-3230 style=margin-left:0.267em;margin-right:0.267em>−</span><span class=MJXp-mfrac id=MJXp-Span-3231 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-3232><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3233>v</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-3234><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3235>c</span></span></span></span></span></span></span><span class=MJXp-mfrac id=MJXp-Span-3236 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-3237><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3238>P</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-3239><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3240>c</span></span></span></span></span></span></span></span></span><span class=MJXp-mtr id=MJXp-Span-3241 style=vertical-align:baseline><span class=MJXp-mtd id=MJXp-Span-3242 style=padding-top:0.431em;text-align:center><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3243>D</span></span><span class=MJXp-mtd id=MJXp-Span-3244 style=padding-left:0.33em;padding-top:0.431em;text-align:center><span class=MJXp-mo id=MJXp-Span-3245 style=margin-left:0.333em;margin-right:0.333em>&gt;</span></span><span class=MJXp-mtd id=MJXp-Span-3246 style=padding-left:0.33em;padding-top:0.431em;text-align:center><span class=MJXp-mfrac id=MJXp-Span-3247 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-3248><span class=MJXp-mn id=MJXp-Span-3249>2</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3250>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3251>n</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3252>L</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-3253><span class=MJXp-msup id=MJXp-Span-3254><span class=MJXp-mrow id=MJXp-Span-3255 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3256>c</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-3257 style=vertical-align:0.5em><span class=MJXp-mn id=MJXp-Span-3258>2</span></span></span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-3259 style=margin-left:0em;margin-right:0.222em>,</span><span class=MJXp-mspace id=MJXp-Span-3260 style=width:1em;height:0em></span><span class=MJXp-mi id=MJXp-Span-3261>Δ</span><span class=MJXp-msup id=MJXp-Span-3262><span class=MJXp-mrow id=MJXp-Span-3263 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3264>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-3265 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-3266>*</span></span></span><span class=MJXp-mrow id=MJXp-Span-3267><span class=MJXp-mo id=MJXp-Span-3268 style=margin-left:0em;margin-right:0em>(</span><span class=MJXp-mrow id=MJXp-Span-3269><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3270>D</span></span><span class=MJXp-mo id=MJXp-Span-3271 style=margin-left:0em;margin-right:0em>)</span></span><span class=MJXp-mo id=MJXp-Span-3272 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-msup id=MJXp-Span-3273><span class=MJXp-mrow id=MJXp-Span-3274 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3275>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-3276 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-3277>*</span></span></span><span class=MJXp-mo id=MJXp-Span-3278 style=margin-left:0.267em;margin-right:0.267em>−</span><span class=MJXp-msub id=MJXp-Span-3279><span class=MJXp-mrow id=MJXp-Span-3280 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3281>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-3282 style=vertical-align:-0.4em><span class=MJXp-mo id=MJXp-Span-3283>⇒</span></span></span><span class=MJXp-mo id=MJXp-Span-3284 style=margin-left:0.333em;margin-right:0.333em>≃</span><span class=MJXp-msubsup id=MJXp-Span-3285><span class=MJXp-mrow id=MJXp-Span-3286 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-3287>Δ</span></span><span class=MJXp-script-box style=height:1.86em;vertical-align:-0.64em><span class=MJXp-script><span><span style=margin-bottom:-0.25em><span class=MJXp-mrow id=MJXp-Span-3290><span class=MJXp-mo id=MJXp-Span-3291>∗</span></span></span></span></span><span class=MJXp-script><span><span style=margin-top:-0.85em><span class=MJXp-mrow id=MJXp-Span-3288><span class=MJXp-mi id=MJXp-Span-3289>Sagn</span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-3292 style=margin-left:0em;margin-right:0.222em>.</span></span></span></span></span></span></span><span class="mjx-chtml MJXc-display MJXc-processing sf-hidden"></span>
</span>
</div><p>
</p>
<p>For the S-RLSE with medium locally at rest with device <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-3293><span class=MJXp-msup id=MJXp-Span-3294><span class=MJXp-mrow id=MJXp-Span-3295 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-3296>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-3297 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-3298>*</span></span></span></span></span><span id=MathJax-Element-307-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>, <a href=#j_phys-2023-0110_fig_004 class="link link-fig" data-bs-target=j_phys-2023-0110_fig_004>Figure 4</a> shows <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-3299><span class=MJXp-mi id=MJXp-Span-3300>Δ</span><span class=MJXp-msup id=MJXp-Span-3301><span class=MJXp-mrow id=MJXp-Span-3302 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3303>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-3304 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-3305>*</span></span></span><span class=MJXp-mo id=MJXp-Span-3306 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-mi id=MJXp-Span-3307>Δ</span><span class=MJXp-msup id=MJXp-Span-3308><span class=MJXp-mrow id=MJXp-Span-3309 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3310>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-3311 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-3312>*</span></span></span><span class=MJXp-mrow id=MJXp-Span-3313><span class=MJXp-mo id=MJXp-Span-3314 style=margin-left:0em;margin-right:0em>(</span><span class=MJXp-mrow id=MJXp-Span-3315><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3316>D</span></span><span class=MJXp-mo id=MJXp-Span-3317 style=margin-left:0em;margin-right:0em>)</span></span></span></span><span id=MathJax-Element-308-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> as a function of <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-3318><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3319>D</span></span></span><span id=MathJax-Element-309-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>. For the Sagnac effect, <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-3320><span class=MJXp-mi id=MJXp-Span-3321>Δ</span><span class=MJXp-msup id=MJXp-Span-3322><span class=MJXp-mrow id=MJXp-Span-3323 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3324>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-3325 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-3326>*</span></span></span><span class=MJXp-mo id=MJXp-Span-3327 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-mi id=MJXp-Span-3328>Δ</span><span class=MJXp-msubsup id=MJXp-Span-3329><span class=MJXp-mrow id=MJXp-Span-3330 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3331>T</span></span><span class=MJXp-script-box style=height:1.86em;vertical-align:-0.64em><span class=MJXp-script><span><span style=margin-bottom:-0.25em><span class=MJXp-mrow id=MJXp-Span-3334><span class=MJXp-mo id=MJXp-Span-3335>*</span></span></span></span></span><span class=MJXp-script><span><span style=margin-top:-0.85em><span class=MJXp-mrow id=MJXp-Span-3332><span class=MJXp-mi id=MJXp-Span-3333>Sagnac</span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-3336 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-msubsup id=MJXp-Span-3337><span class=MJXp-mrow id=MJXp-Span-3338 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-3339>Δ</span></span><span class=MJXp-script-box style=height:1.86em;vertical-align:-0.64em><span class=MJXp-script><span><span style=margin-bottom:-0.25em><span class=MJXp-mrow id=MJXp-Span-3342><span class=MJXp-mo id=MJXp-Span-3343>∗</span></span></span></span></span><span class=MJXp-script><span><span style=margin-top:-0.85em><span class=MJXp-mrow id=MJXp-Span-3340><span class=MJXp-mi id=MJXp-Span-3341>Sagn</span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-3344 style=margin-left:0.333em;margin-right:0.333em>=</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3345>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3346>P</span><span class=MJXp-mo id=MJXp-Span-3347 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class=MJXp-msup id=MJXp-Span-3348><span class=MJXp-mrow id=MJXp-Span-3349 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3350>c</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-3351 style=vertical-align:0.5em><span class=MJXp-mn id=MJXp-Span-3352>2</span></span></span></span></span><span id=MathJax-Element-310-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> is constant. For the S-RLSE, <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-3353><span class=MJXp-mi id=MJXp-Span-3354>Δ</span><span class=MJXp-msup id=MJXp-Span-3355><span class=MJXp-mrow id=MJXp-Span-3356 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3357>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-3358 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-3359>*</span></span></span><span class=MJXp-mrow id=MJXp-Span-3360><span class=MJXp-mo id=MJXp-Span-3361 style=margin-left:0em;margin-right:0em>(</span><span class=MJXp-mrow id=MJXp-Span-3362><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3363>D</span></span><span class=MJXp-mo id=MJXp-Span-3364 style=margin-left:0em;margin-right:0em>)</span></span></span></span><span id=MathJax-Element-311-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> is represented by the solid line that varies as a function of the initial position <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-3365><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3366>D</span></span></span><span id=MathJax-Element-312-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> of clock <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-3367><span class=MJXp-msup id=MJXp-Span-3368><span class=MJXp-mrow id=MJXp-Span-3369 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-3370>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-3371 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-3372>*</span></span></span></span></span><span id=MathJax-Element-313-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>. For the S-RLSE, the LT foresee, the observable dip by <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-3373><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3374>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3375>L</span><span class=MJXp-mo id=MJXp-Span-3376 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class=MJXp-msup id=MJXp-Span-3377><span class=MJXp-mrow id=MJXp-Span-3378 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3379>c</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-3380 style=vertical-align:0.5em><span class=MJXp-mn id=MJXp-Span-3381>2</span></span></span></span></span><span id=MathJax-Element-314-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> in the function <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-3382><span class=MJXp-mi id=MJXp-Span-3383>Δ</span><span class=MJXp-msup id=MJXp-Span-3384><span class=MJXp-mrow id=MJXp-Span-3385 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3386>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-3387 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-3388>*</span></span></span><span class=MJXp-mrow id=MJXp-Span-3389><span class=MJXp-mo id=MJXp-Span-3390 style=margin-left:0em;margin-right:0em>(</span><span class=MJXp-mrow id=MJXp-Span-3391><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3392>D</span></span><span class=MJXp-mo id=MJXp-Span-3393 style=margin-left:0em;margin-right:0em>)</span></span></span></span><span id=MathJax-Element-315-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>. The broken line refers to the S-RLSE of <a href=#j_phys-2023-0110_fig_002 class="link link-fig" data-bs-target=j_phys-2023-0110_fig_002>Figure 2</a>, where <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-3394><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3395>P</span><span class=MJXp-mo id=MJXp-Span-3396 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-mn id=MJXp-Span-3397>2</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3398>L</span></span></span><span id=MathJax-Element-316-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> and the dip is <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-3399><span class=MJXp-mn id=MJXp-Span-3400>2</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3401>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3402>L</span><span class=MJXp-mo id=MJXp-Span-3403 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class=MJXp-msup id=MJXp-Span-3404><span class=MJXp-mrow id=MJXp-Span-3405 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3406>c</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-3407 style=vertical-align:0.5em><span class=MJXp-mn id=MJXp-Span-3408>2</span></span></span></span></span><span id=MathJax-Element-317-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> with <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-3409><span class=MJXp-mi id=MJXp-Span-3410>Δ</span><span class=MJXp-msup id=MJXp-Span-3411><span class=MJXp-mrow id=MJXp-Span-3412 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3413>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-3414 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-3415>*</span></span></span><span class=MJXp-mo id=MJXp-Span-3416 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-mn id=MJXp-Span-3417>0</span></span></span><span id=MathJax-Element-318-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> at <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-3418><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3419>D</span><span class=MJXp-mo id=MJXp-Span-3420 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-msub id=MJXp-Span-3421><span class=MJXp-mrow id=MJXp-Span-3422 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3423>D</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-3424 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-3425>0</span></span></span></span></span><span id=MathJax-Element-319-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>.</p>
<p>
<strong>Expected precision for the S-RLSE</strong>
</p>
<p>The variation <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-3426><span class=MJXp-mi id=MJXp-Span-3427>Δ</span><span class=MJXp-msup id=MJXp-Span-3428><span class=MJXp-mrow id=MJXp-Span-3429 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3430>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-3431 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-3432>*</span></span></span><span class=MJXp-mrow id=MJXp-Span-3433><span class=MJXp-mo id=MJXp-Span-3434 style=margin-left:0em;margin-right:0em>(</span><span class=MJXp-mrow id=MJXp-Span-3435><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3436>D</span></span><span class=MJXp-mo id=MJXp-Span-3437 style=margin-left:0em;margin-right:0em>)</span></span></span></span><span id=MathJax-Element-320-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> may be measured with the techniques of ring interferometry or, after some adaptations, ring lasers [<a href=#j_phys-2023-0110_ref_003 class="link link-bibr" data-bs-target=j_phys-2023-0110_ref_003 data-bs-toggle=tooltip title="[3] Post EJ. Sagnac effect. Rev Mod Phys. 1967;39(2):475–93. 10.1103/RevModPhys.39.475Search in Google Scholar">3</a>]. Ring lasers Sagnac experiments, which can measure the angular velocity <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-3438><span class=MJXp-msub id=MJXp-Span-3439><span class=MJXp-mrow id=MJXp-Span-3440 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3441>ω</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-3442 style=vertical-align:-0.4em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3443>E</span></span></span></span></span><span id=MathJax-Element-321-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> of the Earth with a precision <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-3444><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3445>δ</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3446>ω</span><span class=MJXp-mo id=MJXp-Span-3447 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class=MJXp-msub id=MJXp-Span-3448><span class=MJXp-mrow id=MJXp-Span-3449 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3450>ω</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-3451 style=vertical-align:-0.4em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3452>E</span></span></span><span class=MJXp-mo id=MJXp-Span-3453 style=margin-left:0.333em;margin-right:0.333em>&lt;</span><span class=MJXp-mn id=MJXp-Span-3454>1</span><span class=MJXp-msup id=MJXp-Span-3455><span class=MJXp-mrow id=MJXp-Span-3456 style=margin-right:0.05em><span class=MJXp-mn id=MJXp-Span-3457>0</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-3458 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-3459>−</span><span class=MJXp-mn id=MJXp-Span-3460>8</span></span></span></span></span><span id=MathJax-Element-322-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>, are performed routinely on the Earth [<a href=#j_phys-2023-0110_ref_014 class="link link-bibr" data-bs-target=j_phys-2023-0110_ref_014 data-bs-toggle=tooltip title="[14] Schreiber KU, Gebauer A, Igel H, Wassermann J, Hurst RB, Wells JPR. The centennial of the Sagnac experiment in the optical regime: from a tabletop experiment to the variation of the Earth’s rotation. C R Physique. 2014;15:859–65. http://dx.doi.org/10.1016/j.crhy.2014.10.003. Search in Google Scholar">14</a>,<a href=#j_phys-2023-0110_ref_015 class="link link-bibr" data-bs-target=j_phys-2023-0110_ref_015 data-bs-toggle=tooltip title="[15] Stedman GE. Ring-laser tests of fundamental physics and geophysics. Rep Prog Phys. 1997;60:615. 10.1088/0034-4885/60/6/001Search in Google Scholar">15</a>]. For the effect of refractive index of an optical medium on the rotation frequency of ring lasers and resonators, there are various experimental expressions as functions of <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-3461><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3462>n</span></span></span><span id=MathJax-Element-323-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>, considered by Malykin in ref [<a href=#j_phys-2023-0110_ref_016 class="link link-bibr" data-bs-target=j_phys-2023-0110_ref_016 data-bs-toggle=tooltip title="[16] Malykin GB. The Sagnac effect: correct and incorrect explanations. Phys Uspekhi. 2000;43(12):1229–52. 10.1070/PU2000v043n12ABEH000830Search in Google Scholar">16</a>] (2014).</p>
<p>In relation to the sensitivity of detectors measuring <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-3463><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3464>δ</span><span class=MJXp-msub id=MJXp-Span-3465><span class=MJXp-mrow id=MJXp-Span-3466 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3467>τ</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-3468 style=vertical-align:-0.4em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3469>A</span></span></span></span></span><span id=MathJax-Element-324-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> and the smallest measurable time interval, there are techniques capable of resolving femtosecond (<span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-3470><span class=MJXp-mn id=MJXp-Span-3471>1</span><span class=MJXp-msup id=MJXp-Span-3472><span class=MJXp-mrow id=MJXp-Span-3473 style=margin-right:0.05em><span class=MJXp-mn id=MJXp-Span-3474>0</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-3475 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-3476>−</span><span class=MJXp-mn id=MJXp-Span-3477>15</span></span></span><span class=MJXp-mspace id=MJXp-Span-3478 style=width:0.33em;height:0em></span><span class=MJXp-mi id=MJXp-Span-3479>s</span></span></span><span id=MathJax-Element-325-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>) [<a href=#j_phys-2023-0110_ref_017 class="link link-bibr" data-bs-target=j_phys-2023-0110_ref_017 data-bs-toggle=tooltip title="[17] Ludlow DA, Boyd MM, Ye J, Peik E, Schmidt PO. Optical atomic clocks. Rev Mod Phys. 2015;87:637. 10.1103/RevModPhys.87.637Search in Google Scholar">17</a>] or even attosecond (<span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-3480><span class=MJXp-mn id=MJXp-Span-3481>1</span><span class=MJXp-msup id=MJXp-Span-3482><span class=MJXp-mrow id=MJXp-Span-3483 style=margin-right:0.05em><span class=MJXp-mn id=MJXp-Span-3484>0</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-3485 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-3486>−</span><span class=MJXp-mn id=MJXp-Span-3487>18</span></span></span><span class=MJXp-mspace id=MJXp-Span-3488 style=width:0.33em;height:0em></span><span class=MJXp-mi id=MJXp-Span-3489>s</span></span></span><span id=MathJax-Element-326-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>) [<a href=#j_phys-2023-0110_ref_018 class="link link-bibr" data-bs-target=j_phys-2023-0110_ref_018 data-bs-toggle=tooltip title="[18] Kim J, Chen J, Cox J, Kärtner FX. Attosecond-resolution timing jitter characterization of free-running mode-locked lasers. Optics Lett. 2007;32(24):3519–21; Kwon D, Jeon CG, Shin J, Heo MS, Park SE, Song Y, Kim J. Ultrafast, subnanometre-precision and multifunctional time-of-flight detection. Scientific Reports 2017:7:40917. Search in Google Scholar">18</a>] pulses of laser light, although better limits may be obtained by means of advanced interferometry.</p>
<p>The dip by <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-3490><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3491>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3492>L</span><span class=MJXp-mo id=MJXp-Span-3493 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class=MJXp-msup id=MJXp-Span-3494><span class=MJXp-mrow id=MJXp-Span-3495 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3496>c</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-3497 style=vertical-align:0.5em><span class=MJXp-mn id=MJXp-Span-3498>2</span></span></span></span></span><span id=MathJax-Element-327-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>, to be measured to confirm the prediction of standard relativity based on the LT, is comparable to that measured in the usual experiments testing the Sagnac effect and, thus, well within the range of the sensitivity of available detectors and not too difficult to observe. In the experiment by Wang <em>et al</em>. [<a href=#j_phys-2023-0110_ref_002 class="link link-bibr" data-bs-target=j_phys-2023-0110_ref_002 data-bs-toggle=tooltip title="[2] Wang R, Zhengb Y, Yao A, Langley D. Modified Sagnac experiment for measuring travel-time difference between counter-propagating light beams in a uniformly moving fiber. Phys Lett A. 2003;312:7–10. Wang R, Zheng Y, Yao A. Generalized Sagnac effect. Phys Rev Lett. 2004;93(14):143901.10.1016/S0375-9601(03)00575-9Search in Google Scholar">2</a>], the device <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-3499><span class=MJXp-msup id=MJXp-Span-3500><span class=MJXp-mrow id=MJXp-Span-3501 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-3502>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-3503 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-3504>*</span></span></span></span></span><span id=MathJax-Element-328-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> is in motion relative to the contour. In the S-RLSE, the device <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-3505><span class=MJXp-msup id=MJXp-Span-3506><span class=MJXp-mrow id=MJXp-Span-3507 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-3508>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-3509 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-3510>*</span></span></span></span></span><span id=MathJax-Element-329-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> is stationary and the contour in relative motion. Assuming the same relative velocity, we expect that the sensitivity achievable for our S-RLSE experiment is approximately the same as that achieved in the experiment by Wang <em>et al</em>. [<a href=#j_phys-2023-0110_ref_002 class="link link-bibr" data-bs-target=j_phys-2023-0110_ref_002 data-bs-toggle=tooltip title="[2] Wang R, Zhengb Y, Yao A, Langley D. Modified Sagnac experiment for measuring travel-time difference between counter-propagating light beams in a uniformly moving fiber. Phys Lett A. 2003;312:7–10. Wang R, Zheng Y, Yao A. Generalized Sagnac effect. Phys Rev Lett. 2004;93(14):143901.10.1016/S0375-9601(03)00575-9Search in Google Scholar">2</a>]. The main difference with respect to the experiment by Wang <em>et al</em>. is related to the mechanical difficulties involved with the motion of the contour, which implies more an increase in the complexity and cost of the experiment, rather than a loss in sensitivity.</p>
<p>
<strong>Possible applications of the S-RLSE if confirmed experimentally.</strong>
</p>
<p>After more than a century, the Sagnac effect is employed in current technology and is used in inertial guidance systems, ring laser gyroscope (extremely sensitive to rotations), and other optical systems. Being not yet experimentally confirmed, it might be premature to indicate what kind of applications the RLSE might have. However, considering that the circular Sagnac effect (sensitive to rotations) can detect very accurately the angular velocity of objects, such as the Earth, the RLSE (sensitive to velocity changes) might be suitable to detect velocity variations and also point out the corresponding direction. The realization of these applications requires, however, to take into account other features related to the RLSE that will be considered in a future contribution.</p>
</section>
<section id=j_phys-2023-0110_s_004>
<h2 class=subheading>4 Conclusions</h2>
<p>We have described an optical effect, denoted as RLSE, where the emitter–receiver device is stationary and the contour along which light propagates is in motion. The RLSE provides the same results of the standard Sagnac effect for the round-trip time difference <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-3511><span class=MJXp-mi id=MJXp-Span-3512>Δ</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3513>T</span></span></span><span id=MathJax-Element-330-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> of light signals counter-propagating along the closed contour. However, the RLSE possesses features that are not equivalent to the corresponding ones of the Sagnac effect. When the contour changes velocity, standard special relativity foresees that the round-trip time interval <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-3514><span class=MJXp-msub id=MJXp-Span-3515><span class=MJXp-mrow id=MJXp-Span-3516 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3517>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-3518 style=vertical-align:-0.4em><span class=MJXp-mo id=MJXp-Span-3519>⇒</span></span></span></span></span><span id=MathJax-Element-331-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> of a counter-moving light signal differs from the corresponding one of the Sagnac effect. The difference is observable with our S-RLSE experiment and given by the dip by <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-3520><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3521>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3522>L</span><span class=MJXp-mo id=MJXp-Span-3523 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class=MJXp-msup id=MJXp-Span-3524><span class=MJXp-mrow id=MJXp-Span-3525 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3526>c</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-3527 style=vertical-align:0.5em><span class=MJXp-mn id=MJXp-Span-3528>2</span></span></span></span></span><span id=MathJax-Element-332-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> in the measured round-trip time difference <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-3529><span class=MJXp-mi id=MJXp-Span-3530>Δ</span><span class=MJXp-msup id=MJXp-Span-3531><span class=MJXp-mrow id=MJXp-Span-3532 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3533>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-3534 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-3535>*</span></span></span><span class=MJXp-mrow id=MJXp-Span-3536><span class=MJXp-mo id=MJXp-Span-3537 style=margin-left:0em;margin-right:0em>(</span><span class=MJXp-mrow id=MJXp-Span-3538><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3539>D</span></span><span class=MJXp-mo id=MJXp-Span-3540 style=margin-left:0em;margin-right:0em>)</span></span><span class=MJXp-mo id=MJXp-Span-3541 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-msup id=MJXp-Span-3542><span class=MJXp-mrow id=MJXp-Span-3543 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3544>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-3545 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-3546>*</span></span></span><span class=MJXp-mo id=MJXp-Span-3547 style=margin-left:0.267em;margin-right:0.267em>−</span><span class=MJXp-msub id=MJXp-Span-3548><span class=MJXp-mrow id=MJXp-Span-3549 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3550>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-3551 style=vertical-align:-0.4em><span class=MJXp-mo id=MJXp-Span-3552>⇒</span></span></span></span></span><span id=MathJax-Element-333-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> of counter-propagating photons, plotted in <a href=#j_phys-2023-0110_fig_004 class="link link-fig" data-bs-target=j_phys-2023-0110_fig_004>Figure 4</a>. The dip may be related to the different role played by relative simultaneity in the linear Sagnac effect and the RLSE.</p>
<p>If confirmed experimentally, the S-RLSE stands to be a new relativistic optical effect. In this case, being sensitive to velocity changes, the S-RLSE might have important technological applications in inertial guidance systems by detecting velocity variations and corresponding direction.</p>
<p>In any event, the different features between the standard linear Sagnac effect and the S-RLSE can be exploited for testing Lorentz and light speed invariance.</p>
</section>
</div><div class=contrib-group></div><div class=back>
<ol class=footnote-group>
<li class="footnote footnote-noLabel" id=j_phys-2023-0110_fn_001 fn-type=financial-disclosure>
<p>
<strong>Funding information:</strong> Our research has been supported by the CDCHTA of the Universidad de Los Andes, Mérida, Venezuela, and the ‘Braingain’ grant of the International Center for Theoretical Physics (ICTP), Trieste, Italy, for promoting teaching and researching in Venezuela.</p>
</li>
<li class="footnote footnote-noLabel" id=j_phys-2023-0110_fn_002 fn-type=con>
<p>
<strong>Author contributions:</strong> All authors have accepted responsibility for the entire content of this manuscript and approved its submission.</p>
</li>
<li class="footnote footnote-noLabel" id=j_phys-2023-0110_fn_003 fn-type=conflict>
<p>
<strong>Conflict of interest</strong>: The authors state no conflict of interest.</p>
</li>
</ol>
<span class=app-group>
<div class=app id=j_phys-2023-0110_app_001>
<h2 class=subheading>Appendix</h2>
<section id=j_phys-2023-0110_s_005>
<h3 class=subheading>A.1 Special reciprocal linear Sagnac effect for light propagation in a medium of refracting index <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-3553><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3554>n</span></span></span><span id=MathJax-Element-334-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> on a rectangular contour of sides <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-3555><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3556>L</span></span></span><span id=MathJax-Element-335-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> and <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-3557><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3558>H</span></span></span><span id=MathJax-Element-336-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>
</h3>
<p>For the S-RLSE, the round-trip interval <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-3559><span class=MJXp-msub id=MJXp-Span-3560><span class=MJXp-mrow id=MJXp-Span-3561 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3562>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-3563 style=vertical-align:-0.4em><span class=MJXp-mo id=MJXp-Span-3564>⇒</span></span></span></span></span><span id=MathJax-Element-337-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> differs from the corresponding one of the linear Sagnac effect if, on the contour lower section, to the first order in <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-3565><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3566>v</span><span class=MJXp-mo id=MJXp-Span-3567 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3568>c</span></span></span><span id=MathJax-Element-338-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>, <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-3569><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3570>D</span><span class=MJXp-mo id=MJXp-Span-3571 style=margin-left:0.333em;margin-right:0.333em>≃</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3572>n</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3573>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3574>L</span><span class=MJXp-mo id=MJXp-Span-3575 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3576>c</span></span></span><span id=MathJax-Element-339-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> and the photon reaches the right corner when the left corner reaches <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-3577><span class=MJXp-msup id=MJXp-Span-3578><span class=MJXp-mrow id=MJXp-Span-3579 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-3580>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-3581 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-3582>*</span></span></span></span></span><span id=MathJax-Element-340-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>.</p>
<p>
<strong>S-RLSE with medium locally at rest with the contour.</strong>
<span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-3583><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3584>P</span><span class=MJXp-mo id=MJXp-Span-3585 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-mn id=MJXp-Span-3586>2</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3587>L</span><span class=MJXp-mo id=MJXp-Span-3588 style=margin-left:0.267em;margin-right:0.267em>+</span><span class=MJXp-mn id=MJXp-Span-3589>2</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3590>H</span></span></span><span id=MathJax-Element-341-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>.</p>
<p>For the contour of <a href=#j_phys-2023-0110_fig_005 class="link link-fig" data-bs-target=j_phys-2023-0110_fig_005>Figure A1</a>(a), we calculate with the LT to the first order in <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-3591><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3592>v</span><span class=MJXp-mo id=MJXp-Span-3593 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3594>c</span></span></span><span id=MathJax-Element-342-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> the time intervals taken by the counter-propagating photon to cover the sides of the rectangular contour in motion with velocity <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-3595><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3596>v</span></span></span><span id=MathJax-Element-343-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> relative to the stationary <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-3597><span class=MJXp-msup id=MJXp-Span-3598><span class=MJXp-mrow id=MJXp-Span-3599 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-3600>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-3601 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-3602>*</span></span></span></span></span><span id=MathJax-Element-344-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>.</p>
<p>Position 1: Starting from <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-3603><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3604>D</span><span class=MJXp-mo id=MJXp-Span-3605 style=margin-left:0.333em;margin-right:0.333em>=</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3606>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3607>t</span><span class=MJXp-mo id=MJXp-Span-3608 style=margin-left:0.333em;margin-right:0.333em>≃</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3609>n</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3610>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3611>L</span><span class=MJXp-mo id=MJXp-Span-3612 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3613>c</span></span></span><span id=MathJax-Element-345-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>, and using the equation <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-3614><span class=MJXp-msub id=MJXp-Span-3615><span class=MJXp-mrow id=MJXp-Span-3616 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3617>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-3618 style=vertical-align:-0.4em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3619>n</span></span></span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3620>t</span><span class=MJXp-mo id=MJXp-Span-3621 style=margin-left:0.333em;margin-right:0.333em>=</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3622>L</span><span class=MJXp-mo id=MJXp-Span-3623 style=margin-left:0.267em;margin-right:0.267em>−</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3624>D</span><span class=MJXp-mo id=MJXp-Span-3625 style=margin-left:0.267em;margin-right:0.267em>+</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3626>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3627>t</span></span></span><span id=MathJax-Element-346-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> with <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-3628><span class=MJXp-msub id=MJXp-Span-3629><span class=MJXp-mrow id=MJXp-Span-3630 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3631>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-3632 style=vertical-align:-0.4em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3633>n</span></span></span></span></span><span id=MathJax-Element-347-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> the light speed relative to <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-3634><span class=MJXp-msup id=MJXp-Span-3635><span class=MJXp-mrow id=MJXp-Span-3636 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-3637>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-3638 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-3639>*</span></span></span></span></span><span id=MathJax-Element-348-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>. Then, we have, <div class=formula id=j_phys-2023-0110_eq_009>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class="MJXp-math MJXp-display" id=MJXp-Span-3640><span class=MJXp-mtable id=MJXp-Span-3641><span><span class=MJXp-mtr id=MJXp-Span-3642 style=vertical-align:baseline><span class=MJXp-mtd id=MJXp-Span-3643 style=text-align:center><span class=MJXp-msub id=MJXp-Span-3644><span class=MJXp-mrow id=MJXp-Span-3645 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3646>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-3647 style=vertical-align:-0.4em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3648>n</span></span></span></span><span class=MJXp-mtd id=MJXp-Span-3649 style=padding-left:0.33em;text-align:center><span class=MJXp-mo id=MJXp-Span-3650 style=margin-left:0.333em;margin-right:0.333em>=</span></span><span class=MJXp-mtd id=MJXp-Span-3651 style=padding-left:0.33em;text-align:center><span class=MJXp-mfrac id=MJXp-Span-3652 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-3653><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3654>c</span><span class=MJXp-mo id=MJXp-Span-3655 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3656>n</span><span class=MJXp-mo id=MJXp-Span-3657 style=margin-left:0.267em;margin-right:0.267em>+</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3658>v</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-3659><span class=MJXp-mn id=MJXp-Span-3660>1</span><span class=MJXp-mo id=MJXp-Span-3661 style=margin-left:0.267em;margin-right:0.267em>+</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3662>v</span><span class=MJXp-mo id=MJXp-Span-3663 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3664>n</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3665>c</span></span></span></span></span></span></span></span></span><span class=MJXp-mtr id=MJXp-Span-3666 style=vertical-align:baseline><span class=MJXp-mtd id=MJXp-Span-3667 style=padding-top:0.431em;text-align:center><span class=MJXp-msub id=MJXp-Span-3668><span class=MJXp-mrow id=MJXp-Span-3669 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3670>t</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-3671 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-3672>1</span></span></span></span><span class=MJXp-mtd id=MJXp-Span-3673 style=padding-left:0.33em;padding-top:0.431em;text-align:center><span class=MJXp-mo id=MJXp-Span-3674 style=margin-left:0.333em;margin-right:0.333em>=</span></span><span class=MJXp-mtd id=MJXp-Span-3675 style=padding-left:0.33em;padding-top:0.431em;text-align:center><span class=MJXp-mfrac id=MJXp-Span-3676 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-3677><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3678>L</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-3679><span class=MJXp-msub id=MJXp-Span-3680><span class=MJXp-mrow id=MJXp-Span-3681 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3682>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-3683 style=vertical-align:-0.4em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3684>n</span></span></span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-3685 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-mfrac id=MJXp-Span-3686 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-3687><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3688>n</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3689>L</span><span class=MJXp-mrow id=MJXp-Span-3690><span class=MJXp-mo id=MJXp-Span-3691 style=margin-left:0em;margin-right:0em>(</span><span class=MJXp-mrow id=MJXp-Span-3692><span class=MJXp-mn id=MJXp-Span-3693>1</span><span class=MJXp-mo id=MJXp-Span-3694 style=margin-left:0.267em;margin-right:0.267em>+</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3695>v</span><span class=MJXp-mo id=MJXp-Span-3696 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3697>n</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3698>c</span></span><span class=MJXp-mo id=MJXp-Span-3699 style=margin-left:0em;margin-right:0em>)</span></span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-3700><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3701>c</span><span class=MJXp-mrow id=MJXp-Span-3702><span class=MJXp-mo id=MJXp-Span-3703 style=margin-left:0em;margin-right:0em>(</span><span class=MJXp-mrow id=MJXp-Span-3704><span class=MJXp-mn id=MJXp-Span-3705>1</span><span class=MJXp-mo id=MJXp-Span-3706 style=margin-left:0.267em;margin-right:0.267em>+</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3707>n</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3708>v</span><span class=MJXp-mo id=MJXp-Span-3709 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3710>c</span></span><span class=MJXp-mo id=MJXp-Span-3711 style=margin-left:0em;margin-right:0em>)</span></span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-3712 style=margin-left:0.333em;margin-right:0.333em>≃</span><span class=MJXp-mfrac id=MJXp-Span-3713 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-3714><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3715>n</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3716>L</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-3717><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3718>c</span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-3719 style=margin-left:0.267em;margin-right:0.267em>−</span><span class=MJXp-mfrac id=MJXp-Span-3720 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-3721><span class=MJXp-msup id=MJXp-Span-3722><span class=MJXp-mrow id=MJXp-Span-3723 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3724>n</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-3725 style=vertical-align:0.5em><span class=MJXp-mn id=MJXp-Span-3726>2</span></span></span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3727>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3728>L</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-3729><span class=MJXp-msup id=MJXp-Span-3730><span class=MJXp-mrow id=MJXp-Span-3731 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3732>c</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-3733 style=vertical-align:0.5em><span class=MJXp-mn id=MJXp-Span-3734>2</span></span></span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-3735 style=margin-left:0.267em;margin-right:0.267em>+</span><span class=MJXp-mfrac id=MJXp-Span-3736 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-3737><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3738>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3739>L</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-3740><span class=MJXp-msup id=MJXp-Span-3741><span class=MJXp-mrow id=MJXp-Span-3742 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3743>c</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-3744 style=vertical-align:0.5em><span class=MJXp-mn id=MJXp-Span-3745>2</span></span></span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-3746 style=margin-left:0em;margin-right:0.222em>.</span></span></span></span></span></span></span><span class="mjx-chtml MJXc-display MJXc-processing sf-hidden"></span>
</span>
</div><p>
</p>
<p>Position 2: By means of the equation <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-3747><span class=MJXp-msub id=MJXp-Span-3748><span class=MJXp-mrow id=MJXp-Span-3749 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3750>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-3751 style=vertical-align:-0.4em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3752>n</span></span></span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3753>t</span><span class=MJXp-mo id=MJXp-Span-3754 style=margin-left:0.333em;margin-right:0.333em>=</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3755>H</span><span class=MJXp-mo id=MJXp-Span-3756 style=margin-left:0.267em;margin-right:0.267em>−</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3757>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3758>t</span></span></span><span id=MathJax-Element-350-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>, <div class=formula id=j_phys-2023-0110_eq_010>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class="MJXp-math MJXp-display" id=MJXp-Span-3759><span class=MJXp-mtable id=MJXp-Span-3760><span><span class=MJXp-mtr id=MJXp-Span-3761 style=vertical-align:baseline><span class=MJXp-mtd id=MJXp-Span-3762 style=text-align:center><span class=MJXp-msub id=MJXp-Span-3763><span class=MJXp-mrow id=MJXp-Span-3764 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3765>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-3766 style=vertical-align:-0.4em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3767>n</span></span></span></span><span class=MJXp-mtd id=MJXp-Span-3768 style=padding-left:0.33em;text-align:center><span class=MJXp-mo id=MJXp-Span-3769 style=margin-left:0.333em;margin-right:0.333em>=</span></span><span class=MJXp-mtd id=MJXp-Span-3770 style=padding-left:0.33em;text-align:center><span class=MJXp-mfrac id=MJXp-Span-3771 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-3772><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3773>c</span><span class=MJXp-mo id=MJXp-Span-3774 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3775>n</span><span class=MJXp-mo id=MJXp-Span-3776 style=margin-left:0.267em;margin-right:0.267em>−</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3777>v</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-3778><span class=MJXp-mn id=MJXp-Span-3779>1</span><span class=MJXp-mo id=MJXp-Span-3780 style=margin-left:0.267em;margin-right:0.267em>−</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3781>v</span><span class=MJXp-mo id=MJXp-Span-3782 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3783>n</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3784>c</span></span></span></span></span></span></span></span></span><span class=MJXp-mtr id=MJXp-Span-3785 style=vertical-align:baseline><span class=MJXp-mtd id=MJXp-Span-3786 style=padding-top:0.431em;text-align:center><span class=MJXp-msub id=MJXp-Span-3787><span class=MJXp-mrow id=MJXp-Span-3788 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3789>t</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-3790 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-3791>2</span></span></span></span><span class=MJXp-mtd id=MJXp-Span-3792 style=padding-left:0.33em;padding-top:0.431em;text-align:center><span class=MJXp-mo id=MJXp-Span-3793 style=margin-left:0.333em;margin-right:0.333em>=</span></span><span class=MJXp-mtd id=MJXp-Span-3794 style=padding-left:0.33em;padding-top:0.431em;text-align:center><span class=MJXp-mfrac id=MJXp-Span-3795 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-3796><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3797>H</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-3798><span class=MJXp-msub id=MJXp-Span-3799><span class=MJXp-mrow id=MJXp-Span-3800 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3801>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-3802 style=vertical-align:-0.4em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3803>n</span></span></span><span class=MJXp-mo id=MJXp-Span-3804 style=margin-left:0.267em;margin-right:0.267em>+</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3805>v</span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-3806 style=margin-left:0.333em;margin-right:0.333em>≃</span><span class=MJXp-mfrac id=MJXp-Span-3807 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-3808><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3809>n</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3810>H</span><span class=MJXp-mrow id=MJXp-Span-3811><span class=MJXp-mo id=MJXp-Span-3812 style=margin-left:0em;margin-right:0em>(</span><span class=MJXp-mrow id=MJXp-Span-3813><span class=MJXp-mn id=MJXp-Span-3814>1</span><span class=MJXp-mo id=MJXp-Span-3815 style=margin-left:0.267em;margin-right:0.267em>−</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3816>v</span><span class=MJXp-mo id=MJXp-Span-3817 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3818>n</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3819>c</span></span><span class=MJXp-mo id=MJXp-Span-3820 style=margin-left:0em;margin-right:0em>)</span></span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-3821><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3822>c</span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-3823 style=margin-left:0.333em;margin-right:0.333em>≃</span><span class=MJXp-mfrac id=MJXp-Span-3824 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-3825><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3826>n</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3827>H</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-3828><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3829>c</span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-3830 style=margin-left:0.267em;margin-right:0.267em>−</span><span class=MJXp-mfrac id=MJXp-Span-3831 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-3832><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3833>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3834>H</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-3835><span class=MJXp-msup id=MJXp-Span-3836><span class=MJXp-mrow id=MJXp-Span-3837 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3838>c</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-3839 style=vertical-align:0.5em><span class=MJXp-mn id=MJXp-Span-3840>2</span></span></span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-3841 style=margin-left:0em;margin-right:0.222em>.</span></span></span></span></span></span></span><span class="mjx-chtml MJXc-display MJXc-processing sf-hidden"></span>
</span>
</div><p>
</p>
<p>Position 3: With the equation <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-3842><span class=MJXp-msub id=MJXp-Span-3843><span class=MJXp-mrow id=MJXp-Span-3844 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3845>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-3846 style=vertical-align:-0.4em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3847>n</span></span></span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3848>t</span><span class=MJXp-mo id=MJXp-Span-3849 style=margin-left:0.333em;margin-right:0.333em>=</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3850>L</span></span></span><span id=MathJax-Element-352-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>, <div class=formula id=j_phys-2023-0110_eq_011>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class="MJXp-math MJXp-display" id=MJXp-Span-3851><span class=MJXp-mtable id=MJXp-Span-3852><span><span class=MJXp-mtr id=MJXp-Span-3853 style=vertical-align:baseline><span class=MJXp-mtd id=MJXp-Span-3854 style=text-align:center><span class=MJXp-msub id=MJXp-Span-3855><span class=MJXp-mrow id=MJXp-Span-3856 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3857>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-3858 style=vertical-align:-0.4em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3859>n</span></span></span></span><span class=MJXp-mtd id=MJXp-Span-3860 style=padding-left:0.33em;text-align:center><span class=MJXp-mo id=MJXp-Span-3861 style=margin-left:0.333em;margin-right:0.333em>≃</span></span><span class=MJXp-mtd id=MJXp-Span-3862 style=padding-left:0.33em;text-align:center><span class=MJXp-mfrac id=MJXp-Span-3863 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-3864><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3865>c</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-3866><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3867>n</span></span></span></span></span></span></span></span></span><span class=MJXp-mtr id=MJXp-Span-3868 style=vertical-align:baseline><span class=MJXp-mtd id=MJXp-Span-3869 style=padding-top:0.431em;text-align:center><span class=MJXp-msub id=MJXp-Span-3870><span class=MJXp-mrow id=MJXp-Span-3871 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3872>t</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-3873 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-3874>3</span></span></span></span><span class=MJXp-mtd id=MJXp-Span-3875 style=padding-left:0.33em;padding-top:0.431em;text-align:center><span class=MJXp-mo id=MJXp-Span-3876 style=margin-left:0.333em;margin-right:0.333em>=</span></span><span class=MJXp-mtd id=MJXp-Span-3877 style=padding-left:0.33em;padding-top:0.431em;text-align:center><span class=MJXp-mfrac id=MJXp-Span-3878 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-3879><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3880>L</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-3881><span class=MJXp-msub id=MJXp-Span-3882><span class=MJXp-mrow id=MJXp-Span-3883 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3884>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-3885 style=vertical-align:-0.4em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3886>n</span></span></span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-3887 style=margin-left:0.333em;margin-right:0.333em>≃</span><span class=MJXp-mfrac id=MJXp-Span-3888 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-3889><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3890>n</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3891>L</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-3892><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3893>c</span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-3894 style=margin-left:0em;margin-right:0.222em>.</span></span></span></span></span></span></span><span class="mjx-chtml MJXc-display MJXc-processing sf-hidden"></span>
</span>
</div><p>
</p>
<p>Position 4: By means of the equation, <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-3895><span class=MJXp-msub id=MJXp-Span-3896><span class=MJXp-mrow id=MJXp-Span-3897 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3898>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-3899 style=vertical-align:-0.4em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3900>n</span></span></span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3901>t</span><span class=MJXp-mo id=MJXp-Span-3902 style=margin-left:0.333em;margin-right:0.333em>=</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3903>H</span><span class=MJXp-mo id=MJXp-Span-3904 style=margin-left:0.267em;margin-right:0.267em>−</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3905>v</span><span class=MJXp-mrow id=MJXp-Span-3906><span class=MJXp-mo id=MJXp-Span-3907 style=margin-left:0em;margin-right:0em;vertical-align:-0.244em><span style=font-size:1.978em;margin-left:-0.05em class="MJXp-right MJXp-scale7">(</span></span><span class=MJXp-mrow id=MJXp-Span-3908><span class=MJXp-msub id=MJXp-Span-3909><span class=MJXp-mrow id=MJXp-Span-3910 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3911>t</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-3912 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-3913>2</span></span></span><span class=MJXp-mo id=MJXp-Span-3914 style=margin-left:0.267em;margin-right:0.267em>+</span><span class=MJXp-msub id=MJXp-Span-3915><span class=MJXp-mrow id=MJXp-Span-3916 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3917>t</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-3918 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-3919>3</span></span></span></span><span class=MJXp-mo id=MJXp-Span-3920 style=margin-left:0em;margin-right:0em;vertical-align:-0.244em><span style=font-size:1.978em;margin-left:-0.05em class="MJXp-right MJXp-scale7">)</span></span></span></span></span><span id=MathJax-Element-354-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>, <div class=formula id=j_phys-2023-0110_eq_012>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class="MJXp-math MJXp-display" id=MJXp-Span-3921><span class=MJXp-mtable id=MJXp-Span-3922><span><span class=MJXp-mtr id=MJXp-Span-3923 style=vertical-align:baseline><span class=MJXp-mtd id=MJXp-Span-3924 style=text-align:center><span class=MJXp-msub id=MJXp-Span-3925><span class=MJXp-mrow id=MJXp-Span-3926 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3927>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-3928 style=vertical-align:-0.4em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3929>n</span></span></span></span><span class=MJXp-mtd id=MJXp-Span-3930 style=padding-left:0.33em;text-align:center><span class=MJXp-mo id=MJXp-Span-3931 style=margin-left:0.333em;margin-right:0.333em>=</span></span><span class=MJXp-mtd id=MJXp-Span-3932 style=padding-left:0.33em;text-align:center><span class=MJXp-mfrac id=MJXp-Span-3933 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-3934><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3935>c</span><span class=MJXp-mo id=MJXp-Span-3936 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3937>n</span><span class=MJXp-mo id=MJXp-Span-3938 style=margin-left:0.267em;margin-right:0.267em>+</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3939>v</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-3940><span class=MJXp-mn id=MJXp-Span-3941>1</span><span class=MJXp-mo id=MJXp-Span-3942 style=margin-left:0.267em;margin-right:0.267em>+</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3943>v</span><span class=MJXp-mo id=MJXp-Span-3944 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3945>n</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3946>c</span></span></span></span></span></span></span></span></span><span class=MJXp-mtr id=MJXp-Span-3947 style=vertical-align:baseline><span class=MJXp-mtd id=MJXp-Span-3948 style=padding-top:0.431em;text-align:center><span class=MJXp-msub id=MJXp-Span-3949><span class=MJXp-mrow id=MJXp-Span-3950 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3951>t</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-3952 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-3953>4</span></span></span></span><span class=MJXp-mtd id=MJXp-Span-3954 style=padding-left:0.33em;padding-top:0.431em;text-align:center><span class=MJXp-mo id=MJXp-Span-3955 style=margin-left:0.333em;margin-right:0.333em>=</span></span><span class=MJXp-mtd id=MJXp-Span-3956 style=padding-left:0.33em;padding-top:0.431em;text-align:center><span class=MJXp-mfrac id=MJXp-Span-3957 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-3958><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3959>n</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3960>H</span><span class=MJXp-mrow id=MJXp-Span-3961><span class=MJXp-mo id=MJXp-Span-3962 style=margin-left:0em;margin-right:0em>(</span><span class=MJXp-mrow id=MJXp-Span-3963><span class=MJXp-mn id=MJXp-Span-3964>1</span><span class=MJXp-mo id=MJXp-Span-3965 style=margin-left:0.267em;margin-right:0.267em>+</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3966>v</span><span class=MJXp-mo id=MJXp-Span-3967 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3968>n</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3969>c</span></span><span class=MJXp-mo id=MJXp-Span-3970 style=margin-left:0em;margin-right:0em>)</span></span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-3971><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3972>c</span><span class=MJXp-mrow id=MJXp-Span-3973><span class=MJXp-mo id=MJXp-Span-3974 style=margin-left:0em;margin-right:0em>(</span><span class=MJXp-mrow id=MJXp-Span-3975><span class=MJXp-mn id=MJXp-Span-3976>1</span><span class=MJXp-mo id=MJXp-Span-3977 style=margin-left:0.267em;margin-right:0.267em>+</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3978>n</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3979>v</span><span class=MJXp-mo id=MJXp-Span-3980 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3981>c</span></span><span class=MJXp-mo id=MJXp-Span-3982 style=margin-left:0em;margin-right:0em>)</span></span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-3983 style=margin-left:0.267em;margin-right:0.267em>−</span><span class=MJXp-mfrac id=MJXp-Span-3984 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-3985><span class=MJXp-msup id=MJXp-Span-3986><span class=MJXp-mrow id=MJXp-Span-3987 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3988>n</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-3989 style=vertical-align:0.5em><span class=MJXp-mn id=MJXp-Span-3990>2</span></span></span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3991>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3992>H</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-3993><span class=MJXp-msup id=MJXp-Span-3994><span class=MJXp-mrow id=MJXp-Span-3995 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-3996>c</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-3997 style=vertical-align:0.5em><span class=MJXp-mn id=MJXp-Span-3998>2</span></span></span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-3999 style=margin-left:0.267em;margin-right:0.267em>−</span><span class=MJXp-mfrac id=MJXp-Span-4000 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-4001><span class=MJXp-msup id=MJXp-Span-4002><span class=MJXp-mrow id=MJXp-Span-4003 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4004>n</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-4005 style=vertical-align:0.5em><span class=MJXp-mn id=MJXp-Span-4006>2</span></span></span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4007>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4008>L</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-4009><span class=MJXp-msup id=MJXp-Span-4010><span class=MJXp-mrow id=MJXp-Span-4011 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4012>c</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-4013 style=vertical-align:0.5em><span class=MJXp-mn id=MJXp-Span-4014>2</span></span></span></span></span></span></span></span></span></span></span><span class=MJXp-mtr id=MJXp-Span-4015 style=vertical-align:baseline><span class=MJXp-mtd id=MJXp-Span-4016 style=padding-top:0.431em;text-align:center></span><span class=MJXp-mtd id=MJXp-Span-4017 style=padding-left:0.33em;padding-top:0.431em;text-align:center><span class=MJXp-mo id=MJXp-Span-4018 style=margin-left:0.333em;margin-right:0.333em>=</span></span><span class=MJXp-mtd id=MJXp-Span-4019 style=padding-left:0.33em;padding-top:0.431em;text-align:center><span class=MJXp-mfrac id=MJXp-Span-4020 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-4021><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4022>n</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4023>H</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-4024><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4025>c</span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-4026 style=margin-left:0.267em;margin-right:0.267em>−</span><span class=MJXp-mfrac id=MJXp-Span-4027 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-4028><span class=MJXp-msup id=MJXp-Span-4029><span class=MJXp-mrow id=MJXp-Span-4030 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4031>n</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-4032 style=vertical-align:0.5em><span class=MJXp-mn id=MJXp-Span-4033>2</span></span></span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4034>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4035>H</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-4036><span class=MJXp-msup id=MJXp-Span-4037><span class=MJXp-mrow id=MJXp-Span-4038 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4039>c</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-4040 style=vertical-align:0.5em><span class=MJXp-mn id=MJXp-Span-4041>2</span></span></span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-4042 style=margin-left:0.267em;margin-right:0.267em>+</span><span class=MJXp-mfrac id=MJXp-Span-4043 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-4044><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4045>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4046>H</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-4047><span class=MJXp-msup id=MJXp-Span-4048><span class=MJXp-mrow id=MJXp-Span-4049 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4050>c</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-4051 style=vertical-align:0.5em><span class=MJXp-mn id=MJXp-Span-4052>2</span></span></span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-4053 style=margin-left:0.267em;margin-right:0.267em>−</span><span class=MJXp-mfrac id=MJXp-Span-4054 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-4055><span class=MJXp-msup id=MJXp-Span-4056><span class=MJXp-mrow id=MJXp-Span-4057 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4058>n</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-4059 style=vertical-align:0.5em><span class=MJXp-mn id=MJXp-Span-4060>2</span></span></span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4061>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4062>H</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-4063><span class=MJXp-msup id=MJXp-Span-4064><span class=MJXp-mrow id=MJXp-Span-4065 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4066>c</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-4067 style=vertical-align:0.5em><span class=MJXp-mn id=MJXp-Span-4068>2</span></span></span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-4069 style=margin-left:0.267em;margin-right:0.267em>−</span><span class=MJXp-mfrac id=MJXp-Span-4070 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-4071><span class=MJXp-msup id=MJXp-Span-4072><span class=MJXp-mrow id=MJXp-Span-4073 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4074>n</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-4075 style=vertical-align:0.5em><span class=MJXp-mn id=MJXp-Span-4076>2</span></span></span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4077>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4078>L</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-4079><span class=MJXp-msup id=MJXp-Span-4080><span class=MJXp-mrow id=MJXp-Span-4081 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4082>c</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-4083 style=vertical-align:0.5em><span class=MJXp-mn id=MJXp-Span-4084>2</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span class="mjx-chtml MJXc-display MJXc-processing sf-hidden"></span>
</span>
</div><p>
<div class=formula id=j_phys-2023-0110_eq_013>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class="MJXp-math MJXp-display" id=MJXp-Span-4085><span class=MJXp-msub id=MJXp-Span-4086><span class=MJXp-mrow id=MJXp-Span-4087 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4088>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-4089 style=vertical-align:-0.4em><span class=MJXp-mo id=MJXp-Span-4090>⇒</span></span></span><span class=MJXp-mo id=MJXp-Span-4091 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-msub id=MJXp-Span-4092><span class=MJXp-mrow id=MJXp-Span-4093 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4094>t</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-4095 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-4096>1</span></span></span><span class=MJXp-mo id=MJXp-Span-4097 style=margin-left:0.267em;margin-right:0.267em>+</span><span class=MJXp-msub id=MJXp-Span-4098><span class=MJXp-mrow id=MJXp-Span-4099 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4100>t</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-4101 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-4102>2</span></span></span><span class=MJXp-mo id=MJXp-Span-4103 style=margin-left:0.267em;margin-right:0.267em>+</span><span class=MJXp-msub id=MJXp-Span-4104><span class=MJXp-mrow id=MJXp-Span-4105 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4106>t</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-4107 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-4108>3</span></span></span><span class=MJXp-mo id=MJXp-Span-4109 style=margin-left:0.267em;margin-right:0.267em>+</span><span class=MJXp-msub id=MJXp-Span-4110><span class=MJXp-mrow id=MJXp-Span-4111 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4112>t</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-4113 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-4114>4</span></span></span><span class=MJXp-mo id=MJXp-Span-4115 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-mfrac id=MJXp-Span-4116 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-4117><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4118>n</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4119>P</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-4120><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4121>c</span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-4122 style=margin-left:0.267em;margin-right:0.267em>−</span><span class=MJXp-msup id=MJXp-Span-4123><span class=MJXp-mrow id=MJXp-Span-4124 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4125>n</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-4126 style=vertical-align:0.5em><span class=MJXp-mn id=MJXp-Span-4127>2</span></span></span><span class=MJXp-mfrac id=MJXp-Span-4128 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-4129><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4130>v</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-4131><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4132>c</span></span></span></span></span></span></span><span class=MJXp-mfrac id=MJXp-Span-4133 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-4134><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4135>P</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-4136><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4137>c</span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-4138 style=margin-left:0.267em;margin-right:0.267em>+</span><span class=MJXp-mfrac id=MJXp-Span-4139 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-4140><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4141>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4142>L</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-4143><span class=MJXp-msup id=MJXp-Span-4144><span class=MJXp-mrow id=MJXp-Span-4145 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4146>c</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-4147 style=vertical-align:0.5em><span class=MJXp-mn id=MJXp-Span-4148>2</span></span></span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-4149 style=margin-left:0em;margin-right:0.222em>.</span></span></span><span class="mjx-chtml MJXc-display MJXc-processing sf-hidden"></span>
</span>
</div><p>
</p>
<p>
<strong>S-RLSE medium locally at rest with the device</strong>
<span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-4150><span class=MJXp-msup id=MJXp-Span-4151><span class=MJXp-mrow id=MJXp-Span-4152 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-4153>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-4154 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-4155>*</span></span></span></span></span><span id=MathJax-Element-357-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>. <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-4156><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4157>P</span><span class=MJXp-mo id=MJXp-Span-4158 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-mn id=MJXp-Span-4159>2</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4160>L</span><span class=MJXp-mo id=MJXp-Span-4161 style=margin-left:0.267em;margin-right:0.267em>+</span><span class=MJXp-mn id=MJXp-Span-4162>2</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4163>H</span></span></span><span id=MathJax-Element-358-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>.</p>
<p>For the contour of <a href=#j_phys-2023-0110_fig_005 class="link link-fig" data-bs-target=j_phys-2023-0110_fig_005>Figure A1</a>(b), we calculate with the LT to the first order in <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-4164><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4165>v</span><span class=MJXp-mo id=MJXp-Span-4166 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4167>c</span></span></span><span id=MathJax-Element-359-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> the time intervals taken by the counter-propagating photon to cover the optical fiber sliding on the moving rectangular contour.</p>
<p>Position 1: Starting from <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-4168><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4169>D</span><span class=MJXp-mo id=MJXp-Span-4170 style=margin-left:0.333em;margin-right:0.333em>=</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4171>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4172>t</span></span></span><span id=MathJax-Element-360-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>, by means of the equation <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-4173><span class=MJXp-msub id=MJXp-Span-4174><span class=MJXp-mrow id=MJXp-Span-4175 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4176>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-4177 style=vertical-align:-0.4em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4178>n</span></span></span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4179>t</span><span class=MJXp-mo id=MJXp-Span-4180 style=margin-left:0.333em;margin-right:0.333em>=</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4181>L</span><span class=MJXp-mo id=MJXp-Span-4182 style=margin-left:0.267em;margin-right:0.267em>−</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4183>D</span><span class=MJXp-mo id=MJXp-Span-4184 style=margin-left:0.267em;margin-right:0.267em>+</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4185>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4186>t</span></span></span><span id=MathJax-Element-361-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> with <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-4187><span class=MJXp-msub id=MJXp-Span-4188><span class=MJXp-mrow id=MJXp-Span-4189 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4190>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-4191 style=vertical-align:-0.4em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4192>n</span></span></span></span></span><span id=MathJax-Element-362-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> the light speed relative to <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-4193><span class=MJXp-msup id=MJXp-Span-4194><span class=MJXp-mrow id=MJXp-Span-4195 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-4196>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-4197 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-4198>*</span></span></span></span></span><span id=MathJax-Element-363-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> along the fiber at rest, we have, <div class=formula id=j_phys-2023-0110_eq_014>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class="MJXp-math MJXp-display" id=MJXp-Span-4199><span class=MJXp-mtable id=MJXp-Span-4200><span><span class=MJXp-mtr id=MJXp-Span-4201 style=vertical-align:baseline><span class=MJXp-mtd id=MJXp-Span-4202 style=text-align:center><span class=MJXp-msub id=MJXp-Span-4203><span class=MJXp-mrow id=MJXp-Span-4204 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4205>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-4206 style=vertical-align:-0.4em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4207>n</span></span></span></span><span class=MJXp-mtd id=MJXp-Span-4208 style=padding-left:0.33em;text-align:center><span class=MJXp-mo id=MJXp-Span-4209 style=margin-left:0.333em;margin-right:0.333em>=</span></span><span class=MJXp-mtd id=MJXp-Span-4210 style=padding-left:0.33em;text-align:center><span class=MJXp-mfrac id=MJXp-Span-4211 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-4212><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4213>c</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-4214><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4215>n</span></span></span></span></span></span></span></span></span><span class=MJXp-mtr id=MJXp-Span-4216 style=vertical-align:baseline><span class=MJXp-mtd id=MJXp-Span-4217 style=padding-top:0.431em;text-align:center><span class=MJXp-msub id=MJXp-Span-4218><span class=MJXp-mrow id=MJXp-Span-4219 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4220>t</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-4221 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-4222>1</span></span></span></span><span class=MJXp-mtd id=MJXp-Span-4223 style=padding-left:0.33em;padding-top:0.431em;text-align:center><span class=MJXp-mo id=MJXp-Span-4224 style=margin-left:0.333em;margin-right:0.333em>=</span></span><span class=MJXp-mtd id=MJXp-Span-4225 style=padding-left:0.33em;padding-top:0.431em;text-align:center><span class=MJXp-mfrac id=MJXp-Span-4226 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-4227><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4228>L</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-4229><span class=MJXp-msub id=MJXp-Span-4230><span class=MJXp-mrow id=MJXp-Span-4231 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4232>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-4233 style=vertical-align:-0.4em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4234>n</span></span></span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-4235 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-mfrac id=MJXp-Span-4236 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-4237><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4238>n</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4239>L</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-4240><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4241>c</span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-4242 style=margin-left:0em;margin-right:0.222em>.</span></span></span></span></span></span></span><span class="mjx-chtml MJXc-display MJXc-processing sf-hidden"></span>
</span>
</div><p>
</p>
<p>Position 2: From the equation <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-4243><span class=MJXp-msub id=MJXp-Span-4244><span class=MJXp-mrow id=MJXp-Span-4245 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4246>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-4247 style=vertical-align:-0.4em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4248>n</span></span></span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4249>t</span><span class=MJXp-mo id=MJXp-Span-4250 style=margin-left:0.333em;margin-right:0.333em>=</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4251>H</span><span class=MJXp-mo id=MJXp-Span-4252 style=margin-left:0.267em;margin-right:0.267em>−</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4253>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4254>t</span></span></span><span id=MathJax-Element-365-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> and with the optical fiber at speed <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-4255><span class=MJXp-mn id=MJXp-Span-4256>2</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4257>v</span></span></span><span id=MathJax-Element-366-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> relative to <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-4258><span class=MJXp-msup id=MJXp-Span-4259><span class=MJXp-mrow id=MJXp-Span-4260 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-4261>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-4262 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-4263>*</span></span></span></span></span><span id=MathJax-Element-367-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>, <div class=formula id=j_phys-2023-0110_eq_015>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class="MJXp-math MJXp-display" id=MJXp-Span-4264><span class=MJXp-mtable id=MJXp-Span-4265><span><span class=MJXp-mtr id=MJXp-Span-4266 style=vertical-align:baseline><span class=MJXp-mtd id=MJXp-Span-4267 style=text-align:center><span class=MJXp-msub id=MJXp-Span-4268><span class=MJXp-mrow id=MJXp-Span-4269 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4270>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-4271 style=vertical-align:-0.4em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4272>n</span></span></span></span><span class=MJXp-mtd id=MJXp-Span-4273 style=padding-left:0.33em;text-align:center><span class=MJXp-mo id=MJXp-Span-4274 style=margin-left:0.333em;margin-right:0.333em>=</span></span><span class=MJXp-mtd id=MJXp-Span-4275 style=padding-left:0.33em;text-align:center><span class=MJXp-mfrac id=MJXp-Span-4276 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-4277><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4278>c</span><span class=MJXp-mo id=MJXp-Span-4279 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4280>n</span><span class=MJXp-mo id=MJXp-Span-4281 style=margin-left:0.267em;margin-right:0.267em>−</span><span class=MJXp-mn id=MJXp-Span-4282>2</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4283>v</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-4284><span class=MJXp-mn id=MJXp-Span-4285>1</span><span class=MJXp-mo id=MJXp-Span-4286 style=margin-left:0.267em;margin-right:0.267em>−</span><span class=MJXp-mn id=MJXp-Span-4287>2</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4288>v</span><span class=MJXp-mo id=MJXp-Span-4289 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4290>n</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4291>c</span></span></span></span></span></span></span></span></span><span class=MJXp-mtr id=MJXp-Span-4292 style=vertical-align:baseline><span class=MJXp-mtd id=MJXp-Span-4293 style=padding-top:0.431em;text-align:center><span class=MJXp-msub id=MJXp-Span-4294><span class=MJXp-mrow id=MJXp-Span-4295 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4296>t</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-4297 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-4298>2</span></span></span></span><span class=MJXp-mtd id=MJXp-Span-4299 style=padding-left:0.33em;padding-top:0.431em;text-align:center><span class=MJXp-mo id=MJXp-Span-4300 style=margin-left:0.333em;margin-right:0.333em>=</span></span><span class=MJXp-mtd id=MJXp-Span-4301 style=padding-left:0.33em;padding-top:0.431em;text-align:center><span class=MJXp-mfrac id=MJXp-Span-4302 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-4303><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4304>H</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-4305><span class=MJXp-msub id=MJXp-Span-4306><span class=MJXp-mrow id=MJXp-Span-4307 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4308>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-4309 style=vertical-align:-0.4em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4310>n</span></span></span><span class=MJXp-mo id=MJXp-Span-4311 style=margin-left:0.267em;margin-right:0.267em>+</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4312>v</span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-4313 style=margin-left:0.333em;margin-right:0.333em>≃</span><span class=MJXp-mfrac id=MJXp-Span-4314 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-4315><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4316>n</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4317>H</span><span class=MJXp-mrow id=MJXp-Span-4318><span class=MJXp-mo id=MJXp-Span-4319 style=margin-left:0em;margin-right:0em>(</span><span class=MJXp-mrow id=MJXp-Span-4320><span class=MJXp-mn id=MJXp-Span-4321>1</span><span class=MJXp-mo id=MJXp-Span-4322 style=margin-left:0.267em;margin-right:0.267em>−</span><span class=MJXp-mn id=MJXp-Span-4323>2</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4324>v</span><span class=MJXp-mo id=MJXp-Span-4325 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4326>n</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4327>c</span></span><span class=MJXp-mo id=MJXp-Span-4328 style=margin-left:0em;margin-right:0em>)</span></span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-4329><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4330>c</span><span class=MJXp-mrow id=MJXp-Span-4331><span class=MJXp-mo id=MJXp-Span-4332 style=margin-left:0em;margin-right:0em>(</span><span class=MJXp-mrow id=MJXp-Span-4333><span class=MJXp-mn id=MJXp-Span-4334>1</span><span class=MJXp-mo id=MJXp-Span-4335 style=margin-left:0.267em;margin-right:0.267em>−</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4336>n</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4337>v</span><span class=MJXp-mo id=MJXp-Span-4338 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4339>c</span></span><span class=MJXp-mo id=MJXp-Span-4340 style=margin-left:0em;margin-right:0em>)</span></span></span></span></span></span></span></span></span></span><span class=MJXp-mtr id=MJXp-Span-4341 style=vertical-align:baseline><span class=MJXp-mtd id=MJXp-Span-4342 style=padding-top:0.431em;text-align:center></span><span class=MJXp-mtd id=MJXp-Span-4343 style=padding-left:0.33em;padding-top:0.431em;text-align:center><span class=MJXp-mo id=MJXp-Span-4344 style=margin-left:0.333em;margin-right:0.333em>≃</span></span><span class=MJXp-mtd id=MJXp-Span-4345 style=padding-left:0.33em;padding-top:0.431em;text-align:center><span class=MJXp-mfrac id=MJXp-Span-4346 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-4347><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4348>n</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4349>H</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-4350><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4351>c</span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-4352 style=margin-left:0.267em;margin-right:0.267em>+</span><span class=MJXp-mfrac id=MJXp-Span-4353 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-4354><span class=MJXp-msup id=MJXp-Span-4355><span class=MJXp-mrow id=MJXp-Span-4356 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4357>n</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-4358 style=vertical-align:0.5em><span class=MJXp-mn id=MJXp-Span-4359>2</span></span></span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4360>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4361>H</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-4362><span class=MJXp-msup id=MJXp-Span-4363><span class=MJXp-mrow id=MJXp-Span-4364 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4365>c</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-4366 style=vertical-align:0.5em><span class=MJXp-mn id=MJXp-Span-4367>2</span></span></span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-4368 style=margin-left:0.267em;margin-right:0.267em>−</span><span class=MJXp-mfrac id=MJXp-Span-4369 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-4370><span class=MJXp-mn id=MJXp-Span-4371>2</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4372>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4373>H</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-4374><span class=MJXp-msup id=MJXp-Span-4375><span class=MJXp-mrow id=MJXp-Span-4376 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4377>c</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-4378 style=vertical-align:0.5em><span class=MJXp-mn id=MJXp-Span-4379>2</span></span></span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-4380 style=margin-left:0em;margin-right:0.222em>.</span></span></span></span></span></span></span><span class="mjx-chtml MJXc-display MJXc-processing sf-hidden"></span>
</span>
</div><p>
</p>
<div class=figure-wrapper id=j_phys-2023-0110_fig_005><div class="figure w-100"><div class=graphic><img loading=lazy 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" alt="Figure A1
(a) Optical fiber of index
n
n
locally at rest on the rectangular contour moving with velocity
v
v
relative to the stationary clock
C
*
{{\rm{C}}}^{* }
. The photon starts from
C
*
{{\rm{C}}}^{* }
at the distance
D
D
from the contour left side
H
H
and returns to
C
*
{{\rm{C}}}^{* }
in the interval
T
⇒
{T}_{\Rightarrow }
after traveling along the contour sides at different speeds
C
n
{C}_{n}
relative to
C
*
{{\rm{C}}}^{* }
. (b) Optical fiber of index
n
n
locally at rest with
C
*
{{\rm{C}}}^{* }
and sliding on the rectangular contour moving with velocity
v
v
relative to the stationary clock
C
*
{{\rm{C}}}^{* }
. In position 1, the fiber in the lower contour section is at rest relative to
C
*
{{\rm{C}}}^{* }
. In 2, the sliding fiber has speed
2
v
2v
relative to
C
*
{{\rm{C}}}^{* }
. In 3, the relative speed is
v
v
and in 4, the fiber is at rest relative to
C
*
{{\rm{C}}}^{* }
.
"></div><div class="figure-description mb-3"><div class="figure-label h3"><span class=label>Figure A1</span></div><div class="figure-caption mb-2"><span class=caption><p>(a) Optical fiber of index <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-4381><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4382>n</span></span></span><span id=MathJax-Element-369-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> locally at rest on the rectangular contour moving with velocity <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-4383><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4384>v</span></span></span><span id=MathJax-Element-370-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> relative to the stationary clock <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-4385><span class=MJXp-msup id=MJXp-Span-4386><span class=MJXp-mrow id=MJXp-Span-4387 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-4388>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-4389 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-4390>*</span></span></span></span></span><span id=MathJax-Element-371-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>. The photon starts from <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-4391><span class=MJXp-msup id=MJXp-Span-4392><span class=MJXp-mrow id=MJXp-Span-4393 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-4394>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-4395 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-4396>*</span></span></span></span></span><span id=MathJax-Element-372-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> at the distance <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-4397><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4398>D</span></span></span><span id=MathJax-Element-373-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> from the contour left side <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-4399><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4400>H</span></span></span><span id=MathJax-Element-374-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> and returns to <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-4401><span class=MJXp-msup id=MJXp-Span-4402><span class=MJXp-mrow id=MJXp-Span-4403 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-4404>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-4405 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-4406>*</span></span></span></span></span><span id=MathJax-Element-375-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> in the interval <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-4407><span class=MJXp-msub id=MJXp-Span-4408><span class=MJXp-mrow id=MJXp-Span-4409 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4410>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-4411 style=vertical-align:-0.4em><span class=MJXp-mo id=MJXp-Span-4412>⇒</span></span></span></span></span><span id=MathJax-Element-376-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> after traveling along the contour sides at different speeds <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-4413><span class=MJXp-msub id=MJXp-Span-4414><span class=MJXp-mrow id=MJXp-Span-4415 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4416>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-4417 style=vertical-align:-0.4em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4418>n</span></span></span></span></span><span id=MathJax-Element-377-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> relative to <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-4419><span class=MJXp-msup id=MJXp-Span-4420><span class=MJXp-mrow id=MJXp-Span-4421 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-4422>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-4423 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-4424>*</span></span></span></span></span><span id=MathJax-Element-378-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>. (b) Optical fiber of index <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-4425><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4426>n</span></span></span><span id=MathJax-Element-379-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> locally at rest with <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-4427><span class=MJXp-msup id=MJXp-Span-4428><span class=MJXp-mrow id=MJXp-Span-4429 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-4430>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-4431 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-4432>*</span></span></span></span></span><span id=MathJax-Element-380-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> and sliding on the rectangular contour moving with velocity <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-4433><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4434>v</span></span></span><span id=MathJax-Element-381-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> relative to the stationary clock <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-4435><span class=MJXp-msup id=MJXp-Span-4436><span class=MJXp-mrow id=MJXp-Span-4437 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-4438>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-4439 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-4440>*</span></span></span></span></span><span id=MathJax-Element-382-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>. In position 1, the fiber in the lower contour section is at rest relative to <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-4441><span class=MJXp-msup id=MJXp-Span-4442><span class=MJXp-mrow id=MJXp-Span-4443 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-4444>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-4445 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-4446>*</span></span></span></span></span><span id=MathJax-Element-383-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>. In 2, the sliding fiber has speed <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-4447><span class=MJXp-mn id=MJXp-Span-4448>2</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4449>v</span></span></span><span id=MathJax-Element-384-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> relative to <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-4450><span class=MJXp-msup id=MJXp-Span-4451><span class=MJXp-mrow id=MJXp-Span-4452 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-4453>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-4454 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-4455>*</span></span></span></span></span><span id=MathJax-Element-385-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>. In 3, the relative speed is <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-4456><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4457>v</span></span></span><span id=MathJax-Element-386-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> and in 4, the fiber is at rest relative to <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-4458><span class=MJXp-msup id=MJXp-Span-4459><span class=MJXp-mrow id=MJXp-Span-4460 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-4461>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-4462 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-4463>*</span></span></span></span></span><span id=MathJax-Element-387-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>.</p></span></div></div></div></div>
<p>Position 3: By means of the equation <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-4464><span class=MJXp-msub id=MJXp-Span-4465><span class=MJXp-mrow id=MJXp-Span-4466 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4467>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-4468 style=vertical-align:-0.4em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4469>n</span></span></span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4470>t</span><span class=MJXp-mo id=MJXp-Span-4471 style=margin-left:0.333em;margin-right:0.333em>=</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4472>L</span></span></span><span id=MathJax-Element-388-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> and with the optical fiber at speed <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-4473><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4474>v</span></span></span><span id=MathJax-Element-389-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>, <div class=formula id=j_phys-2023-0110_eq_016>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class="MJXp-math MJXp-display" id=MJXp-Span-4475><span class=MJXp-mtable id=MJXp-Span-4476><span><span class=MJXp-mtr id=MJXp-Span-4477 style=vertical-align:baseline><span class=MJXp-mtd id=MJXp-Span-4478 style=text-align:center><span class=MJXp-msub id=MJXp-Span-4479><span class=MJXp-mrow id=MJXp-Span-4480 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4481>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-4482 style=vertical-align:-0.4em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4483>n</span></span></span></span><span class=MJXp-mtd id=MJXp-Span-4484 style=padding-left:0.33em;text-align:center><span class=MJXp-mo id=MJXp-Span-4485 style=margin-left:0.333em;margin-right:0.333em>≃</span></span><span class=MJXp-mtd id=MJXp-Span-4486 style=padding-left:0.33em;text-align:center><span class=MJXp-mfrac id=MJXp-Span-4487 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-4488><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4489>c</span><span class=MJXp-mo id=MJXp-Span-4490 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4491>n</span><span class=MJXp-mo id=MJXp-Span-4492 style=margin-left:0.267em;margin-right:0.267em>−</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4493>v</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-4494><span class=MJXp-mn id=MJXp-Span-4495>1</span><span class=MJXp-mo id=MJXp-Span-4496 style=margin-left:0.267em;margin-right:0.267em>−</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4497>v</span><span class=MJXp-mo id=MJXp-Span-4498 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4499>n</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4500>c</span></span></span></span></span></span></span></span></span><span class=MJXp-mtr id=MJXp-Span-4501 style=vertical-align:baseline><span class=MJXp-mtd id=MJXp-Span-4502 style=padding-top:0.431em;text-align:center><span class=MJXp-msub id=MJXp-Span-4503><span class=MJXp-mrow id=MJXp-Span-4504 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4505>t</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-4506 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-4507>3</span></span></span></span><span class=MJXp-mtd id=MJXp-Span-4508 style=padding-left:0.33em;padding-top:0.431em;text-align:center><span class=MJXp-mo id=MJXp-Span-4509 style=margin-left:0.333em;margin-right:0.333em>=</span></span><span class=MJXp-mtd id=MJXp-Span-4510 style=padding-left:0.33em;padding-top:0.431em;text-align:center><span class=MJXp-mfrac id=MJXp-Span-4511 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-4512><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4513>L</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-4514><span class=MJXp-msub id=MJXp-Span-4515><span class=MJXp-mrow id=MJXp-Span-4516 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4517>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-4518 style=vertical-align:-0.4em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4519>n</span></span></span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-4520 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-mfrac id=MJXp-Span-4521 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-4522><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4523>n</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4524>L</span><span class=MJXp-mrow id=MJXp-Span-4525><span class=MJXp-mo id=MJXp-Span-4526 style=margin-left:0em;margin-right:0em>(</span><span class=MJXp-mrow id=MJXp-Span-4527><span class=MJXp-mn id=MJXp-Span-4528>1</span><span class=MJXp-mo id=MJXp-Span-4529 style=margin-left:0.267em;margin-right:0.267em>−</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4530>v</span><span class=MJXp-mo id=MJXp-Span-4531 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4532>n</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4533>c</span></span><span class=MJXp-mo id=MJXp-Span-4534 style=margin-left:0em;margin-right:0em>)</span></span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-4535><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4536>c</span><span class=MJXp-mrow id=MJXp-Span-4537><span class=MJXp-mo id=MJXp-Span-4538 style=margin-left:0em;margin-right:0em>(</span><span class=MJXp-mrow id=MJXp-Span-4539><span class=MJXp-mn id=MJXp-Span-4540>1</span><span class=MJXp-mo id=MJXp-Span-4541 style=margin-left:0.267em;margin-right:0.267em>−</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4542>n</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4543>v</span><span class=MJXp-mo id=MJXp-Span-4544 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4545>c</span></span><span class=MJXp-mo id=MJXp-Span-4546 style=margin-left:0em;margin-right:0em>)</span></span></span></span></span></span></span></span></span></span><span class=MJXp-mtr id=MJXp-Span-4547 style=vertical-align:baseline><span class=MJXp-mtd id=MJXp-Span-4548 style=padding-top:0.431em;text-align:center></span><span class=MJXp-mtd id=MJXp-Span-4549 style=padding-left:0.33em;padding-top:0.431em;text-align:center><span class=MJXp-mo id=MJXp-Span-4550 style=margin-left:0.333em;margin-right:0.333em>≃</span></span><span class=MJXp-mtd id=MJXp-Span-4551 style=padding-left:0.33em;padding-top:0.431em;text-align:center><span class=MJXp-mfrac id=MJXp-Span-4552 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-4553><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4554>n</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4555>L</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-4556><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4557>c</span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-4558 style=margin-left:0.267em;margin-right:0.267em>+</span><span class=MJXp-mfrac id=MJXp-Span-4559 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-4560><span class=MJXp-msup id=MJXp-Span-4561><span class=MJXp-mrow id=MJXp-Span-4562 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4563>n</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-4564 style=vertical-align:0.5em><span class=MJXp-mn id=MJXp-Span-4565>2</span></span></span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4566>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4567>L</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-4568><span class=MJXp-msup id=MJXp-Span-4569><span class=MJXp-mrow id=MJXp-Span-4570 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4571>c</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-4572 style=vertical-align:0.5em><span class=MJXp-mn id=MJXp-Span-4573>2</span></span></span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-4574 style=margin-left:0.267em;margin-right:0.267em>−</span><span class=MJXp-mfrac id=MJXp-Span-4575 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-4576><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4577>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4578>L</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-4579><span class=MJXp-msup id=MJXp-Span-4580><span class=MJXp-mrow id=MJXp-Span-4581 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4582>c</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-4583 style=vertical-align:0.5em><span class=MJXp-mn id=MJXp-Span-4584>2</span></span></span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-4585 style=margin-left:0em;margin-right:0.222em>.</span></span></span></span></span></span></span><span class="mjx-chtml MJXc-display MJXc-processing sf-hidden"></span>
</span>
</div><p>
</p>
<p>Position 4: From the equation <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-4586><span class=MJXp-msub id=MJXp-Span-4587><span class=MJXp-mrow id=MJXp-Span-4588 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4589>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-4590 style=vertical-align:-0.4em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4591>n</span></span></span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4592>t</span><span class=MJXp-mo id=MJXp-Span-4593 style=margin-left:0.333em;margin-right:0.333em>=</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4594>H</span><span class=MJXp-mo id=MJXp-Span-4595 style=margin-left:0.267em;margin-right:0.267em>−</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4596>v</span><span class=MJXp-mrow id=MJXp-Span-4597><span class=MJXp-mo id=MJXp-Span-4598 style=margin-left:0em;margin-right:0em;vertical-align:-0.244em><span style=font-size:1.978em;margin-left:-0.05em class="MJXp-right MJXp-scale7">(</span></span><span class=MJXp-mrow id=MJXp-Span-4599><span class=MJXp-msub id=MJXp-Span-4600><span class=MJXp-mrow id=MJXp-Span-4601 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4602>t</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-4603 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-4604>2</span></span></span><span class=MJXp-mo id=MJXp-Span-4605 style=margin-left:0.267em;margin-right:0.267em>+</span><span class=MJXp-msub id=MJXp-Span-4606><span class=MJXp-mrow id=MJXp-Span-4607 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4608>t</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-4609 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-4610>3</span></span></span></span><span class=MJXp-mo id=MJXp-Span-4611 style=margin-left:0em;margin-right:0em;vertical-align:-0.244em><span style=font-size:1.978em;margin-left:-0.05em class="MJXp-right MJXp-scale7">)</span></span></span></span></span><span id=MathJax-Element-391-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> and with the optical fiber at rest, <div class=formula id=j_phys-2023-0110_eq_017>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class="MJXp-math MJXp-display" id=MJXp-Span-4612><span class=MJXp-msub id=MJXp-Span-4613><span class=MJXp-mrow id=MJXp-Span-4614 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4615>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-4616 style=vertical-align:-0.4em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4617>n</span></span></span><span class=MJXp-mo id=MJXp-Span-4618 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-mfrac id=MJXp-Span-4619 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-4620><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4621>c</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-4622><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4623>n</span></span></span></span></span></span></span><span class=MJXp-msub id=MJXp-Span-4624><span class=MJXp-mrow id=MJXp-Span-4625 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4626>t</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-4627 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-4628>4</span></span></span><span class=MJXp-mo id=MJXp-Span-4629 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-mfrac id=MJXp-Span-4630 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-4631><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4632>n</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4633>H</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-4634><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4635>c</span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-4636 style=margin-left:0.267em;margin-right:0.267em>−</span><span class=MJXp-mfrac id=MJXp-Span-4637 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-4638><span class=MJXp-msup id=MJXp-Span-4639><span class=MJXp-mrow id=MJXp-Span-4640 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4641>n</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-4642 style=vertical-align:0.5em><span class=MJXp-mn id=MJXp-Span-4643>2</span></span></span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4644>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4645>H</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-4646><span class=MJXp-msup id=MJXp-Span-4647><span class=MJXp-mrow id=MJXp-Span-4648 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4649>c</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-4650 style=vertical-align:0.5em><span class=MJXp-mn id=MJXp-Span-4651>2</span></span></span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-4652 style=margin-left:0.267em;margin-right:0.267em>−</span><span class=MJXp-mfrac id=MJXp-Span-4653 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-4654><span class=MJXp-msup id=MJXp-Span-4655><span class=MJXp-mrow id=MJXp-Span-4656 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4657>n</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-4658 style=vertical-align:0.5em><span class=MJXp-mn id=MJXp-Span-4659>2</span></span></span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4660>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4661>L</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-4662><span class=MJXp-msup id=MJXp-Span-4663><span class=MJXp-mrow id=MJXp-Span-4664 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4665>c</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-4666 style=vertical-align:0.5em><span class=MJXp-mn id=MJXp-Span-4667>2</span></span></span></span></span></span></span></span></span></span></span><span class="mjx-chtml MJXc-display MJXc-processing sf-hidden"></span>
</span>
</div><p>
<div class=formula id=j_phys-2023-0110_eq_018>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class="MJXp-math MJXp-display" id=MJXp-Span-4668><span class=MJXp-msub id=MJXp-Span-4669><span class=MJXp-mrow id=MJXp-Span-4670 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4671>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-4672 style=vertical-align:-0.4em><span class=MJXp-mo id=MJXp-Span-4673>⇒</span></span></span><span class=MJXp-mo id=MJXp-Span-4674 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-msub id=MJXp-Span-4675><span class=MJXp-mrow id=MJXp-Span-4676 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4677>t</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-4678 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-4679>1</span></span></span><span class=MJXp-mo id=MJXp-Span-4680 style=margin-left:0.267em;margin-right:0.267em>+</span><span class=MJXp-msub id=MJXp-Span-4681><span class=MJXp-mrow id=MJXp-Span-4682 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4683>t</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-4684 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-4685>2</span></span></span><span class=MJXp-mo id=MJXp-Span-4686 style=margin-left:0.267em;margin-right:0.267em>+</span><span class=MJXp-msub id=MJXp-Span-4687><span class=MJXp-mrow id=MJXp-Span-4688 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4689>t</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-4690 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-4691>3</span></span></span><span class=MJXp-mo id=MJXp-Span-4692 style=margin-left:0.267em;margin-right:0.267em>+</span><span class=MJXp-msub id=MJXp-Span-4693><span class=MJXp-mrow id=MJXp-Span-4694 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4695>t</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-4696 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-4697>4</span></span></span><span class=MJXp-mo id=MJXp-Span-4698 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-mfrac id=MJXp-Span-4699 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-4700><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4701>P</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-4702><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4703>c</span></span></span></span></span></span></span><span class=MJXp-mfenced id=MJXp-Span-4704><span class=MJXp-mo id=MJXp-Span-4705 style=margin-left:0em;margin-right:0em;vertical-align:-0.5em><span style=font-size:3em;margin-left:-0.13em class="MJXp-right MJXp-scale5">(</span></span><span class=MJXp-mrow id=MJXp-Span-4706><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4707>n</span><span class=MJXp-mo id=MJXp-Span-4708 style=margin-left:0.267em;margin-right:0.267em>−</span><span class=MJXp-mfrac id=MJXp-Span-4709 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-4710><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4711>v</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-4712><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4713>c</span></span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-4714 style=margin-left:0em;margin-right:0em;vertical-align:-0.5em><span style=font-size:3em;margin-left:-0.13em class="MJXp-right MJXp-scale5">)</span></span></span><span class=MJXp-mo id=MJXp-Span-4715 style=margin-left:0.267em;margin-right:0.267em>+</span><span class=MJXp-mfrac id=MJXp-Span-4716 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-4717><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4718>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4719>L</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-4720><span class=MJXp-msup id=MJXp-Span-4721><span class=MJXp-mrow id=MJXp-Span-4722 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4723>c</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-4724 style=vertical-align:0.5em><span class=MJXp-mn id=MJXp-Span-4725>2</span></span></span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-4726 style=margin-left:0em;margin-right:0.222em>.</span></span></span><span class="mjx-chtml MJXc-display MJXc-processing sf-hidden"></span>
</span>
</div><p>
</p>
</section>
<section id=j_phys-2023-0110_s_006>
<h3 class=subheading>A.2 Interpreting optical effects and the RLSE in the scenario of relativistic theories</h3>
<p>Several authors [<a href=#j_phys-2023-0110_ref_004 class="link link-bibr" data-bs-target=j_phys-2023-0110_ref_004 data-bs-toggle=tooltip title="[4] Lee C. Simultaneity in cylindrical spacetime. Am J Phys. 2020;88:131. 10.1119/10.0000002Search in Google Scholar">4</a>,<a href=#j_phys-2023-0110_ref_013 class="link link-bibr" data-bs-target=j_phys-2023-0110_ref_013 data-bs-toggle=tooltip title="[13] Mansouri R, Sexl RU. A test theory of special relativity: I. Simultaneity and clock synchronization. Gen Rel Grav. 1977;8:497, 515, 809. 10.1007/BF00762634Search in Google Scholar">13</a>,<a href=#j_phys-2023-0110_ref_019 class="link link-bibr" data-bs-target=j_phys-2023-0110_ref_019 data-bs-toggle=tooltip title="[19] Tangherlini FR. An introduction to the general theory of relativity. Nuovo Cimento Suppl. 1961;20:1. 10.1007/BF02746778Search in Google Scholar">19</a>–<a href=#j_phys-2023-0110_ref_023 class="link link-bibr" data-bs-target=j_phys-2023-0110_ref_023 data-bs-toggle=tooltip title="[23] Anderson R, Vetharaniam I, Stedman GE. Conventionality of synchronisation, gauge dependence and test theories of relativity. Phys Rep. 1998;295:93–180. 10.1016/S0370-1573(97)00051-3Search in Google Scholar">23</a>] argue that the LT are physically equivalent to alternative coordinate transformations that differ from the LT by an arbitrary clock synchronization parameter only. Thus, these authors claim that the one-way light speed is undetermined, or conventional, when measured by two spatially separated clocks that can be arbitrarily synchronized. In the framework of relativistic theories [<a href=#j_phys-2023-0110_ref_013 class="link link-bibr" data-bs-target=j_phys-2023-0110_ref_013 data-bs-toggle=tooltip title="[13] Mansouri R, Sexl RU. A test theory of special relativity: I. Simultaneity and clock synchronization. Gen Rel Grav. 1977;8:497, 515, 809. 10.1007/BF00762634Search in Google Scholar">13</a>], the coordinate transformations alternative to the LT, more often used to describe physical phenomena, are denoted as LTs based on absolute simultaneity (LTA). The LT and the LTA are expressed as, <div class=formula id=j_phys-2023-0110_eq_019>
<span class=label>(A1)</span>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class="MJXp-math MJXp-display" id=MJXp-Span-4727><span class=MJXp-mtable id=MJXp-Span-4728><span><span class=MJXp-mtr id=MJXp-Span-4729 style=vertical-align:baseline><span class=MJXp-mtd id=MJXp-Span-4730 style=text-align:center><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4731>L</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4732>T</span><span class=MJXp-mspace id=MJXp-Span-4733 style=width:1em;height:0em></span><span class=MJXp-msup id=MJXp-Span-4734><span class=MJXp-mrow id=MJXp-Span-4735 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4736>t</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-4737 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-4738>′</span></span></span></span><span class=MJXp-mtd id=MJXp-Span-4739 style=padding-left:0.33em;text-align:center><span class=MJXp-mo id=MJXp-Span-4740 style=margin-left:0.333em;margin-right:0.333em>=</span></span><span class=MJXp-mtd id=MJXp-Span-4741 style=padding-left:0.33em;text-align:center><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4742>γ</span><span class=MJXp-mrow id=MJXp-Span-4743><span class=MJXp-mo id=MJXp-Span-4744 style=margin-left:0em;margin-right:0em;vertical-align:-0.289em><span style=font-size:2.156em;margin-left:-0.09em class="MJXp-right MJXp-scale6">(</span></span><span class=MJXp-mrow id=MJXp-Span-4745><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4746>t</span><span class=MJXp-mo id=MJXp-Span-4747 style=margin-left:0.267em;margin-right:0.267em>−</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4748>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4749>x</span><span class=MJXp-mo id=MJXp-Span-4750 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class=MJXp-msup id=MJXp-Span-4751><span class=MJXp-mrow id=MJXp-Span-4752 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4753>c</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-4754 style=vertical-align:0.5em><span class=MJXp-mn id=MJXp-Span-4755>2</span></span></span></span><span class=MJXp-mo id=MJXp-Span-4756 style=margin-left:0em;margin-right:0em;vertical-align:-0.289em><span style=font-size:2.156em;margin-left:-0.09em class="MJXp-right MJXp-scale6">)</span></span></span><span class=MJXp-mspace id=MJXp-Span-4757 style=width:1em;height:0em></span><span class=MJXp-msup id=MJXp-Span-4758><span class=MJXp-mrow id=MJXp-Span-4759 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4760>x</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-4761 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-4762>′</span></span></span><span class=MJXp-mo id=MJXp-Span-4763 style=margin-left:0.333em;margin-right:0.333em>=</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4764>γ</span><span class=MJXp-mrow id=MJXp-Span-4765><span class=MJXp-mo id=MJXp-Span-4766 style=margin-left:0em;margin-right:0em>(</span><span class=MJXp-mrow id=MJXp-Span-4767><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4768>x</span><span class=MJXp-mo id=MJXp-Span-4769 style=margin-left:0.267em;margin-right:0.267em>−</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4770>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4771>t</span></span><span class=MJXp-mo id=MJXp-Span-4772 style=margin-left:0em;margin-right:0em>)</span></span></span></span><span class=MJXp-mtr id=MJXp-Span-4773 style=vertical-align:baseline><span class=MJXp-mtd id=MJXp-Span-4774 style=padding-top:0.431em;text-align:center><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4775>L</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4776>T</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4777>A</span><span class=MJXp-mspace id=MJXp-Span-4778 style=width:1em;height:0em></span><span class=MJXp-msup id=MJXp-Span-4779><span class=MJXp-mrow id=MJXp-Span-4780 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4781>t</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-4782 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-4783>′</span></span></span></span><span class=MJXp-mtd id=MJXp-Span-4784 style=padding-left:0.33em;padding-top:0.431em;text-align:center><span class=MJXp-mo id=MJXp-Span-4785 style=margin-left:0.333em;margin-right:0.333em>=</span></span><span class=MJXp-mtd id=MJXp-Span-4786 style=padding-left:0.33em;padding-top:0.431em;text-align:center><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4787>t</span><span class=MJXp-mo id=MJXp-Span-4788 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4789>γ</span><span class=MJXp-mspace id=MJXp-Span-4790 style=width:1em;height:0em></span><span class=MJXp-msup id=MJXp-Span-4791><span class=MJXp-mrow id=MJXp-Span-4792 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4793>x</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-4794 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-4795>′</span></span></span><span class=MJXp-mo id=MJXp-Span-4796 style=margin-left:0.333em;margin-right:0.333em>=</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4797>γ</span><span class=MJXp-mrow id=MJXp-Span-4798><span class=MJXp-mo id=MJXp-Span-4799 style=margin-left:0em;margin-right:0em>(</span><span class=MJXp-mrow id=MJXp-Span-4800><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4801>x</span><span class=MJXp-mo id=MJXp-Span-4802 style=margin-left:0.267em;margin-right:0.267em>−</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4803>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4804>t</span></span><span class=MJXp-mo id=MJXp-Span-4805 style=margin-left:0em;margin-right:0em>)</span></span><span class=MJXp-mo id=MJXp-Span-4806 style=margin-left:0em;margin-right:0.222em>,</span></span></span></span></span></span></span><span class="mjx-chtml MJXc-display MJXc-processing sf-hidden"></span>
</span>
</div><p> where in (<a href=#j_phys-2023-0110_eq_019 class="link link-disp-formula" data-bs-target=j_phys-2023-0110_eq_019>A1</a>)<span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-4807><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4808>v</span></span></span><span id=MathJax-Element-395-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> indicates the velocity of frame <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-4809><span class=MJXp-msup id=MJXp-Span-4810><span class=MJXp-mrow id=MJXp-Span-4811 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4812>S</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-4813 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-4814>′</span></span></span></span></span><span id=MathJax-Element-396-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> relative to frame <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-4815><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4816>S</span></span></span><span id=MathJax-Element-397-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> and the transformations <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-4817><span class=MJXp-msup id=MJXp-Span-4818><span class=MJXp-mrow id=MJXp-Span-4819 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4820>y</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-4821 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-4822>′</span></span></span><span class=MJXp-mo id=MJXp-Span-4823 style=margin-left:0.333em;margin-right:0.333em>=</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4824>y</span><span class=MJXp-mo id=MJXp-Span-4825 style=margin-left:0em;margin-right:0.222em>;</span><span class=MJXp-mspace id=MJXp-Span-4826 style=width:0.33em;height:0em></span><span class=MJXp-msup id=MJXp-Span-4827><span class=MJXp-mrow id=MJXp-Span-4828 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4829>z</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-4830 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-4831>′</span></span></span><span class=MJXp-mo id=MJXp-Span-4832 style=margin-left:0.333em;margin-right:0.333em>=</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4833>z</span></span></span><span id=MathJax-Element-398-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> are understood. With the factor <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-4834><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4835>γ</span><span class=MJXp-mo id=MJXp-Span-4836 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-msup id=MJXp-Span-4837><span class=MJXp-mrow id=MJXp-Span-4838 style=margin-right:0.05em><span class=MJXp-mrow id=MJXp-Span-4839><span class=MJXp-mo id=MJXp-Span-4840 style=margin-left:0em;margin-right:0em;vertical-align:-0.289em><span style=font-size:2.156em;margin-left:-0.09em class="MJXp-right MJXp-scale6">(</span></span><span class=MJXp-mrow id=MJXp-Span-4841><span class=MJXp-mn id=MJXp-Span-4842>1</span><span class=MJXp-mo id=MJXp-Span-4843 style=margin-left:0.267em;margin-right:0.267em>−</span><span class=MJXp-msup id=MJXp-Span-4844><span class=MJXp-mrow id=MJXp-Span-4845 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4846>v</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-4847 style=vertical-align:0.5em><span class=MJXp-mn id=MJXp-Span-4848>2</span></span></span><span class=MJXp-mo id=MJXp-Span-4849 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class=MJXp-msup id=MJXp-Span-4850><span class=MJXp-mrow id=MJXp-Span-4851 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4852>c</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-4853 style=vertical-align:0.5em><span class=MJXp-mn id=MJXp-Span-4854>2</span></span></span></span><span class=MJXp-mo id=MJXp-Span-4855 style=margin-left:0em;margin-right:0em;vertical-align:-0.289em><span style=font-size:2.156em;margin-left:-0.09em class="MJXp-right MJXp-scale6">)</span></span></span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-4856 style=vertical-align:0.82em><span class=MJXp-mo id=MJXp-Span-4857>−</span><span class=MJXp-mn id=MJXp-Span-4858>1</span><span class=MJXp-mo id=MJXp-Span-4859>⁄</span><span class=MJXp-mn id=MJXp-Span-4860>2</span></span></span></span></span><span id=MathJax-Element-399-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> depending on <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-4861><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4862>v</span></span></span><span id=MathJax-Element-400-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>, LT stands for the LTs, based on standard synchrony and relative simultaneity. LTA stands for the LTs based on absolute synchrony and simultaneity. To the first order in <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-4863><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4864>v</span><span class=MJXp-mo id=MJXp-Span-4865 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4866>c</span></span></span><span id=MathJax-Element-401-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>, the LTA coincides with the Galileo transformations. The LTA (or ALT in Ref. [<a href=#j_phys-2023-0110_ref_009 class="link link-bibr" data-bs-target=j_phys-2023-0110_ref_009 data-bs-toggle=tooltip title="[9] Kipreos ET, Balachandran RS. An approach to directly probe simultaneity. Modern Phys Lett A. 2016;31(26):1650157; Assessment of the relativistic rotational transformations. Modern Physics Letters A. 2021;36(16):2150113. Search in Google Scholar">9</a>]) are known in literature also as the Tangherlini–Selleri transformations [<a href=#j_phys-2023-0110_ref_006 class="link link-bibr" data-bs-target=j_phys-2023-0110_ref_006 data-bs-toggle=tooltip title="[6] Selleri F. Noninvariant one-way velocity of light. Found Phys. 1996;26:641. Noninvariant one-way speed of light and locally equivalent reference frames. Found Phys Lett. 1997;10:73–83. 10.1007/BF02764121Search in Google Scholar">6</a>,<a href=#j_phys-2023-0110_ref_019 class="link link-bibr" data-bs-target=j_phys-2023-0110_ref_019 data-bs-toggle=tooltip title="[19] Tangherlini FR. An introduction to the general theory of relativity. Nuovo Cimento Suppl. 1961;20:1. 10.1007/BF02746778Search in Google Scholar">19</a>,<a href=#j_phys-2023-0110_ref_020 class="link link-bibr" data-bs-target=j_phys-2023-0110_ref_020 data-bs-toggle=tooltip title="[20] Spavieri G, Rodriguez M, Sanchez A. Thought experiment discriminating special relativity from preferred frame theories. J Phys Commun. 2018;2:085009. 10.1088/2399-6528/aad5fa. Search in Google Scholar">20</a>], used by several authors [<a href=#j_phys-2023-0110_ref_004 class="link link-bibr" data-bs-target=j_phys-2023-0110_ref_004 data-bs-toggle=tooltip title="[4] Lee C. Simultaneity in cylindrical spacetime. Am J Phys. 2020;88:131. 10.1119/10.0000002Search in Google Scholar">4</a>–<a href=#j_phys-2023-0110_ref_009 class="link link-bibr" data-bs-target=j_phys-2023-0110_ref_009 data-bs-toggle=tooltip title="[9] Kipreos ET, Balachandran RS. An approach to directly probe simultaneity. Modern Phys Lett A. 2016;31(26):1650157; Assessment of the relativistic rotational transformations. Modern Physics Letters A. 2021;36(16):2150113. Search in Google Scholar">9</a>].</p>
<p>Because of the arbitrariness of synchronization and one-way light speed, many physicists consider the LT and LTA to be physically equivalent and, according to them, the LTA can be used to interpret all the experiments supporting standard special relativity [<a href=#j_phys-2023-0110_ref_013 class="link link-bibr" data-bs-target=j_phys-2023-0110_ref_013 data-bs-toggle=tooltip title="[13] Mansouri R, Sexl RU. A test theory of special relativity: I. Simultaneity and clock synchronization. Gen Rel Grav. 1977;8:497, 515, 809. 10.1007/BF00762634Search in Google Scholar">13</a>,<a href=#j_phys-2023-0110_ref_021 class="link link-bibr" data-bs-target=j_phys-2023-0110_ref_021 data-bs-toggle=tooltip title="[21] de AbreuR, Guerra V. On the consistency between the assumption of a special system of reference and special relativity. Found Phys. 2006;36:1826–45. 10.1007/s10701-006-9085-5Search in Google Scholar">21</a>–<a href=#j_phys-2023-0110_ref_023 class="link link-bibr" data-bs-target=j_phys-2023-0110_ref_023 data-bs-toggle=tooltip title="[23] Anderson R, Vetharaniam I, Stedman GE. Conventionality of synchronisation, gauge dependence and test theories of relativity. Phys Rep. 1998;295:93–180. 10.1016/S0370-1573(97)00051-3Search in Google Scholar">23</a>]. Certainly, the equivalence should hold in the cases when the one-way light speed is conventional because measured by two spatially separated clocks that are arbitrarily synchronized. However, in the Sagnac effects, the one-way speed of light around the contour can be determined with the single clock <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-4867><span class=MJXp-msup id=MJXp-Span-4868><span class=MJXp-mrow id=MJXp-Span-4869 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-4870>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-4871 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-4872>*</span></span></span></span></span><span id=MathJax-Element-402-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> and no arbitrary clock synchronization is involved. Thus, in relation to the difficulties pointed out in the interpretations of the Sagnac effect [<a href=#j_phys-2023-0110_ref_006 class="link link-bibr" data-bs-target=j_phys-2023-0110_ref_006 data-bs-toggle=tooltip title="[6] Selleri F. Noninvariant one-way velocity of light. Found Phys. 1996;26:641. Noninvariant one-way speed of light and locally equivalent reference frames. Found Phys Lett. 1997;10:73–83. 10.1007/BF02764121Search in Google Scholar">6</a>–<a href=#j_phys-2023-0110_ref_009 class="link link-bibr" data-bs-target=j_phys-2023-0110_ref_009 data-bs-toggle=tooltip title="[9] Kipreos ET, Balachandran RS. An approach to directly probe simultaneity. Modern Phys Lett A. 2016;31(26):1650157; Assessment of the relativistic rotational transformations. Modern Physics Letters A. 2021;36(16):2150113. Search in Google Scholar">9</a>,<a href=#j_phys-2023-0110_ref_011 class="link link-bibr" data-bs-target=j_phys-2023-0110_ref_011 data-bs-toggle=tooltip title="[11] Lundberg R. Critique of the Einstein clock variable. Phys essays. 2019;32:237; Travelling light. J Mod Opt. 2021;68(14). doi: 10.1080/09500340.2021.1945154. Search in Google Scholar">11</a>], several authors [<a href=#j_phys-2023-0110_ref_004 class="link link-bibr" data-bs-target=j_phys-2023-0110_ref_004 data-bs-toggle=tooltip title="[4] Lee C. Simultaneity in cylindrical spacetime. Am J Phys. 2020;88:131. 10.1119/10.0000002Search in Google Scholar">4</a>–<a href=#j_phys-2023-0110_ref_009 class="link link-bibr" data-bs-target=j_phys-2023-0110_ref_009 data-bs-toggle=tooltip title="[9] Kipreos ET, Balachandran RS. An approach to directly probe simultaneity. Modern Phys Lett A. 2016;31(26):1650157; Assessment of the relativistic rotational transformations. Modern Physics Letters A. 2021;36(16):2150113. Search in Google Scholar">9</a>] have shown that the difficulties are surmounted if, in lieu of the LT based on relative simultaneity, coordinate transformations based on conservation of simultaneity (LTA) are adopted.</p>
<p>Nevertheless, epistemologists [<a href=#j_phys-2023-0110_ref_024 class="link link-bibr" data-bs-target=j_phys-2023-0110_ref_024 data-bs-toggle=tooltip title="[24] Popper K. Conjectures and refutations. London: Routledge; 1963; Kuhn TS, The structure of scientific revolutions. Chicago, Illinois: University of Chicago Press; 1962. Search in Google Scholar">24</a>] claim that the basic postulates of a meaningful physical theory must be testable (<em>i.e.</em>, falsifiable). Then, if one of its basic postulates is not falsifiable, it may be argued by physicists and epistemologists [<a href=#j_phys-2023-0110_ref_024 class="link link-bibr" data-bs-target=j_phys-2023-0110_ref_024 data-bs-toggle=tooltip title="[24] Popper K. Conjectures and refutations. London: Routledge; 1963; Kuhn TS, The structure of scientific revolutions. Chicago, Illinois: University of Chicago Press; 1962. Search in Google Scholar">24</a>] that the theory is not physically meaningful. If the LT (with relative simultaneity) are equivalent to the LTA (with absolute simultaneity) and the speed of light is conventional, the <em>standard</em> theory of special relativity has a drawback because its fundamental postulate of one-way light speed invariance cannot be tested [<a href=#j_phys-2023-0110_ref_013 class="link link-bibr" data-bs-target=j_phys-2023-0110_ref_013 data-bs-toggle=tooltip title="[13] Mansouri R, Sexl RU. A test theory of special relativity: I. Simultaneity and clock synchronization. Gen Rel Grav. 1977;8:497, 515, 809. 10.1007/BF00762634Search in Google Scholar">13</a>,<a href=#j_phys-2023-0110_ref_019 class="link link-bibr" data-bs-target=j_phys-2023-0110_ref_019 data-bs-toggle=tooltip title="[19] Tangherlini FR. An introduction to the general theory of relativity. Nuovo Cimento Suppl. 1961;20:1. 10.1007/BF02746778Search in Google Scholar">19</a>–<a href=#j_phys-2023-0110_ref_023 class="link link-bibr" data-bs-target=j_phys-2023-0110_ref_023 data-bs-toggle=tooltip title="[23] Anderson R, Vetharaniam I, Stedman GE. Conventionality of synchronisation, gauge dependence and test theories of relativity. Phys Rep. 1998;295:93–180. 10.1016/S0370-1573(97)00051-3Search in Google Scholar">23</a>]. For this reason, in the more recent formulation of special relativity found in mainstream physics journals where light speed is conventional [<a href=#j_phys-2023-0110_ref_004 class="link link-bibr" data-bs-target=j_phys-2023-0110_ref_004 data-bs-toggle=tooltip title="[4] Lee C. Simultaneity in cylindrical spacetime. Am J Phys. 2020;88:131. 10.1119/10.0000002Search in Google Scholar">4</a>], the constant <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-4873><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4874>c</span></span></span><span id=MathJax-Element-403-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> in the second postulate is no longer the one-way light speed, but “<em>the round-trip speed of light (<em>i.e.</em>, the average speed of light during the round-trip from A to B and then back to A)</em>,” which is observable.</p>
<p>Nevertheless, <em>standard</em> special relativity is based on the LT and, for determining the good standing of this theory and the LT, it is essential to establish whether the LTA and the LT are, or are not, physically equivalent.</p>
<p>It is worth mentioning that in practically all the experiments supporting special relativity what is being tested are effects related to relativistic time dilation and length contraction, equally foreseen by the LT and the LTA [<a href=#j_phys-2023-0110_ref_004 class="link link-bibr" data-bs-target=j_phys-2023-0110_ref_004 data-bs-toggle=tooltip title="[4] Lee C. Simultaneity in cylindrical spacetime. Am J Phys. 2020;88:131. 10.1119/10.0000002Search in Google Scholar">4</a>–<a href=#j_phys-2023-0110_ref_009 class="link link-bibr" data-bs-target=j_phys-2023-0110_ref_009 data-bs-toggle=tooltip title="[9] Kipreos ET, Balachandran RS. An approach to directly probe simultaneity. Modern Phys Lett A. 2016;31(26):1650157; Assessment of the relativistic rotational transformations. Modern Physics Letters A. 2021;36(16):2150113. Search in Google Scholar">9</a>,<a href=#j_phys-2023-0110_ref_013 class="link link-bibr" data-bs-target=j_phys-2023-0110_ref_013 data-bs-toggle=tooltip title="[13] Mansouri R, Sexl RU. A test theory of special relativity: I. Simultaneity and clock synchronization. Gen Rel Grav. 1977;8:497, 515, 809. 10.1007/BF00762634Search in Google Scholar">13</a>]. Special relativity is a very well tested theory confirmed by high precision experiments [<a href=#j_phys-2023-0110_ref_013 class="link link-bibr" data-bs-target=j_phys-2023-0110_ref_013 data-bs-toggle=tooltip title="[13] Mansouri R, Sexl RU. A test theory of special relativity: I. Simultaneity and clock synchronization. Gen Rel Grav. 1977;8:497, 515, 809. 10.1007/BF00762634Search in Google Scholar">13</a>,<a href=#j_phys-2023-0110_ref_025 class="link link-bibr" data-bs-target=j_phys-2023-0110_ref_025 data-bs-toggle=tooltip title="[25] Eisele C, Nevsky AY, Schiller S. Laboratory test of the isotropy of light propagation at the 10−17 level. Phys Rev Lett. 2009;103:090401. 10.1103/PhysRevLett.103.090401Search in Google Scholar
PubMed
">25</a>–<a href=#j_phys-2023-0110_ref_028 class="link link-bibr" data-bs-target=j_phys-2023-0110_ref_028 data-bs-toggle=tooltip title="[28] Pruttivarasin T, Ramm M, Porsev SG, Tupitsyn II, Safronova MS, Hohensee MA, et al. Häffner H. Michelson-Morley analogue for electrons using trapped ions to test Lorentz symmetry. Nature. 2015;517:592–5. 10.1038/nature14091. Search in Google Scholar
PubMed
">28</a>]. The experiments performed so far are likely suitable to test [<a href=#j_phys-2023-0110_ref_013 class="link link-bibr" data-bs-target=j_phys-2023-0110_ref_013 data-bs-toggle=tooltip title="[13] Mansouri R, Sexl RU. A test theory of special relativity: I. Simultaneity and clock synchronization. Gen Rel Grav. 1977;8:497, 515, 809. 10.1007/BF00762634Search in Google Scholar">13</a>] the so-called relativistic effects only, which are of second (or higher) order in <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-4875><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4876>v</span><span class=MJXp-mo id=MJXp-Span-4877 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4878>c</span></span></span><span id=MathJax-Element-404-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> and are not dedicated experiments capable of testing the special different features of the LT and LTA, relative versus absolute simultaneity, because these differences vanish on average. In literature, there are proposals of dedicated experiments of first order in <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-4879><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4880>v</span><span class=MJXp-mo id=MJXp-Span-4881 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4882>c</span></span></span><span id=MathJax-Element-405-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> that might test the different features of simultaneity, relative or absolute (see, for example, [<a href=#j_phys-2023-0110_ref_007 class="link link-bibr" data-bs-target=j_phys-2023-0110_ref_007 data-bs-toggle=tooltip title="[7] Spavieri G, Gillies GT, GaarderHaug E, Sanchez A. Light propagation and local speed in the linear Sagnac effect. J Modern Optics. 2019;66(21):2131–41. 10.1080/09500340.2019.1695005. Spavieri G, Gillies GT, Gaarder Haug E. The Sagnac effect and the role of simultaneity in relativity theory. J Mod Opt. 2021. doi: 10.1080/09500340.2021.1887384. Spavieri G. On measuring the one-way speed of light. Eur Phys J D. 2012;66:76. doi: 10.1140/epjd/e2012-20524-8; Spavieri G. Light propagation on a moving closed contour and the role of simultaneity in special relativity. Eur J Appl Phys. 2021;3:4:48. doi :10.24018/ejphysics.2021.3.4.99; Spavieri G, Gaarder Haug E. Testing light speed invariance by measuring the one-way light speed on earth. Physics Open 2022;12:100113. doi: 10.1016/j.physo.2022.100113. Search in Google Scholar">7</a>,<a href=#j_phys-2023-0110_ref_020 class="link link-bibr" data-bs-target=j_phys-2023-0110_ref_020 data-bs-toggle=tooltip title="[20] Spavieri G, Rodriguez M, Sanchez A. Thought experiment discriminating special relativity from preferred frame theories. J Phys Commun. 2018;2:085009. 10.1088/2399-6528/aad5fa. Search in Google Scholar">20</a>]). However, up to now and as far as we know, no experiments of this type have been performed. Yet, as shown below, these different features can be tested by means of the RLSE also.</p>
<section id=j_phys-2023-0110_s_006_s_001>
<h4 class=subheading>A.2.1 The LTA and LT foresee different results for the RLSE</h4>
<p>In the interpretation of the optical effects of the Sagnac type with the LTA, we are looking for the preferred frame where the one-way light speed can be assumed to be <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-4883><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4884>c</span></span></span><span id=MathJax-Element-406-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>. The natural choice is given by the contour inertial rest frame <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-4885><span class=MJXp-msub id=MJXp-Span-4886><span class=MJXp-mrow id=MJXp-Span-4887 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4888>S</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-4889 style=vertical-align:-0.4em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4890>c</span></span></span></span></span><span id=MathJax-Element-407-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> where Maxwell’s equations are valid, and the electromagnetic waves, locked on the contour, propagate at speed <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-4891><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4892>c</span></span></span><span id=MathJax-Element-408-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>. With this choice of the preferred frame, from the contour inertial frame <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-4893><span class=MJXp-msub id=MJXp-Span-4894><span class=MJXp-mrow id=MJXp-Span-4895 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4896>S</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-4897 style=vertical-align:-0.4em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4898>c</span></span></span></span></span><span id=MathJax-Element-409-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>, the LTA and LT provide an equivalent interpretation with the same results.</p>
<p>If, for the RLSE of <a href=#j_phys-2023-0110_fig_002 class="link link-fig" data-bs-target=j_phys-2023-0110_fig_002>Figure 2</a>, we choose again the contour to be the preferred frame, then, we may assume that while moving with uniform velocity relative to <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-4899><span class=MJXp-msup id=MJXp-Span-4900><span class=MJXp-mrow id=MJXp-Span-4901 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-4902>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-4903 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-4904>*</span></span></span></span></span><span id=MathJax-Element-410-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> the contour is carrying along the electromagnetic waves, always propagating at the local speed <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-4905><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4906>c</span></span></span><span id=MathJax-Element-411-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> relative to the contour. With the aforementioned assumptions, we find that in the framework of the LTA, the RLSE is fully reciprocal to the linear Sagnac effect. In fact, save for the negligible time interval <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-4907><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4908>η</span></span></span><span id=MathJax-Element-412-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> when the contour changes velocity, the observer <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-4909><span class=MJXp-msub id=MJXp-Span-4910><span class=MJXp-mrow id=MJXp-Span-4911 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4912>S</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-4913 style=vertical-align:-0.4em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4914>c</span></span></span></span></span><span id=MathJax-Element-413-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> comoving with the contour of <a href=#j_phys-2023-0110_fig_002 class="link link-fig" data-bs-target=j_phys-2023-0110_fig_002>Figure 2</a> is on an inertial frame before and after the interval <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-4915><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4916>η</span></span></span><span id=MathJax-Element-414-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>. Then, as far as the RLSE is concerned, the result is independent of whether the relative change of motion is performed by <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-4917><span class=MJXp-msup id=MJXp-Span-4918><span class=MJXp-mrow id=MJXp-Span-4919 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-4920>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-4921 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-4922>*</span></span></span></span></span><span id=MathJax-Element-415-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> or the contour. Since simultaneity is conserved with the LTA, when the contour changes velocity, there are no variations in the relative positions of photon and <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-4923><span class=MJXp-msup id=MJXp-Span-4924><span class=MJXp-mrow id=MJXp-Span-4925 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-4926>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-4927 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-4928>*</span></span></span></span></span><span id=MathJax-Element-416-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>, unlike what happens with relative simultaneity in <a href=#j_phys-2023-0110_fig_003 class="link link-fig" data-bs-target=j_phys-2023-0110_fig_003>Figure 3</a>. Therefore, if calculated from the contour frame <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-4929><span class=MJXp-msub id=MJXp-Span-4930><span class=MJXp-mrow id=MJXp-Span-4931 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4932>S</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-4933 style=vertical-align:-0.4em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4934>c</span></span></span></span></span><span id=MathJax-Element-417-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>, the invariant proper time interval <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-4935><span class=MJXp-msub id=MJXp-Span-4936><span class=MJXp-mrow id=MJXp-Span-4937 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4938>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-4939 style=vertical-align:-0.4em><span class=MJXp-mo id=MJXp-Span-4940>⇒</span></span></span></span></span><span id=MathJax-Element-418-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> is the same as in the linear Sagnac effect. However, when calculated from clock frame <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-4941><span class=MJXp-msub id=MJXp-Span-4942><span class=MJXp-mrow id=MJXp-Span-4943 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4944>S</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-4945 style=vertical-align:-0.4em><span class=MJXp-msup id=MJXp-Span-4946><span class=MJXp-mrow id=MJXp-Span-4947 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-4948>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-4949 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-4950>*</span></span></span></span></span></span></span><span id=MathJax-Element-419-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> we have to take into account that with the LTA light speed is no longer invariant.</p>
<p>To verify that, with the LTA, the invariant interval <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-4951><span class=MJXp-msub id=MJXp-Span-4952><span class=MJXp-mrow id=MJXp-Span-4953 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4954>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-4955 style=vertical-align:-0.4em><span class=MJXp-mo id=MJXp-Span-4956>⇒</span></span></span></span></span><span id=MathJax-Element-420-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> in the RLSE is independent of <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-4957><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4958>D</span></span></span><span id=MathJax-Element-421-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> and the same as in the linear Sagnac effect, we calculate it from the clock frame <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-4959><span class=MJXp-msub id=MJXp-Span-4960><span class=MJXp-mrow id=MJXp-Span-4961 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4962>S</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-4963 style=vertical-align:-0.4em><span class=MJXp-msup id=MJXp-Span-4964><span class=MJXp-mrow id=MJXp-Span-4965 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-4966>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-4967 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-4968>*</span></span></span></span></span></span></span><span id=MathJax-Element-422-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> for the case when the contour changes velocity in the interval <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-4969><span class=MJXp-msub id=MJXp-Span-4970><span class=MJXp-mrow id=MJXp-Span-4971 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4972>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-4973 style=vertical-align:-0.4em><span class=MJXp-mo id=MJXp-Span-4974>⇒</span></span></span></span></span><span id=MathJax-Element-423-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>, as in <a href=#j_phys-2023-0110_fig_002 class="link link-fig" data-bs-target=j_phys-2023-0110_fig_002>Figure 2</a>. Let the photon start from <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-4975><span class=MJXp-msup id=MJXp-Span-4976><span class=MJXp-mrow id=MJXp-Span-4977 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-4978>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-4979 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-4980>*</span></span></span></span></span><span id=MathJax-Element-424-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> at <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-4981><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4982>D</span></span></span><span id=MathJax-Element-425-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> and travel toward point B moving to the right (<a href=#j_phys-2023-0110_fig_002 class="link link-fig" data-bs-target=j_phys-2023-0110_fig_002>Figure 2</a>(a)). Relative to <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-4983><span class=MJXp-msup id=MJXp-Span-4984><span class=MJXp-mrow id=MJXp-Span-4985 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-4986>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-4987 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-4988>*</span></span></span></span></span><span id=MathJax-Element-426-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>, by addition of velocities, the light speed along the moving contour is <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-4989><span class=MJXp-mo id=MJXp-Span-4990 style=margin-left:0.333em;margin-right:0.333em>≃</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4991>c</span><span class=MJXp-mo id=MJXp-Span-4992 style=margin-left:0.267em;margin-right:0.267em>+</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4993>v</span></span></span><span id=MathJax-Element-427-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>, where for simplicity we use the first-order approximation in <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-4994><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4995>v</span><span class=MJXp-mo id=MJXp-Span-4996 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4997>c</span></span></span><span id=MathJax-Element-428-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>. In the out trip and at time <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-4998><span class="MJXp-mi MJXp-italic" id=MJXp-Span-4999>t</span></span></span><span id=MathJax-Element-429-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>, point B is at the position <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-5000><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5001>L</span><span class=MJXp-mo id=MJXp-Span-5002 style=margin-left:0.267em;margin-right:0.267em>−</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5003>D</span><span class=MJXp-mo id=MJXp-Span-5004 style=margin-left:0.267em;margin-right:0.267em>+</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5005>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5006>t</span></span></span><span id=MathJax-Element-430-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> to the right of <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-5007><span class=MJXp-msup id=MJXp-Span-5008><span class=MJXp-mrow id=MJXp-Span-5009 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-5010>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-5011 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-5012>*</span></span></span></span></span><span id=MathJax-Element-431-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> and the photon reaches B when <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-5013><span class=MJXp-mrow id=MJXp-Span-5014><span class=MJXp-mo id=MJXp-Span-5015 style=margin-left:0em;margin-right:0em>(</span><span class=MJXp-mrow id=MJXp-Span-5016><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5017>c</span><span class=MJXp-mo id=MJXp-Span-5018 style=margin-left:0.267em;margin-right:0.267em>+</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5019>v</span></span><span class=MJXp-mo id=MJXp-Span-5020 style=margin-left:0em;margin-right:0em>)</span></span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5021>t</span><span class=MJXp-mo id=MJXp-Span-5022 style=margin-left:0.333em;margin-right:0.333em>=</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5023>L</span><span class=MJXp-mo id=MJXp-Span-5024 style=margin-left:0.267em;margin-right:0.267em>−</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5025>D</span><span class=MJXp-mo id=MJXp-Span-5026 style=margin-left:0.267em;margin-right:0.267em>+</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5027>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5028>t</span></span></span><span id=MathJax-Element-432-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>. Considering first the special case when simultaneity takes place, we set <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-5029><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5030>D</span><span class=MJXp-mo id=MJXp-Span-5031 style=margin-left:0.333em;margin-right:0.333em>=</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5032>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5033>t</span></span></span><span id=MathJax-Element-433-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> and, thus, <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-5034><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5035>t</span><span class=MJXp-mo id=MJXp-Span-5036 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-msub id=MJXp-Span-5037><span class=MJXp-mrow id=MJXp-Span-5038 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5039>t</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-5040 style=vertical-align:-0.4em><span class=MJXp-mi id=MJXp-Span-5041>out</span></span></span><span class=MJXp-mo id=MJXp-Span-5042 style=margin-left:0.333em;margin-right:0.333em>=</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5043>L</span><span class=MJXp-mo id=MJXp-Span-5044 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class=MJXp-mrow id=MJXp-Span-5045><span class=MJXp-mo id=MJXp-Span-5046 style=margin-left:0em;margin-right:0em>(</span><span class=MJXp-mrow id=MJXp-Span-5047><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5048>c</span><span class=MJXp-mo id=MJXp-Span-5049 style=margin-left:0.267em;margin-right:0.267em>+</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5050>v</span></span><span class=MJXp-mo id=MJXp-Span-5051 style=margin-left:0em;margin-right:0em>)</span></span></span></span><span id=MathJax-Element-434-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> and <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-5052><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5053>D</span><span class=MJXp-mo id=MJXp-Span-5054 style=margin-left:0.333em;margin-right:0.333em>=</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5055>v</span><span class=MJXp-msub id=MJXp-Span-5056><span class=MJXp-mrow id=MJXp-Span-5057 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5058>t</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-5059 style=vertical-align:-0.4em><span class=MJXp-mi id=MJXp-Span-5060>out</span></span></span><span class=MJXp-mo id=MJXp-Span-5061 style=margin-left:0.333em;margin-right:0.333em>≃</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5062>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5063>L</span><span class=MJXp-mo id=MJXp-Span-5064 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5065>c</span></span></span><span id=MathJax-Element-435-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>. Then, the two events “photon at B” and “A at <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-5066><span class=MJXp-msup id=MJXp-Span-5067><span class=MJXp-mrow id=MJXp-Span-5068 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-5069>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-5070 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-5071>*</span></span></span></span></span><span id=MathJax-Element-436-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>” are simultaneous in every frame. In the return trip on the upper section (<a href=#j_phys-2023-0110_fig_002 class="link link-fig" data-bs-target=j_phys-2023-0110_fig_002>Figure 2</a>(b)), the contour is now moving to the left, while the photon travels on the upper section toward the stationary <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-5072><span class=MJXp-msup id=MJXp-Span-5073><span class=MJXp-mrow id=MJXp-Span-5074 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-5075>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-5076 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-5077>*</span></span></span></span></span><span id=MathJax-Element-437-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> at the speed <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-5078><span class=MJXp-mo id=MJXp-Span-5079 style=margin-left:0.333em;margin-right:0.333em>≃</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5080>c</span><span class=MJXp-mo id=MJXp-Span-5081 style=margin-left:0.267em;margin-right:0.267em>+</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5082>v</span></span></span><span id=MathJax-Element-438-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>. With the photon coming from B at <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-5083><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5084>L</span></span></span><span id=MathJax-Element-439-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>, the return time interval is <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-5085><span class=MJXp-msub id=MJXp-Span-5086><span class=MJXp-mrow id=MJXp-Span-5087 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5088>t</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-5089 style=vertical-align:-0.4em><span class=MJXp-mi id=MJXp-Span-5090>ret</span></span></span><span class=MJXp-mo id=MJXp-Span-5091 style=margin-left:0.333em;margin-right:0.333em>=</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5092>L</span><span class=MJXp-mo id=MJXp-Span-5093 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class=MJXp-mrow id=MJXp-Span-5094><span class=MJXp-mo id=MJXp-Span-5095 style=margin-left:0em;margin-right:0em>(</span><span class=MJXp-mrow id=MJXp-Span-5096><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5097>c</span><span class=MJXp-mo id=MJXp-Span-5098 style=margin-left:0.267em;margin-right:0.267em>+</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5099>v</span></span><span class=MJXp-mo id=MJXp-Span-5100 style=margin-left:0em;margin-right:0em>)</span></span></span></span><span id=MathJax-Element-440-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> and the round-trip is <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-5101><span class=MJXp-msub id=MJXp-Span-5102><span class=MJXp-mrow id=MJXp-Span-5103 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5104>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-5105 style=vertical-align:-0.4em><span class=MJXp-mo id=MJXp-Span-5106>⇒</span></span></span><span class=MJXp-mo id=MJXp-Span-5107 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-msub id=MJXp-Span-5108><span class=MJXp-mrow id=MJXp-Span-5109 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5110>t</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-5111 style=vertical-align:-0.4em><span class=MJXp-mi id=MJXp-Span-5112>out</span></span></span><span class=MJXp-mo id=MJXp-Span-5113 style=margin-left:0.267em;margin-right:0.267em>+</span><span class=MJXp-msub id=MJXp-Span-5114><span class=MJXp-mrow id=MJXp-Span-5115 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5116>t</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-5117 style=vertical-align:-0.4em><span class=MJXp-mi id=MJXp-Span-5118>ret</span></span></span><span class=MJXp-mo id=MJXp-Span-5119 style=margin-left:0.333em;margin-right:0.333em>≃</span><span class=MJXp-mn id=MJXp-Span-5120>2</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5121>L</span><span class=MJXp-mo id=MJXp-Span-5122 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class=MJXp-mrow id=MJXp-Span-5123><span class=MJXp-mo id=MJXp-Span-5124 style=margin-left:0em;margin-right:0em>(</span><span class=MJXp-mrow id=MJXp-Span-5125><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5126>c</span><span class=MJXp-mo id=MJXp-Span-5127 style=margin-left:0.267em;margin-right:0.267em>+</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5128>v</span></span><span class=MJXp-mo id=MJXp-Span-5129 style=margin-left:0em;margin-right:0em>)</span></span></span></span><span id=MathJax-Element-441-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>, which is the same as in the linear Sagnac effect shown in (<a href=#j_phys-2023-0110_eq_002 class="link link-disp-formula" data-bs-target=j_phys-2023-0110_eq_002>2</a>).</p>
<p>It can be shown that the same result, independent of <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-5130><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5131>D</span></span></span><span id=MathJax-Element-442-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>, is obtained in general, <em>e.g.</em>, when the photon reaches B before A reaching <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-5132><span class=MJXp-msup id=MJXp-Span-5133><span class=MJXp-mrow id=MJXp-Span-5134 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-5135>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-5136 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-5137>*</span></span></span></span></span><span id=MathJax-Element-443-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> (or when A reaches <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-5138><span class=MJXp-msup id=MJXp-Span-5139><span class=MJXp-mrow id=MJXp-Span-5140 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-5141>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-5142 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-5143>*</span></span></span></span></span><span id=MathJax-Element-444-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> before the photon reaching B) and when <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-5144><span class=MJXp-msup id=MJXp-Span-5145><span class=MJXp-mrow id=MJXp-Span-5146 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-5147>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-5148 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-5149>*</span></span></span></span></span><span id=MathJax-Element-445-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> is always on the lower (or upper) section of the contour in the round-trip interval <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-5150><span class=MJXp-msub id=MJXp-Span-5151><span class=MJXp-mrow id=MJXp-Span-5152 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5153>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-5154 style=vertical-align:-0.4em><span class=MJXp-mo id=MJXp-Span-5155>⇒</span></span></span></span></span><span id=MathJax-Element-446-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>.</p>
<p>In conclusion, with the LTA based on absolute simultaneity, the RLSE is fully equivalent to the linear Sagnac effect and the relativity principle is holding. For the S-RLSE experiments described earlier, contrary to the LT, the LTA foresee that the variant (for the LT) function <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-5156><span class=MJXp-mi id=MJXp-Span-5157>Δ</span><span class=MJXp-msup id=MJXp-Span-5158><span class=MJXp-mrow id=MJXp-Span-5159 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5160>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-5161 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-5162>*</span></span></span><span class=MJXp-mrow id=MJXp-Span-5163><span class=MJXp-mo id=MJXp-Span-5164 style=margin-left:0em;margin-right:0em>(</span><span class=MJXp-mrow id=MJXp-Span-5165><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5166>D</span></span><span class=MJXp-mo id=MJXp-Span-5167 style=margin-left:0em;margin-right:0em>)</span></span></span></span><span id=MathJax-Element-447-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> is (for the LTA) always <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-5168><span class=MJXp-mi id=MJXp-Span-5169>Δ</span><span class=MJXp-msup id=MJXp-Span-5170><span class=MJXp-mrow id=MJXp-Span-5171 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5172>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-5173 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-5174>*</span></span></span><span class=MJXp-mo id=MJXp-Span-5175 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-mi id=MJXp-Span-5176>Δ</span><span class=MJXp-msubsup id=MJXp-Span-5177><span class=MJXp-mrow id=MJXp-Span-5178 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5179>T</span></span><span class=MJXp-script-box style=height:1.86em;vertical-align:-0.64em><span class=MJXp-script><span><span style=margin-bottom:-0.25em><span class=MJXp-mrow id=MJXp-Span-5182><span class=MJXp-mo id=MJXp-Span-5183>*</span></span></span></span></span><span class=MJXp-script><span><span style=margin-top:-0.85em><span class=MJXp-mrow id=MJXp-Span-5180><span class=MJXp-mi id=MJXp-Span-5181>Sagnac</span></span></span></span></span></span></span></span></span><span id=MathJax-Element-448-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>, independent of <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-5184><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5185>D</span></span></span><span id=MathJax-Element-449-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>. It follows that, by means of the S-RLSE, the different predictions of the LT and LTA, and light speed invariance, can be tested.</p>
<p>Another example indicating that the LT and LTA are not equivalent, and cannot be arbitrarily interchanged in the description of physical phenomena, is given by the Thomas precession, discussed below.</p>
</section>
<section id=j_phys-2023-0110_s_006_s_002>
<h4 class=subheading>A.2.2 Using the Thomas precession to discriminate relative (LT) from absolute (LTA) simultaneity</h4>
<p>In the following, we consider the relativistic phenomenon of the Thomas precession [<a href=#j_phys-2023-0110_ref_029 class="link link-bibr" data-bs-target=j_phys-2023-0110_ref_029 data-bs-toggle=tooltip title="[29] Thomas LH. The motion of the spinning electron. Nature (London). 1926;117:514; The kinematics of an electron with an axis. Phil Mag. 1927;3:1–22. Search in Google Scholar">29</a>] and find that it is predicted by the LT but not by the LTA. Since the spacetime symmetry of the LT differs from that of the LTA, it is not surprising that the two transformations predict different results. Standard special relativity is routinely used in several areas of modern physics employing the symmetry of the LTs based on relative simultaneity and the Thomas precession derived from the LT is well known for predicting the correct spin–orbit interaction energy splitting [<a href=#j_phys-2023-0110_ref_029 class="link link-bibr" data-bs-target=j_phys-2023-0110_ref_029 data-bs-toggle=tooltip title="[29] Thomas LH. The motion of the spinning electron. Nature (London). 1926;117:514; The kinematics of an electron with an axis. Phil Mag. 1927;3:1–22. Search in Google Scholar">29</a>,<a href=#j_phys-2023-0110_ref_030 class="link link-bibr" data-bs-target=j_phys-2023-0110_ref_030 data-bs-toggle=tooltip title="[30] Jackson JD. Classical Electrodynamics, Sect. 11.8. 2nd edn. New York: John Wiley &amp; Sons, Inc; 1975. Search in Google Scholar">30</a>] and is thus considered to be observable. Moreover, Thomas’ precession is included in the equation of spin motion of the BMT equation of elementary particle physics [<a href=#j_phys-2023-0110_ref_031 class="link link-bibr" data-bs-target=j_phys-2023-0110_ref_031 data-bs-toggle=tooltip title="[31] Bargmann V, Michel L, Telegdi VL. Precession of the polarization of particles moving in a homogeneous electromagnetic field. Phys Rev Lett. 1959;2:435. 10.1103/PhysRevLett.2.435Search in Google Scholar">31</a>]. However, so far there are no direct tests of the Thomas precession.</p>
<p>
<strong>Deriving the Thomas precession with the LT</strong>
</p>
<p>Here, we consider the textbook derivation made by Jackson [<a href=#j_phys-2023-0110_ref_030 class="link link-bibr" data-bs-target=j_phys-2023-0110_ref_030 data-bs-toggle=tooltip title="[30] Jackson JD. Classical Electrodynamics, Sect. 11.8. 2nd edn. New York: John Wiley &amp; Sons, Inc; 1975. Search in Google Scholar">30</a>] and indicate schematically the steps that lead to the Thomas precession. In deriving the spin precession for the case of spin–orbit interaction, Thomas considers an electron orbiting on a plane at the peripheral velocity <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-5186><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5187>v</span></span></span><span id=MathJax-Element-450-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> around the nucleus of an atom. Thomas shows that, because of the motion of the electron in its circular orbit with the acceleration <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-5188><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5189>a</span></span></span><span id=MathJax-Element-451-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> due to the Coulomb field, the electron spin acquires an extra angular velocity <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-5190><span class=MJXp-msub id=MJXp-Span-5191><span class=MJXp-mrow id=MJXp-Span-5192 style=margin-right:0.05em><span class="MJXp-mi MJXp-bold MJXp-italic" id=MJXp-Span-5193>ω</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-5194 style=vertical-align:-0.4em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5195>T</span></span></span></span></span><span id=MathJax-Element-452-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> of purely relativistic kinematical origin. The Thomas angular velocity <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-5196><span class=MJXp-msub id=MJXp-Span-5197><span class=MJXp-mrow id=MJXp-Span-5198 style=margin-right:0.05em><span class="MJXp-mi MJXp-bold MJXp-italic" id=MJXp-Span-5199>ω</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-5200 style=vertical-align:-0.4em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5201>T</span></span></span></span></span><span id=MathJax-Element-453-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>, corresponding to the rotation per unit of time of the electron frame, can be calculated from the infinitesimal LT along the electron path (shown in <a href=#j_phys-2023-0110_fig_006 class="link link-fig" data-bs-target=j_phys-2023-0110_fig_006>Figure A2</a>), indicating that successive transformations consist of a pure boost and a rotation.</p>
<div class=figure-wrapper id=j_phys-2023-0110_fig_006><div class="figure w-100"><div class=graphic><img loading=lazy 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" alt="Figure A2
An object (electron) is in accelerated motion along a curvilinear path under the action of external forces. The moving frames
S
′
{S}^{^{\prime} }
and
S
″
{S}^{^{\prime\prime} }
represent successive rest frames of the object. Starting from the origin of the laboratory frame
S
S
, the velocity of the rest frame
S
′
{S}^{^{\prime} }
at time
t
t
is
v
(
t
)
=
c
β
{\bf{v}}\left(t)=c\beta
and at time
t
+
δ
t
t+\delta t
the velocity of the rest frame
S
″
{S}^{^{\prime\prime} }
is
v
(
t
+
δ
t
)
=
c
β
+
c
δ
β
v\left(t+\delta t)=c\beta +c\delta \beta
. The resulting infinitesimal LT from
S
′
{S}^{^{\prime} }
to
S
″
{S}^{^{\prime\prime} }
consists of a boost and a rotation, indicating that the object acquires a precession at the Thomas angular velocity
ω
T
{{\boldsymbol{\omega }}}_{T}
of purely relativistic kinematical origin independent of other effects.
"></div><div class="figure-description mb-3"><div class="figure-label h3"><span class=label>Figure A2</span></div><div class="figure-caption mb-2"><span class=caption><p>An object (electron) is in accelerated motion along a curvilinear path under the action of external forces. The moving frames <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-5202><span class=MJXp-msup id=MJXp-Span-5203><span class=MJXp-mrow id=MJXp-Span-5204 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5205>S</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-5206 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-5207>′</span></span></span></span></span><span id=MathJax-Element-454-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> and <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-5208><span class=MJXp-msup id=MJXp-Span-5209><span class=MJXp-mrow id=MJXp-Span-5210 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5211>S</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-5212 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-5213>″</span></span></span></span></span><span id=MathJax-Element-455-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> represent successive rest frames of the object. Starting from the origin of the laboratory frame <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-5214><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5215>S</span></span></span><span id=MathJax-Element-456-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>, the velocity of the rest frame <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-5216><span class=MJXp-msup id=MJXp-Span-5217><span class=MJXp-mrow id=MJXp-Span-5218 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5219>S</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-5220 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-5221>′</span></span></span></span></span><span id=MathJax-Element-457-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> at time <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-5222><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5223>t</span></span></span><span id=MathJax-Element-458-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> is <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-5224><span class="MJXp-mi MJXp-bold" id=MJXp-Span-5225>v</span><span class=MJXp-mrow id=MJXp-Span-5226><span class=MJXp-mo id=MJXp-Span-5227 style=margin-left:0em;margin-right:0em>(</span><span class=MJXp-mrow id=MJXp-Span-5228><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5229>t</span></span><span class=MJXp-mo id=MJXp-Span-5230 style=margin-left:0em;margin-right:0em>)</span></span><span class=MJXp-mo id=MJXp-Span-5231 style=margin-left:0.333em;margin-right:0.333em>=</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5232>c</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5233>β</span></span></span><span id=MathJax-Element-459-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> and at time <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-5234><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5235>t</span><span class=MJXp-mo id=MJXp-Span-5236 style=margin-left:0.267em;margin-right:0.267em>+</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5237>δ</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5238>t</span></span></span><span id=MathJax-Element-460-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> the velocity of the rest frame <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-5239><span class=MJXp-msup id=MJXp-Span-5240><span class=MJXp-mrow id=MJXp-Span-5241 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5242>S</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-5243 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-5244>″</span></span></span></span></span><span id=MathJax-Element-461-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> is <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-5245><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5246>v</span><span class=MJXp-mrow id=MJXp-Span-5247><span class=MJXp-mo id=MJXp-Span-5248 style=margin-left:0em;margin-right:0em>(</span><span class=MJXp-mrow id=MJXp-Span-5249><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5250>t</span><span class=MJXp-mo id=MJXp-Span-5251 style=margin-left:0.267em;margin-right:0.267em>+</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5252>δ</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5253>t</span></span><span class=MJXp-mo id=MJXp-Span-5254 style=margin-left:0em;margin-right:0em>)</span></span><span class=MJXp-mo id=MJXp-Span-5255 style=margin-left:0.333em;margin-right:0.333em>=</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5256>c</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5257>β</span><span class=MJXp-mo id=MJXp-Span-5258 style=margin-left:0.267em;margin-right:0.267em>+</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5259>c</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5260>δ</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5261>β</span></span></span><span id=MathJax-Element-462-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>. The resulting infinitesimal LT from <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-5262><span class=MJXp-msup id=MJXp-Span-5263><span class=MJXp-mrow id=MJXp-Span-5264 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5265>S</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-5266 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-5267>′</span></span></span></span></span><span id=MathJax-Element-463-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> to <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-5268><span class=MJXp-msup id=MJXp-Span-5269><span class=MJXp-mrow id=MJXp-Span-5270 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5271>S</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-5272 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-5273>″</span></span></span></span></span><span id=MathJax-Element-464-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> consists of a boost and a rotation, indicating that the object acquires a precession at the Thomas angular velocity <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-5274><span class=MJXp-msub id=MJXp-Span-5275><span class=MJXp-mrow id=MJXp-Span-5276 style=margin-right:0.05em><span class="MJXp-mi MJXp-bold" id=MJXp-Span-5277>ω</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-5278 style=vertical-align:-0.4em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5279>T</span></span></span></span></span><span id=MathJax-Element-465-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> of purely relativistic kinematical origin independent of other effects.</p></span></div></div></div></div>
<p>To point out the origin of the rotation of the particle rest frame <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-5280><span class=MJXp-msup id=MJXp-Span-5281><span class=MJXp-mrow id=MJXp-Span-5282 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5283>S</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-5284 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-5285>″</span></span></span></span></span><span id=MathJax-Element-466-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>, in his approach to the Thomas precession, Jackson starts from the LT between the two frames <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-5286><span class=MJXp-msup id=MJXp-Span-5287><span class=MJXp-mrow id=MJXp-Span-5288 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5289>S</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-5290 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-5291>″</span></span></span></span></span><span id=MathJax-Element-467-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> and <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-5292><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5293>S</span></span></span><span id=MathJax-Element-468-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> given by (Ref. [<a href=#j_phys-2023-0110_ref_030 class="link link-bibr" data-bs-target=j_phys-2023-0110_ref_030 data-bs-toggle=tooltip title="[30] Jackson JD. Classical Electrodynamics, Sect. 11.8. 2nd edn. New York: John Wiley &amp; Sons, Inc; 1975. Search in Google Scholar">30</a>], Section 11.19),<div class=formula id=j_phys-2023-0110_eq_020>
<span class=label>(A2)</span>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class="MJXp-math MJXp-display" id=MJXp-Span-5294><span class=MJXp-mtable id=MJXp-Span-5295><span><span class=MJXp-mtr id=MJXp-Span-5296 style=vertical-align:baseline><span class=MJXp-mtd id=MJXp-Span-5297 style=text-align:center><span class=MJXp-msubsup id=MJXp-Span-5298><span class=MJXp-mrow id=MJXp-Span-5299 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5300>x</span></span><span class=MJXp-script-box style=height:1.86em;vertical-align:-0.64em><span class=MJXp-script><span><span style=margin-bottom:-0.25em><span class=MJXp-mrow id=MJXp-Span-5303><span class=MJXp-mo id=MJXp-Span-5304>″</span></span></span></span></span><span class=MJXp-script><span><span style=margin-top:-0.85em><span class=MJXp-mrow id=MJXp-Span-5301><span class=MJXp-mn id=MJXp-Span-5302>0</span></span></span></span></span></span></span></span><span class=MJXp-mtd id=MJXp-Span-5305 style=padding-left:0.33em;text-align:center><span class=MJXp-mo id=MJXp-Span-5306 style=margin-left:0.333em;margin-right:0.333em>=</span></span><span class=MJXp-mtd id=MJXp-Span-5307 style=padding-left:0.33em;text-align:center><span class=MJXp-msub id=MJXp-Span-5308><span class=MJXp-mrow id=MJXp-Span-5309 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5310>γ</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-5311 style=vertical-align:-0.4em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5312>u</span></span></span><span class=MJXp-mrow id=MJXp-Span-5313><span class=MJXp-mo id=MJXp-Span-5314 style=margin-left:0em;margin-right:0em;vertical-align:-0.244em><span style=font-size:1.978em;margin-left:-0.05em class="MJXp-right MJXp-scale7">(</span></span><span class=MJXp-mrow id=MJXp-Span-5315><span class=MJXp-msub id=MJXp-Span-5316><span class=MJXp-mrow id=MJXp-Span-5317 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5318>x</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-5319 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-5320>0</span></span></span><span class=MJXp-mo id=MJXp-Span-5321 style=margin-left:0.267em;margin-right:0.267em>−</span><span class="MJXp-mi MJXp-bold MJXp-italic" id=MJXp-Span-5322>β</span><span class=MJXp-mo id=MJXp-Span-5323 style=margin-left:0.267em;margin-right:0.267em>⋅</span><span class="MJXp-mi MJXp-bold" id=MJXp-Span-5324>x</span></span><span class=MJXp-mo id=MJXp-Span-5325 style=margin-left:0em;margin-right:0em;vertical-align:-0.244em><span style=font-size:1.978em;margin-left:-0.05em class="MJXp-right MJXp-scale7">)</span></span></span><span class=MJXp-mo id=MJXp-Span-5326 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-msub id=MJXp-Span-5327><span class=MJXp-mrow id=MJXp-Span-5328 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5329>γ</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-5330 style=vertical-align:-0.4em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5331>u</span></span></span><span class=MJXp-mrow id=MJXp-Span-5332><span class=MJXp-mo id=MJXp-Span-5333 style=margin-left:0em;margin-right:0em;vertical-align:-0.244em><span style=font-size:1.978em;margin-left:-0.05em class="MJXp-right MJXp-scale7">(</span></span><span class=MJXp-mrow id=MJXp-Span-5334><span class=MJXp-msub id=MJXp-Span-5335><span class=MJXp-mrow id=MJXp-Span-5336 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5337>x</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-5338 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-5339>0</span></span></span><span class=MJXp-mo id=MJXp-Span-5340 style=margin-left:0.267em;margin-right:0.267em>−</span><span class=MJXp-msub id=MJXp-Span-5341><span class=MJXp-mrow id=MJXp-Span-5342 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5343>β</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-5344 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-5345>1</span></span></span><span class=MJXp-msub id=MJXp-Span-5346><span class=MJXp-mrow id=MJXp-Span-5347 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5348>x</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-5349 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-5350>1</span></span></span><span class=MJXp-mo id=MJXp-Span-5351 style=margin-left:0.267em;margin-right:0.267em>−</span><span class=MJXp-msub id=MJXp-Span-5352><span class=MJXp-mrow id=MJXp-Span-5353 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5354>β</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-5355 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-5356>2</span></span></span><span class=MJXp-msub id=MJXp-Span-5357><span class=MJXp-mrow id=MJXp-Span-5358 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5359>x</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-5360 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-5361>2</span></span></span></span><span class=MJXp-mo id=MJXp-Span-5362 style=margin-left:0em;margin-right:0em;vertical-align:-0.244em><span style=font-size:1.978em;margin-left:-0.05em class="MJXp-right MJXp-scale7">)</span></span></span></span></span><span class=MJXp-mtr id=MJXp-Span-5363 style=vertical-align:baseline><span class=MJXp-mtd id=MJXp-Span-5364 style=padding-top:0.431em;text-align:center><span class=MJXp-msubsup id=MJXp-Span-5365><span class=MJXp-mrow id=MJXp-Span-5366 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5367>x</span></span><span class=MJXp-script-box style=height:1.86em;vertical-align:-0.64em><span class=MJXp-script><span><span style=margin-bottom:-0.25em><span class=MJXp-mrow id=MJXp-Span-5370><span class=MJXp-mo id=MJXp-Span-5371>″</span></span></span></span></span><span class=MJXp-script><span><span style=margin-top:-0.85em><span class=MJXp-mrow id=MJXp-Span-5368><span class=MJXp-mn id=MJXp-Span-5369>1</span></span></span></span></span></span></span></span><span class=MJXp-mtd id=MJXp-Span-5372 style=padding-left:0.33em;padding-top:0.431em;text-align:center><span class=MJXp-mo id=MJXp-Span-5373 style=margin-left:0.333em;margin-right:0.333em>=</span></span><span class=MJXp-mtd id=MJXp-Span-5374 style=padding-left:0.33em;padding-top:0.431em;text-align:center><span class=MJXp-msub id=MJXp-Span-5375><span class=MJXp-mrow id=MJXp-Span-5376 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5377>x</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-5378 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-5379>1</span></span></span><span class=MJXp-mo id=MJXp-Span-5380 style=margin-left:0.267em;margin-right:0.267em>+</span><span class=MJXp-mfrac id=MJXp-Span-5381 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-5382><span class=MJXp-msub id=MJXp-Span-5383><span class=MJXp-mrow id=MJXp-Span-5384 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5385>γ</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-5386 style=vertical-align:-0.4em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5387>u</span></span></span><span class=MJXp-mo id=MJXp-Span-5388 style=margin-left:0.267em;margin-right:0.267em>−</span><span class=MJXp-mn id=MJXp-Span-5389>1</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-5390><span class=MJXp-msup id=MJXp-Span-5391><span class=MJXp-mrow id=MJXp-Span-5392 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5393>β</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-5394 style=vertical-align:0.5em><span class=MJXp-mn id=MJXp-Span-5395>2</span></span></span></span></span></span></span></span></span><span class=MJXp-mrow id=MJXp-Span-5396><span class=MJXp-mo id=MJXp-Span-5397 style=margin-left:0em;margin-right:0em;vertical-align:-0.244em><span style=font-size:1.978em;margin-left:-0.05em class="MJXp-right MJXp-scale7">(</span></span><span class=MJXp-mrow id=MJXp-Span-5398><span class=MJXp-msub id=MJXp-Span-5399><span class=MJXp-mrow id=MJXp-Span-5400 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5401>β</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-5402 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-5403>1</span></span></span><span class=MJXp-msub id=MJXp-Span-5404><span class=MJXp-mrow id=MJXp-Span-5405 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5406>x</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-5407 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-5408>1</span></span></span><span class=MJXp-mo id=MJXp-Span-5409 style=margin-left:0.267em;margin-right:0.267em>+</span><span class=MJXp-msub id=MJXp-Span-5410><span class=MJXp-mrow id=MJXp-Span-5411 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5412>β</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-5413 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-5414>2</span></span></span><span class=MJXp-msub id=MJXp-Span-5415><span class=MJXp-mrow id=MJXp-Span-5416 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5417>x</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-5418 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-5419>2</span></span></span></span><span class=MJXp-mo id=MJXp-Span-5420 style=margin-left:0em;margin-right:0em;vertical-align:-0.244em><span style=font-size:1.978em;margin-left:-0.05em class="MJXp-right MJXp-scale7">)</span></span></span><span class=MJXp-msub id=MJXp-Span-5421><span class=MJXp-mrow id=MJXp-Span-5422 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5423>β</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-5424 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-5425>1</span></span></span><span class=MJXp-mo id=MJXp-Span-5426 style=margin-left:0.267em;margin-right:0.267em>−</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5427>γ</span><span class=MJXp-msub id=MJXp-Span-5428><span class=MJXp-mrow id=MJXp-Span-5429 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5430>β</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-5431 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-5432>1</span></span></span><span class=MJXp-msub id=MJXp-Span-5433><span class=MJXp-mrow id=MJXp-Span-5434 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5435>x</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-5436 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-5437>0</span></span></span></span></span><span class=MJXp-mtr id=MJXp-Span-5438 style=vertical-align:baseline><span class=MJXp-mtd id=MJXp-Span-5439 style=padding-top:0.431em;text-align:center><span class=MJXp-msubsup id=MJXp-Span-5440><span class=MJXp-mrow id=MJXp-Span-5441 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5442>x</span></span><span class=MJXp-script-box style=height:1.86em;vertical-align:-0.64em><span class=MJXp-script><span><span style=margin-bottom:-0.25em><span class=MJXp-mrow id=MJXp-Span-5445><span class=MJXp-mo id=MJXp-Span-5446>″</span></span></span></span></span><span class=MJXp-script><span><span style=margin-top:-0.85em><span class=MJXp-mrow id=MJXp-Span-5443><span class=MJXp-mn id=MJXp-Span-5444>2</span></span></span></span></span></span></span></span><span class=MJXp-mtd id=MJXp-Span-5447 style=padding-left:0.33em;padding-top:0.431em;text-align:center><span class=MJXp-mo id=MJXp-Span-5448 style=margin-left:0.333em;margin-right:0.333em>=</span></span><span class=MJXp-mtd id=MJXp-Span-5449 style=padding-left:0.33em;padding-top:0.431em;text-align:center><span class=MJXp-msub id=MJXp-Span-5450><span class=MJXp-mrow id=MJXp-Span-5451 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5452>x</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-5453 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-5454>2</span></span></span><span class=MJXp-mo id=MJXp-Span-5455 style=margin-left:0.267em;margin-right:0.267em>+</span><span class=MJXp-mfrac id=MJXp-Span-5456 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-5457><span class=MJXp-msub id=MJXp-Span-5458><span class=MJXp-mrow id=MJXp-Span-5459 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5460>γ</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-5461 style=vertical-align:-0.4em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5462>u</span></span></span><span class=MJXp-mo id=MJXp-Span-5463 style=margin-left:0.267em;margin-right:0.267em>−</span><span class=MJXp-mn id=MJXp-Span-5464>1</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-5465><span class=MJXp-msup id=MJXp-Span-5466><span class=MJXp-mrow id=MJXp-Span-5467 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5468>β</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-5469 style=vertical-align:0.5em><span class=MJXp-mn id=MJXp-Span-5470>2</span></span></span></span></span></span></span></span></span><span class=MJXp-mrow id=MJXp-Span-5471><span class=MJXp-mo id=MJXp-Span-5472 style=margin-left:0em;margin-right:0em;vertical-align:-0.244em><span style=font-size:1.978em;margin-left:-0.05em class="MJXp-right MJXp-scale7">(</span></span><span class=MJXp-mrow id=MJXp-Span-5473><span class=MJXp-msub id=MJXp-Span-5474><span class=MJXp-mrow id=MJXp-Span-5475 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5476>β</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-5477 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-5478>1</span></span></span><span class=MJXp-msub id=MJXp-Span-5479><span class=MJXp-mrow id=MJXp-Span-5480 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5481>x</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-5482 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-5483>1</span></span></span><span class=MJXp-mo id=MJXp-Span-5484 style=margin-left:0.267em;margin-right:0.267em>+</span><span class=MJXp-msub id=MJXp-Span-5485><span class=MJXp-mrow id=MJXp-Span-5486 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5487>β</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-5488 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-5489>2</span></span></span><span class=MJXp-msub id=MJXp-Span-5490><span class=MJXp-mrow id=MJXp-Span-5491 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5492>x</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-5493 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-5494>2</span></span></span></span><span class=MJXp-mo id=MJXp-Span-5495 style=margin-left:0em;margin-right:0em;vertical-align:-0.244em><span style=font-size:1.978em;margin-left:-0.05em class="MJXp-right MJXp-scale7">)</span></span></span><span class=MJXp-msub id=MJXp-Span-5496><span class=MJXp-mrow id=MJXp-Span-5497 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5498>β</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-5499 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-5500>2</span></span></span><span class=MJXp-mo id=MJXp-Span-5501 style=margin-left:0.267em;margin-right:0.267em>−</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5502>γ</span><span class=MJXp-msub id=MJXp-Span-5503><span class=MJXp-mrow id=MJXp-Span-5504 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5505>β</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-5506 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-5507>2</span></span></span><span class=MJXp-msub id=MJXp-Span-5508><span class=MJXp-mrow id=MJXp-Span-5509 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5510>x</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-5511 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-5512>0</span></span></span></span></span><span class=MJXp-mtr id=MJXp-Span-5513 style=vertical-align:baseline><span class=MJXp-mtd id=MJXp-Span-5514 style=padding-top:0.431em;text-align:center><span class=MJXp-msubsup id=MJXp-Span-5515><span class=MJXp-mrow id=MJXp-Span-5516 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5517>x</span></span><span class=MJXp-script-box style=height:1.86em;vertical-align:-0.64em><span class=MJXp-script><span><span style=margin-bottom:-0.25em><span class=MJXp-mrow id=MJXp-Span-5520><span class=MJXp-mo id=MJXp-Span-5521>″</span></span></span></span></span><span class=MJXp-script><span><span style=margin-top:-0.85em><span class=MJXp-mrow id=MJXp-Span-5518><span class=MJXp-mn id=MJXp-Span-5519>3</span></span></span></span></span></span></span></span><span class=MJXp-mtd id=MJXp-Span-5522 style=padding-left:0.33em;padding-top:0.431em;text-align:center><span class=MJXp-mo id=MJXp-Span-5523 style=margin-left:0.333em;margin-right:0.333em>=</span></span><span class=MJXp-mtd id=MJXp-Span-5524 style=padding-left:0.33em;padding-top:0.431em;text-align:center><span class=MJXp-msub id=MJXp-Span-5525><span class=MJXp-mrow id=MJXp-Span-5526 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5527>x</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-5528 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-5529>3</span></span></span><span class=MJXp-mo id=MJXp-Span-5530 style=margin-left:0em;margin-right:0.222em>,</span></span></span></span></span></span></span><span class="mjx-chtml MJXc-display MJXc-processing sf-hidden"></span>
</span>
</div><p> where, as shown in Figure A2, <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-5531><span class=MJXp-msup id=MJXp-Span-5532><span class=MJXp-mrow id=MJXp-Span-5533 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5534>S</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-5535 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-5536>″</span></span></span></span></span><span id=MathJax-Element-470-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> is in motion with velocity components <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-5537><span class=MJXp-msub id=MJXp-Span-5538><span class=MJXp-mrow id=MJXp-Span-5539 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5540>u</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-5541 style=vertical-align:-0.4em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5542>x</span></span></span><span class=MJXp-mo id=MJXp-Span-5543 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-msub id=MJXp-Span-5544><span class=MJXp-mrow id=MJXp-Span-5545 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5546>u</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-5547 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-5548>1</span></span></span></span></span><span id=MathJax-Element-471-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> and <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-5549><span class=MJXp-msub id=MJXp-Span-5550><span class=MJXp-mrow id=MJXp-Span-5551 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5552>u</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-5553 style=vertical-align:-0.4em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5554>y</span></span></span><span class=MJXp-mo id=MJXp-Span-5555 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-msub id=MJXp-Span-5556><span class=MJXp-mrow id=MJXp-Span-5557 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5558>u</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-5559 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-5560>2</span></span></span></span></span><span id=MathJax-Element-472-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> relative to the laboratory frame <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-5561><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5562>S</span></span></span><span id=MathJax-Element-473-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> and in (<a href=#j_phys-2023-0110_eq_020 class="link link-disp-formula" data-bs-target=j_phys-2023-0110_eq_020>A2</a>)<span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-5563><span class=MJXp-msub id=MJXp-Span-5564><span class=MJXp-mrow id=MJXp-Span-5565 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5566>γ</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-5567 style=vertical-align:-0.4em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5568>u</span></span></span><span class=MJXp-mo id=MJXp-Span-5569 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-msup id=MJXp-Span-5570><span class=MJXp-mrow id=MJXp-Span-5571 style=margin-right:0.05em><span class=MJXp-mrow id=MJXp-Span-5572><span class=MJXp-mo id=MJXp-Span-5573 style=margin-left:0em;margin-right:0em;vertical-align:-0.289em><span style=font-size:2.156em;margin-left:-0.09em class="MJXp-right MJXp-scale6">(</span></span><span class=MJXp-mrow id=MJXp-Span-5574><span class=MJXp-mn id=MJXp-Span-5575>1</span><span class=MJXp-mo id=MJXp-Span-5576 style=margin-left:0.267em;margin-right:0.267em>−</span><span class=MJXp-msup id=MJXp-Span-5577><span class=MJXp-mrow id=MJXp-Span-5578 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5579>u</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-5580 style=vertical-align:0.5em><span class=MJXp-mn id=MJXp-Span-5581>2</span></span></span><span class=MJXp-mo id=MJXp-Span-5582 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class=MJXp-msup id=MJXp-Span-5583><span class=MJXp-mrow id=MJXp-Span-5584 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5585>c</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-5586 style=vertical-align:0.5em><span class=MJXp-mn id=MJXp-Span-5587>2</span></span></span></span><span class=MJXp-mo id=MJXp-Span-5588 style=margin-left:0em;margin-right:0em;vertical-align:-0.289em><span style=font-size:2.156em;margin-left:-0.09em class="MJXp-right MJXp-scale6">)</span></span></span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-5589 style=vertical-align:0.82em><span class=MJXp-mo id=MJXp-Span-5590>−</span><span class=MJXp-mn id=MJXp-Span-5591>1</span><span class=MJXp-mo id=MJXp-Span-5592>⁄</span><span class=MJXp-mn id=MJXp-Span-5593>2</span></span></span></span></span><span id=MathJax-Element-474-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>, <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-5594><span class=MJXp-msup id=MJXp-Span-5595><span class=MJXp-mrow id=MJXp-Span-5596 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5597>u</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-5598 style=vertical-align:0.5em><span class=MJXp-mn id=MJXp-Span-5599>2</span></span></span><span class=MJXp-mo id=MJXp-Span-5600 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-msubsup id=MJXp-Span-5601><span class=MJXp-mrow id=MJXp-Span-5602 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5603>u</span></span><span class=MJXp-script-box style=height:1.86em;vertical-align:-0.64em><span class=MJXp-script><span><span style=margin-bottom:-0.25em><span class=MJXp-mrow id=MJXp-Span-5606><span class=MJXp-mn id=MJXp-Span-5607>2</span></span></span></span></span><span class=MJXp-script><span><span style=margin-top:-0.85em><span class=MJXp-mrow id=MJXp-Span-5604><span class=MJXp-mn id=MJXp-Span-5605>1</span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-5608 style=margin-left:0.267em;margin-right:0.267em>+</span><span class=MJXp-msubsup id=MJXp-Span-5609><span class=MJXp-mrow id=MJXp-Span-5610 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5611>u</span></span><span class=MJXp-script-box style=height:1.86em;vertical-align:-0.64em><span class=MJXp-script><span><span style=margin-bottom:-0.25em><span class=MJXp-mrow id=MJXp-Span-5614><span class=MJXp-mn id=MJXp-Span-5615>2</span></span></span></span></span><span class=MJXp-script><span><span style=margin-top:-0.85em><span class=MJXp-mrow id=MJXp-Span-5612><span class=MJXp-mn id=MJXp-Span-5613>2</span></span></span></span></span></span></span></span></span><span id=MathJax-Element-475-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>, <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-5616><span class=MJXp-msub id=MJXp-Span-5617><span class=MJXp-mrow id=MJXp-Span-5618 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5619>β</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-5620 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-5621>1</span></span></span><span class=MJXp-mo id=MJXp-Span-5622 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-msub id=MJXp-Span-5623><span class=MJXp-mrow id=MJXp-Span-5624 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5625>u</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-5626 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-5627>1</span></span></span><span class=MJXp-mo id=MJXp-Span-5628 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5629>c</span></span></span><span id=MathJax-Element-476-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>, and <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-5630><span class=MJXp-msub id=MJXp-Span-5631><span class=MJXp-mrow id=MJXp-Span-5632 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5633>β</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-5634 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-5635>2</span></span></span><span class=MJXp-mo id=MJXp-Span-5636 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-msub id=MJXp-Span-5637><span class=MJXp-mrow id=MJXp-Span-5638 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5639>u</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-5640 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-5641>2</span></span></span><span class=MJXp-mo id=MJXp-Span-5642 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5643>c</span></span></span><span id=MathJax-Element-477-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>.</p>
<p>The connection between the two sets of rest frame coordinates, <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-5644><span class=MJXp-msup id=MJXp-Span-5645><span class=MJXp-mrow id=MJXp-Span-5646 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5647>x</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-5648 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-5649>′</span></span></span></span></span><span id=MathJax-Element-478-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> at time <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-5650><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5651>t</span></span></span><span id=MathJax-Element-479-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> and <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-5652><span class=MJXp-msup id=MJXp-Span-5653><span class=MJXp-mrow id=MJXp-Span-5654 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5655>x</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-5656 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-5657>″</span></span></span></span></span><span id=MathJax-Element-480-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> at time <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-5658><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5659>t</span><span class=MJXp-mo id=MJXp-Span-5660 style=margin-left:0.267em;margin-right:0.267em>+</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5661>δ</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5662>t</span></span></span><span id=MathJax-Element-481-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>, corresponding to the frames instantaneously co-moving with the particle in its accelerated motion, are given by, <div class=formula id=j_phys-2023-0110_eq_021>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class="MJXp-math MJXp-display" id=MJXp-Span-5663><span class=MJXp-mtable id=MJXp-Span-5664><span><span class=MJXp-mtr id=MJXp-Span-5665 style=vertical-align:baseline><span class=MJXp-mtd id=MJXp-Span-5666 style=text-align:center><span class=MJXp-msup id=MJXp-Span-5667><span class=MJXp-mrow id=MJXp-Span-5668 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5669>x</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-5670 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-5671>′</span></span></span></span><span class=MJXp-mtd id=MJXp-Span-5672 style=padding-left:0.33em;text-align:center><span class=MJXp-mo id=MJXp-Span-5673 style=margin-left:0.333em;margin-right:0.333em>=</span></span><span class=MJXp-mtd id=MJXp-Span-5674 style=padding-left:0.33em;text-align:center><span class=MJXp-msub id=MJXp-Span-5675><span class=MJXp-mrow id=MJXp-Span-5676 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5677>A</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-5678 style=vertical-align:-0.4em><span class=MJXp-mi id=MJXp-Span-5679>boost</span></span></span><span class=MJXp-mrow id=MJXp-Span-5680><span class=MJXp-mo id=MJXp-Span-5681 style=margin-left:0em;margin-right:0em>(</span><span class=MJXp-mrow id=MJXp-Span-5682><span class="MJXp-mi MJXp-bold MJXp-italic" id=MJXp-Span-5683>β</span></span><span class=MJXp-mo id=MJXp-Span-5684 style=margin-left:0em;margin-right:0em>)</span></span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5685>x</span></span></span><span class=MJXp-mtr id=MJXp-Span-5686 style=vertical-align:baseline><span class=MJXp-mtd id=MJXp-Span-5687 style=padding-top:0.431em;text-align:center><span class=MJXp-msup id=MJXp-Span-5688><span class=MJXp-mrow id=MJXp-Span-5689 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5690>x</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-5691 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-5692>″</span></span></span></span><span class=MJXp-mtd id=MJXp-Span-5693 style=padding-left:0.33em;padding-top:0.431em;text-align:center><span class=MJXp-mo id=MJXp-Span-5694 style=margin-left:0.333em;margin-right:0.333em>=</span></span><span class=MJXp-mtd id=MJXp-Span-5695 style=padding-left:0.33em;padding-top:0.431em;text-align:center><span class=MJXp-msub id=MJXp-Span-5696><span class=MJXp-mrow id=MJXp-Span-5697 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5698>A</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-5699 style=vertical-align:-0.4em><span class=MJXp-mi id=MJXp-Span-5700>boost</span></span></span><span class=MJXp-mrow id=MJXp-Span-5701><span class=MJXp-mo id=MJXp-Span-5702 style=margin-left:0em;margin-right:0em>(</span><span class=MJXp-mrow id=MJXp-Span-5703><span class="MJXp-mi MJXp-bold MJXp-italic" id=MJXp-Span-5704>β</span><span class=MJXp-mo id=MJXp-Span-5705 style=margin-left:0.267em;margin-right:0.267em>+</span><span class="MJXp-mi MJXp-bold MJXp-italic" id=MJXp-Span-5706>δ</span><span class="MJXp-mi MJXp-bold MJXp-italic" id=MJXp-Span-5707>β</span></span><span class=MJXp-mo id=MJXp-Span-5708 style=margin-left:0em;margin-right:0em>)</span></span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5709>x</span><span class=MJXp-mo id=MJXp-Span-5710 style=margin-left:0em;margin-right:0.222em>,</span></span></span></span></span></span></span><span class="mjx-chtml MJXc-display MJXc-processing sf-hidden"></span>
</span>
</div><p> where <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-5711><span class="MJXp-mi MJXp-bold MJXp-italic" id=MJXp-Span-5712>β</span><span class=MJXp-mo id=MJXp-Span-5713 style=margin-left:0.333em;margin-right:0.333em>=</span><span class="MJXp-mi MJXp-bold" id=MJXp-Span-5714>v</span><span class=MJXp-mo id=MJXp-Span-5715 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5716>c</span></span></span><span id=MathJax-Element-483-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> and <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-5717><span class="MJXp-mi MJXp-bold MJXp-italic" id=MJXp-Span-5718>β</span><span class=MJXp-mo id=MJXp-Span-5719 style=margin-left:0.267em;margin-right:0.267em>+</span><span class="MJXp-mi MJXp-bold MJXp-italic" id=MJXp-Span-5720>δ</span><span class="MJXp-mi MJXp-bold MJXp-italic" id=MJXp-Span-5721>β</span><span class=MJXp-mo id=MJXp-Span-5722 style=margin-left:0.333em;margin-right:0.333em>=</span><span class="MJXp-mi MJXp-bold" id=MJXp-Span-5723>u</span><span class=MJXp-mo id=MJXp-Span-5724 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5725>c</span><span class=MJXp-mo id=MJXp-Span-5726 style=margin-left:0.333em;margin-right:0.333em>=</span><span class="MJXp-mi MJXp-bold" id=MJXp-Span-5727>v</span><span class=MJXp-mo id=MJXp-Span-5728 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5729>c</span><span class=MJXp-mo id=MJXp-Span-5730 style=margin-left:0.267em;margin-right:0.267em>+</span><span class="MJXp-mi MJXp-bold MJXp-italic" id=MJXp-Span-5731>δ</span><span class="MJXp-mi MJXp-bold MJXp-italic" id=MJXp-Span-5732>β</span></span></span><span id=MathJax-Element-484-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>, with the factor <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-5733><span class=MJXp-msub id=MJXp-Span-5734><span class=MJXp-mrow id=MJXp-Span-5735 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5736>γ</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-5737 style=vertical-align:-0.4em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5738>u</span></span></span><span class=MJXp-mo id=MJXp-Span-5739 style=margin-left:0.333em;margin-right:0.333em>=</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5740>γ</span><span class=MJXp-mo id=MJXp-Span-5741 style=margin-left:0.267em;margin-right:0.267em>+</span><span class=MJXp-msup id=MJXp-Span-5742><span class=MJXp-mrow id=MJXp-Span-5743 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5744>γ</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-5745 style=vertical-align:0.5em><span class=MJXp-mn id=MJXp-Span-5746>3</span></span></span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5747>β</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5748>δ</span><span class=MJXp-msub id=MJXp-Span-5749><span class=MJXp-mrow id=MJXp-Span-5750 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5751>β</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-5752 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-5753>1</span></span></span></span></span><span id=MathJax-Element-485-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> to the first order in <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-5754><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5755>δ</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5756>β</span></span></span><span id=MathJax-Element-486-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>. The resulting infinitesimal transformation between <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-5757><span class=MJXp-msup id=MJXp-Span-5758><span class=MJXp-mrow id=MJXp-Span-5759 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5760>S</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-5761 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-5762>′</span></span></span></span></span><span id=MathJax-Element-487-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> and <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-5763><span class=MJXp-msup id=MJXp-Span-5764><span class=MJXp-mrow id=MJXp-Span-5765 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5766>S</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-5767 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-5768>″</span></span></span></span></span><span id=MathJax-Element-488-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> is, <div class=formula id=j_phys-2023-0110_eq_022>
<span class=label>(A3)</span>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class="MJXp-math MJXp-display" id=MJXp-Span-5769><span class=MJXp-msup id=MJXp-Span-5770><span class=MJXp-mrow id=MJXp-Span-5771 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5772>x</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-5773 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-5774>″</span></span></span><span class=MJXp-mo id=MJXp-Span-5775 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-msub id=MJXp-Span-5776><span class=MJXp-mrow id=MJXp-Span-5777 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5778>A</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-5779 style=vertical-align:-0.4em><span class=MJXp-mi id=MJXp-Span-5780>LT</span></span></span><span class=MJXp-msup id=MJXp-Span-5781><span class=MJXp-mrow id=MJXp-Span-5782 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5783>x</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-5784 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-5785>′</span></span></span><span class=MJXp-mo id=MJXp-Span-5786 style=margin-left:0em;margin-right:0.222em>,</span></span></span><span class="mjx-chtml MJXc-display MJXc-processing sf-hidden"></span>
</span>
</div><p> where the transformation matrix, <div class=formula id=j_phys-2023-0110_eq_023>
<span class=label>(A4)</span>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class="MJXp-math MJXp-display" id=MJXp-Span-5787><span class=MJXp-msub id=MJXp-Span-5788><span class=MJXp-mrow id=MJXp-Span-5789 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5790>A</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-5791 style=vertical-align:-0.4em><span class=MJXp-mo id=MJXp-Span-5792>L</span><span class=MJXp-mo id=MJXp-Span-5793>T</span></span></span><span class=MJXp-mo id=MJXp-Span-5794 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-msub id=MJXp-Span-5795><span class=MJXp-mrow id=MJXp-Span-5796 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5797>A</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-5798 style=vertical-align:-0.4em><span class=MJXp-mi id=MJXp-Span-5799>boost</span></span></span><span class=MJXp-mrow id=MJXp-Span-5800><span class=MJXp-mo id=MJXp-Span-5801 style=margin-left:0em;margin-right:0em>(</span><span class=MJXp-mrow id=MJXp-Span-5802><span class="MJXp-mi MJXp-bold MJXp-italic" id=MJXp-Span-5803>β</span><span class=MJXp-mo id=MJXp-Span-5804 style=margin-left:0.267em;margin-right:0.267em>+</span><span class="MJXp-mi MJXp-bold MJXp-italic" id=MJXp-Span-5805>δ</span><span class="MJXp-mi MJXp-bold MJXp-italic" id=MJXp-Span-5806>β</span></span><span class=MJXp-mo id=MJXp-Span-5807 style=margin-left:0em;margin-right:0em>)</span></span><span class=MJXp-msubsup id=MJXp-Span-5808><span class=MJXp-mrow id=MJXp-Span-5809 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5810>A</span></span><span class=MJXp-script-box style=height:1.86em;vertical-align:-0.64em><span class=MJXp-script><span><span style=margin-bottom:-0.25em><span class=MJXp-mrow id=MJXp-Span-5813><span class=MJXp-mo id=MJXp-Span-5814>−</span><span class=MJXp-mn id=MJXp-Span-5815>1</span></span></span></span></span><span class=MJXp-script><span><span style=margin-top:-0.85em><span class=MJXp-mrow id=MJXp-Span-5811><span class=MJXp-mi id=MJXp-Span-5812>boost</span></span></span></span></span></span></span><span class=MJXp-mrow id=MJXp-Span-5816><span class=MJXp-mo id=MJXp-Span-5817 style=margin-left:0em;margin-right:0em>(</span><span class=MJXp-mrow id=MJXp-Span-5818><span class="MJXp-mi MJXp-bold MJXp-italic" id=MJXp-Span-5819>β</span></span><span class=MJXp-mo id=MJXp-Span-5820 style=margin-left:0em;margin-right:0em>)</span></span><span class=MJXp-mo id=MJXp-Span-5821 style=margin-left:0em;margin-right:0.222em>,</span></span></span><span class="mjx-chtml MJXc-display MJXc-processing sf-hidden"></span>
</span>
</div><p> is, <div class=formula id=j_phys-2023-0110_eq_024>
<span class=label>(A5)</span>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class="MJXp-math MJXp-display" id=MJXp-Span-5822><span class=MJXp-msub id=MJXp-Span-5823><span class=MJXp-mrow id=MJXp-Span-5824 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5825>A</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-5826 style=vertical-align:-0.4em><span class=MJXp-mi id=MJXp-Span-5827>LT</span></span></span><span class=MJXp-mo id=MJXp-Span-5828 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-mfenced id=MJXp-Span-5829><span class=MJXp-mo id=MJXp-Span-5830 style=margin-left:0em;margin-right:0em;vertical-align:-2.459em><span style=font-size:10.835em;margin-left:-0.25em class="MJXp-right MJXp-scale2">(</span></span><span class=MJXp-mrow id=MJXp-Span-5831><span class=MJXp-mtable id=MJXp-Span-5832><span><span class=MJXp-mtr id=MJXp-Span-5833 style=vertical-align:baseline><span class=MJXp-mtd id=MJXp-Span-5834 style=text-align:center><span class=MJXp-mn id=MJXp-Span-5835>1</span></span><span class=MJXp-mtd id=MJXp-Span-5836 style=padding-left:0.8em;text-align:center><span class=MJXp-mo id=MJXp-Span-5837 style=margin-left:0em;margin-right:0.111em>−</span><span class=MJXp-msup id=MJXp-Span-5838><span class=MJXp-mrow id=MJXp-Span-5839 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5840>γ</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-5841 style=vertical-align:0.5em><span class=MJXp-mn id=MJXp-Span-5842>2</span></span></span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5843>δ</span><span class=MJXp-msub id=MJXp-Span-5844><span class=MJXp-mrow id=MJXp-Span-5845 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5846>β</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-5847 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-5848>1</span></span></span></span><span class=MJXp-mtd id=MJXp-Span-5849 style=padding-left:0.8em;text-align:center><span class=MJXp-mo id=MJXp-Span-5850 style=margin-left:0em;margin-right:0.111em>−</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5851>γ</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5852>δ</span><span class=MJXp-msub id=MJXp-Span-5853><span class=MJXp-mrow id=MJXp-Span-5854 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5855>β</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-5856 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-5857>2</span></span></span></span><span class=MJXp-mtd id=MJXp-Span-5858 style=padding-left:0.8em;text-align:center><span class=MJXp-mn id=MJXp-Span-5859>0</span></span></span><span class=MJXp-mtr id=MJXp-Span-5860 style=vertical-align:baseline><span class=MJXp-mtd id=MJXp-Span-5861 style=padding-top:0.431em;text-align:center><span class=MJXp-mo id=MJXp-Span-5862 style=margin-left:0em;margin-right:0.111em>−</span><span class=MJXp-msup id=MJXp-Span-5863><span class=MJXp-mrow id=MJXp-Span-5864 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5865>γ</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-5866 style=vertical-align:0.5em><span class=MJXp-mn id=MJXp-Span-5867>2</span></span></span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5868>δ</span><span class=MJXp-msub id=MJXp-Span-5869><span class=MJXp-mrow id=MJXp-Span-5870 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5871>β</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-5872 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-5873>1</span></span></span></span><span class=MJXp-mtd id=MJXp-Span-5874 style=padding-left:0.8em;padding-top:0.431em;text-align:center><span class=MJXp-mn id=MJXp-Span-5875>1</span></span><span class=MJXp-mtd id=MJXp-Span-5876 style=padding-left:0.8em;padding-top:0.431em;text-align:center><span class=MJXp-mstyle id=MJXp-Span-5877><span class=MJXp-mtext id=MJXp-Span-5878></span></span><span class=MJXp-mfrac id=MJXp-Span-5879 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-5880><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5881>γ</span><span class=MJXp-mo id=MJXp-Span-5882 style=margin-left:0.267em;margin-right:0.267em>−</span><span class=MJXp-mn id=MJXp-Span-5883>1</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-5884><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5885>β</span></span></span></span></span></span></span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5886>δ</span><span class=MJXp-msub id=MJXp-Span-5887><span class=MJXp-mrow id=MJXp-Span-5888 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5889>β</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-5890 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-5891>2</span></span></span></span><span class=MJXp-mtd id=MJXp-Span-5892 style=padding-left:0.8em;padding-top:0.431em;text-align:center><span class=MJXp-mn id=MJXp-Span-5893>0</span></span></span><span class=MJXp-mtr id=MJXp-Span-5894 style=vertical-align:baseline><span class=MJXp-mtd id=MJXp-Span-5895 style=padding-top:0.431em;text-align:center><span class=MJXp-mo id=MJXp-Span-5896 style=margin-left:0em;margin-right:0.111em>−</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5897>γ</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5898>δ</span><span class=MJXp-msub id=MJXp-Span-5899><span class=MJXp-mrow id=MJXp-Span-5900 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5901>β</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-5902 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-5903>2</span></span></span></span><span class=MJXp-mtd id=MJXp-Span-5904 style=padding-left:0.8em;padding-top:0.431em;text-align:center><span class=MJXp-mo id=MJXp-Span-5905 style=margin-left:0em;margin-right:0.111em>−</span><span class=MJXp-mfrac id=MJXp-Span-5906 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-5907><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5908>γ</span><span class=MJXp-mo id=MJXp-Span-5909 style=margin-left:0.267em;margin-right:0.267em>−</span><span class=MJXp-mn id=MJXp-Span-5910>1</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-5911><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5912>β</span></span></span></span></span></span></span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5913>δ</span><span class=MJXp-msub id=MJXp-Span-5914><span class=MJXp-mrow id=MJXp-Span-5915 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5916>β</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-5917 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-5918>2</span></span></span></span><span class=MJXp-mtd id=MJXp-Span-5919 style=padding-left:0.8em;padding-top:0.431em;text-align:center><span class=MJXp-mn id=MJXp-Span-5920>1</span></span><span class=MJXp-mtd id=MJXp-Span-5921 style=padding-left:0.8em;padding-top:0.431em;text-align:center><span class=MJXp-mn id=MJXp-Span-5922>0</span></span></span><span class=MJXp-mtr id=MJXp-Span-5923 style=vertical-align:baseline><span class=MJXp-mtd id=MJXp-Span-5924 style=padding-top:0.431em;text-align:center><span class=MJXp-mn id=MJXp-Span-5925>0</span></span><span class=MJXp-mtd id=MJXp-Span-5926 style=padding-left:0.8em;padding-top:0.431em;text-align:center><span class=MJXp-mn id=MJXp-Span-5927>0</span></span><span class=MJXp-mtd id=MJXp-Span-5928 style=padding-left:0.8em;padding-top:0.431em;text-align:center><span class=MJXp-mn id=MJXp-Span-5929>0</span></span><span class=MJXp-mtd id=MJXp-Span-5930 style=padding-left:0.8em;padding-top:0.431em;text-align:center><span class=MJXp-mn id=MJXp-Span-5931>1</span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-5932 style=margin-left:0em;margin-right:0em;vertical-align:-2.459em><span style=font-size:10.835em;margin-left:-0.25em class="MJXp-right MJXp-scale2">)</span></span></span><span class=MJXp-mo id=MJXp-Span-5933 style=margin-left:0em;margin-right:0.222em>.</span></span></span><span class="mjx-chtml MJXc-display MJXc-processing sf-hidden"></span>
</span>
</div><p>
</p>
<p>As shown by Jackson [<a href=#j_phys-2023-0110_ref_030 class="link link-bibr" data-bs-target=j_phys-2023-0110_ref_030 data-bs-toggle=tooltip title="[30] Jackson JD. Classical Electrodynamics, Sect. 11.8. 2nd edn. New York: John Wiley &amp; Sons, Inc; 1975. Search in Google Scholar">30</a>], the resulting infinitesimal Lorentz transformation (<a href=#j_phys-2023-0110_eq_022 class="link link-disp-formula" data-bs-target=j_phys-2023-0110_eq_022>A3</a>) consists of a boost with velocity <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-5934><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5935>c</span><span class="MJXp-mi MJXp-bold" id=MJXp-Span-5936>Δ</span><span class="MJXp-mi MJXp-bold MJXp-italic" id=MJXp-Span-5937>β</span></span></span><span id=MathJax-Element-492-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> and a rotation <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-5938><span class=MJXp-mi id=MJXp-Span-5939>Δ</span><span class="MJXp-mi MJXp-bold" id=MJXp-Span-5940>Ω</span></span></span><span id=MathJax-Element-493-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> given by, <div class=formula id=j_phys-2023-0110_eq_025>
<span class=label>(A6)</span>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class="MJXp-math MJXp-display" id=MJXp-Span-5941><span class=MJXp-mi id=MJXp-Span-5942>Δ</span><span class="MJXp-mi MJXp-bold" id=MJXp-Span-5943>Ω</span><span class=MJXp-mo id=MJXp-Span-5944 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-mfrac id=MJXp-Span-5945 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-5946><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5947>γ</span><span class=MJXp-mo id=MJXp-Span-5948 style=margin-left:0.267em;margin-right:0.267em>−</span><span class=MJXp-mn id=MJXp-Span-5949>1</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-5950><span class=MJXp-msup id=MJXp-Span-5951><span class=MJXp-mrow id=MJXp-Span-5952 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5953>β</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-5954 style=vertical-align:0.5em><span class=MJXp-mn id=MJXp-Span-5955>2</span></span></span></span></span></span></span></span></span><span class="MJXp-mi MJXp-bold MJXp-italic" id=MJXp-Span-5956>β</span><span class=MJXp-mo id=MJXp-Span-5957 style=margin-left:0.267em;margin-right:0.267em>×</span><span class="MJXp-mi MJXp-bold MJXp-italic" id=MJXp-Span-5958>δ</span><span class="MJXp-mi MJXp-bold MJXp-italic" id=MJXp-Span-5959>β</span><span class=MJXp-mo id=MJXp-Span-5960 style=margin-left:0em;margin-right:0.222em>.</span></span></span><span class="mjx-chtml MJXc-display MJXc-processing sf-hidden"></span>
</span>
</div><p>
</p>
<p>The rotation is highlighted by the two antisymmetric matrix elements <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-5961><span class=MJXp-msub id=MJXp-Span-5962><span class=MJXp-mrow id=MJXp-Span-5963 style=margin-right:0.05em><span class=MJXp-mrow id=MJXp-Span-5964><span class=MJXp-mo id=MJXp-Span-5965 style=margin-left:0em;margin-right:0em;vertical-align:-0.244em><span style=font-size:1.978em;margin-left:-0.05em class="MJXp-right MJXp-scale7">(</span></span><span class=MJXp-mrow id=MJXp-Span-5966><span class=MJXp-msub id=MJXp-Span-5967><span class=MJXp-mrow id=MJXp-Span-5968 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5969>A</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-5970 style=vertical-align:-0.4em><span class=MJXp-mi id=MJXp-Span-5971>LT</span></span></span></span><span class=MJXp-mo id=MJXp-Span-5972 style=margin-left:0em;margin-right:0em;vertical-align:-0.244em><span style=font-size:1.978em;margin-left:-0.05em class="MJXp-right MJXp-scale7">)</span></span></span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-5973 style=vertical-align:-0.74em><span class=MJXp-mn id=MJXp-Span-5974>23</span></span></span></span></span><span id=MathJax-Element-495-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> and <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-5975><span class=MJXp-msub id=MJXp-Span-5976><span class=MJXp-mrow id=MJXp-Span-5977 style=margin-right:0.05em><span class=MJXp-mrow id=MJXp-Span-5978><span class=MJXp-mo id=MJXp-Span-5979 style=margin-left:0em;margin-right:0em;vertical-align:-0.244em><span style=font-size:1.978em;margin-left:-0.05em class="MJXp-right MJXp-scale7">(</span></span><span class=MJXp-mrow id=MJXp-Span-5980><span class=MJXp-msub id=MJXp-Span-5981><span class=MJXp-mrow id=MJXp-Span-5982 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5983>A</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-5984 style=vertical-align:-0.4em><span class=MJXp-mi id=MJXp-Span-5985>LT</span></span></span></span><span class=MJXp-mo id=MJXp-Span-5986 style=margin-left:0em;margin-right:0em;vertical-align:-0.244em><span style=font-size:1.978em;margin-left:-0.05em class="MJXp-right MJXp-scale7">)</span></span></span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-5987 style=vertical-align:-0.74em><span class=MJXp-mn id=MJXp-Span-5988>32</span></span></span></span></span><span id=MathJax-Element-496-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> of <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-5989><span class=MJXp-msub id=MJXp-Span-5990><span class=MJXp-mrow id=MJXp-Span-5991 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-5992>A</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-5993 style=vertical-align:-0.4em><span class=MJXp-msub id=MJXp-Span-5994><span class=MJXp-mrow id=MJXp-Span-5995 style=margin-right:0.05em></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-5996 style=vertical-align:-0.2em><span class=MJXp-mi id=MJXp-Span-5997>LT</span></span></span></span></span></span></span><span id=MathJax-Element-497-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>, <div class=formula id=j_phys-2023-0110_eq_026>
<span class=label>(A7)</span>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class="MJXp-math MJXp-display" id=MJXp-Span-5998><span class=MJXp-msub id=MJXp-Span-5999><span class=MJXp-mrow id=MJXp-Span-6000 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6001>A</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-6002 style=vertical-align:-0.4em><span class=MJXp-mi id=MJXp-Span-6003>LT</span></span></span><span class=MJXp-mo id=MJXp-Span-6004 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-mfenced id=MJXp-Span-6005><span class=MJXp-mo id=MJXp-Span-6006 style=margin-left:0em;margin-right:0em;vertical-align:-2.275em><span style=font-size:10.102em;margin-left:-0.25em class="MJXp-right MJXp-scale2">(</span></span><span class=MJXp-mrow id=MJXp-Span-6007><span class=MJXp-mtable id=MJXp-Span-6008><span><span class=MJXp-mtr id=MJXp-Span-6009 style=vertical-align:baseline><span class=MJXp-mtd id=MJXp-Span-6010 style=text-align:center><span class=MJXp-mo id=MJXp-Span-6011 style=margin-left:0em;margin-right:0em>⋯</span><span class=MJXp-mspace id=MJXp-Span-6012 style=width:0.33em;height:0em></span></span><span class=MJXp-mtd id=MJXp-Span-6013 style=padding-left:0.8em;text-align:center><span class=MJXp-mo id=MJXp-Span-6014 style=margin-left:0em;margin-right:0em>⋯</span><span class=MJXp-mspace id=MJXp-Span-6015 style=width:0.33em;height:0em></span></span><span class=MJXp-mtd id=MJXp-Span-6016 style=padding-left:0.8em;text-align:center><span class=MJXp-mo id=MJXp-Span-6017 style=margin-left:0em;margin-right:0em>⋯</span><span class=MJXp-mspace id=MJXp-Span-6018 style=width:0.33em;height:0em></span></span><span class=MJXp-mtd id=MJXp-Span-6019 style=padding-left:0.8em;text-align:center><span class=MJXp-mo id=MJXp-Span-6020 style=margin-left:0em;margin-right:0em>⋯</span></span></span><span class=MJXp-mtr id=MJXp-Span-6021 style=vertical-align:baseline><span class=MJXp-mtd id=MJXp-Span-6022 style=padding-top:0.431em;text-align:center><span class=MJXp-mo id=MJXp-Span-6023 style=margin-left:0em;margin-right:0em>⋯</span><span class=MJXp-mspace id=MJXp-Span-6024 style=width:0.33em;height:0em></span></span><span class=MJXp-mtd id=MJXp-Span-6025 style=padding-left:0.8em;padding-top:0.431em;text-align:center><span class=MJXp-mo id=MJXp-Span-6026 style=margin-left:0em;margin-right:0em>⋯</span><span class=MJXp-mspace id=MJXp-Span-6027 style=width:0.33em;height:0em></span></span><span class=MJXp-mtd id=MJXp-Span-6028 style=padding-left:0.8em;padding-top:0.431em;text-align:center><span class=MJXp-mstyle id=MJXp-Span-6029><span class=MJXp-mtext id=MJXp-Span-6030></span></span><span class=MJXp-mfrac id=MJXp-Span-6031 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-6032><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6033>γ</span><span class=MJXp-mo id=MJXp-Span-6034 style=margin-left:0.267em;margin-right:0.267em>−</span><span class=MJXp-mn id=MJXp-Span-6035>1</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-6036><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6037>β</span></span></span></span></span></span></span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6038>δ</span><span class=MJXp-msub id=MJXp-Span-6039><span class=MJXp-mrow id=MJXp-Span-6040 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6041>β</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-6042 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-6043>2</span></span></span></span><span class=MJXp-mtd id=MJXp-Span-6044 style=padding-left:0.8em;padding-top:0.431em;text-align:center><span class=MJXp-mo id=MJXp-Span-6045 style=margin-left:0em;margin-right:0em>⋯</span></span></span><span class=MJXp-mtr id=MJXp-Span-6046 style=vertical-align:baseline><span class=MJXp-mtd id=MJXp-Span-6047 style=padding-top:0.431em;text-align:center><span class=MJXp-mo id=MJXp-Span-6048 style=margin-left:0em;margin-right:0em>⋯</span><span class=MJXp-mspace id=MJXp-Span-6049 style=width:0.33em;height:0em></span></span><span class=MJXp-mtd id=MJXp-Span-6050 style=padding-left:0.8em;padding-top:0.431em;text-align:center><span class=MJXp-mo id=MJXp-Span-6051 style=margin-left:0em;margin-right:0.111em>−</span><span class=MJXp-mfrac id=MJXp-Span-6052 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-6053><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6054>γ</span><span class=MJXp-mo id=MJXp-Span-6055 style=margin-left:0.267em;margin-right:0.267em>−</span><span class=MJXp-mn id=MJXp-Span-6056>1</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-6057><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6058>β</span></span></span></span></span></span></span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6059>δ</span><span class=MJXp-msub id=MJXp-Span-6060><span class=MJXp-mrow id=MJXp-Span-6061 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6062>β</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-6063 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-6064>2</span></span></span></span><span class=MJXp-mtd id=MJXp-Span-6065 style=padding-left:0.8em;padding-top:0.431em;text-align:center><span class=MJXp-mo id=MJXp-Span-6066 style=margin-left:0em;margin-right:0em>⋯</span><span class=MJXp-mspace id=MJXp-Span-6067 style=width:0.33em;height:0em></span></span><span class=MJXp-mtd id=MJXp-Span-6068 style=padding-left:0.8em;padding-top:0.431em;text-align:center><span class=MJXp-mo id=MJXp-Span-6069 style=margin-left:0em;margin-right:0em>⋯</span></span></span><span class=MJXp-mtr id=MJXp-Span-6070 style=vertical-align:baseline><span class=MJXp-mtd id=MJXp-Span-6071 style=padding-top:0.431em;text-align:center><span class=MJXp-mo id=MJXp-Span-6072 style=margin-left:0em;margin-right:0em>⋯</span><span class=MJXp-mspace id=MJXp-Span-6073 style=width:0.33em;height:0em></span></span><span class=MJXp-mtd id=MJXp-Span-6074 style=padding-left:0.8em;padding-top:0.431em;text-align:center><span class=MJXp-mo id=MJXp-Span-6075 style=margin-left:0em;margin-right:0em>⋯</span><span class=MJXp-mspace id=MJXp-Span-6076 style=width:0.33em;height:0em></span></span><span class=MJXp-mtd id=MJXp-Span-6077 style=padding-left:0.8em;padding-top:0.431em;text-align:center><span class=MJXp-mo id=MJXp-Span-6078 style=margin-left:0em;margin-right:0em>⋯</span><span class=MJXp-mspace id=MJXp-Span-6079 style=width:0.33em;height:0em></span></span><span class=MJXp-mtd id=MJXp-Span-6080 style=padding-left:0.8em;padding-top:0.431em;text-align:center><span class=MJXp-mo id=MJXp-Span-6081 style=margin-left:0em;margin-right:0em>⋯</span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-6082 style=margin-left:0em;margin-right:0em;vertical-align:-2.275em><span style=font-size:10.102em;margin-left:-0.25em class="MJXp-right MJXp-scale2">)</span></span></span><span class=MJXp-mo id=MJXp-Span-6083 style=margin-left:0em;margin-right:0.222em>,</span></span></span><span class="mjx-chtml MJXc-display MJXc-processing sf-hidden"></span>
</span>
</div><p> indicating the existence of a rotation of the electron rest frame <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-6084><span class=MJXp-msup id=MJXp-Span-6085><span class=MJXp-mrow id=MJXp-Span-6086 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6087>S</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-6088 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-6089>″</span></span></span></span></span><span id=MathJax-Element-499-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> by <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-6090><span class=MJXp-mi id=MJXp-Span-6091>Δ</span><span class=MJXp-mi id=MJXp-Span-6092>Ω</span></span></span><span id=MathJax-Element-500-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> about the <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-6093><span class=MJXp-msub id=MJXp-Span-6094><span class=MJXp-mrow id=MJXp-Span-6095 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6096>x</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-6097 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-6098>3</span></span></span></span></span><span id=MathJax-Element-501-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> axis. Because of the spacetime symmetry of the LT in (<a href=#j_phys-2023-0110_eq_020 class="link link-disp-formula" data-bs-target=j_phys-2023-0110_eq_020>A2</a>), the parameter time depends on space, <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-6099><span class=MJXp-msup id=MJXp-Span-6100><span class=MJXp-mrow id=MJXp-Span-6101 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6102>t</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-6103 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-6104>″</span></span></span><span class=MJXp-mo id=MJXp-Span-6105 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-msup id=MJXp-Span-6106><span class=MJXp-mrow id=MJXp-Span-6107 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6108>t</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-6109 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-6110>″</span></span></span><span class=MJXp-mrow id=MJXp-Span-6111><span class=MJXp-mo id=MJXp-Span-6112 style=margin-left:0em;margin-right:0em>(</span><span class=MJXp-mrow id=MJXp-Span-6113><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6114>t</span><span class=MJXp-mo id=MJXp-Span-6115 style=margin-left:0em;margin-right:0.222em>,</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6116>x</span></span><span class=MJXp-mo id=MJXp-Span-6117 style=margin-left:0em;margin-right:0em>)</span></span></span></span><span id=MathJax-Element-502-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> and <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-6118><span class=MJXp-msup id=MJXp-Span-6119><span class=MJXp-mrow id=MJXp-Span-6120 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6121>t</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-6122 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-6123>′</span></span></span><span class=MJXp-mo id=MJXp-Span-6124 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-msup id=MJXp-Span-6125><span class=MJXp-mrow id=MJXp-Span-6126 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6127>t</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-6128 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-6129>′</span></span></span><span class=MJXp-mrow id=MJXp-Span-6130><span class=MJXp-mo id=MJXp-Span-6131 style=margin-left:0em;margin-right:0em>(</span><span class=MJXp-mrow id=MJXp-Span-6132><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6133>t</span><span class=MJXp-mo id=MJXp-Span-6134 style=margin-left:0em;margin-right:0.222em>,</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6135>x</span></span><span class=MJXp-mo id=MJXp-Span-6136 style=margin-left:0em;margin-right:0em>)</span></span></span></span><span id=MathJax-Element-503-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>. Therefore, through the matrix multiplication (<a href=#j_phys-2023-0110_eq_023 class="link link-disp-formula" data-bs-target=j_phys-2023-0110_eq_023>A4</a>), we can see that the time dependence on space, related to relative simultaneity, is essential for providing the resulting antisymmetric matrix elements <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-6137><span class=MJXp-msub id=MJXp-Span-6138><span class=MJXp-mrow id=MJXp-Span-6139 style=margin-right:0.05em><span class=MJXp-mrow id=MJXp-Span-6140><span class=MJXp-mo id=MJXp-Span-6141 style=margin-left:0em;margin-right:0em;vertical-align:-0.244em><span style=font-size:1.978em;margin-left:-0.05em class="MJXp-right MJXp-scale7">(</span></span><span class=MJXp-mrow id=MJXp-Span-6142><span class=MJXp-msub id=MJXp-Span-6143><span class=MJXp-mrow id=MJXp-Span-6144 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6145>A</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-6146 style=vertical-align:-0.4em><span class=MJXp-mi id=MJXp-Span-6147>LT</span></span></span></span><span class=MJXp-mo id=MJXp-Span-6148 style=margin-left:0em;margin-right:0em;vertical-align:-0.244em><span style=font-size:1.978em;margin-left:-0.05em class="MJXp-right MJXp-scale7">)</span></span></span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-6149 style=vertical-align:-0.74em><span class=MJXp-mn id=MJXp-Span-6150>23</span></span></span></span></span><span id=MathJax-Element-504-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> and <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-6151><span class=MJXp-msub id=MJXp-Span-6152><span class=MJXp-mrow id=MJXp-Span-6153 style=margin-right:0.05em><span class=MJXp-mrow id=MJXp-Span-6154><span class=MJXp-mo id=MJXp-Span-6155 style=margin-left:0em;margin-right:0em;vertical-align:-0.244em><span style=font-size:1.978em;margin-left:-0.05em class="MJXp-right MJXp-scale7">(</span></span><span class=MJXp-mrow id=MJXp-Span-6156><span class=MJXp-msub id=MJXp-Span-6157><span class=MJXp-mrow id=MJXp-Span-6158 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6159>A</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-6160 style=vertical-align:-0.4em><span class=MJXp-mi id=MJXp-Span-6161>LT</span></span></span></span><span class=MJXp-mo id=MJXp-Span-6162 style=margin-left:0em;margin-right:0em;vertical-align:-0.244em><span style=font-size:1.978em;margin-left:-0.05em class="MJXp-right MJXp-scale7">)</span></span></span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-6163 style=vertical-align:-0.74em><span class=MJXp-mn id=MJXp-Span-6164>32</span></span></span></span></span><span id=MathJax-Element-505-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> of <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-6165><span class=MJXp-msub id=MJXp-Span-6166><span class=MJXp-mrow id=MJXp-Span-6167 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6168>A</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-6169 style=vertical-align:-0.4em><span class=MJXp-msub id=MJXp-Span-6170><span class=MJXp-mrow id=MJXp-Span-6171 style=margin-right:0.05em></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-6172 style=vertical-align:-0.2em><span class=MJXp-mi id=MJXp-Span-6173>LT</span></span></span></span></span></span></span><span id=MathJax-Element-506-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> shown in (<a href=#j_phys-2023-0110_eq_026 class="link link-disp-formula" data-bs-target=j_phys-2023-0110_eq_026>A7</a>).</p>
<p>A direct consequence of expression (<a href=#j_phys-2023-0110_eq_025 class="link link-disp-formula" data-bs-target=j_phys-2023-0110_eq_025>A6</a>) is the resulting Thomas precession acquired by the object at the angular velocity, <div class=formula id=j_phys-2023-0110_eq_027>
<span class=label>(A8)</span>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class="MJXp-math MJXp-display" id=MJXp-Span-6174><span class=MJXp-msub id=MJXp-Span-6175><span class=MJXp-mrow id=MJXp-Span-6176 style=margin-right:0.05em><span class="MJXp-mi MJXp-bold MJXp-italic" id=MJXp-Span-6177>ω</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-6178 style=vertical-align:-0.4em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6179>T</span></span></span><span class=MJXp-mo id=MJXp-Span-6180 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-mo id=MJXp-Span-6181 style=margin-left:0.267em;margin-right:0.267em>−</span><span class=MJXp-munder id=MJXp-Span-6182><span><span class=MJXp-mrow id=MJXp-Span-6183><span class=MJXp-mi id=MJXp-Span-6184>lim</span></span></span><span class=MJXp-script><span class=MJXp-mrow id=MJXp-Span-6185 style=margin-left:0px><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6186>δ</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6187>t</span><span class=MJXp-mo id=MJXp-Span-6188>→</span><span class=MJXp-mn id=MJXp-Span-6189>0</span></span></span></span><span class=MJXp-mfrac id=MJXp-Span-6190 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-6191><span class=MJXp-mi id=MJXp-Span-6192>Δ</span><span class="MJXp-mi MJXp-bold" id=MJXp-Span-6193>Ω</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-6194><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6195>δ</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6196>t</span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-6197 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-mfrac id=MJXp-Span-6198 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-6199><span class=MJXp-msup id=MJXp-Span-6200><span class=MJXp-mrow id=MJXp-Span-6201 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6202>γ</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-6203 style=vertical-align:0.5em><span class=MJXp-mn id=MJXp-Span-6204>2</span></span></span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-6205><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6206>γ</span><span class=MJXp-mo id=MJXp-Span-6207 style=margin-left:0.267em;margin-right:0.267em>+</span><span class=MJXp-mn id=MJXp-Span-6208>1</span></span></span></span></span></span></span><span class=MJXp-mfrac id=MJXp-Span-6209 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-6210><span class="MJXp-mi MJXp-bold" id=MJXp-Span-6211>a</span><span class=MJXp-mo id=MJXp-Span-6212 style=margin-left:0.267em;margin-right:0.267em>×</span><span class="MJXp-mi MJXp-bold" id=MJXp-Span-6213>v</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-6214><span class=MJXp-msup id=MJXp-Span-6215><span class=MJXp-mrow id=MJXp-Span-6216 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6217>c</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-6218 style=vertical-align:0.5em><span class=MJXp-mn id=MJXp-Span-6219>2</span></span></span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-6220 style=margin-left:0em;margin-right:0.222em>.</span></span></span><span class="mjx-chtml MJXc-display MJXc-processing sf-hidden"></span>
</span>
</div><p> Then, if the rotating object has a component of <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-6221><span class="MJXp-mi MJXp-bold" id=MJXp-Span-6222>a</span></span></span><span id=MathJax-Element-508-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> perpendicular to <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-6223><span class="MJXp-mi MJXp-bold" id=MJXp-Span-6224>v</span></span></span><span id=MathJax-Element-509-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>, the object acquires a Thomas precession of purely kinematical origin, independent of other effects.</p>
<p>
<strong>The LTA based on absolute simultaneity predict no Thomas precession</strong>
</p>
<p>The LTs based on absolute simultaneity (LTA) between frame <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-6225><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6226>S</span></span></span><span id=MathJax-Element-510-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> and <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-6227><span class=MJXp-msup id=MJXp-Span-6228><span class=MJXp-mrow id=MJXp-Span-6229 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6230>S</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-6231 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-6232>″</span></span></span></span></span><span id=MathJax-Element-511-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> are given by, <div class=formula id=j_phys-2023-0110_eq_028>
<span class=label>(A9)</span>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class="MJXp-math MJXp-display" id=MJXp-Span-6233><span class=MJXp-mtable id=MJXp-Span-6234><span><span class=MJXp-mtr id=MJXp-Span-6235 style=vertical-align:baseline><span class=MJXp-mtd id=MJXp-Span-6236 style=text-align:center><span class=MJXp-msubsup id=MJXp-Span-6237><span class=MJXp-mrow id=MJXp-Span-6238 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6239>x</span></span><span class=MJXp-script-box style=height:1.86em;vertical-align:-0.64em><span class=MJXp-script><span><span style=margin-bottom:-0.25em><span class=MJXp-mrow id=MJXp-Span-6242><span class=MJXp-mo id=MJXp-Span-6243>″</span></span></span></span></span><span class=MJXp-script><span><span style=margin-top:-0.85em><span class=MJXp-mrow id=MJXp-Span-6240><span class=MJXp-mn id=MJXp-Span-6241>0</span></span></span></span></span></span></span></span><span class=MJXp-mtd id=MJXp-Span-6244 style=padding-left:0.33em;text-align:center><span class=MJXp-mo id=MJXp-Span-6245 style=margin-left:0.333em;margin-right:0.333em>=</span></span><span class=MJXp-mtd id=MJXp-Span-6246 style=padding-left:0.33em;text-align:center><span class=MJXp-msubsup id=MJXp-Span-6247><span class=MJXp-mrow id=MJXp-Span-6248 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6249>γ</span></span><span class=MJXp-script-box style=height:1.86em;vertical-align:-0.64em><span class=MJXp-script><span><span style=margin-bottom:-0.25em><span class=MJXp-mrow id=MJXp-Span-6252><span class=MJXp-mo id=MJXp-Span-6253>−</span><span class=MJXp-mn id=MJXp-Span-6254>1</span></span></span></span></span><span class=MJXp-script><span><span style=margin-top:-0.85em><span class=MJXp-mrow id=MJXp-Span-6250><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6251>u</span></span></span></span></span></span></span><span class=MJXp-msub id=MJXp-Span-6255><span class=MJXp-mrow id=MJXp-Span-6256 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6257>x</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-6258 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-6259>0</span></span></span></span></span><span class=MJXp-mtr id=MJXp-Span-6260 style=vertical-align:baseline><span class=MJXp-mtd id=MJXp-Span-6261 style=padding-top:0.431em;text-align:center><span class=MJXp-msubsup id=MJXp-Span-6262><span class=MJXp-mrow id=MJXp-Span-6263 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6264>x</span></span><span class=MJXp-script-box style=height:1.86em;vertical-align:-0.64em><span class=MJXp-script><span><span style=margin-bottom:-0.25em><span class=MJXp-mrow id=MJXp-Span-6267><span class=MJXp-mo id=MJXp-Span-6268>″</span></span></span></span></span><span class=MJXp-script><span><span style=margin-top:-0.85em><span class=MJXp-mrow id=MJXp-Span-6265><span class=MJXp-mn id=MJXp-Span-6266>1</span></span></span></span></span></span></span></span><span class=MJXp-mtd id=MJXp-Span-6269 style=padding-left:0.33em;padding-top:0.431em;text-align:center><span class=MJXp-mo id=MJXp-Span-6270 style=margin-left:0.333em;margin-right:0.333em>=</span></span><span class=MJXp-mtd id=MJXp-Span-6271 style=padding-left:0.33em;padding-top:0.431em;text-align:center><span class=MJXp-msub id=MJXp-Span-6272><span class=MJXp-mrow id=MJXp-Span-6273 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6274>x</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-6275 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-6276>1</span></span></span><span class=MJXp-mo id=MJXp-Span-6277 style=margin-left:0.267em;margin-right:0.267em>+</span><span class=MJXp-mfrac id=MJXp-Span-6278 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-6279><span class=MJXp-msub id=MJXp-Span-6280><span class=MJXp-mrow id=MJXp-Span-6281 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6282>γ</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-6283 style=vertical-align:-0.4em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6284>u</span></span></span><span class=MJXp-mo id=MJXp-Span-6285 style=margin-left:0.267em;margin-right:0.267em>−</span><span class=MJXp-mn id=MJXp-Span-6286>1</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-6287><span class=MJXp-msup id=MJXp-Span-6288><span class=MJXp-mrow id=MJXp-Span-6289 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6290>β</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-6291 style=vertical-align:0.5em><span class=MJXp-mn id=MJXp-Span-6292>2</span></span></span></span></span></span></span></span></span><span class=MJXp-mrow id=MJXp-Span-6293><span class=MJXp-mo id=MJXp-Span-6294 style=margin-left:0em;margin-right:0em;vertical-align:-0.244em><span style=font-size:1.978em;margin-left:-0.05em class="MJXp-right MJXp-scale7">(</span></span><span class=MJXp-mrow id=MJXp-Span-6295><span class=MJXp-msub id=MJXp-Span-6296><span class=MJXp-mrow id=MJXp-Span-6297 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6298>β</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-6299 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-6300>1</span></span></span><span class=MJXp-msub id=MJXp-Span-6301><span class=MJXp-mrow id=MJXp-Span-6302 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6303>x</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-6304 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-6305>1</span></span></span><span class=MJXp-mo id=MJXp-Span-6306 style=margin-left:0.267em;margin-right:0.267em>+</span><span class=MJXp-msub id=MJXp-Span-6307><span class=MJXp-mrow id=MJXp-Span-6308 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6309>β</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-6310 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-6311>2</span></span></span><span class=MJXp-msub id=MJXp-Span-6312><span class=MJXp-mrow id=MJXp-Span-6313 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6314>x</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-6315 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-6316>2</span></span></span></span><span class=MJXp-mo id=MJXp-Span-6317 style=margin-left:0em;margin-right:0em;vertical-align:-0.244em><span style=font-size:1.978em;margin-left:-0.05em class="MJXp-right MJXp-scale7">)</span></span></span><span class=MJXp-msub id=MJXp-Span-6318><span class=MJXp-mrow id=MJXp-Span-6319 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6320>β</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-6321 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-6322>1</span></span></span><span class=MJXp-mo id=MJXp-Span-6323 style=margin-left:0.267em;margin-right:0.267em>−</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6324>γ</span><span class=MJXp-msub id=MJXp-Span-6325><span class=MJXp-mrow id=MJXp-Span-6326 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6327>β</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-6328 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-6329>1</span></span></span><span class=MJXp-msub id=MJXp-Span-6330><span class=MJXp-mrow id=MJXp-Span-6331 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6332>x</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-6333 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-6334>0</span></span></span></span></span><span class=MJXp-mtr id=MJXp-Span-6335 style=vertical-align:baseline><span class=MJXp-mtd id=MJXp-Span-6336 style=padding-top:0.431em;text-align:center><span class=MJXp-msubsup id=MJXp-Span-6337><span class=MJXp-mrow id=MJXp-Span-6338 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6339>x</span></span><span class=MJXp-script-box style=height:1.86em;vertical-align:-0.64em><span class=MJXp-script><span><span style=margin-bottom:-0.25em><span class=MJXp-mrow id=MJXp-Span-6342><span class=MJXp-mo id=MJXp-Span-6343>″</span></span></span></span></span><span class=MJXp-script><span><span style=margin-top:-0.85em><span class=MJXp-mrow id=MJXp-Span-6340><span class=MJXp-mn id=MJXp-Span-6341>2</span></span></span></span></span></span></span></span><span class=MJXp-mtd id=MJXp-Span-6344 style=padding-left:0.33em;padding-top:0.431em;text-align:center><span class=MJXp-mo id=MJXp-Span-6345 style=margin-left:0.333em;margin-right:0.333em>=</span></span><span class=MJXp-mtd id=MJXp-Span-6346 style=padding-left:0.33em;padding-top:0.431em;text-align:center><span class=MJXp-msub id=MJXp-Span-6347><span class=MJXp-mrow id=MJXp-Span-6348 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6349>x</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-6350 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-6351>2</span></span></span><span class=MJXp-mo id=MJXp-Span-6352 style=margin-left:0.267em;margin-right:0.267em>+</span><span class=MJXp-mfrac id=MJXp-Span-6353 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-6354><span class=MJXp-msub id=MJXp-Span-6355><span class=MJXp-mrow id=MJXp-Span-6356 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6357>γ</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-6358 style=vertical-align:-0.4em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6359>u</span></span></span><span class=MJXp-mo id=MJXp-Span-6360 style=margin-left:0.267em;margin-right:0.267em>−</span><span class=MJXp-mn id=MJXp-Span-6361>1</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-6362><span class=MJXp-msup id=MJXp-Span-6363><span class=MJXp-mrow id=MJXp-Span-6364 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6365>β</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-6366 style=vertical-align:0.5em><span class=MJXp-mn id=MJXp-Span-6367>2</span></span></span></span></span></span></span></span></span><span class=MJXp-mrow id=MJXp-Span-6368><span class=MJXp-mo id=MJXp-Span-6369 style=margin-left:0em;margin-right:0em;vertical-align:-0.244em><span style=font-size:1.978em;margin-left:-0.05em class="MJXp-right MJXp-scale7">(</span></span><span class=MJXp-mrow id=MJXp-Span-6370><span class=MJXp-msub id=MJXp-Span-6371><span class=MJXp-mrow id=MJXp-Span-6372 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6373>β</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-6374 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-6375>1</span></span></span><span class=MJXp-msub id=MJXp-Span-6376><span class=MJXp-mrow id=MJXp-Span-6377 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6378>x</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-6379 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-6380>1</span></span></span><span class=MJXp-mo id=MJXp-Span-6381 style=margin-left:0.267em;margin-right:0.267em>+</span><span class=MJXp-msub id=MJXp-Span-6382><span class=MJXp-mrow id=MJXp-Span-6383 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6384>β</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-6385 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-6386>2</span></span></span><span class=MJXp-msub id=MJXp-Span-6387><span class=MJXp-mrow id=MJXp-Span-6388 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6389>x</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-6390 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-6391>2</span></span></span></span><span class=MJXp-mo id=MJXp-Span-6392 style=margin-left:0em;margin-right:0em;vertical-align:-0.244em><span style=font-size:1.978em;margin-left:-0.05em class="MJXp-right MJXp-scale7">)</span></span></span><span class=MJXp-msub id=MJXp-Span-6393><span class=MJXp-mrow id=MJXp-Span-6394 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6395>β</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-6396 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-6397>2</span></span></span><span class=MJXp-mo id=MJXp-Span-6398 style=margin-left:0.267em;margin-right:0.267em>−</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6399>γ</span><span class=MJXp-msub id=MJXp-Span-6400><span class=MJXp-mrow id=MJXp-Span-6401 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6402>β</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-6403 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-6404>2</span></span></span><span class=MJXp-msub id=MJXp-Span-6405><span class=MJXp-mrow id=MJXp-Span-6406 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6407>x</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-6408 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-6409>0</span></span></span></span></span><span class=MJXp-mtr id=MJXp-Span-6410 style=vertical-align:baseline><span class=MJXp-mtd id=MJXp-Span-6411 style=padding-top:0.431em;text-align:center><span class=MJXp-msubsup id=MJXp-Span-6412><span class=MJXp-mrow id=MJXp-Span-6413 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6414>x</span></span><span class=MJXp-script-box style=height:1.86em;vertical-align:-0.64em><span class=MJXp-script><span><span style=margin-bottom:-0.25em><span class=MJXp-mrow id=MJXp-Span-6417><span class=MJXp-mo id=MJXp-Span-6418>″</span></span></span></span></span><span class=MJXp-script><span><span style=margin-top:-0.85em><span class=MJXp-mrow id=MJXp-Span-6415><span class=MJXp-mn id=MJXp-Span-6416>3</span></span></span></span></span></span></span></span><span class=MJXp-mtd id=MJXp-Span-6419 style=padding-left:0.33em;padding-top:0.431em;text-align:center><span class=MJXp-mo id=MJXp-Span-6420 style=margin-left:0.333em;margin-right:0.333em>=</span></span><span class=MJXp-mtd id=MJXp-Span-6421 style=padding-left:0.33em;padding-top:0.431em;text-align:center><span class=MJXp-msub id=MJXp-Span-6422><span class=MJXp-mrow id=MJXp-Span-6423 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6424>x</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-6425 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-6426>3</span></span></span><span class=MJXp-mo id=MJXp-Span-6427 style=margin-left:0em;margin-right:0.222em>,</span></span></span></span></span></span></span><span class="mjx-chtml MJXc-display MJXc-processing sf-hidden"></span>
</span>
</div><p> which are the same as the LT in (<a href=#j_phys-2023-0110_eq_020 class="link link-disp-formula" data-bs-target=j_phys-2023-0110_eq_020>A2</a>), save for the fact that the time parameter does not depend on space (absolute simultaneity) and is given by <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-6428><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6429>c</span><span class=MJXp-msup id=MJXp-Span-6430><span class=MJXp-mrow id=MJXp-Span-6431 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6432>τ</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-6433 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-6434>″</span></span></span><span class=MJXp-mo id=MJXp-Span-6435 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-msubsup id=MJXp-Span-6436><span class=MJXp-mrow id=MJXp-Span-6437 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6438>x</span></span><span class=MJXp-script-box style=height:1.86em;vertical-align:-0.64em><span class=MJXp-script><span><span style=margin-bottom:-0.25em><span class=MJXp-mrow id=MJXp-Span-6441><span class=MJXp-mo id=MJXp-Span-6442>″</span></span></span></span></span><span class=MJXp-script><span><span style=margin-top:-0.85em><span class=MJXp-mrow id=MJXp-Span-6439><span class=MJXp-mn id=MJXp-Span-6440>0</span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-6443 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-msubsup id=MJXp-Span-6444><span class=MJXp-mrow id=MJXp-Span-6445 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6446>γ</span></span><span class=MJXp-script-box style=height:1.86em;vertical-align:-0.64em><span class=MJXp-script><span><span style=margin-bottom:-0.25em><span class=MJXp-mrow id=MJXp-Span-6449><span class=MJXp-mo id=MJXp-Span-6450>−</span><span class=MJXp-mn id=MJXp-Span-6451>1</span></span></span></span></span><span class=MJXp-script><span><span style=margin-top:-0.85em><span class=MJXp-mrow id=MJXp-Span-6447><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6448>u</span></span></span></span></span></span></span><span class=MJXp-msub id=MJXp-Span-6452><span class=MJXp-mrow id=MJXp-Span-6453 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6454>x</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-6455 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-6456>0</span></span></span></span></span><span id=MathJax-Element-513-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>, being <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-6457><span class=MJXp-msup id=MJXp-Span-6458><span class=MJXp-mrow id=MJXp-Span-6459 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6460>τ</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-6461 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-6462>″</span></span></span></span></span><span id=MathJax-Element-514-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> the proper time on the particle rest frame <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-6463><span class=MJXp-msup id=MJXp-Span-6464><span class=MJXp-mrow id=MJXp-Span-6465 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6466>S</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-6467 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-6468>″</span></span></span></span></span><span id=MathJax-Element-515-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>.</p>
<p>Obviously, the spacetime symmetry of the LT is different from that of the LTA and, therefore, for observables that depend on symmetry, different predictions may be expected from the two different transformations.</p>
<p>Following the procedure adopted earlier, we proceed by calculating the connection, <div class=formula id=j_phys-2023-0110_eq_029>
<span class=label>(A10)</span>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class="MJXp-math MJXp-display" id=MJXp-Span-6469><span class=MJXp-msup id=MJXp-Span-6470><span class=MJXp-mrow id=MJXp-Span-6471 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6472>x</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-6473 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-6474>″</span></span></span><span class=MJXp-mo id=MJXp-Span-6475 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-msub id=MJXp-Span-6476><span class=MJXp-mrow id=MJXp-Span-6477 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6478>A</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-6479 style=vertical-align:-0.4em><span class=MJXp-mi id=MJXp-Span-6480>LTA</span></span></span><span class=MJXp-mspace id=MJXp-Span-6481 style=width:0.33em;height:0em></span><span class=MJXp-msup id=MJXp-Span-6482><span class=MJXp-mrow id=MJXp-Span-6483 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6484>x</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-6485 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-6486>′</span></span></span><span class=MJXp-mo id=MJXp-Span-6487 style=margin-left:0em;margin-right:0.222em>,</span></span></span><span class="mjx-chtml MJXc-display MJXc-processing sf-hidden"></span>
</span>
</div><p> using the LTA (instead of the LT) and derive the corresponding matrix <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-6488><span class=MJXp-msub id=MJXp-Span-6489><span class=MJXp-mrow id=MJXp-Span-6490 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6491>A</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-6492 style=vertical-align:-0.4em><span class=MJXp-mi id=MJXp-Span-6493>LTA</span></span></span></span></span><span id=MathJax-Element-517-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> (<a href=#j_phys-2023-0110_eq_033 class="link link-disp-formula" data-bs-target=j_phys-2023-0110_eq_033>A14</a>).</p>
<p>The transformations between frame <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-6494><span class=MJXp-msup id=MJXp-Span-6495><span class=MJXp-mrow id=MJXp-Span-6496 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6497>S</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-6498 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-6499>′</span></span></span></span></span><span id=MathJax-Element-518-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> and <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-6500><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6501>S</span></span></span><span id=MathJax-Element-519-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> are, <div class=formula id=j_phys-2023-0110_eq_030>
<span class=label>(A11)</span>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class="MJXp-math MJXp-display" id=MJXp-Span-6502><span class=MJXp-mtable id=MJXp-Span-6503><span><span class=MJXp-mtr id=MJXp-Span-6504 style=vertical-align:baseline><span class=MJXp-mtd id=MJXp-Span-6505 style=text-align:center><span class=MJXp-msubsup id=MJXp-Span-6506><span class=MJXp-mrow id=MJXp-Span-6507 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6508>x</span></span><span class=MJXp-script-box style=height:1.86em;vertical-align:-0.64em><span class=MJXp-script><span><span style=margin-bottom:-0.25em><span class=MJXp-mrow id=MJXp-Span-6511><span class=MJXp-mo id=MJXp-Span-6512>′</span></span></span></span></span><span class=MJXp-script><span><span style=margin-top:-0.85em><span class=MJXp-mrow id=MJXp-Span-6509><span class=MJXp-mn id=MJXp-Span-6510>0</span></span></span></span></span></span></span></span><span class=MJXp-mtd id=MJXp-Span-6513 style=padding-left:0.33em;text-align:center><span class=MJXp-mo id=MJXp-Span-6514 style=margin-left:0.333em;margin-right:0.333em>=</span></span><span class=MJXp-mtd id=MJXp-Span-6515 style=padding-left:0.33em;text-align:center><span class=MJXp-msup id=MJXp-Span-6516><span class=MJXp-mrow id=MJXp-Span-6517 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6518>γ</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-6519 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-6520>−</span><span class=MJXp-mn id=MJXp-Span-6521>1</span></span></span><span class=MJXp-msub id=MJXp-Span-6522><span class=MJXp-mrow id=MJXp-Span-6523 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6524>x</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-6525 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-6526>0</span></span></span><span class=MJXp-mo id=MJXp-Span-6527 style=margin-left:0.333em;margin-right:0.333em>⇒</span><span class=MJXp-msub id=MJXp-Span-6528><span class=MJXp-mrow id=MJXp-Span-6529 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6530>x</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-6531 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-6532>0</span></span></span><span class=MJXp-mo id=MJXp-Span-6533 style=margin-left:0.333em;margin-right:0.333em>=</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6534>γ</span><span class=MJXp-msubsup id=MJXp-Span-6535><span class=MJXp-mrow id=MJXp-Span-6536 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6537>x</span></span><span class=MJXp-script-box style=height:1.86em;vertical-align:-0.64em><span class=MJXp-script><span><span style=margin-bottom:-0.25em><span class=MJXp-mrow id=MJXp-Span-6540><span class=MJXp-mo id=MJXp-Span-6541>′</span></span></span></span></span><span class=MJXp-script><span><span style=margin-top:-0.85em><span class=MJXp-mrow id=MJXp-Span-6538><span class=MJXp-mn id=MJXp-Span-6539>0</span></span></span></span></span></span></span></span></span><span class=MJXp-mtr id=MJXp-Span-6542 style=vertical-align:baseline><span class=MJXp-mtd id=MJXp-Span-6543 style=padding-top:0.431em;text-align:center><span class=MJXp-msubsup id=MJXp-Span-6544><span class=MJXp-mrow id=MJXp-Span-6545 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6546>x</span></span><span class=MJXp-script-box style=height:1.86em;vertical-align:-0.64em><span class=MJXp-script><span><span style=margin-bottom:-0.25em><span class=MJXp-mrow id=MJXp-Span-6549><span class=MJXp-mo id=MJXp-Span-6550>′</span></span></span></span></span><span class=MJXp-script><span><span style=margin-top:-0.85em><span class=MJXp-mrow id=MJXp-Span-6547><span class=MJXp-mn id=MJXp-Span-6548>1</span></span></span></span></span></span></span></span><span class=MJXp-mtd id=MJXp-Span-6551 style=padding-left:0.33em;padding-top:0.431em;text-align:center><span class=MJXp-mo id=MJXp-Span-6552 style=margin-left:0.333em;margin-right:0.333em>=</span></span><span class=MJXp-mtd id=MJXp-Span-6553 style=padding-left:0.33em;padding-top:0.431em;text-align:center><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6554>γ</span><span class=MJXp-mrow id=MJXp-Span-6555><span class=MJXp-mo id=MJXp-Span-6556 style=margin-left:0em;margin-right:0em;vertical-align:-0.244em><span style=font-size:1.978em;margin-left:-0.05em class="MJXp-right MJXp-scale7">(</span></span><span class=MJXp-mrow id=MJXp-Span-6557><span class=MJXp-msub id=MJXp-Span-6558><span class=MJXp-mrow id=MJXp-Span-6559 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6560>x</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-6561 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-6562>1</span></span></span><span class=MJXp-mo id=MJXp-Span-6563 style=margin-left:0.267em;margin-right:0.267em>−</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6564>β</span><span class=MJXp-msub id=MJXp-Span-6565><span class=MJXp-mrow id=MJXp-Span-6566 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6567>x</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-6568 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-6569>0</span></span></span></span><span class=MJXp-mo id=MJXp-Span-6570 style=margin-left:0em;margin-right:0em;vertical-align:-0.244em><span style=font-size:1.978em;margin-left:-0.05em class="MJXp-right MJXp-scale7">)</span></span></span><span class=MJXp-mo id=MJXp-Span-6571 style=margin-left:0.333em;margin-right:0.333em>⇒</span><span class=MJXp-msub id=MJXp-Span-6572><span class=MJXp-mrow id=MJXp-Span-6573 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6574>x</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-6575 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-6576>1</span></span></span><span class=MJXp-mo id=MJXp-Span-6577 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-msup id=MJXp-Span-6578><span class=MJXp-mrow id=MJXp-Span-6579 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6580>γ</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-6581 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-6582>−</span><span class=MJXp-mn id=MJXp-Span-6583>1</span></span></span><span class=MJXp-msubsup id=MJXp-Span-6584><span class=MJXp-mrow id=MJXp-Span-6585 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6586>x</span></span><span class=MJXp-script-box style=height:1.86em;vertical-align:-0.64em><span class=MJXp-script><span><span style=margin-bottom:-0.25em><span class=MJXp-mrow id=MJXp-Span-6589><span class=MJXp-mo id=MJXp-Span-6590>′</span></span></span></span></span><span class=MJXp-script><span><span style=margin-top:-0.85em><span class=MJXp-mrow id=MJXp-Span-6587><span class=MJXp-mn id=MJXp-Span-6588>1</span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-6591 style=margin-left:0.267em;margin-right:0.267em>+</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6592>γ</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6593>β</span><span class=MJXp-msubsup id=MJXp-Span-6594><span class=MJXp-mrow id=MJXp-Span-6595 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6596>x</span></span><span class=MJXp-script-box style=height:1.86em;vertical-align:-0.64em><span class=MJXp-script><span><span style=margin-bottom:-0.25em><span class=MJXp-mrow id=MJXp-Span-6599><span class=MJXp-mo id=MJXp-Span-6600>′</span></span></span></span></span><span class=MJXp-script><span><span style=margin-top:-0.85em><span class=MJXp-mrow id=MJXp-Span-6597><span class=MJXp-mn id=MJXp-Span-6598>0</span></span></span></span></span></span></span></span></span><span class=MJXp-mtr id=MJXp-Span-6601 style=vertical-align:baseline><span class=MJXp-mtd id=MJXp-Span-6602 style=padding-top:0.431em;text-align:center><span class=MJXp-msubsup id=MJXp-Span-6603><span class=MJXp-mrow id=MJXp-Span-6604 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6605>x</span></span><span class=MJXp-script-box style=height:1.86em;vertical-align:-0.64em><span class=MJXp-script><span><span style=margin-bottom:-0.25em><span class=MJXp-mrow id=MJXp-Span-6608><span class=MJXp-mo id=MJXp-Span-6609>′</span></span></span></span></span><span class=MJXp-script><span><span style=margin-top:-0.85em><span class=MJXp-mrow id=MJXp-Span-6606><span class=MJXp-mn id=MJXp-Span-6607>2</span></span></span></span></span></span></span></span><span class=MJXp-mtd id=MJXp-Span-6610 style=padding-left:0.33em;padding-top:0.431em;text-align:center><span class=MJXp-mo id=MJXp-Span-6611 style=margin-left:0.333em;margin-right:0.333em>=</span></span><span class=MJXp-mtd id=MJXp-Span-6612 style=padding-left:0.33em;padding-top:0.431em;text-align:center><span class=MJXp-msub id=MJXp-Span-6613><span class=MJXp-mrow id=MJXp-Span-6614 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6615>x</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-6616 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-6617>2</span></span></span><span class=MJXp-mo id=MJXp-Span-6618 style=margin-left:0.333em;margin-right:0.333em>⇒</span><span class=MJXp-msub id=MJXp-Span-6619><span class=MJXp-mrow id=MJXp-Span-6620 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6621>x</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-6622 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-6623>2</span></span></span><span class=MJXp-mo id=MJXp-Span-6624 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-msubsup id=MJXp-Span-6625><span class=MJXp-mrow id=MJXp-Span-6626 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6627>x</span></span><span class=MJXp-script-box style=height:1.86em;vertical-align:-0.64em><span class=MJXp-script><span><span style=margin-bottom:-0.25em><span class=MJXp-mrow id=MJXp-Span-6630><span class=MJXp-mo id=MJXp-Span-6631>′</span></span></span></span></span><span class=MJXp-script><span><span style=margin-top:-0.85em><span class=MJXp-mrow id=MJXp-Span-6628><span class=MJXp-mn id=MJXp-Span-6629>2</span></span></span></span></span></span></span></span></span><span class=MJXp-mtr id=MJXp-Span-6632 style=vertical-align:baseline><span class=MJXp-mtd id=MJXp-Span-6633 style=padding-top:0.431em;text-align:center><span class=MJXp-msubsup id=MJXp-Span-6634><span class=MJXp-mrow id=MJXp-Span-6635 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6636>x</span></span><span class=MJXp-script-box style=height:1.86em;vertical-align:-0.64em><span class=MJXp-script><span><span style=margin-bottom:-0.25em><span class=MJXp-mrow id=MJXp-Span-6639><span class=MJXp-mo id=MJXp-Span-6640>′</span></span></span></span></span><span class=MJXp-script><span><span style=margin-top:-0.85em><span class=MJXp-mrow id=MJXp-Span-6637><span class=MJXp-mn id=MJXp-Span-6638>3</span></span></span></span></span></span></span></span><span class=MJXp-mtd id=MJXp-Span-6641 style=padding-left:0.33em;padding-top:0.431em;text-align:center><span class=MJXp-mo id=MJXp-Span-6642 style=margin-left:0.333em;margin-right:0.333em>=</span></span><span class=MJXp-mtd id=MJXp-Span-6643 style=padding-left:0.33em;padding-top:0.431em;text-align:center><span class=MJXp-msub id=MJXp-Span-6644><span class=MJXp-mrow id=MJXp-Span-6645 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6646>x</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-6647 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-6648>3</span></span></span><span class=MJXp-mo id=MJXp-Span-6649 style=margin-left:0.333em;margin-right:0.333em>⇒</span><span class=MJXp-msub id=MJXp-Span-6650><span class=MJXp-mrow id=MJXp-Span-6651 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6652>x</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-6653 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-6654>3</span></span></span><span class=MJXp-mo id=MJXp-Span-6655 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-msubsup id=MJXp-Span-6656><span class=MJXp-mrow id=MJXp-Span-6657 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6658>x</span></span><span class=MJXp-script-box style=height:1.86em;vertical-align:-0.64em><span class=MJXp-script><span><span style=margin-bottom:-0.25em><span class=MJXp-mrow id=MJXp-Span-6661><span class=MJXp-mo id=MJXp-Span-6662>′</span></span></span></span></span><span class=MJXp-script><span><span style=margin-top:-0.85em><span class=MJXp-mrow id=MJXp-Span-6659><span class=MJXp-mn id=MJXp-Span-6660>3</span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-6663 style=margin-left:0em;margin-right:0.222em>.</span></span></span></span></span></span></span><span class="mjx-chtml MJXc-display MJXc-processing sf-hidden"></span>
</span>
</div><p>
</p>
<p>After substituting <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-6664><span class=MJXp-msub id=MJXp-Span-6665><span class=MJXp-mrow id=MJXp-Span-6666 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6667>x</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-6668 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-6669>0</span></span></span></span></span><span id=MathJax-Element-521-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> and <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-6670><span class=MJXp-msub id=MJXp-Span-6671><span class=MJXp-mrow id=MJXp-Span-6672 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6673>x</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-6674 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-6675>1</span></span></span></span></span><span id=MathJax-Element-522-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> given by (<a href=#j_phys-2023-0110_eq_030 class="link link-disp-formula" data-bs-target=j_phys-2023-0110_eq_030>A11</a>) in expression (<a href=#j_phys-2023-0110_eq_028 class="link link-disp-formula" data-bs-target=j_phys-2023-0110_eq_028>A9</a>), the connection <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-6676><span class=MJXp-msup id=MJXp-Span-6677><span class=MJXp-mrow id=MJXp-Span-6678 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6679>x</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-6680 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-6681>″</span></span></span><span class=MJXp-mo id=MJXp-Span-6682 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-msub id=MJXp-Span-6683><span class=MJXp-mrow id=MJXp-Span-6684 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6685>A</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-6686 style=vertical-align:-0.4em><span class=MJXp-mi id=MJXp-Span-6687>LTA</span></span></span><span class=MJXp-mspace id=MJXp-Span-6688 style=width:0.33em;height:0em></span><span class=MJXp-msup id=MJXp-Span-6689><span class=MJXp-mrow id=MJXp-Span-6690 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6691>x</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-6692 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-6693>′</span></span></span></span></span><span id=MathJax-Element-523-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> of (<a href=#j_phys-2023-0110_eq_029 class="link link-disp-formula" data-bs-target=j_phys-2023-0110_eq_029>A10</a>) to the first order in <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-6694><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6695>δ</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6696>β</span></span></span><span id=MathJax-Element-524-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> is found to be, <div class=formula id=j_phys-2023-0110_eq_031>
<span class=label>(A12)</span>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class="MJXp-math MJXp-display" id=MJXp-Span-6697><span class=MJXp-mtable id=MJXp-Span-6698><span><span class=MJXp-mtr id=MJXp-Span-6699 style=vertical-align:baseline><span class=MJXp-mtd id=MJXp-Span-6700 style=text-align:center><span class=MJXp-msubsup id=MJXp-Span-6701><span class=MJXp-mrow id=MJXp-Span-6702 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6703>x</span></span><span class=MJXp-script-box style=height:1.86em;vertical-align:-0.64em><span class=MJXp-script><span><span style=margin-bottom:-0.25em><span class=MJXp-mrow id=MJXp-Span-6706><span class=MJXp-mo id=MJXp-Span-6707>″</span></span></span></span></span><span class=MJXp-script><span><span style=margin-top:-0.85em><span class=MJXp-mrow id=MJXp-Span-6704><span class=MJXp-mn id=MJXp-Span-6705>0</span></span></span></span></span></span></span></span><span class=MJXp-mtd id=MJXp-Span-6708 style=padding-left:0.33em;text-align:center><span class=MJXp-mo id=MJXp-Span-6709 style=margin-left:0.333em;margin-right:0.333em>=</span></span><span class=MJXp-mtd id=MJXp-Span-6710 style=padding-left:0.33em;text-align:center><span class=MJXp-msubsup id=MJXp-Span-6711><span class=MJXp-mrow id=MJXp-Span-6712 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6713>γ</span></span><span class=MJXp-script-box style=height:1.86em;vertical-align:-0.64em><span class=MJXp-script><span><span style=margin-bottom:-0.25em><span class=MJXp-mrow id=MJXp-Span-6716><span class=MJXp-mo id=MJXp-Span-6717>−</span><span class=MJXp-mn id=MJXp-Span-6718>1</span></span></span></span></span><span class=MJXp-script><span><span style=margin-top:-0.85em><span class=MJXp-mrow id=MJXp-Span-6714><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6715>u</span></span></span></span></span></span></span><span class=MJXp-msub id=MJXp-Span-6719><span class=MJXp-mrow id=MJXp-Span-6720 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6721>x</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-6722 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-6723>0</span></span></span><span class=MJXp-mo id=MJXp-Span-6724 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-msubsup id=MJXp-Span-6725><span class=MJXp-mrow id=MJXp-Span-6726 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6727>γ</span></span><span class=MJXp-script-box style=height:1.86em;vertical-align:-0.64em><span class=MJXp-script><span><span style=margin-bottom:-0.25em><span class=MJXp-mrow id=MJXp-Span-6730><span class=MJXp-mo id=MJXp-Span-6731>−</span><span class=MJXp-mn id=MJXp-Span-6732>1</span></span></span></span></span><span class=MJXp-script><span><span style=margin-top:-0.85em><span class=MJXp-mrow id=MJXp-Span-6728><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6729>u</span></span></span></span></span></span></span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6733>γ</span><span class=MJXp-msubsup id=MJXp-Span-6734><span class=MJXp-mrow id=MJXp-Span-6735 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6736>x</span></span><span class=MJXp-script-box style=height:1.86em;vertical-align:-0.64em><span class=MJXp-script><span><span style=margin-bottom:-0.25em><span class=MJXp-mrow id=MJXp-Span-6739><span class=MJXp-mo id=MJXp-Span-6740>′</span></span></span></span></span><span class=MJXp-script><span><span style=margin-top:-0.85em><span class=MJXp-mrow id=MJXp-Span-6737><span class=MJXp-mn id=MJXp-Span-6738>0</span></span></span></span></span></span></span></span></span><span class=MJXp-mtr id=MJXp-Span-6741 style=vertical-align:baseline><span class=MJXp-mtd id=MJXp-Span-6742 style=padding-top:0.431em;text-align:center><span class=MJXp-msubsup id=MJXp-Span-6743><span class=MJXp-mrow id=MJXp-Span-6744 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6745>x</span></span><span class=MJXp-script-box style=height:1.86em;vertical-align:-0.64em><span class=MJXp-script><span><span style=margin-bottom:-0.25em><span class=MJXp-mrow id=MJXp-Span-6748><span class=MJXp-mo id=MJXp-Span-6749>″</span></span></span></span></span><span class=MJXp-script><span><span style=margin-top:-0.85em><span class=MJXp-mrow id=MJXp-Span-6746><span class=MJXp-mn id=MJXp-Span-6747>1</span></span></span></span></span></span></span></span><span class=MJXp-mtd id=MJXp-Span-6750 style=padding-left:0.33em;padding-top:0.431em;text-align:center><span class=MJXp-mo id=MJXp-Span-6751 style=margin-left:0.333em;margin-right:0.333em>=</span></span><span class=MJXp-mtd id=MJXp-Span-6752 style=padding-left:0.33em;padding-top:0.431em;text-align:center><span class=MJXp-mo id=MJXp-Span-6753 style=margin-left:0em;margin-right:0.111em>−</span><span class=MJXp-msub id=MJXp-Span-6754><span class=MJXp-mrow id=MJXp-Span-6755 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6756>γ</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-6757 style=vertical-align:-0.4em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6758>u</span></span></span><span class=MJXp-msub id=MJXp-Span-6759><span class=MJXp-mrow id=MJXp-Span-6760 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6761>β</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-6762 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-6763>1</span></span></span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6764>γ</span><span class=MJXp-msubsup id=MJXp-Span-6765><span class=MJXp-mrow id=MJXp-Span-6766 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6767>x</span></span><span class=MJXp-script-box style=height:1.86em;vertical-align:-0.64em><span class=MJXp-script><span><span style=margin-bottom:-0.25em><span class=MJXp-mrow id=MJXp-Span-6770><span class=MJXp-mo id=MJXp-Span-6771>′</span></span></span></span></span><span class=MJXp-script><span><span style=margin-top:-0.85em><span class=MJXp-mrow id=MJXp-Span-6768><span class=MJXp-mn id=MJXp-Span-6769>0</span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-6772 style=margin-left:0.267em;margin-right:0.267em>+</span><span class=MJXp-mfenced id=MJXp-Span-6773><span class=MJXp-mo id=MJXp-Span-6774 style=margin-left:0em;margin-right:0em;vertical-align:-0.689em><span style=font-size:3.756em;margin-left:-0.17em class="MJXp-right MJXp-scale4">(</span></span><span class=MJXp-mrow id=MJXp-Span-6775><span class=MJXp-mn id=MJXp-Span-6776>1</span><span class=MJXp-mo id=MJXp-Span-6777 style=margin-left:0.267em;margin-right:0.267em>+</span><span class=MJXp-mfrac id=MJXp-Span-6778 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-6779><span class=MJXp-msub id=MJXp-Span-6780><span class=MJXp-mrow id=MJXp-Span-6781 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6782>γ</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-6783 style=vertical-align:-0.4em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6784>u</span></span></span><span class=MJXp-mo id=MJXp-Span-6785 style=margin-left:0.267em;margin-right:0.267em>−</span><span class=MJXp-mn id=MJXp-Span-6786>1</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-6787><span class=MJXp-msup id=MJXp-Span-6788><span class=MJXp-mrow id=MJXp-Span-6789 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6790>β</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-6791 style=vertical-align:0.5em><span class=MJXp-mn id=MJXp-Span-6792>2</span></span></span></span></span></span></span></span></span><span class=MJXp-msub id=MJXp-Span-6793><span class=MJXp-mrow id=MJXp-Span-6794 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6795>β</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-6796 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-6797>1</span></span></span><span class=MJXp-msub id=MJXp-Span-6798><span class=MJXp-mrow id=MJXp-Span-6799 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6800>β</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-6801 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-6802>1</span></span></span></span><span class=MJXp-mo id=MJXp-Span-6803 style=margin-left:0em;margin-right:0em;vertical-align:-0.689em><span style=font-size:3.756em;margin-left:-0.17em class="MJXp-right MJXp-scale4">)</span></span></span><span class=MJXp-mrow id=MJXp-Span-6804><span class=MJXp-mo id=MJXp-Span-6805 style=margin-left:0em;margin-right:0em;vertical-align:-0.289em><span style=font-size:2.156em;margin-left:-0.09em class="MJXp-right MJXp-scale6">(</span></span><span class=MJXp-mrow id=MJXp-Span-6806><span class=MJXp-msup id=MJXp-Span-6807><span class=MJXp-mrow id=MJXp-Span-6808 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6809>γ</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-6810 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-6811>−</span><span class=MJXp-mn id=MJXp-Span-6812>1</span></span></span><span class=MJXp-msubsup id=MJXp-Span-6813><span class=MJXp-mrow id=MJXp-Span-6814 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6815>x</span></span><span class=MJXp-script-box style=height:1.86em;vertical-align:-0.64em><span class=MJXp-script><span><span style=margin-bottom:-0.25em><span class=MJXp-mrow id=MJXp-Span-6818><span class=MJXp-mo id=MJXp-Span-6819>′</span></span></span></span></span><span class=MJXp-script><span><span style=margin-top:-0.85em><span class=MJXp-mrow id=MJXp-Span-6816><span class=MJXp-mn id=MJXp-Span-6817>1</span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-6820 style=margin-left:0.267em;margin-right:0.267em>+</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6821>β</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6822>γ</span><span class=MJXp-msubsup id=MJXp-Span-6823><span class=MJXp-mrow id=MJXp-Span-6824 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6825>x</span></span><span class=MJXp-script-box style=height:1.86em;vertical-align:-0.64em><span class=MJXp-script><span><span style=margin-bottom:-0.25em><span class=MJXp-mrow id=MJXp-Span-6828><span class=MJXp-mo id=MJXp-Span-6829>′</span></span></span></span></span><span class=MJXp-script><span><span style=margin-top:-0.85em><span class=MJXp-mrow id=MJXp-Span-6826><span class=MJXp-mn id=MJXp-Span-6827>0</span></span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-6830 style=margin-left:0em;margin-right:0em;vertical-align:-0.289em><span style=font-size:2.156em;margin-left:-0.09em class="MJXp-right MJXp-scale6">)</span></span></span></span></span><span class=MJXp-mtr id=MJXp-Span-6831 style=vertical-align:baseline><span class=MJXp-mtd id=MJXp-Span-6832 style=padding-top:0.431em;text-align:center></span><span class=MJXp-mtd id=MJXp-Span-6833 style=padding-left:0.33em;padding-top:0.431em;text-align:center></span><span class=MJXp-mtd id=MJXp-Span-6834 style=padding-left:0.33em;padding-top:0.431em;text-align:center><span class=MJXp-mo id=MJXp-Span-6835 style=margin-left:0em;margin-right:0.111em>+</span><span class=MJXp-mfrac id=MJXp-Span-6836 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-6837><span class=MJXp-msub id=MJXp-Span-6838><span class=MJXp-mrow id=MJXp-Span-6839 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6840>γ</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-6841 style=vertical-align:-0.4em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6842>u</span></span></span><span class=MJXp-mo id=MJXp-Span-6843 style=margin-left:0.267em;margin-right:0.267em>−</span><span class=MJXp-mn id=MJXp-Span-6844>1</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-6845><span class=MJXp-msup id=MJXp-Span-6846><span class=MJXp-mrow id=MJXp-Span-6847 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6848>β</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-6849 style=vertical-align:0.5em><span class=MJXp-mn id=MJXp-Span-6850>2</span></span></span></span></span></span></span></span></span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6851>δ</span><span class=MJXp-msub id=MJXp-Span-6852><span class=MJXp-mrow id=MJXp-Span-6853 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6854>β</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-6855 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-6856>2</span></span></span><span class=MJXp-msub id=MJXp-Span-6857><span class=MJXp-mrow id=MJXp-Span-6858 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6859>β</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-6860 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-6861>1</span></span></span><span class=MJXp-msubsup id=MJXp-Span-6862><span class=MJXp-mrow id=MJXp-Span-6863 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6864>x</span></span><span class=MJXp-script-box style=height:1.86em;vertical-align:-0.64em><span class=MJXp-script><span><span style=margin-bottom:-0.25em><span class=MJXp-mrow id=MJXp-Span-6867><span class=MJXp-mo id=MJXp-Span-6868>′</span></span></span></span></span><span class=MJXp-script><span><span style=margin-top:-0.85em><span class=MJXp-mrow id=MJXp-Span-6865><span class=MJXp-mn id=MJXp-Span-6866>2</span></span></span></span></span></span></span></span></span><span class=MJXp-mtr id=MJXp-Span-6869 style=vertical-align:baseline><span class=MJXp-mtd id=MJXp-Span-6870 style=padding-top:0.431em;text-align:center><span class=MJXp-msubsup id=MJXp-Span-6871><span class=MJXp-mrow id=MJXp-Span-6872 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6873>x</span></span><span class=MJXp-script-box style=height:1.86em;vertical-align:-0.64em><span class=MJXp-script><span><span style=margin-bottom:-0.25em><span class=MJXp-mrow id=MJXp-Span-6876><span class=MJXp-mo id=MJXp-Span-6877>″</span></span></span></span></span><span class=MJXp-script><span><span style=margin-top:-0.85em><span class=MJXp-mrow id=MJXp-Span-6874><span class=MJXp-mn id=MJXp-Span-6875>2</span></span></span></span></span></span></span></span><span class=MJXp-mtd id=MJXp-Span-6878 style=padding-left:0.33em;padding-top:0.431em;text-align:center><span class=MJXp-mo id=MJXp-Span-6879 style=margin-left:0.333em;margin-right:0.333em>=</span></span><span class=MJXp-mtd id=MJXp-Span-6880 style=padding-left:0.33em;padding-top:0.431em;text-align:center><span class=MJXp-mo id=MJXp-Span-6881 style=margin-left:0em;margin-right:0.111em>−</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6882>γ</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6883>δ</span><span class=MJXp-msub id=MJXp-Span-6884><span class=MJXp-mrow id=MJXp-Span-6885 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6886>β</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-6887 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-6888>2</span></span></span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6889>γ</span><span class=MJXp-msubsup id=MJXp-Span-6890><span class=MJXp-mrow id=MJXp-Span-6891 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6892>x</span></span><span class=MJXp-script-box style=height:1.86em;vertical-align:-0.64em><span class=MJXp-script><span><span style=margin-bottom:-0.25em><span class=MJXp-mrow id=MJXp-Span-6895><span class=MJXp-mo id=MJXp-Span-6896>′</span></span></span></span></span><span class=MJXp-script><span><span style=margin-top:-0.85em><span class=MJXp-mrow id=MJXp-Span-6893><span class=MJXp-mn id=MJXp-Span-6894>0</span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-6897 style=margin-left:0.267em;margin-right:0.267em>+</span><span class=MJXp-mfrac id=MJXp-Span-6898 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-6899><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6900>γ</span><span class=MJXp-mo id=MJXp-Span-6901 style=margin-left:0.267em;margin-right:0.267em>−</span><span class=MJXp-mn id=MJXp-Span-6902>1</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-6903><span class=MJXp-msup id=MJXp-Span-6904><span class=MJXp-mrow id=MJXp-Span-6905 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6906>β</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-6907 style=vertical-align:0.5em><span class=MJXp-mn id=MJXp-Span-6908>2</span></span></span></span></span></span></span></span></span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6909>δ</span><span class=MJXp-msub id=MJXp-Span-6910><span class=MJXp-mrow id=MJXp-Span-6911 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6912>β</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-6913 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-6914>2</span></span></span><span class=MJXp-msub id=MJXp-Span-6915><span class=MJXp-mrow id=MJXp-Span-6916 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6917>β</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-6918 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-6919>1</span></span></span><span class=MJXp-mrow id=MJXp-Span-6920><span class=MJXp-mo id=MJXp-Span-6921 style=margin-left:0em;margin-right:0em;vertical-align:-0.289em><span style=font-size:2.156em;margin-left:-0.09em class="MJXp-right MJXp-scale6">(</span></span><span class=MJXp-mrow id=MJXp-Span-6922><span class=MJXp-msup id=MJXp-Span-6923><span class=MJXp-mrow id=MJXp-Span-6924 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6925>γ</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-6926 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-6927>−</span><span class=MJXp-mn id=MJXp-Span-6928>1</span></span></span><span class=MJXp-msubsup id=MJXp-Span-6929><span class=MJXp-mrow id=MJXp-Span-6930 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6931>x</span></span><span class=MJXp-script-box style=height:1.86em;vertical-align:-0.64em><span class=MJXp-script><span><span style=margin-bottom:-0.25em><span class=MJXp-mrow id=MJXp-Span-6934><span class=MJXp-mo id=MJXp-Span-6935>′</span></span></span></span></span><span class=MJXp-script><span><span style=margin-top:-0.85em><span class=MJXp-mrow id=MJXp-Span-6932><span class=MJXp-mn id=MJXp-Span-6933>1</span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-6936 style=margin-left:0.267em;margin-right:0.267em>+</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6937>β</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6938>γ</span><span class=MJXp-msubsup id=MJXp-Span-6939><span class=MJXp-mrow id=MJXp-Span-6940 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6941>x</span></span><span class=MJXp-script-box style=height:1.86em;vertical-align:-0.64em><span class=MJXp-script><span><span style=margin-bottom:-0.25em><span class=MJXp-mrow id=MJXp-Span-6944><span class=MJXp-mo id=MJXp-Span-6945>′</span></span></span></span></span><span class=MJXp-script><span><span style=margin-top:-0.85em><span class=MJXp-mrow id=MJXp-Span-6942><span class=MJXp-mn id=MJXp-Span-6943>0</span></span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-6946 style=margin-left:0em;margin-right:0em;vertical-align:-0.289em><span style=font-size:2.156em;margin-left:-0.09em class="MJXp-right MJXp-scale6">)</span></span></span><span class=MJXp-mo id=MJXp-Span-6947 style=margin-left:0.267em;margin-right:0.267em>+</span><span class=MJXp-msubsup id=MJXp-Span-6948><span class=MJXp-mrow id=MJXp-Span-6949 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6950>x</span></span><span class=MJXp-script-box style=height:1.86em;vertical-align:-0.64em><span class=MJXp-script><span><span style=margin-bottom:-0.25em><span class=MJXp-mrow id=MJXp-Span-6953><span class=MJXp-mo id=MJXp-Span-6954>′</span></span></span></span></span><span class=MJXp-script><span><span style=margin-top:-0.85em><span class=MJXp-mrow id=MJXp-Span-6951><span class=MJXp-mn id=MJXp-Span-6952>2</span></span></span></span></span></span></span></span></span><span class=MJXp-mtr id=MJXp-Span-6955 style=vertical-align:baseline><span class=MJXp-mtd id=MJXp-Span-6956 style=padding-top:0.431em;text-align:center><span class=MJXp-msubsup id=MJXp-Span-6957><span class=MJXp-mrow id=MJXp-Span-6958 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6959>x</span></span><span class=MJXp-script-box style=height:1.86em;vertical-align:-0.64em><span class=MJXp-script><span><span style=margin-bottom:-0.25em><span class=MJXp-mrow id=MJXp-Span-6962><span class=MJXp-mo id=MJXp-Span-6963>″</span></span></span></span></span><span class=MJXp-script><span><span style=margin-top:-0.85em><span class=MJXp-mrow id=MJXp-Span-6960><span class=MJXp-mn id=MJXp-Span-6961>3</span></span></span></span></span></span></span></span><span class=MJXp-mtd id=MJXp-Span-6964 style=padding-left:0.33em;padding-top:0.431em;text-align:center><span class=MJXp-mo id=MJXp-Span-6965 style=margin-left:0.333em;margin-right:0.333em>=</span></span><span class=MJXp-mtd id=MJXp-Span-6966 style=padding-left:0.33em;padding-top:0.431em;text-align:center><span class=MJXp-msub id=MJXp-Span-6967><span class=MJXp-mrow id=MJXp-Span-6968 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6969>x</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-6970 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-6971>3</span></span></span><span class=MJXp-mo id=MJXp-Span-6972 style=margin-left:0em;margin-right:0.222em>.</span></span></span></span></span></span></span><span class="mjx-chtml MJXc-display MJXc-processing sf-hidden"></span>
</span>
</div><p>
</p>
<p>For the matrix elements <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-6973><span class=MJXp-msub id=MJXp-Span-6974><span class=MJXp-mrow id=MJXp-Span-6975 style=margin-right:0.05em><span class=MJXp-mrow id=MJXp-Span-6976><span class=MJXp-mo id=MJXp-Span-6977 style=margin-left:0em;margin-right:0em;vertical-align:-0.244em><span style=font-size:1.978em;margin-left:-0.05em class="MJXp-right MJXp-scale7">(</span></span><span class=MJXp-mrow id=MJXp-Span-6978><span class=MJXp-msub id=MJXp-Span-6979><span class=MJXp-mrow id=MJXp-Span-6980 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6981>A</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-6982 style=vertical-align:-0.4em><span class=MJXp-mi id=MJXp-Span-6983>LTA</span></span></span></span><span class=MJXp-mo id=MJXp-Span-6984 style=margin-left:0em;margin-right:0em;vertical-align:-0.244em><span style=font-size:1.978em;margin-left:-0.05em class="MJXp-right MJXp-scale7">)</span></span></span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-6985 style=vertical-align:-0.74em><span class=MJXp-mn id=MJXp-Span-6986>23</span></span></span></span></span><span id=MathJax-Element-526-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> and <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-6987><span class=MJXp-msub id=MJXp-Span-6988><span class=MJXp-mrow id=MJXp-Span-6989 style=margin-right:0.05em><span class=MJXp-mrow id=MJXp-Span-6990><span class=MJXp-mo id=MJXp-Span-6991 style=margin-left:0em;margin-right:0em;vertical-align:-0.244em><span style=font-size:1.978em;margin-left:-0.05em class="MJXp-right MJXp-scale7">(</span></span><span class=MJXp-mrow id=MJXp-Span-6992><span class=MJXp-msub id=MJXp-Span-6993><span class=MJXp-mrow id=MJXp-Span-6994 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-6995>A</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-6996 style=vertical-align:-0.4em><span class=MJXp-mi id=MJXp-Span-6997>LTA</span></span></span></span><span class=MJXp-mo id=MJXp-Span-6998 style=margin-left:0em;margin-right:0em;vertical-align:-0.244em><span style=font-size:1.978em;margin-left:-0.05em class="MJXp-right MJXp-scale7">)</span></span></span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-6999 style=vertical-align:-0.74em><span class=MJXp-mn id=MJXp-Span-7000>32</span></span></span></span></span><span id=MathJax-Element-527-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>, we may take into account that the velocity of <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-7001><span class=MJXp-msup id=MJXp-Span-7002><span class=MJXp-mrow id=MJXp-Span-7003 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7004>S</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-7005 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-7006>″</span></span></span></span></span><span id=MathJax-Element-528-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> relative to <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-7007><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7008>S</span></span></span><span id=MathJax-Element-529-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> is <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-7009><span class=MJXp-msub id=MJXp-Span-7010><span class=MJXp-mrow id=MJXp-Span-7011 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7012>β</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-7013 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-7014>1</span></span></span><span class=MJXp-mo id=MJXp-Span-7015 style=margin-left:0.333em;margin-right:0.333em>=</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7016>β</span><span class=MJXp-mo id=MJXp-Span-7017 style=margin-left:0.267em;margin-right:0.267em>+</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7018>δ</span><span class=MJXp-msub id=MJXp-Span-7019><span class=MJXp-mrow id=MJXp-Span-7020 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7021>β</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-7022 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-7023>1</span></span></span></span></span><span id=MathJax-Element-530-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> and <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-7024><span class=MJXp-msub id=MJXp-Span-7025><span class=MJXp-mrow id=MJXp-Span-7026 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7027>β</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-7028 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-7029>2</span></span></span><span class=MJXp-mo id=MJXp-Span-7030 style=margin-left:0.333em;margin-right:0.333em>=</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7031>δ</span><span class=MJXp-msub id=MJXp-Span-7032><span class=MJXp-mrow id=MJXp-Span-7033 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7034>β</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-7035 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-7036>2</span></span></span></span></span><span id=MathJax-Element-531-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> and <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-7037><span class=MJXp-msub id=MJXp-Span-7038><span class=MJXp-mrow id=MJXp-Span-7039 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7040>γ</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-7041 style=vertical-align:-0.4em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7042>u</span></span></span><span class=MJXp-mo id=MJXp-Span-7043 style=margin-left:0.333em;margin-right:0.333em>≃</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7044>γ</span></span></span><span id=MathJax-Element-532-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> to the first order in <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-7045><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7046>δ</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7047>β</span></span></span><span id=MathJax-Element-533-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>. Then, (<a href=#j_phys-2023-0110_eq_031 class="link link-disp-formula" data-bs-target=j_phys-2023-0110_eq_031>A12</a>) becomes, <div class=formula id=j_phys-2023-0110_eq_032>
<span class=label>(A13)</span>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class="MJXp-math MJXp-display" id=MJXp-Span-7048><span class=MJXp-mtable id=MJXp-Span-7049><span><span class=MJXp-mtr id=MJXp-Span-7050 style=vertical-align:baseline><span class=MJXp-mtd id=MJXp-Span-7051 style=text-align:center><span class=MJXp-msubsup id=MJXp-Span-7052><span class=MJXp-mrow id=MJXp-Span-7053 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7054>x</span></span><span class=MJXp-script-box style=height:1.86em;vertical-align:-0.64em><span class=MJXp-script><span><span style=margin-bottom:-0.25em><span class=MJXp-mrow id=MJXp-Span-7057><span class=MJXp-mo id=MJXp-Span-7058>″</span></span></span></span></span><span class=MJXp-script><span><span style=margin-top:-0.85em><span class=MJXp-mrow id=MJXp-Span-7055><span class=MJXp-mn id=MJXp-Span-7056>0</span></span></span></span></span></span></span></span><span class=MJXp-mtd id=MJXp-Span-7059 style=padding-left:0.33em;text-align:center><span class=MJXp-mo id=MJXp-Span-7060 style=margin-left:0.333em;margin-right:0.333em>=</span></span><span class=MJXp-mtd id=MJXp-Span-7061 style=padding-left:0.33em;text-align:center><span class=MJXp-msubsup id=MJXp-Span-7062><span class=MJXp-mrow id=MJXp-Span-7063 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7064>γ</span></span><span class=MJXp-script-box style=height:1.86em;vertical-align:-0.64em><span class=MJXp-script><span><span style=margin-bottom:-0.25em><span class=MJXp-mrow id=MJXp-Span-7067><span class=MJXp-mo id=MJXp-Span-7068>−</span><span class=MJXp-mn id=MJXp-Span-7069>1</span></span></span></span></span><span class=MJXp-script><span><span style=margin-top:-0.85em><span class=MJXp-mrow id=MJXp-Span-7065><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7066>u</span></span></span></span></span></span></span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7070>γ</span><span class=MJXp-msubsup id=MJXp-Span-7071><span class=MJXp-mrow id=MJXp-Span-7072 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7073>x</span></span><span class=MJXp-script-box style=height:1.86em;vertical-align:-0.64em><span class=MJXp-script><span><span style=margin-bottom:-0.25em><span class=MJXp-mrow id=MJXp-Span-7076><span class=MJXp-mo id=MJXp-Span-7077>′</span></span></span></span></span><span class=MJXp-script><span><span style=margin-top:-0.85em><span class=MJXp-mrow id=MJXp-Span-7074><span class=MJXp-mn id=MJXp-Span-7075>0</span></span></span></span></span></span></span></span></span><span class=MJXp-mtr id=MJXp-Span-7078 style=vertical-align:baseline><span class=MJXp-mtd id=MJXp-Span-7079 style=padding-top:0.431em;text-align:center><span class=MJXp-msubsup id=MJXp-Span-7080><span class=MJXp-mrow id=MJXp-Span-7081 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7082>x</span></span><span class=MJXp-script-box style=height:1.86em;vertical-align:-0.64em><span class=MJXp-script><span><span style=margin-bottom:-0.25em><span class=MJXp-mrow id=MJXp-Span-7085><span class=MJXp-mo id=MJXp-Span-7086>″</span></span></span></span></span><span class=MJXp-script><span><span style=margin-top:-0.85em><span class=MJXp-mrow id=MJXp-Span-7083><span class=MJXp-mn id=MJXp-Span-7084>1</span></span></span></span></span></span></span></span><span class=MJXp-mtd id=MJXp-Span-7087 style=padding-left:0.33em;padding-top:0.431em;text-align:center><span class=MJXp-mo id=MJXp-Span-7088 style=margin-left:0.333em;margin-right:0.333em>=</span></span><span class=MJXp-mtd id=MJXp-Span-7089 style=padding-left:0.33em;padding-top:0.431em;text-align:center><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7090>γ</span><span class=MJXp-mrow id=MJXp-Span-7091><span class=MJXp-mo id=MJXp-Span-7092 style=margin-left:0em;margin-right:0em;vertical-align:-0.689em><span style=font-size:3.756em;margin-left:-0.17em class="MJXp-right MJXp-scale4">(</span></span><span class=MJXp-mrow id=MJXp-Span-7093><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7094>β</span><span class=MJXp-mo id=MJXp-Span-7095 style=margin-left:0.267em;margin-right:0.267em>+</span><span class=MJXp-mfrac id=MJXp-Span-7096 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-7097><span class=MJXp-msub id=MJXp-Span-7098><span class=MJXp-mrow id=MJXp-Span-7099 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7100>γ</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-7101 style=vertical-align:-0.4em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7102>u</span></span></span><span class=MJXp-mo id=MJXp-Span-7103 style=margin-left:0.267em;margin-right:0.267em>−</span><span class=MJXp-mn id=MJXp-Span-7104>1</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-7105><span class=MJXp-msup id=MJXp-Span-7106><span class=MJXp-mrow id=MJXp-Span-7107 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7108>β</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-7109 style=vertical-align:0.5em><span class=MJXp-mn id=MJXp-Span-7110>2</span></span></span></span></span></span></span></span></span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7111>β</span><span class=MJXp-msub id=MJXp-Span-7112><span class=MJXp-mrow id=MJXp-Span-7113 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7114>β</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-7115 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-7116>1</span></span></span><span class=MJXp-msub id=MJXp-Span-7117><span class=MJXp-mrow id=MJXp-Span-7118 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7119>β</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-7120 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-7121>1</span></span></span><span class=MJXp-mo id=MJXp-Span-7122 style=margin-left:0.267em;margin-right:0.267em>−</span><span class=MJXp-msub id=MJXp-Span-7123><span class=MJXp-mrow id=MJXp-Span-7124 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7125>γ</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-7126 style=vertical-align:-0.4em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7127>u</span></span></span><span class=MJXp-msub id=MJXp-Span-7128><span class=MJXp-mrow id=MJXp-Span-7129 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7130>β</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-7131 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-7132>1</span></span></span></span><span class=MJXp-mo id=MJXp-Span-7133 style=margin-left:0em;margin-right:0em;vertical-align:-0.689em><span style=font-size:3.756em;margin-left:-0.17em class="MJXp-right MJXp-scale4">)</span></span></span><span class=MJXp-msubsup id=MJXp-Span-7134><span class=MJXp-mrow id=MJXp-Span-7135 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7136>x</span></span><span class=MJXp-script-box style=height:1.86em;vertical-align:-0.64em><span class=MJXp-script><span><span style=margin-bottom:-0.25em><span class=MJXp-mrow id=MJXp-Span-7139><span class=MJXp-mo id=MJXp-Span-7140>′</span></span></span></span></span><span class=MJXp-script><span><span style=margin-top:-0.85em><span class=MJXp-mrow id=MJXp-Span-7137><span class=MJXp-mn id=MJXp-Span-7138>0</span></span></span></span></span></span></span></span></span><span class=MJXp-mtr id=MJXp-Span-7141 style=vertical-align:baseline><span class=MJXp-mtd id=MJXp-Span-7142 style=padding-top:0.431em;text-align:center></span><span class=MJXp-mtd id=MJXp-Span-7143 style=padding-left:0.33em;padding-top:0.431em;text-align:center></span><span class=MJXp-mtd id=MJXp-Span-7144 style=padding-left:0.33em;padding-top:0.431em;text-align:center><span class=MJXp-mo id=MJXp-Span-7145 style=margin-left:0em;margin-right:0.111em>+</span><span class=MJXp-mrow id=MJXp-Span-7146><span class=MJXp-mo id=MJXp-Span-7147 style=margin-left:0em;margin-right:0em;vertical-align:-0.689em><span style=font-size:3.756em;margin-left:-0.17em class="MJXp-right MJXp-scale4">(</span></span><span class=MJXp-mrow id=MJXp-Span-7148><span class=MJXp-mn id=MJXp-Span-7149>1</span><span class=MJXp-mo id=MJXp-Span-7150 style=margin-left:0.267em;margin-right:0.267em>+</span><span class=MJXp-mfrac id=MJXp-Span-7151 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-7152><span class=MJXp-msub id=MJXp-Span-7153><span class=MJXp-mrow id=MJXp-Span-7154 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7155>γ</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-7156 style=vertical-align:-0.4em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7157>u</span></span></span><span class=MJXp-mo id=MJXp-Span-7158 style=margin-left:0.267em;margin-right:0.267em>−</span><span class=MJXp-mn id=MJXp-Span-7159>1</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-7160><span class=MJXp-msup id=MJXp-Span-7161><span class=MJXp-mrow id=MJXp-Span-7162 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7163>β</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-7164 style=vertical-align:0.5em><span class=MJXp-mn id=MJXp-Span-7165>2</span></span></span></span></span></span></span></span></span><span class=MJXp-msub id=MJXp-Span-7166><span class=MJXp-mrow id=MJXp-Span-7167 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7168>β</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-7169 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-7170>1</span></span></span><span class=MJXp-msub id=MJXp-Span-7171><span class=MJXp-mrow id=MJXp-Span-7172 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7173>β</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-7174 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-7175>1</span></span></span></span><span class=MJXp-mo id=MJXp-Span-7176 style=margin-left:0em;margin-right:0em;vertical-align:-0.689em><span style=font-size:3.756em;margin-left:-0.17em class="MJXp-right MJXp-scale4">)</span></span></span><span class=MJXp-msup id=MJXp-Span-7177><span class=MJXp-mrow id=MJXp-Span-7178 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7179>γ</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-7180 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-7181>−</span><span class=MJXp-mn id=MJXp-Span-7182>1</span></span></span><span class=MJXp-msubsup id=MJXp-Span-7183><span class=MJXp-mrow id=MJXp-Span-7184 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7185>x</span></span><span class=MJXp-script-box style=height:1.86em;vertical-align:-0.64em><span class=MJXp-script><span><span style=margin-bottom:-0.25em><span class=MJXp-mrow id=MJXp-Span-7188><span class=MJXp-mo id=MJXp-Span-7189>′</span></span></span></span></span><span class=MJXp-script><span><span style=margin-top:-0.85em><span class=MJXp-mrow id=MJXp-Span-7186><span class=MJXp-mn id=MJXp-Span-7187>1</span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-7190 style=margin-left:0.267em;margin-right:0.267em>+</span><span class=MJXp-mfrac id=MJXp-Span-7191 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-7192><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7193>γ</span><span class=MJXp-mo id=MJXp-Span-7194 style=margin-left:0.267em;margin-right:0.267em>−</span><span class=MJXp-mn id=MJXp-Span-7195>1</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-7196><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7197>β</span></span></span></span></span></span></span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7198>δ</span><span class=MJXp-msub id=MJXp-Span-7199><span class=MJXp-mrow id=MJXp-Span-7200 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7201>β</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-7202 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-7203>2</span></span></span><span class=MJXp-msubsup id=MJXp-Span-7204><span class=MJXp-mrow id=MJXp-Span-7205 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7206>x</span></span><span class=MJXp-script-box style=height:1.86em;vertical-align:-0.64em><span class=MJXp-script><span><span style=margin-bottom:-0.25em><span class=MJXp-mrow id=MJXp-Span-7209><span class=MJXp-mo id=MJXp-Span-7210>′</span></span></span></span></span><span class=MJXp-script><span><span style=margin-top:-0.85em><span class=MJXp-mrow id=MJXp-Span-7207><span class=MJXp-mn id=MJXp-Span-7208>2</span></span></span></span></span></span></span></span></span><span class=MJXp-mtr id=MJXp-Span-7211 style=vertical-align:baseline><span class=MJXp-mtd id=MJXp-Span-7212 style=padding-top:0.431em;text-align:center><span class=MJXp-msubsup id=MJXp-Span-7213><span class=MJXp-mrow id=MJXp-Span-7214 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7215>x</span></span><span class=MJXp-script-box style=height:1.86em;vertical-align:-0.64em><span class=MJXp-script><span><span style=margin-bottom:-0.25em><span class=MJXp-mrow id=MJXp-Span-7218><span class=MJXp-mo id=MJXp-Span-7219>″</span></span></span></span></span><span class=MJXp-script><span><span style=margin-top:-0.85em><span class=MJXp-mrow id=MJXp-Span-7216><span class=MJXp-mn id=MJXp-Span-7217>2</span></span></span></span></span></span></span></span><span class=MJXp-mtd id=MJXp-Span-7220 style=padding-left:0.33em;padding-top:0.431em;text-align:center><span class=MJXp-mo id=MJXp-Span-7221 style=margin-left:0.333em;margin-right:0.333em>=</span></span><span class=MJXp-mtd id=MJXp-Span-7222 style=padding-left:0.33em;padding-top:0.431em;text-align:center><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7223>γ</span><span class=MJXp-mrow id=MJXp-Span-7224><span class=MJXp-mo id=MJXp-Span-7225 style=margin-left:0em;margin-right:0em;vertical-align:-0.5em><span style=font-size:3em;margin-left:-0.13em class="MJXp-right MJXp-scale5">(</span></span><span class=MJXp-mrow id=MJXp-Span-7226><span class=MJXp-mfrac id=MJXp-Span-7227 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-7228><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7229>γ</span><span class=MJXp-mo id=MJXp-Span-7230 style=margin-left:0.267em;margin-right:0.267em>−</span><span class=MJXp-mn id=MJXp-Span-7231>1</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-7232><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7233>β</span></span></span></span></span></span></span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7234>δ</span><span class=MJXp-msub id=MJXp-Span-7235><span class=MJXp-mrow id=MJXp-Span-7236 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7237>β</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-7238 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-7239>2</span></span></span><span class=MJXp-msub id=MJXp-Span-7240><span class=MJXp-mrow id=MJXp-Span-7241 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7242>β</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-7243 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-7244>1</span></span></span><span class=MJXp-mo id=MJXp-Span-7245 style=margin-left:0.267em;margin-right:0.267em>−</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7246>γ</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7247>δ</span><span class=MJXp-msub id=MJXp-Span-7248><span class=MJXp-mrow id=MJXp-Span-7249 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7250>β</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-7251 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-7252>2</span></span></span></span><span class=MJXp-mo id=MJXp-Span-7253 style=margin-left:0em;margin-right:0em;vertical-align:-0.5em><span style=font-size:3em;margin-left:-0.13em class="MJXp-right MJXp-scale5">)</span></span></span><span class=MJXp-msubsup id=MJXp-Span-7254><span class=MJXp-mrow id=MJXp-Span-7255 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7256>x</span></span><span class=MJXp-script-box style=height:1.86em;vertical-align:-0.64em><span class=MJXp-script><span><span style=margin-bottom:-0.25em><span class=MJXp-mrow id=MJXp-Span-7259><span class=MJXp-mo id=MJXp-Span-7260>′</span></span></span></span></span><span class=MJXp-script><span><span style=margin-top:-0.85em><span class=MJXp-mrow id=MJXp-Span-7257><span class=MJXp-mn id=MJXp-Span-7258>0</span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-7261 style=margin-left:0.267em;margin-right:0.267em>+</span><span class=MJXp-mfrac id=MJXp-Span-7262 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-7263><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7264>γ</span><span class=MJXp-mo id=MJXp-Span-7265 style=margin-left:0.267em;margin-right:0.267em>−</span><span class=MJXp-mn id=MJXp-Span-7266>1</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-7267><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7268>γ</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7269>β</span></span></span></span></span></span></span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7270>δ</span><span class=MJXp-msub id=MJXp-Span-7271><span class=MJXp-mrow id=MJXp-Span-7272 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7273>β</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-7274 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-7275>2</span></span></span><span class=MJXp-msubsup id=MJXp-Span-7276><span class=MJXp-mrow id=MJXp-Span-7277 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7278>x</span></span><span class=MJXp-script-box style=height:1.86em;vertical-align:-0.64em><span class=MJXp-script><span><span style=margin-bottom:-0.25em><span class=MJXp-mrow id=MJXp-Span-7281><span class=MJXp-mo id=MJXp-Span-7282>′</span></span></span></span></span><span class=MJXp-script><span><span style=margin-top:-0.85em><span class=MJXp-mrow id=MJXp-Span-7279><span class=MJXp-mn id=MJXp-Span-7280>1</span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-7283 style=margin-left:0.267em;margin-right:0.267em>+</span><span class=MJXp-msubsup id=MJXp-Span-7284><span class=MJXp-mrow id=MJXp-Span-7285 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7286>x</span></span><span class=MJXp-script-box style=height:1.86em;vertical-align:-0.64em><span class=MJXp-script><span><span style=margin-bottom:-0.25em><span class=MJXp-mrow id=MJXp-Span-7289><span class=MJXp-mo id=MJXp-Span-7290>′</span></span></span></span></span><span class=MJXp-script><span><span style=margin-top:-0.85em><span class=MJXp-mrow id=MJXp-Span-7287><span class=MJXp-mn id=MJXp-Span-7288>2</span></span></span></span></span></span></span></span></span><span class=MJXp-mtr id=MJXp-Span-7291 style=vertical-align:baseline><span class=MJXp-mtd id=MJXp-Span-7292 style=padding-top:0.431em;text-align:center><span class=MJXp-msubsup id=MJXp-Span-7293><span class=MJXp-mrow id=MJXp-Span-7294 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7295>x</span></span><span class=MJXp-script-box style=height:1.86em;vertical-align:-0.64em><span class=MJXp-script><span><span style=margin-bottom:-0.25em><span class=MJXp-mrow id=MJXp-Span-7298><span class=MJXp-mo id=MJXp-Span-7299>″</span></span></span></span></span><span class=MJXp-script><span><span style=margin-top:-0.85em><span class=MJXp-mrow id=MJXp-Span-7296><span class=MJXp-mn id=MJXp-Span-7297>3</span></span></span></span></span></span></span></span><span class=MJXp-mtd id=MJXp-Span-7300 style=padding-left:0.33em;padding-top:0.431em;text-align:center><span class=MJXp-mo id=MJXp-Span-7301 style=margin-left:0.333em;margin-right:0.333em>=</span></span><span class=MJXp-mtd id=MJXp-Span-7302 style=padding-left:0.33em;padding-top:0.431em;text-align:center><span class=MJXp-msub id=MJXp-Span-7303><span class=MJXp-mrow id=MJXp-Span-7304 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7305>x</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-7306 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-7307>3</span></span></span><span class=MJXp-mo id=MJXp-Span-7308 style=margin-left:0em;margin-right:0.222em>.</span></span></span></span></span></span></span><span class="mjx-chtml MJXc-display MJXc-processing sf-hidden"></span>
</span>
</div><p> From the connection <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-7309><span class=MJXp-msup id=MJXp-Span-7310><span class=MJXp-mrow id=MJXp-Span-7311 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7312>x</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-7313 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-7314>″</span></span></span><span class=MJXp-mo id=MJXp-Span-7315 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-msub id=MJXp-Span-7316><span class=MJXp-mrow id=MJXp-Span-7317 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7318>A</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-7319 style=vertical-align:-0.4em><span class=MJXp-mi id=MJXp-Span-7320>LTA</span></span></span><span class=MJXp-mspace id=MJXp-Span-7321 style=width:0.33em;height:0em></span><span class=MJXp-msup id=MJXp-Span-7322><span class=MJXp-mrow id=MJXp-Span-7323 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7324>x</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-7325 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-7326>′</span></span></span></span></span><span id=MathJax-Element-535-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> given by Eq. (<a href=#j_phys-2023-0110_eq_032 class="link link-disp-formula" data-bs-target=j_phys-2023-0110_eq_032>A13</a>), we find that the elements of the corresponding matrix <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-7327><span class=MJXp-msub id=MJXp-Span-7328><span class=MJXp-mrow id=MJXp-Span-7329 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7330>A</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-7331 style=vertical-align:-0.4em><span class=MJXp-mi id=MJXp-Span-7332>LTA</span></span></span></span></span><span id=MathJax-Element-536-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> relevant to our case are, <div class=formula id=j_phys-2023-0110_eq_033>
<span class=label>(A14)</span>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class="MJXp-math MJXp-display" id=MJXp-Span-7333><span class=MJXp-msub id=MJXp-Span-7334><span class=MJXp-mrow id=MJXp-Span-7335 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7336>A</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-7337 style=vertical-align:-0.4em><span class=MJXp-mi id=MJXp-Span-7338>LTA</span></span></span><span class=MJXp-mo id=MJXp-Span-7339 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-mfenced id=MJXp-Span-7340><span class=MJXp-mo id=MJXp-Span-7341 style=margin-left:0em;margin-right:0em;vertical-align:-2.275em><span style=font-size:10.102em;margin-left:-0.25em class="MJXp-right MJXp-scale2">(</span></span><span class=MJXp-mrow id=MJXp-Span-7342><span class=MJXp-mtable id=MJXp-Span-7343><span><span class=MJXp-mtr id=MJXp-Span-7344 style=vertical-align:baseline><span class=MJXp-mtd id=MJXp-Span-7345 style=text-align:center><span class=MJXp-mo id=MJXp-Span-7346 style=margin-left:0em;margin-right:0em>⋯</span><span class=MJXp-mspace id=MJXp-Span-7347 style=width:0.33em;height:0em></span></span><span class=MJXp-mtd id=MJXp-Span-7348 style=padding-left:0.8em;text-align:center><span class=MJXp-mo id=MJXp-Span-7349 style=margin-left:0em;margin-right:0em>⋯</span><span class=MJXp-mspace id=MJXp-Span-7350 style=width:0.33em;height:0em></span></span><span class=MJXp-mtd id=MJXp-Span-7351 style=padding-left:0.8em;text-align:center><span class=MJXp-mo id=MJXp-Span-7352 style=margin-left:0em;margin-right:0em>⋯</span><span class=MJXp-mspace id=MJXp-Span-7353 style=width:0.33em;height:0em></span></span><span class=MJXp-mtd id=MJXp-Span-7354 style=padding-left:0.8em;text-align:center><span class=MJXp-mo id=MJXp-Span-7355 style=margin-left:0em;margin-right:0em>⋯</span></span></span><span class=MJXp-mtr id=MJXp-Span-7356 style=vertical-align:baseline><span class=MJXp-mtd id=MJXp-Span-7357 style=padding-top:0.431em;text-align:center><span class=MJXp-mo id=MJXp-Span-7358 style=margin-left:0em;margin-right:0em>⋯</span><span class=MJXp-mspace id=MJXp-Span-7359 style=width:0.33em;height:0em></span></span><span class=MJXp-mtd id=MJXp-Span-7360 style=padding-left:0.8em;padding-top:0.431em;text-align:center><span class=MJXp-mo id=MJXp-Span-7361 style=margin-left:0em;margin-right:0em>⋯</span><span class=MJXp-mspace id=MJXp-Span-7362 style=width:0.33em;height:0em></span></span><span class=MJXp-mtd id=MJXp-Span-7363 style=padding-left:0.8em;padding-top:0.431em;text-align:center><span class=MJXp-mfrac id=MJXp-Span-7364 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-7365><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7366>γ</span><span class=MJXp-mo id=MJXp-Span-7367 style=margin-left:0.267em;margin-right:0.267em>−</span><span class=MJXp-mn id=MJXp-Span-7368>1</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-7369><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7370>β</span></span></span></span></span></span></span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7371>δ</span><span class=MJXp-msub id=MJXp-Span-7372><span class=MJXp-mrow id=MJXp-Span-7373 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7374>β</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-7375 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-7376>2</span></span></span></span><span class=MJXp-mtd id=MJXp-Span-7377 style=padding-left:0.8em;padding-top:0.431em;text-align:center><span class=MJXp-mo id=MJXp-Span-7378 style=margin-left:0em;margin-right:0em>⋯</span></span></span><span class=MJXp-mtr id=MJXp-Span-7379 style=vertical-align:baseline><span class=MJXp-mtd id=MJXp-Span-7380 style=padding-top:0.431em;text-align:center><span class=MJXp-mo id=MJXp-Span-7381 style=margin-left:0em;margin-right:0em>⋯</span><span class=MJXp-mspace id=MJXp-Span-7382 style=width:0.33em;height:0em></span></span><span class=MJXp-mtd id=MJXp-Span-7383 style=padding-left:0.8em;padding-top:0.431em;text-align:center><span class=MJXp-mfrac id=MJXp-Span-7384 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-7385><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7386>γ</span><span class=MJXp-mo id=MJXp-Span-7387 style=margin-left:0.267em;margin-right:0.267em>−</span><span class=MJXp-mn id=MJXp-Span-7388>1</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-7389><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7390>γ</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7391>β</span></span></span></span></span></span></span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7392>δ</span><span class=MJXp-msub id=MJXp-Span-7393><span class=MJXp-mrow id=MJXp-Span-7394 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7395>β</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-7396 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-7397>2</span></span></span></span><span class=MJXp-mtd id=MJXp-Span-7398 style=padding-left:0.8em;padding-top:0.431em;text-align:center><span class=MJXp-mo id=MJXp-Span-7399 style=margin-left:0em;margin-right:0em>⋯</span><span class=MJXp-mspace id=MJXp-Span-7400 style=width:0.33em;height:0em></span></span><span class=MJXp-mtd id=MJXp-Span-7401 style=padding-left:0.8em;padding-top:0.431em;text-align:center><span class=MJXp-mo id=MJXp-Span-7402 style=margin-left:0em;margin-right:0em>⋯</span></span></span><span class=MJXp-mtr id=MJXp-Span-7403 style=vertical-align:baseline><span class=MJXp-mtd id=MJXp-Span-7404 style=padding-top:0.431em;text-align:center><span class=MJXp-mo id=MJXp-Span-7405 style=margin-left:0em;margin-right:0em>⋯</span><span class=MJXp-mspace id=MJXp-Span-7406 style=width:0.33em;height:0em></span></span><span class=MJXp-mtd id=MJXp-Span-7407 style=padding-left:0.8em;padding-top:0.431em;text-align:center><span class=MJXp-mo id=MJXp-Span-7408 style=margin-left:0em;margin-right:0em>⋯</span><span class=MJXp-mspace id=MJXp-Span-7409 style=width:0.33em;height:0em></span></span><span class=MJXp-mtd id=MJXp-Span-7410 style=padding-left:0.8em;padding-top:0.431em;text-align:center><span class=MJXp-mo id=MJXp-Span-7411 style=margin-left:0em;margin-right:0em>⋯</span><span class=MJXp-mspace id=MJXp-Span-7412 style=width:0.33em;height:0em></span></span><span class=MJXp-mtd id=MJXp-Span-7413 style=padding-left:0.8em;padding-top:0.431em;text-align:center><span class=MJXp-mo id=MJXp-Span-7414 style=margin-left:0em;margin-right:0em>⋯</span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-7415 style=margin-left:0em;margin-right:0em;vertical-align:-2.275em><span style=font-size:10.102em;margin-left:-0.25em class="MJXp-right MJXp-scale2">)</span></span></span><span class=MJXp-mo id=MJXp-Span-7416 style=margin-left:0em;margin-right:0.222em>,</span></span></span><span class="mjx-chtml MJXc-display MJXc-processing sf-hidden"></span>
</span>
</div><p> indicating that both the matrix elements <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-7417><span class=MJXp-msub id=MJXp-Span-7418><span class=MJXp-mrow id=MJXp-Span-7419 style=margin-right:0.05em><span class=MJXp-mrow id=MJXp-Span-7420><span class=MJXp-mo id=MJXp-Span-7421 style=margin-left:0em;margin-right:0em;vertical-align:-0.244em><span style=font-size:1.978em;margin-left:-0.05em class="MJXp-right MJXp-scale7">(</span></span><span class=MJXp-mrow id=MJXp-Span-7422><span class=MJXp-msub id=MJXp-Span-7423><span class=MJXp-mrow id=MJXp-Span-7424 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7425>A</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-7426 style=vertical-align:-0.4em><span class=MJXp-mi id=MJXp-Span-7427>LTA</span></span></span></span><span class=MJXp-mo id=MJXp-Span-7428 style=margin-left:0em;margin-right:0em;vertical-align:-0.244em><span style=font-size:1.978em;margin-left:-0.05em class="MJXp-right MJXp-scale7">)</span></span></span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-7429 style=vertical-align:-0.74em><span class=MJXp-mn id=MJXp-Span-7430>23</span></span></span></span></span><span id=MathJax-Element-538-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> and <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-7431><span class=MJXp-msub id=MJXp-Span-7432><span class=MJXp-mrow id=MJXp-Span-7433 style=margin-right:0.05em><span class=MJXp-mrow id=MJXp-Span-7434><span class=MJXp-mo id=MJXp-Span-7435 style=margin-left:0em;margin-right:0em;vertical-align:-0.244em><span style=font-size:1.978em;margin-left:-0.05em class="MJXp-right MJXp-scale7">(</span></span><span class=MJXp-mrow id=MJXp-Span-7436><span class=MJXp-msub id=MJXp-Span-7437><span class=MJXp-mrow id=MJXp-Span-7438 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7439>A</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-7440 style=vertical-align:-0.4em><span class=MJXp-mi id=MJXp-Span-7441>LTA</span></span></span></span><span class=MJXp-mo id=MJXp-Span-7442 style=margin-left:0em;margin-right:0em;vertical-align:-0.244em><span style=font-size:1.978em;margin-left:-0.05em class="MJXp-right MJXp-scale7">)</span></span></span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-7443 style=vertical-align:-0.74em><span class=MJXp-mn id=MJXp-Span-7444>32</span></span></span></span></span><span id=MathJax-Element-539-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> are positive, not antisymmetric, and do not reflect the existence of a rotation about the <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-7445><span class=MJXp-msub id=MJXp-Span-7446><span class=MJXp-mrow id=MJXp-Span-7447 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7448>x</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-7449 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-7450>3</span></span></span></span></span><span id=MathJax-Element-540-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> axis, as it is the case for the corresponding elements of the matrix <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-7451><span class=MJXp-msub id=MJXp-Span-7452><span class=MJXp-mrow id=MJXp-Span-7453 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7454>A</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-7455 style=vertical-align:-0.4em><span class=MJXp-mi id=MJXp-Span-7456>LT</span></span></span></span></span><span id=MathJax-Element-541-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> Eq. (<a href=#j_phys-2023-0110_eq_024 class="link link-disp-formula" data-bs-target=j_phys-2023-0110_eq_024>A5</a>) derived with the LT. In fact, the matrix elements <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-7457><span class=MJXp-msub id=MJXp-Span-7458><span class=MJXp-mrow id=MJXp-Span-7459 style=margin-right:0.05em><span class=MJXp-mrow id=MJXp-Span-7460><span class=MJXp-mo id=MJXp-Span-7461 style=margin-left:0em;margin-right:0em;vertical-align:-0.244em><span style=font-size:1.978em;margin-left:-0.05em class="MJXp-right MJXp-scale7">(</span></span><span class=MJXp-mrow id=MJXp-Span-7462><span class=MJXp-msub id=MJXp-Span-7463><span class=MJXp-mrow id=MJXp-Span-7464 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7465>A</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-7466 style=vertical-align:-0.4em><span class=MJXp-mi id=MJXp-Span-7467>LTA</span></span></span></span><span class=MJXp-mo id=MJXp-Span-7468 style=margin-left:0em;margin-right:0em;vertical-align:-0.244em><span style=font-size:1.978em;margin-left:-0.05em class="MJXp-right MJXp-scale7">)</span></span></span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-7469 style=vertical-align:-0.74em><span class=MJXp-mn id=MJXp-Span-7470>23</span></span></span></span></span><span id=MathJax-Element-542-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> and <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-7471><span class=MJXp-msub id=MJXp-Span-7472><span class=MJXp-mrow id=MJXp-Span-7473 style=margin-right:0.05em><span class=MJXp-mrow id=MJXp-Span-7474><span class=MJXp-mo id=MJXp-Span-7475 style=margin-left:0em;margin-right:0em;vertical-align:-0.244em><span style=font-size:1.978em;margin-left:-0.05em class="MJXp-right MJXp-scale7">(</span></span><span class=MJXp-mrow id=MJXp-Span-7476><span class=MJXp-msub id=MJXp-Span-7477><span class=MJXp-mrow id=MJXp-Span-7478 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7479>A</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-7480 style=vertical-align:-0.4em><span class=MJXp-mi id=MJXp-Span-7481>LTA</span></span></span></span><span class=MJXp-mo id=MJXp-Span-7482 style=margin-left:0em;margin-right:0em;vertical-align:-0.244em><span style=font-size:1.978em;margin-left:-0.05em class="MJXp-right MJXp-scale7">)</span></span></span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-7483 style=vertical-align:-0.74em><span class=MJXp-mn id=MJXp-Span-7484>32</span></span></span></span></span><span id=MathJax-Element-543-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> indicate a relative distortion of axes due to length contraction in the direction of motion, but no relative rotation about the <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-7485><span class=MJXp-msub id=MJXp-Span-7486><span class=MJXp-mrow id=MJXp-Span-7487 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7488>x</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-7489 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-7490>3</span></span></span></span></span><span id=MathJax-Element-544-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> axis.</p>
<p>In conclusion, standard special relativity predicts the existence of the Thomas precession, which is related to the spacetime symmetry properties of the LT based on relative simultaneity. Instead, the LTA, based on conservation of simultaneity, predicts that the Thomas precession does not exist. With the examples of the Thomas precession, the RLSE, and other phenomena [<a href=#j_phys-2023-0110_ref_006 class="link link-bibr" data-bs-target=j_phys-2023-0110_ref_006 data-bs-toggle=tooltip title="[6] Selleri F. Noninvariant one-way velocity of light. Found Phys. 1996;26:641. Noninvariant one-way speed of light and locally equivalent reference frames. Found Phys Lett. 1997;10:73–83. 10.1007/BF02764121Search in Google Scholar">6</a>–<a href=#j_phys-2023-0110_ref_009 class="link link-bibr" data-bs-target=j_phys-2023-0110_ref_009 data-bs-toggle=tooltip title="[9] Kipreos ET, Balachandran RS. An approach to directly probe simultaneity. Modern Phys Lett A. 2016;31(26):1650157; Assessment of the relativistic rotational transformations. Modern Physics Letters A. 2021;36(16):2150113. Search in Google Scholar">9</a>], we may infer that the LTA are not in general physically equivalent to the LT. Hence, the two transformations – and absolute and relative simultaneity – cannot be interchanged arbitrarily.</p>
</section>
</section>
<section id=j_phys-2023-0110_s_007>
<h3 class=subheading>A.3 Calculating with the Lorentz transformations the intervals <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-7491><span class=MJXp-msub id=MJXp-Span-7492><span class=MJXp-mrow id=MJXp-Span-7493 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7494>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-7495 style=vertical-align:-0.4em><span class=MJXp-mo id=MJXp-Span-7496>⇐</span></span></span></span></span><span id=MathJax-Element-545-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>, <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-7497><span class=MJXp-msub id=MJXp-Span-7498><span class=MJXp-mrow id=MJXp-Span-7499 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7500>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-7501 style=vertical-align:-0.4em><span class=MJXp-mo id=MJXp-Span-7502>⇒</span></span></span></span></span><span id=MathJax-Element-546-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> and <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-7503><span class=MJXp-mi id=MJXp-Span-7504>Δ</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7505>T</span><span class=MJXp-mo id=MJXp-Span-7506 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-msub id=MJXp-Span-7507><span class=MJXp-mrow id=MJXp-Span-7508 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7509>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-7510 style=vertical-align:-0.4em><span class=MJXp-mo id=MJXp-Span-7511>⇐</span></span></span><span class=MJXp-mo id=MJXp-Span-7512 style=margin-left:0em;margin-right:0.222em>‒</span><span class=MJXp-msub id=MJXp-Span-7513><span class=MJXp-mrow id=MJXp-Span-7514 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7515>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-7516 style=vertical-align:-0.4em><span class=MJXp-mo id=MJXp-Span-7517>⇒</span></span></span></span></span><span id=MathJax-Element-547-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> for the RLSE</h3>
<section id=j_phys-2023-0110_s_007_s_001>
<h4 class=subheading>A.3.1 Showing that, for <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-7518><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7519>D</span><span class=MJXp-mo id=MJXp-Span-7520 style=margin-left:0.333em;margin-right:0.333em>&gt;</span><span class=MJXp-mn id=MJXp-Span-7521>2</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7522>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7523>L</span><span class=MJXp-mo id=MJXp-Span-7524 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7525>c</span></span></span><span id=MathJax-Element-548-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> and <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-7526><span class=MJXp-msup id=MJXp-Span-7527><span class=MJXp-mrow id=MJXp-Span-7528 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-7529>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-7530 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-7531>*</span></span></span></span></span><span id=MathJax-Element-549-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> on the same (upper or lower) contour section, in the RLSE the round-trip time interval <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-7532><span class=MJXp-msub id=MJXp-Span-7533><span class=MJXp-mrow id=MJXp-Span-7534 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7535>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-7536 style=vertical-align:-0.4em><span class=MJXp-mo id=MJXp-Span-7537>⇒</span></span></span></span></span><span id=MathJax-Element-550-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> for the counter-moving photon is independent of <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-7538><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7539>D</span></span></span><span id=MathJax-Element-551-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> and the same as in the standard linear Sagnac effect</h4>
<p>With reference to <a href=#j_phys-2023-0110_fig_001 class="link link-fig" data-bs-target=j_phys-2023-0110_fig_001>Figures 1</a>(b) and <a href=#j_phys-2023-0110_fig_002 class="link link-fig" data-bs-target=j_phys-2023-0110_fig_002>2</a>(a), we assume that the counter-moving photon is emitted by <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-7540><span class=MJXp-msup id=MJXp-Span-7541><span class=MJXp-mrow id=MJXp-Span-7542 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-7543>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-7544 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-7545>*</span></span></span></span></span><span id=MathJax-Element-552-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> when <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-7546><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7547>D</span><span class=MJXp-mo id=MJXp-Span-7548 style=margin-left:0.333em;margin-right:0.333em>&gt;</span><span class=MJXp-mn id=MJXp-Span-7549>2</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7550>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7551>L</span><span class=MJXp-mo id=MJXp-Span-7552 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7553>c</span></span></span><span id=MathJax-Element-553-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>, so that <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-7554><span class=MJXp-msup id=MJXp-Span-7555><span class=MJXp-mrow id=MJXp-Span-7556 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-7557>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-7558 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-7559>*</span></span></span></span></span><span id=MathJax-Element-554-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> is always on the lower track during the round-trip interval <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-7560><span class=MJXp-msub id=MJXp-Span-7561><span class=MJXp-mrow id=MJXp-Span-7562 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7563>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-7564 style=vertical-align:-0.4em><span class=MJXp-mo id=MJXp-Span-7565>⇒</span></span></span></span></span><span id=MathJax-Element-555-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>. In this case, the contour is always moving at speed <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-7566><span class=MJXp-mo id=MJXp-Span-7567 style=margin-left:0em;margin-right:0.111em>+</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7568>v</span></span></span><span id=MathJax-Element-556-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> relative to <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-7569><span class=MJXp-msup id=MJXp-Span-7570><span class=MJXp-mrow id=MJXp-Span-7571 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-7572>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-7573 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-7574>*</span></span></span></span></span><span id=MathJax-Element-557-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>. Then, the photon moving at speed <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-7575><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7576>c</span></span></span><span id=MathJax-Element-558-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> reaches point B when <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-7577><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7578>c</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7579>t</span><span class=MJXp-mo id=MJXp-Span-7580 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-mrow id=MJXp-Span-7581><span class=MJXp-mo id=MJXp-Span-7582 style=margin-left:0em;margin-right:0em>(</span><span class=MJXp-mrow id=MJXp-Span-7583><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7584>L</span><span class=MJXp-mo id=MJXp-Span-7585 style=margin-left:0.267em;margin-right:0.267em>−</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7586>D</span></span><span class=MJXp-mo id=MJXp-Span-7587 style=margin-left:0em;margin-right:0em>)</span></span><span class=MJXp-mo id=MJXp-Span-7588 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7589>γ</span><span class=MJXp-mo id=MJXp-Span-7590 style=margin-left:0.267em;margin-right:0.267em>+</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7591>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7592>t</span></span></span><span id=MathJax-Element-559-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>, <em>i.e.</em>, at, <div class=formula id=j_phys-2023-0110_eq_034>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class="MJXp-math MJXp-display" id=MJXp-Span-7593><span class=MJXp-msub id=MJXp-Span-7594><span class=MJXp-mrow id=MJXp-Span-7595 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7596>t</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-7597 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-7598>1</span></span></span><span class=MJXp-mo id=MJXp-Span-7599 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-mfrac id=MJXp-Span-7600 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-7601><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7602>L</span><span class=MJXp-mo id=MJXp-Span-7603 style=margin-left:0.267em;margin-right:0.267em>−</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7604>D</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-7605><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7606>γ</span><span class=MJXp-mrow id=MJXp-Span-7607><span class=MJXp-mo id=MJXp-Span-7608 style=margin-left:0em;margin-right:0em>(</span><span class=MJXp-mrow id=MJXp-Span-7609><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7610>c</span><span class=MJXp-mo id=MJXp-Span-7611 style=margin-left:0.267em;margin-right:0.267em>−</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7612>v</span></span><span class=MJXp-mo id=MJXp-Span-7613 style=margin-left:0em;margin-right:0em>)</span></span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-7614 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-mfrac id=MJXp-Span-7615 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-7616><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7617>γ</span><span class=MJXp-mrow id=MJXp-Span-7618><span class=MJXp-mo id=MJXp-Span-7619 style=margin-left:0em;margin-right:0em>(</span><span class=MJXp-mrow id=MJXp-Span-7620><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7621>L</span><span class=MJXp-mo id=MJXp-Span-7622 style=margin-left:0.267em;margin-right:0.267em>−</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7623>D</span></span><span class=MJXp-mo id=MJXp-Span-7624 style=margin-left:0em;margin-right:0em>)</span></span><span class=MJXp-mrow id=MJXp-Span-7625><span class=MJXp-mo id=MJXp-Span-7626 style=margin-left:0em;margin-right:0em>(</span><span class=MJXp-mrow id=MJXp-Span-7627><span class=MJXp-mn id=MJXp-Span-7628>1</span><span class=MJXp-mo id=MJXp-Span-7629 style=margin-left:0.267em;margin-right:0.267em>+</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7630>v</span><span class=MJXp-mo id=MJXp-Span-7631 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7632>c</span></span><span class=MJXp-mo id=MJXp-Span-7633 style=margin-left:0em;margin-right:0em>)</span></span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-7634><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7635>c</span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-7636 style=margin-left:0em;margin-right:0.222em>,</span></span></span><span class="mjx-chtml MJXc-display MJXc-processing sf-hidden"></span>
</span>
</div><p> where we have used the relation <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-7637><span class=MJXp-mn id=MJXp-Span-7638>1</span><span class=MJXp-mo id=MJXp-Span-7639 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class=MJXp-msup id=MJXp-Span-7640><span class=MJXp-mrow id=MJXp-Span-7641 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7642>γ</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-7643 style=vertical-align:0.5em><span class=MJXp-mn id=MJXp-Span-7644>2</span></span></span><span class=MJXp-mo id=MJXp-Span-7645 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-mrow id=MJXp-Span-7646><span class=MJXp-mo id=MJXp-Span-7647 style=margin-left:0em;margin-right:0em>(</span><span class=MJXp-mrow id=MJXp-Span-7648><span class=MJXp-mn id=MJXp-Span-7649>1</span><span class=MJXp-mo id=MJXp-Span-7650 style=margin-left:0.267em;margin-right:0.267em>−</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7651>v</span><span class=MJXp-mo id=MJXp-Span-7652 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7653>c</span></span><span class=MJXp-mo id=MJXp-Span-7654 style=margin-left:0em;margin-right:0em>)</span></span><span class=MJXp-mrow id=MJXp-Span-7655><span class=MJXp-mo id=MJXp-Span-7656 style=margin-left:0em;margin-right:0em>(</span><span class=MJXp-mrow id=MJXp-Span-7657><span class=MJXp-mn id=MJXp-Span-7658>1</span><span class=MJXp-mo id=MJXp-Span-7659 style=margin-left:0.267em;margin-right:0.267em>+</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7660>v</span><span class=MJXp-mo id=MJXp-Span-7661 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7662>c</span></span><span class=MJXp-mo id=MJXp-Span-7663 style=margin-left:0em;margin-right:0em>)</span></span><span class=MJXp-mo id=MJXp-Span-7664 style=margin-left:0.333em;margin-right:0.333em>=</span></span></span><span id=MathJax-Element-561-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>
<span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-7665><span class=MJXp-mn id=MJXp-Span-7666>1</span><span class=MJXp-mo id=MJXp-Span-7667 style=margin-left:0.267em;margin-right:0.267em>−</span><span class=MJXp-msup id=MJXp-Span-7668><span class=MJXp-mrow id=MJXp-Span-7669 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7670>v</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-7671 style=vertical-align:0.5em><span class=MJXp-mn id=MJXp-Span-7672>2</span></span></span><span class=MJXp-mo id=MJXp-Span-7673 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class=MJXp-msup id=MJXp-Span-7674><span class=MJXp-mrow id=MJXp-Span-7675 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7676>c</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-7677 style=vertical-align:0.5em><span class=MJXp-mn id=MJXp-Span-7678>2</span></span></span></span></span><span id=MathJax-Element-562-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>.</p>
<p>Moving now on the upper track, the photon travels from B toward A and reaches A when <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-7679><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7680>L</span><span class=MJXp-mo id=MJXp-Span-7681 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7682>γ</span><span class=MJXp-mo id=MJXp-Span-7683 style=margin-left:0.267em;margin-right:0.267em>−</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7684>c</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7685>t</span><span class=MJXp-mo id=MJXp-Span-7686 style=margin-left:0.333em;margin-right:0.333em>=</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7687>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7688>t</span></span></span><span id=MathJax-Element-563-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> after the interval, <div class=formula id=j_phys-2023-0110_eq_035>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class="MJXp-math MJXp-display" id=MJXp-Span-7689><span class=MJXp-msub id=MJXp-Span-7690><span class=MJXp-mrow id=MJXp-Span-7691 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7692>t</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-7693 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-7694>2</span></span></span><span class=MJXp-mo id=MJXp-Span-7695 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-mfrac id=MJXp-Span-7696 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-7697><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7698>L</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-7699><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7700>γ</span><span class=MJXp-mrow id=MJXp-Span-7701><span class=MJXp-mo id=MJXp-Span-7702 style=margin-left:0em;margin-right:0em>(</span><span class=MJXp-mrow id=MJXp-Span-7703><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7704>c</span><span class=MJXp-mo id=MJXp-Span-7705 style=margin-left:0.267em;margin-right:0.267em>+</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7706>v</span></span><span class=MJXp-mo id=MJXp-Span-7707 style=margin-left:0em;margin-right:0em>)</span></span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-7708 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-mfrac id=MJXp-Span-7709 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-7710><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7711>γ</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7712>L</span><span class=MJXp-mrow id=MJXp-Span-7713><span class=MJXp-mo id=MJXp-Span-7714 style=margin-left:0em;margin-right:0em>(</span><span class=MJXp-mrow id=MJXp-Span-7715><span class=MJXp-mn id=MJXp-Span-7716>1</span><span class=MJXp-mo id=MJXp-Span-7717 style=margin-left:0.267em;margin-right:0.267em>−</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7718>v</span><span class=MJXp-mo id=MJXp-Span-7719 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7720>c</span></span><span class=MJXp-mo id=MJXp-Span-7721 style=margin-left:0em;margin-right:0em>)</span></span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-7722><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7723>c</span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-7724 style=margin-left:0em;margin-right:0.222em>.</span></span></span><span class="mjx-chtml MJXc-display MJXc-processing sf-hidden"></span>
</span>
</div><p>
</p>
<p>After reaching A, the photon starts moving on the lower track to return to C*. Since point A has been moving at speed <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-7725><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7726>v</span></span></span><span id=MathJax-Element-565-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> toward <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-7727><span class=MJXp-msup id=MJXp-Span-7728><span class=MJXp-mrow id=MJXp-Span-7729 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-7730>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-7731 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-7732>*</span></span></span></span></span><span id=MathJax-Element-566-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> during the interval <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-7733><span class=MJXp-msub id=MJXp-Span-7734><span class=MJXp-mrow id=MJXp-Span-7735 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7736>t</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-7737 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-7738>1</span></span></span><span class=MJXp-mo id=MJXp-Span-7739 style=margin-left:0.267em;margin-right:0.267em>+</span><span class=MJXp-msub id=MJXp-Span-7740><span class=MJXp-mrow id=MJXp-Span-7741 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7742>t</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-7743 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-7744>2</span></span></span></span></span><span id=MathJax-Element-567-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>, the position of A relative to <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-7745><span class=MJXp-msup id=MJXp-Span-7746><span class=MJXp-mrow id=MJXp-Span-7747 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-7748>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-7749 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-7750>*</span></span></span></span></span><span id=MathJax-Element-568-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> is now <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-7751><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7752>D</span><span class=MJXp-mo id=MJXp-Span-7753 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7754>γ</span><span class=MJXp-mo id=MJXp-Span-7755 style=margin-left:0.267em;margin-right:0.267em>−</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7756>v</span><span class=MJXp-mrow id=MJXp-Span-7757><span class=MJXp-mo id=MJXp-Span-7758 style=margin-left:0em;margin-right:0em;vertical-align:-0.244em><span style=font-size:1.978em;margin-left:-0.05em class="MJXp-right MJXp-scale7">(</span></span><span class=MJXp-mrow id=MJXp-Span-7759><span class=MJXp-msub id=MJXp-Span-7760><span class=MJXp-mrow id=MJXp-Span-7761 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7762>t</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-7763 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-7764>1</span></span></span><span class=MJXp-mo id=MJXp-Span-7765 style=margin-left:0.267em;margin-right:0.267em>+</span><span class=MJXp-msub id=MJXp-Span-7766><span class=MJXp-mrow id=MJXp-Span-7767 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7768>t</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-7769 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-7770>2</span></span></span></span><span class=MJXp-mo id=MJXp-Span-7771 style=margin-left:0em;margin-right:0em;vertical-align:-0.244em><span style=font-size:1.978em;margin-left:-0.05em class="MJXp-right MJXp-scale7">)</span></span></span></span></span><span id=MathJax-Element-569-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> and the photon reaches <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-7772><span class=MJXp-msup id=MJXp-Span-7773><span class=MJXp-mrow id=MJXp-Span-7774 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-7775>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-7776 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-7777>*</span></span></span></span></span><span id=MathJax-Element-570-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> when <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-7778><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7779>D</span><span class=MJXp-mo id=MJXp-Span-7780 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7781>γ</span><span class=MJXp-mo id=MJXp-Span-7782 style=margin-left:0.267em;margin-right:0.267em>−</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7783>v</span><span class=MJXp-mrow id=MJXp-Span-7784><span class=MJXp-mo id=MJXp-Span-7785 style=margin-left:0em;margin-right:0em;vertical-align:-0.244em><span style=font-size:1.978em;margin-left:-0.05em class="MJXp-right MJXp-scale7">(</span></span><span class=MJXp-mrow id=MJXp-Span-7786><span class=MJXp-msub id=MJXp-Span-7787><span class=MJXp-mrow id=MJXp-Span-7788 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7789>t</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-7790 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-7791>1</span></span></span><span class=MJXp-mo id=MJXp-Span-7792 style=margin-left:0.267em;margin-right:0.267em>+</span><span class=MJXp-msub id=MJXp-Span-7793><span class=MJXp-mrow id=MJXp-Span-7794 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7795>t</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-7796 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-7797>2</span></span></span></span><span class=MJXp-mo id=MJXp-Span-7798 style=margin-left:0em;margin-right:0em;vertical-align:-0.244em><span style=font-size:1.978em;margin-left:-0.05em class="MJXp-right MJXp-scale7">)</span></span></span><span class=MJXp-mo id=MJXp-Span-7799 style=margin-left:0.333em;margin-right:0.333em>=</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7800>c</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7801>t</span></span></span><span id=MathJax-Element-571-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>, after the interval, <div class=formula id=j_phys-2023-0110_eq_036>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class="MJXp-math MJXp-display" id=MJXp-Span-7802><span class=MJXp-mtable id=MJXp-Span-7803><span><span class=MJXp-mtr id=MJXp-Span-7804 style=vertical-align:baseline><span class=MJXp-mtd id=MJXp-Span-7805 style=text-align:center><span class=MJXp-msub id=MJXp-Span-7806><span class=MJXp-mrow id=MJXp-Span-7807 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7808>t</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-7809 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-7810>3</span></span></span></span><span class=MJXp-mtd id=MJXp-Span-7811 style=padding-left:0.33em;text-align:center><span class=MJXp-mo id=MJXp-Span-7812 style=margin-left:0.333em;margin-right:0.333em>=</span></span><span class=MJXp-mtd id=MJXp-Span-7813 style=padding-left:0.33em;text-align:center><span class=MJXp-mfrac id=MJXp-Span-7814 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-7815><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7816>D</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-7817><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7818>γ</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7819>c</span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-7820 style=margin-left:0.267em;margin-right:0.267em>−</span><span class=MJXp-mfrac id=MJXp-Span-7821 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-7822><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7823>v</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-7824><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7825>c</span></span></span></span></span></span></span><span class=MJXp-mrow id=MJXp-Span-7826><span class=MJXp-mo id=MJXp-Span-7827 style=margin-left:0em;margin-right:0em;vertical-align:-0.244em><span style=font-size:1.978em;margin-left:-0.05em class="MJXp-right MJXp-scale7">(</span></span><span class=MJXp-mrow id=MJXp-Span-7828><span class=MJXp-msub id=MJXp-Span-7829><span class=MJXp-mrow id=MJXp-Span-7830 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7831>t</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-7832 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-7833>1</span></span></span><span class=MJXp-mo id=MJXp-Span-7834 style=margin-left:0.267em;margin-right:0.267em>+</span><span class=MJXp-msub id=MJXp-Span-7835><span class=MJXp-mrow id=MJXp-Span-7836 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7837>t</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-7838 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-7839>2</span></span></span></span><span class=MJXp-mo id=MJXp-Span-7840 style=margin-left:0em;margin-right:0em;vertical-align:-0.244em><span style=font-size:1.978em;margin-left:-0.05em class="MJXp-right MJXp-scale7">)</span></span></span></span></span><span class=MJXp-mtr id=MJXp-Span-7841 style=vertical-align:baseline><span class=MJXp-mtd id=MJXp-Span-7842 style=padding-top:0.431em;text-align:center></span><span class=MJXp-mtd id=MJXp-Span-7843 style=padding-left:0.33em;padding-top:0.431em;text-align:center><span class=MJXp-mo id=MJXp-Span-7844 style=margin-left:0.333em;margin-right:0.333em>=</span></span><span class=MJXp-mtd id=MJXp-Span-7845 style=padding-left:0.33em;padding-top:0.431em;text-align:center><span class=MJXp-mfrac id=MJXp-Span-7846 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-7847><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7848>D</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-7849><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7850>γ</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7851>c</span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-7852 style=margin-left:0.267em;margin-right:0.267em>−</span><span class=MJXp-mfrac id=MJXp-Span-7853 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-7854><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7855>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7856>γ</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-7857><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7858>c</span></span></span></span></span></span></span><span class=MJXp-mfenced id=MJXp-Span-7859><span class=MJXp-mo id=MJXp-Span-7860 style=margin-left:0em;margin-right:0em;vertical-align:-0.5em><span style=font-size:3em;margin-left:-0.13em class="MJXp-right MJXp-scale5">(</span></span><span class=MJXp-mrow id=MJXp-Span-7861><span class=MJXp-mfrac id=MJXp-Span-7862 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-7863><span class=MJXp-mrow id=MJXp-Span-7864><span class=MJXp-mo id=MJXp-Span-7865 style=margin-left:0em;margin-right:0em>(</span><span class=MJXp-mrow id=MJXp-Span-7866><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7867>L</span><span class=MJXp-mo id=MJXp-Span-7868 style=margin-left:0.267em;margin-right:0.267em>−</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7869>D</span></span><span class=MJXp-mo id=MJXp-Span-7870 style=margin-left:0em;margin-right:0em>)</span></span><span class=MJXp-mrow id=MJXp-Span-7871><span class=MJXp-mo id=MJXp-Span-7872 style=margin-left:0em;margin-right:0em>(</span><span class=MJXp-mrow id=MJXp-Span-7873><span class=MJXp-mn id=MJXp-Span-7874>1</span><span class=MJXp-mo id=MJXp-Span-7875 style=margin-left:0.267em;margin-right:0.267em>+</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7876>v</span><span class=MJXp-mo id=MJXp-Span-7877 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7878>c</span></span><span class=MJXp-mo id=MJXp-Span-7879 style=margin-left:0em;margin-right:0em>)</span></span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-7880><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7881>c</span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-7882 style=margin-left:0.267em;margin-right:0.267em>+</span><span class=MJXp-mfrac id=MJXp-Span-7883 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-7884><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7885>L</span><span class=MJXp-mrow id=MJXp-Span-7886><span class=MJXp-mo id=MJXp-Span-7887 style=margin-left:0em;margin-right:0em>(</span><span class=MJXp-mrow id=MJXp-Span-7888><span class=MJXp-mn id=MJXp-Span-7889>1</span><span class=MJXp-mo id=MJXp-Span-7890 style=margin-left:0.267em;margin-right:0.267em>−</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7891>v</span><span class=MJXp-mo id=MJXp-Span-7892 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7893>c</span></span><span class=MJXp-mo id=MJXp-Span-7894 style=margin-left:0em;margin-right:0em>)</span></span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-7895><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7896>c</span></span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-7897 style=margin-left:0em;margin-right:0em;vertical-align:-0.5em><span style=font-size:3em;margin-left:-0.13em class="MJXp-right MJXp-scale5">)</span></span></span></span></span><span class=MJXp-mtr id=MJXp-Span-7898 style=vertical-align:baseline><span class=MJXp-mtd id=MJXp-Span-7899 style=padding-top:0.431em;text-align:center></span><span class=MJXp-mtd id=MJXp-Span-7900 style=padding-left:0.33em;padding-top:0.431em;text-align:center><span class=MJXp-mo id=MJXp-Span-7901 style=margin-left:0.333em;margin-right:0.333em>=</span></span><span class=MJXp-mtd id=MJXp-Span-7902 style=padding-left:0.33em;padding-top:0.431em;text-align:center><span class=MJXp-mfrac id=MJXp-Span-7903 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-7904><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7905>γ</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7906>D</span><span class=MJXp-mrow id=MJXp-Span-7907><span class=MJXp-mo id=MJXp-Span-7908 style=margin-left:0em;margin-right:0em;vertical-align:-0.289em><span style=font-size:2.156em;margin-left:-0.09em class="MJXp-right MJXp-scale6">(</span></span><span class=MJXp-mrow id=MJXp-Span-7909><span class=MJXp-mn id=MJXp-Span-7910>1</span><span class=MJXp-mo id=MJXp-Span-7911 style=margin-left:0.267em;margin-right:0.267em>−</span><span class=MJXp-msup id=MJXp-Span-7912><span class=MJXp-mrow id=MJXp-Span-7913 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7914>v</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-7915 style=vertical-align:0.5em><span class=MJXp-mn id=MJXp-Span-7916>2</span></span></span><span class=MJXp-mo id=MJXp-Span-7917 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class=MJXp-msup id=MJXp-Span-7918><span class=MJXp-mrow id=MJXp-Span-7919 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7920>c</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-7921 style=vertical-align:0.5em><span class=MJXp-mn id=MJXp-Span-7922>2</span></span></span></span><span class=MJXp-mo id=MJXp-Span-7923 style=margin-left:0em;margin-right:0em;vertical-align:-0.289em><span style=font-size:2.156em;margin-left:-0.09em class="MJXp-right MJXp-scale6">)</span></span></span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-7924><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7925>c</span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-7926 style=margin-left:0.267em;margin-right:0.267em>−</span><span class=MJXp-mfrac id=MJXp-Span-7927 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-7928><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7929>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7930>γ</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-7931><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7932>c</span></span></span></span></span></span></span><span class=MJXp-mfrac id=MJXp-Span-7933 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-7934><span class=MJXp-mn id=MJXp-Span-7935>2</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7936>L</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-7937><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7938>c</span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-7939 style=margin-left:0.267em;margin-right:0.267em>+</span><span class=MJXp-mfrac id=MJXp-Span-7940 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-7941><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7942>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7943>γ</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-7944><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7945>c</span></span></span></span></span></span></span><span class=MJXp-mfrac id=MJXp-Span-7946 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-7947><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7948>D</span><span class=MJXp-mrow id=MJXp-Span-7949><span class=MJXp-mo id=MJXp-Span-7950 style=margin-left:0em;margin-right:0em>(</span><span class=MJXp-mrow id=MJXp-Span-7951><span class=MJXp-mn id=MJXp-Span-7952>1</span><span class=MJXp-mo id=MJXp-Span-7953 style=margin-left:0.267em;margin-right:0.267em>+</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7954>v</span><span class=MJXp-mo id=MJXp-Span-7955 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7956>c</span></span><span class=MJXp-mo id=MJXp-Span-7957 style=margin-left:0em;margin-right:0em>)</span></span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-7958><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7959>c</span></span></span></span></span></span></span></span></span><span class=MJXp-mtr id=MJXp-Span-7960 style=vertical-align:baseline><span class=MJXp-mtd id=MJXp-Span-7961 style=padding-top:0.431em;text-align:center></span><span class=MJXp-mtd id=MJXp-Span-7962 style=padding-left:0.33em;padding-top:0.431em;text-align:center><span class=MJXp-mo id=MJXp-Span-7963 style=margin-left:0.333em;margin-right:0.333em>=</span></span><span class=MJXp-mtd id=MJXp-Span-7964 style=padding-left:0.33em;padding-top:0.431em;text-align:center><span class=MJXp-mfrac id=MJXp-Span-7965 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-7966><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7967>γ</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7968>D</span><span class=MJXp-mrow id=MJXp-Span-7969><span class=MJXp-mo id=MJXp-Span-7970 style=margin-left:0em;margin-right:0em>(</span><span class=MJXp-mrow id=MJXp-Span-7971><span class=MJXp-mn id=MJXp-Span-7972>1</span><span class=MJXp-mo id=MJXp-Span-7973 style=margin-left:0.267em;margin-right:0.267em>+</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7974>v</span><span class=MJXp-mo id=MJXp-Span-7975 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7976>c</span></span><span class=MJXp-mo id=MJXp-Span-7977 style=margin-left:0em;margin-right:0em>)</span></span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-7978><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7979>c</span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-7980 style=margin-left:0.267em;margin-right:0.267em>−</span><span class=MJXp-mfrac id=MJXp-Span-7981 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-7982><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7983>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7984>γ</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-7985><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7986>c</span></span></span></span></span></span></span><span class=MJXp-mfrac id=MJXp-Span-7987 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-7988><span class=MJXp-mn id=MJXp-Span-7989>2</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7990>L</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-7991><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7992>c</span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-7993 style=margin-left:0em;margin-right:0.222em>.</span></span></span></span></span></span></span><span class="mjx-chtml MJXc-display MJXc-processing sf-hidden"></span>
</span>
</div><p> The resulting round-trip interval <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-7994><span class=MJXp-msub id=MJXp-Span-7995><span class=MJXp-mrow id=MJXp-Span-7996 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-7997>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-7998 style=vertical-align:-0.4em><span class=MJXp-mo id=MJXp-Span-7999>⇒</span></span></span></span></span><span id=MathJax-Element-573-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> is, <div class=formula id=j_phys-2023-0110_eq_037>
<span class=label>(A15)</span>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class="MJXp-math MJXp-display" id=MJXp-Span-8000><span class=MJXp-mtable id=MJXp-Span-8001><span><span class=MJXp-mtr id=MJXp-Span-8002 style=vertical-align:baseline><span class=MJXp-mtd id=MJXp-Span-8003 style=text-align:center><span class=MJXp-msub id=MJXp-Span-8004><span class=MJXp-mrow id=MJXp-Span-8005 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8006>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-8007 style=vertical-align:-0.4em><span class=MJXp-mo id=MJXp-Span-8008>⇒</span></span></span></span><span class=MJXp-mtd id=MJXp-Span-8009 style=padding-left:0.33em;text-align:center><span class=MJXp-mo id=MJXp-Span-8010 style=margin-left:0.333em;margin-right:0.333em>=</span></span><span class=MJXp-mtd id=MJXp-Span-8011 style=padding-left:0.33em;text-align:center><span class=MJXp-msub id=MJXp-Span-8012><span class=MJXp-mrow id=MJXp-Span-8013 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8014>t</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-8015 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-8016>1</span></span></span><span class=MJXp-mo id=MJXp-Span-8017 style=margin-left:0.267em;margin-right:0.267em>+</span><span class=MJXp-msub id=MJXp-Span-8018><span class=MJXp-mrow id=MJXp-Span-8019 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8020>t</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-8021 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-8022>2</span></span></span><span class=MJXp-mo id=MJXp-Span-8023 style=margin-left:0.267em;margin-right:0.267em>+</span><span class=MJXp-msub id=MJXp-Span-8024><span class=MJXp-mrow id=MJXp-Span-8025 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8026>t</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-8027 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-8028>3</span></span></span></span></span><span class=MJXp-mtr id=MJXp-Span-8029 style=vertical-align:baseline><span class=MJXp-mtd id=MJXp-Span-8030 style=padding-top:0.431em;text-align:center></span><span class=MJXp-mtd id=MJXp-Span-8031 style=padding-left:0.33em;padding-top:0.431em;text-align:center><span class=MJXp-mo id=MJXp-Span-8032 style=margin-left:0.333em;margin-right:0.333em>=</span></span><span class=MJXp-mtd id=MJXp-Span-8033 style=padding-left:0.33em;padding-top:0.431em;text-align:center><span class=MJXp-mfrac id=MJXp-Span-8034 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-8035><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8036>γ</span><span class=MJXp-mrow id=MJXp-Span-8037><span class=MJXp-mo id=MJXp-Span-8038 style=margin-left:0em;margin-right:0em>(</span><span class=MJXp-mrow id=MJXp-Span-8039><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8040>L</span><span class=MJXp-mo id=MJXp-Span-8041 style=margin-left:0.267em;margin-right:0.267em>−</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8042>D</span></span><span class=MJXp-mo id=MJXp-Span-8043 style=margin-left:0em;margin-right:0em>)</span></span><span class=MJXp-mrow id=MJXp-Span-8044><span class=MJXp-mo id=MJXp-Span-8045 style=margin-left:0em;margin-right:0em>(</span><span class=MJXp-mrow id=MJXp-Span-8046><span class=MJXp-mn id=MJXp-Span-8047>1</span><span class=MJXp-mo id=MJXp-Span-8048 style=margin-left:0.267em;margin-right:0.267em>+</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8049>v</span><span class=MJXp-mo id=MJXp-Span-8050 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8051>c</span></span><span class=MJXp-mo id=MJXp-Span-8052 style=margin-left:0em;margin-right:0em>)</span></span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-8053><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8054>c</span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-8055 style=margin-left:0.267em;margin-right:0.267em>+</span><span class=MJXp-mfrac id=MJXp-Span-8056 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-8057><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8058>γ</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8059>L</span><span class=MJXp-mrow id=MJXp-Span-8060><span class=MJXp-mo id=MJXp-Span-8061 style=margin-left:0em;margin-right:0em>(</span><span class=MJXp-mrow id=MJXp-Span-8062><span class=MJXp-mn id=MJXp-Span-8063>1</span><span class=MJXp-mo id=MJXp-Span-8064 style=margin-left:0.267em;margin-right:0.267em>−</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8065>v</span><span class=MJXp-mo id=MJXp-Span-8066 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8067>c</span></span><span class=MJXp-mo id=MJXp-Span-8068 style=margin-left:0em;margin-right:0em>)</span></span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-8069><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8070>c</span></span></span></span></span></span></span></span></span><span class=MJXp-mtr id=MJXp-Span-8071 style=vertical-align:baseline><span class=MJXp-mtd id=MJXp-Span-8072 style=padding-top:0.431em;text-align:center></span><span class=MJXp-mtd id=MJXp-Span-8073 style=padding-left:0.33em;padding-top:0.431em;text-align:center></span><span class=MJXp-mtd id=MJXp-Span-8074 style=padding-left:0.33em;padding-top:0.431em;text-align:center><span class=MJXp-mo id=MJXp-Span-8075 style=margin-left:0em;margin-right:0.111em>+</span><span class=MJXp-mfrac id=MJXp-Span-8076 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-8077><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8078>γ</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8079>D</span><span class=MJXp-mrow id=MJXp-Span-8080><span class=MJXp-mo id=MJXp-Span-8081 style=margin-left:0em;margin-right:0em>(</span><span class=MJXp-mrow id=MJXp-Span-8082><span class=MJXp-mn id=MJXp-Span-8083>1</span><span class=MJXp-mo id=MJXp-Span-8084 style=margin-left:0.267em;margin-right:0.267em>+</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8085>v</span><span class=MJXp-mo id=MJXp-Span-8086 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8087>c</span></span><span class=MJXp-mo id=MJXp-Span-8088 style=margin-left:0em;margin-right:0em>)</span></span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-8089><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8090>c</span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-8091 style=margin-left:0.267em;margin-right:0.267em>−</span><span class=MJXp-mfrac id=MJXp-Span-8092 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-8093><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8094>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8095>γ</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-8096><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8097>c</span></span></span></span></span></span></span><span class=MJXp-mfrac id=MJXp-Span-8098 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-8099><span class=MJXp-mn id=MJXp-Span-8100>2</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8101>L</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-8102><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8103>c</span></span></span></span></span></span></span></span></span><span class=MJXp-mtr id=MJXp-Span-8104 style=vertical-align:baseline><span class=MJXp-mtd id=MJXp-Span-8105 style=padding-top:0.431em;text-align:center></span><span class=MJXp-mtd id=MJXp-Span-8106 style=padding-left:0.33em;padding-top:0.431em;text-align:center><span class=MJXp-mo id=MJXp-Span-8107 style=margin-left:0.333em;margin-right:0.333em>=</span></span><span class=MJXp-mtd id=MJXp-Span-8108 style=padding-left:0.33em;padding-top:0.431em;text-align:center><span class=MJXp-mfrac id=MJXp-Span-8109 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-8110><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8111>γ</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8112>L</span><span class=MJXp-mrow id=MJXp-Span-8113><span class=MJXp-mo id=MJXp-Span-8114 style=margin-left:0em;margin-right:0em>(</span><span class=MJXp-mrow id=MJXp-Span-8115><span class=MJXp-mn id=MJXp-Span-8116>1</span><span class=MJXp-mo id=MJXp-Span-8117 style=margin-left:0.267em;margin-right:0.267em>+</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8118>v</span><span class=MJXp-mo id=MJXp-Span-8119 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8120>c</span></span><span class=MJXp-mo id=MJXp-Span-8121 style=margin-left:0em;margin-right:0em>)</span></span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-8122><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8123>c</span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-8124 style=margin-left:0.267em;margin-right:0.267em>+</span><span class=MJXp-mfrac id=MJXp-Span-8125 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-8126><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8127>γ</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8128>L</span><span class=MJXp-mrow id=MJXp-Span-8129><span class=MJXp-mo id=MJXp-Span-8130 style=margin-left:0em;margin-right:0em>(</span><span class=MJXp-mrow id=MJXp-Span-8131><span class=MJXp-mn id=MJXp-Span-8132>1</span><span class=MJXp-mo id=MJXp-Span-8133 style=margin-left:0.267em;margin-right:0.267em>−</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8134>v</span><span class=MJXp-mo id=MJXp-Span-8135 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8136>c</span></span><span class=MJXp-mo id=MJXp-Span-8137 style=margin-left:0em;margin-right:0em>)</span></span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-8138><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8139>c</span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-8140 style=margin-left:0.267em;margin-right:0.267em>−</span><span class=MJXp-mfrac id=MJXp-Span-8141 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-8142><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8143>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8144>γ</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-8145><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8146>c</span></span></span></span></span></span></span><span class=MJXp-mfrac id=MJXp-Span-8147 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-8148><span class=MJXp-mn id=MJXp-Span-8149>2</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8150>L</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-8151><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8152>c</span></span></span></span></span></span></span></span></span><span class=MJXp-mtr id=MJXp-Span-8153 style=vertical-align:baseline><span class=MJXp-mtd id=MJXp-Span-8154 style=padding-top:0.431em;text-align:center></span><span class=MJXp-mtd id=MJXp-Span-8155 style=padding-left:0.33em;padding-top:0.431em;text-align:center></span><span class=MJXp-mtd id=MJXp-Span-8156 style=padding-left:0.33em;padding-top:0.431em;text-align:center><span class=MJXp-mo id=MJXp-Span-8157 style=margin-left:0em;margin-right:0.111em>−</span><span class=MJXp-mfrac id=MJXp-Span-8158 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-8159><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8160>γ</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8161>D</span><span class=MJXp-mrow id=MJXp-Span-8162><span class=MJXp-mo id=MJXp-Span-8163 style=margin-left:0em;margin-right:0em>(</span><span class=MJXp-mrow id=MJXp-Span-8164><span class=MJXp-mn id=MJXp-Span-8165>1</span><span class=MJXp-mo id=MJXp-Span-8166 style=margin-left:0.267em;margin-right:0.267em>+</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8167>v</span><span class=MJXp-mo id=MJXp-Span-8168 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8169>c</span></span><span class=MJXp-mo id=MJXp-Span-8170 style=margin-left:0em;margin-right:0em>)</span></span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-8171><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8172>c</span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-8173 style=margin-left:0.267em;margin-right:0.267em>+</span><span class=MJXp-mfrac id=MJXp-Span-8174 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-8175><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8176>γ</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8177>D</span><span class=MJXp-mrow id=MJXp-Span-8178><span class=MJXp-mo id=MJXp-Span-8179 style=margin-left:0em;margin-right:0em>(</span><span class=MJXp-mrow id=MJXp-Span-8180><span class=MJXp-mn id=MJXp-Span-8181>1</span><span class=MJXp-mo id=MJXp-Span-8182 style=margin-left:0.267em;margin-right:0.267em>+</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8183>v</span><span class=MJXp-mo id=MJXp-Span-8184 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8185>c</span></span><span class=MJXp-mo id=MJXp-Span-8186 style=margin-left:0em;margin-right:0em>)</span></span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-8187><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8188>c</span></span></span></span></span></span></span></span></span><span class=MJXp-mtr id=MJXp-Span-8189 style=vertical-align:baseline><span class=MJXp-mtd id=MJXp-Span-8190 style=padding-top:0.431em;text-align:center></span><span class=MJXp-mtd id=MJXp-Span-8191 style=padding-left:0.33em;padding-top:0.431em;text-align:center><span class=MJXp-mo id=MJXp-Span-8192 style=margin-left:0.333em;margin-right:0.333em>=</span></span><span class=MJXp-mtd id=MJXp-Span-8193 style=padding-left:0.33em;padding-top:0.431em;text-align:center><span class=MJXp-mfrac id=MJXp-Span-8194 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-8195><span class=MJXp-mn id=MJXp-Span-8196>2</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8197>γ</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8198>L</span><span class=MJXp-mrow id=MJXp-Span-8199><span class=MJXp-mo id=MJXp-Span-8200 style=margin-left:0em;margin-right:0em>(</span><span class=MJXp-mrow id=MJXp-Span-8201><span class=MJXp-mn id=MJXp-Span-8202>1</span><span class=MJXp-mo id=MJXp-Span-8203 style=margin-left:0.267em;margin-right:0.267em>−</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8204>v</span><span class=MJXp-mo id=MJXp-Span-8205 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8206>c</span></span><span class=MJXp-mo id=MJXp-Span-8207 style=margin-left:0em;margin-right:0em>)</span></span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-8208><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8209>c</span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-8210 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-mfrac id=MJXp-Span-8211 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-8212><span class=MJXp-mn id=MJXp-Span-8213>2</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8214>L</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-8215><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8216>γ</span><span class=MJXp-mrow id=MJXp-Span-8217><span class=MJXp-mo id=MJXp-Span-8218 style=margin-left:0em;margin-right:0em>(</span><span class=MJXp-mrow id=MJXp-Span-8219><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8220>c</span><span class=MJXp-mo id=MJXp-Span-8221 style=margin-left:0.267em;margin-right:0.267em>+</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8222>v</span></span><span class=MJXp-mo id=MJXp-Span-8223 style=margin-left:0em;margin-right:0em>)</span></span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-8224 style=margin-left:0em;margin-right:0.222em>,</span></span></span></span></span></span></span><span class="mjx-chtml MJXc-display MJXc-processing sf-hidden"></span>
</span>
</div><p> showing that, for <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-8225><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8226>D</span><span class=MJXp-mo id=MJXp-Span-8227 style=margin-left:0.333em;margin-right:0.333em>&gt;</span><span class=MJXp-mn id=MJXp-Span-8228>2</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8229>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8230>L</span><span class=MJXp-mo id=MJXp-Span-8231 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8232>c</span></span></span><span id=MathJax-Element-575-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>, in the RLSE <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-8233><span class=MJXp-msub id=MJXp-Span-8234><span class=MJXp-mrow id=MJXp-Span-8235 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8236>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-8237 style=vertical-align:-0.4em><span class=MJXp-mo id=MJXp-Span-8238>⇒</span></span></span></span></span><span id=MathJax-Element-576-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>, is <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-8239><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8240>D</span></span></span><span id=MathJax-Element-577-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>-independent and the same as that of the standard linear Sagnac effect in Eq. (<a href=#j_phys-2023-0110_eq_001 class="link link-disp-formula" data-bs-target=j_phys-2023-0110_eq_001>1</a>). The same conclusion holds for the round-trip <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-8241><span class=MJXp-msub id=MJXp-Span-8242><span class=MJXp-mrow id=MJXp-Span-8243 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8244>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-8245 style=vertical-align:-0.4em><span class=MJXp-mo id=MJXp-Span-8246>⇐</span></span></span></span></span><span id=MathJax-Element-578-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> of the co-propagating photon.</p>
</section>
<section id=j_phys-2023-0110_s_007_s_002>
<h4 class=subheading>A.3.2 Showing that in general, for the RLSE the round trips intervals <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-8247><span class=MJXp-msub id=MJXp-Span-8248><span class=MJXp-mrow id=MJXp-Span-8249 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8250>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-8251 style=vertical-align:-0.4em><span class=MJXp-mo id=MJXp-Span-8252>⇐</span></span></span></span></span><span id=MathJax-Element-579-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> and <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-8253><span class=MJXp-msub id=MJXp-Span-8254><span class=MJXp-mrow id=MJXp-Span-8255 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8256>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-8257 style=vertical-align:-0.4em><span class=MJXp-mo id=MJXp-Span-8258>⇒</span></span></span></span></span><span id=MathJax-Element-580-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> depend on <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-8259><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8260>D</span></span></span><span id=MathJax-Element-581-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>. For two counter-propagating photons, the standard RLSE provides the same <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-8261><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8262>D</span></span></span><span id=MathJax-Element-582-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>-independent result <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-8263><span class=MJXp-mi id=MJXp-Span-8264>Δ</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8265>T</span></span></span><span id=MathJax-Element-583-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> of the standard linear Sagnac effect.</h4>
<p>When during the round-trip interval <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-8266><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8267>T</span></span></span><span id=MathJax-Element-584-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> the device <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-8268><span class=MJXp-msup id=MJXp-Span-8269><span class=MJXp-mrow id=MJXp-Span-8270 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-8271>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-8272 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-8273>*</span></span></span></span></span><span id=MathJax-Element-585-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> keeps on the same track (lower or upper contour section), there is no problem in deriving (as shown earlier) for <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-8274><span class=MJXp-mi id=MJXp-Span-8275>Δ</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8276>T</span><span class=MJXp-mo id=MJXp-Span-8277 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-msub id=MJXp-Span-8278><span class=MJXp-mrow id=MJXp-Span-8279 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8280>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-8281 style=vertical-align:-0.4em><span class=MJXp-mo id=MJXp-Span-8282>⇐</span></span></span><span class=MJXp-mo id=MJXp-Span-8283 style=margin-left:0.267em;margin-right:0.267em>−</span><span class=MJXp-msub id=MJXp-Span-8284><span class=MJXp-mrow id=MJXp-Span-8285 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8286>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-8287 style=vertical-align:-0.4em><span class=MJXp-mo id=MJXp-Span-8288>⇒</span></span></span></span></span><span id=MathJax-Element-586-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> the <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-8289><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8290>D</span></span></span><span id=MathJax-Element-587-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>-independent results (<a href=#j_phys-2023-0110_eq_001 class="link link-disp-formula" data-bs-target=j_phys-2023-0110_eq_001>1</a>)–(<a href=#j_phys-2023-0110_eq_003 class="link link-disp-formula" data-bs-target=j_phys-2023-0110_eq_003>3</a>), which are the same as those that can be found in literature. The calculations become quite complicated when the device <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-8291><span class=MJXp-msup id=MJXp-Span-8292><span class=MJXp-mrow id=MJXp-Span-8293 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-8294>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-8295 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-8296>*</span></span></span></span></span><span id=MathJax-Element-588-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> passes, e.g., from the lower to the upper track and we wish to find results in general. Since in the variant S-RLSE, the round-trip <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-8297><span class=MJXp-msub id=MJXp-Span-8298><span class=MJXp-mrow id=MJXp-Span-8299 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8300>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-8301 style=vertical-align:-0.4em><span class=MJXp-mo id=MJXp-Span-8302>⇒</span></span></span></span></span><span id=MathJax-Element-589-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> has its maximum when the photon covers the maximum length <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-8303><span class=MJXp-mn id=MJXp-Span-8304>2</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8305>L</span><span class=MJXp-mo id=MJXp-Span-8306 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8307>γ</span></span></span><span id=MathJax-Element-590-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> (occurring when <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-8308><span class=MJXp-msub id=MJXp-Span-8309><span class=MJXp-mrow id=MJXp-Span-8310 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8311>D</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-8312 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-8313>0</span></span></span><span class=MJXp-mo id=MJXp-Span-8314 style=margin-left:0.333em;margin-right:0.333em>=</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8315>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8316>L</span><span class=MJXp-mo id=MJXp-Span-8317 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class=MJXp-mrow id=MJXp-Span-8318><span class=MJXp-mo id=MJXp-Span-8319 style=margin-left:0em;margin-right:0em>(</span><span class=MJXp-mrow id=MJXp-Span-8320><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8321>γ</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8322>c</span></span><span class=MJXp-mo id=MJXp-Span-8323 style=margin-left:0em;margin-right:0em>)</span></span></span></span><span id=MathJax-Element-591-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>), we consider here this special case and perform the calculations for deriving the round-trip <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-8324><span class=MJXp-msub id=MJXp-Span-8325><span class=MJXp-mrow id=MJXp-Span-8326 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8327>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-8328 style=vertical-align:-0.4em><span class=MJXp-mo id=MJXp-Span-8329>⇐</span></span></span></span></span><span id=MathJax-Element-592-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> of the co-moving photon and determine <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-8330><span class=MJXp-mi id=MJXp-Span-8331>Δ</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8332>T</span></span></span><span id=MathJax-Element-593-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> of (<a href=#j_phys-2023-0110_eq_003 class="link link-disp-formula" data-bs-target=j_phys-2023-0110_eq_003>3</a>). For the co-moving photon, we have first to find its position at <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-8333><span class=MJXp-msub id=MJXp-Span-8334><span class=MJXp-mrow id=MJXp-Span-8335 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8336>t</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-8337 style=vertical-align:-0.4em><span class=MJXp-mi id=MJXp-Span-8338>out</span></span></span><span class=MJXp-mo id=MJXp-Span-8339 style=margin-left:0.333em;margin-right:0.333em>=</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8340>L</span><span class=MJXp-mo id=MJXp-Span-8341 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class=MJXp-mrow id=MJXp-Span-8342><span class=MJXp-mo id=MJXp-Span-8343 style=margin-left:0em;margin-right:0em>(</span><span class=MJXp-mrow id=MJXp-Span-8344><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8345>γ</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8346>c</span></span><span class=MJXp-mo id=MJXp-Span-8347 style=margin-left:0em;margin-right:0em>)</span></span></span></span><span id=MathJax-Element-594-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> when point A reaches <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-8348><span class=MJXp-msup id=MJXp-Span-8349><span class=MJXp-mrow id=MJXp-Span-8350 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-8351>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-8352 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-8353>*</span></span></span></span></span><span id=MathJax-Element-595-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> and the rod changes the direction of motion. With reference to <a href=#j_phys-2023-0110_fig_007 class="link link-fig" data-bs-target=j_phys-2023-0110_fig_007>Figure A3</a>(a), starting from <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-8354><span class=MJXp-msup id=MJXp-Span-8355><span class=MJXp-mrow id=MJXp-Span-8356 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-8357>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-8358 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-8359>*</span></span></span></span></span><span id=MathJax-Element-596-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> and moving to the left at speed <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-8360><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8361>c</span></span></span><span id=MathJax-Element-597-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> toward point A, the photon reaches A when <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-8362><span class=MJXp-mo id=MJXp-Span-8363 style=margin-left:0em;margin-right:0.111em>−</span><span class=MJXp-msub id=MJXp-Span-8364><span class=MJXp-mrow id=MJXp-Span-8365 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8366>D</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-8367 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-8368>0</span></span></span><span class=MJXp-mo id=MJXp-Span-8369 style=margin-left:0.267em;margin-right:0.267em>+</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8370>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8371>t</span><span class=MJXp-mo id=MJXp-Span-8372 style=margin-left:0.333em;margin-right:0.333em>=</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8373>c</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8374>t</span></span></span><span id=MathJax-Element-598-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>, <em>i.e.</em>, <div class=formula id=j_phys-2023-0110_eq_038>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class="MJXp-math MJXp-display" id=MJXp-Span-8375><span class=MJXp-msub id=MJXp-Span-8376><span class=MJXp-mrow id=MJXp-Span-8377 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8378>t</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-8379 style=vertical-align:-0.4em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8380>A</span></span></span><span class=MJXp-mo id=MJXp-Span-8381 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-mfrac id=MJXp-Span-8382 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-8383><span class=MJXp-msub id=MJXp-Span-8384><span class=MJXp-mrow id=MJXp-Span-8385 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8386>D</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-8387 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-8388>0</span></span></span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-8389><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8390>c</span><span class=MJXp-mo id=MJXp-Span-8391 style=margin-left:0.267em;margin-right:0.267em>+</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8392>v</span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-8393 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-mfrac id=MJXp-Span-8394 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-8395><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8396>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8397>L</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-8398><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8399>γ</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8400>c</span><span class=MJXp-mrow id=MJXp-Span-8401><span class=MJXp-mo id=MJXp-Span-8402 style=margin-left:0em;margin-right:0em>(</span><span class=MJXp-mrow id=MJXp-Span-8403><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8404>c</span><span class=MJXp-mo id=MJXp-Span-8405 style=margin-left:0.267em;margin-right:0.267em>+</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8406>v</span></span><span class=MJXp-mo id=MJXp-Span-8407 style=margin-left:0em;margin-right:0em>)</span></span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-8408 style=margin-left:0em;margin-right:0.222em>.</span></span></span><span class="mjx-chtml MJXc-display MJXc-processing sf-hidden"></span>
</span>
</div><p> After reaching A (<a href=#j_phys-2023-0110_fig_007 class="link link-fig" data-bs-target=j_phys-2023-0110_fig_007>Figure A3</a>(b)), the photon moves to the upper track and, in the remaining interval, <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-8409><span class=MJXp-mi id=MJXp-Span-8410>Δ</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8411>t</span><span class=MJXp-mo id=MJXp-Span-8412 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-msub id=MJXp-Span-8413><span class=MJXp-mrow id=MJXp-Span-8414 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8415>t</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-8416 style=vertical-align:-0.4em><span class=MJXp-mi id=MJXp-Span-8417>out</span></span></span><span class=MJXp-mo id=MJXp-Span-8418 style=margin-left:0.267em;margin-right:0.267em>−</span><span class=MJXp-msub id=MJXp-Span-8419><span class=MJXp-mrow id=MJXp-Span-8420 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8421>t</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-8422 style=vertical-align:-0.4em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8423>A</span></span></span></span></span><span id=MathJax-Element-600-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> propagates on the upper track toward point B while the rod is still moving to the right at speed <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-8424><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8425>v</span></span></span><span id=MathJax-Element-601-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>. Then, since A is moving at speed <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-8426><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8427>v</span></span></span><span id=MathJax-Element-602-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>, after the interval <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-8428><span class=MJXp-mi id=MJXp-Span-8429>Δ</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8430>t</span></span></span><span id=MathJax-Element-603-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>, the position of the photon relative to A is, <div class=formula id=j_phys-2023-0110_eq_039>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class="MJXp-math MJXp-display" id=MJXp-Span-8431><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8432>h</span><span class=MJXp-mo id=MJXp-Span-8433 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-mrow id=MJXp-Span-8434><span class=MJXp-mo id=MJXp-Span-8435 style=margin-left:0em;margin-right:0em>(</span><span class=MJXp-mrow id=MJXp-Span-8436><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8437>c</span><span class=MJXp-mo id=MJXp-Span-8438 style=margin-left:0.267em;margin-right:0.267em>−</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8439>v</span></span><span class=MJXp-mo id=MJXp-Span-8440 style=margin-left:0em;margin-right:0em>)</span></span><span class=MJXp-mi id=MJXp-Span-8441>Δ</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8442>t</span><span class=MJXp-mo id=MJXp-Span-8443 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-mrow id=MJXp-Span-8444><span class=MJXp-mo id=MJXp-Span-8445 style=margin-left:0em;margin-right:0em>(</span><span class=MJXp-mrow id=MJXp-Span-8446><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8447>c</span><span class=MJXp-mo id=MJXp-Span-8448 style=margin-left:0.267em;margin-right:0.267em>−</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8449>v</span></span><span class=MJXp-mo id=MJXp-Span-8450 style=margin-left:0em;margin-right:0em>)</span></span><span class=MJXp-mrow id=MJXp-Span-8451><span class=MJXp-mo id=MJXp-Span-8452 style=margin-left:0em;margin-right:0em;vertical-align:-0.244em><span style=font-size:1.978em;margin-left:-0.05em class="MJXp-right MJXp-scale7">(</span></span><span class=MJXp-mrow id=MJXp-Span-8453><span class=MJXp-msub id=MJXp-Span-8454><span class=MJXp-mrow id=MJXp-Span-8455 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8456>t</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-8457 style=vertical-align:-0.4em><span class=MJXp-mi id=MJXp-Span-8458>out</span></span></span><span class=MJXp-mo id=MJXp-Span-8459 style=margin-left:0.267em;margin-right:0.267em>−</span><span class=MJXp-msub id=MJXp-Span-8460><span class=MJXp-mrow id=MJXp-Span-8461 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8462>t</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-8463 style=vertical-align:-0.4em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8464>A</span></span></span></span><span class=MJXp-mo id=MJXp-Span-8465 style=margin-left:0em;margin-right:0em;vertical-align:-0.244em><span style=font-size:1.978em;margin-left:-0.05em class="MJXp-right MJXp-scale7">)</span></span></span><span class=MJXp-mo id=MJXp-Span-8466 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-mfrac id=MJXp-Span-8467 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-8468><span class=MJXp-mrow id=MJXp-Span-8469><span class=MJXp-mo id=MJXp-Span-8470 style=margin-left:0em;margin-right:0em>(</span><span class=MJXp-mrow id=MJXp-Span-8471><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8472>c</span><span class=MJXp-mo id=MJXp-Span-8473 style=margin-left:0.267em;margin-right:0.267em>−</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8474>v</span></span><span class=MJXp-mo id=MJXp-Span-8475 style=margin-left:0em;margin-right:0em>)</span></span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8476>L</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-8477><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8478>γ</span><span class=MJXp-mrow id=MJXp-Span-8479><span class=MJXp-mo id=MJXp-Span-8480 style=margin-left:0em;margin-right:0em>(</span><span class=MJXp-mrow id=MJXp-Span-8481><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8482>c</span><span class=MJXp-mo id=MJXp-Span-8483 style=margin-left:0.267em;margin-right:0.267em>+</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8484>v</span></span><span class=MJXp-mo id=MJXp-Span-8485 style=margin-left:0em;margin-right:0em>)</span></span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-8486 style=margin-left:0em;margin-right:0.222em>,</span></span></span><span class="mjx-chtml MJXc-display MJXc-processing sf-hidden"></span>
</span>
</div><p> as shown in <a href=#j_phys-2023-0110_fig_007 class="link link-fig" data-bs-target=j_phys-2023-0110_fig_007>Figure A3</a>(c).</p>
<div class=figure-wrapper id=j_phys-2023-0110_fig_007><div class="figure w-100"><div class=graphic><img loading=lazy 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" alt="Figure A3
Relative positions of photon and clock
C
*
{{\rm{C}}}^{* }
during light co-propagation in the round-trip interval
T
⇐
{T}_{\Leftarrow }
.
"></div><div class="figure-description mb-3"><div class="figure-label h3"><span class=label>Figure A3</span></div><div class="figure-caption mb-2"><span class=caption><p>Relative positions of photon and clock <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-8487><span class=MJXp-msup id=MJXp-Span-8488><span class=MJXp-mrow id=MJXp-Span-8489 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-8490>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-8491 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-8492>*</span></span></span></span></span><span id=MathJax-Element-605-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> during light co-propagation in the round-trip interval <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-8493><span class=MJXp-msub id=MJXp-Span-8494><span class=MJXp-mrow id=MJXp-Span-8495 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8496>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-8497 style=vertical-align:-0.4em><span class=MJXp-mo id=MJXp-Span-8498>⇐</span></span></span></span></span><span id=MathJax-Element-606-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>.</p></span></div></div></div></div>
<p>With the photon at distance <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-8499><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8500>h</span></span></span><span id=MathJax-Element-607-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> from A and the device <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-8501><span class=MJXp-msup id=MJXp-Span-8502><span class=MJXp-mrow id=MJXp-Span-8503 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-8504>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-8505 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-8506>*</span></span></span></span></span><span id=MathJax-Element-608-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> coinciding with A and displaying the reading <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-8507><span class=MJXp-msub id=MJXp-Span-8508><span class=MJXp-mrow id=MJXp-Span-8509 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8510>t</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-8511 style=vertical-align:-0.4em><span class=MJXp-mi id=MJXp-Span-8512>out</span></span></span></span></span><span id=MathJax-Element-609-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>, the contour changes direction of motion. Then, from <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-8513><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8514>h</span></span></span><span id=MathJax-Element-610-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>, the photon reaches B when, <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-8515><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8516>h</span><span class=MJXp-mo id=MJXp-Span-8517 style=margin-left:0.267em;margin-right:0.267em>+</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8518>c</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8519>t</span><span class=MJXp-mo id=MJXp-Span-8520 style=margin-left:0.333em;margin-right:0.333em>=</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8521>L</span><span class=MJXp-mo id=MJXp-Span-8522 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8523>γ</span><span class=MJXp-mo id=MJXp-Span-8524 style=margin-left:0.267em;margin-right:0.267em>−</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8525>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8526>t</span></span></span><span id=MathJax-Element-611-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>, <em>i.e.</em>, after the interval, <div class=formula id=j_phys-2023-0110_eq_040>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class="MJXp-math MJXp-display" id=MJXp-Span-8527><span class=MJXp-msub id=MJXp-Span-8528><span class=MJXp-mrow id=MJXp-Span-8529 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8530>t</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-8531 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-8532>2</span></span></span><span class=MJXp-mo id=MJXp-Span-8533 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-mfrac id=MJXp-Span-8534 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-8535><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8536>L</span><span class=MJXp-mo id=MJXp-Span-8537 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8538>γ</span><span class=MJXp-mo id=MJXp-Span-8539 style=margin-left:0.267em;margin-right:0.267em>−</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8540>h</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-8541><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8542>c</span><span class=MJXp-mo id=MJXp-Span-8543 style=margin-left:0.267em;margin-right:0.267em>+</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8544>v</span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-8545 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-mfrac id=MJXp-Span-8546 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-8547><span class=MJXp-mn id=MJXp-Span-8548>1</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-8549><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8550>c</span><span class=MJXp-mo id=MJXp-Span-8551 style=margin-left:0.267em;margin-right:0.267em>+</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8552>v</span></span></span></span></span></span></span><span class=MJXp-mfenced id=MJXp-Span-8553><span class=MJXp-mo id=MJXp-Span-8554 style=margin-left:0em;margin-right:0em;vertical-align:-0.5em><span style=font-size:3em;margin-left:-0.13em class="MJXp-right MJXp-scale5">[</span></span><span class=MJXp-mrow id=MJXp-Span-8555><span class=MJXp-mfrac id=MJXp-Span-8556 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-8557><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8558>L</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-8559><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8560>γ</span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-8561 style=margin-left:0.267em;margin-right:0.267em>−</span><span class=MJXp-mfrac id=MJXp-Span-8562 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-8563><span class=MJXp-mrow id=MJXp-Span-8564><span class=MJXp-mo id=MJXp-Span-8565 style=margin-left:0em;margin-right:0em>(</span><span class=MJXp-mrow id=MJXp-Span-8566><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8567>c</span><span class=MJXp-mo id=MJXp-Span-8568 style=margin-left:0.267em;margin-right:0.267em>−</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8569>v</span></span><span class=MJXp-mo id=MJXp-Span-8570 style=margin-left:0em;margin-right:0em>)</span></span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8571>L</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-8572><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8573>γ</span><span class=MJXp-mrow id=MJXp-Span-8574><span class=MJXp-mo id=MJXp-Span-8575 style=margin-left:0em;margin-right:0em>(</span><span class=MJXp-mrow id=MJXp-Span-8576><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8577>c</span><span class=MJXp-mo id=MJXp-Span-8578 style=margin-left:0.267em;margin-right:0.267em>+</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8579>v</span></span><span class=MJXp-mo id=MJXp-Span-8580 style=margin-left:0em;margin-right:0em>)</span></span></span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-8581 style=margin-left:0em;margin-right:0em;vertical-align:-0.5em><span style=font-size:3em;margin-left:-0.13em class="MJXp-right MJXp-scale5">]</span></span></span><span class=MJXp-mo id=MJXp-Span-8582 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-mfrac id=MJXp-Span-8583 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-8584><span class=MJXp-mn id=MJXp-Span-8585>2</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8586>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8587>L</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-8588><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8589>γ</span><span class=MJXp-msup id=MJXp-Span-8590><span class=MJXp-mrow id=MJXp-Span-8591 style=margin-right:0.05em><span class=MJXp-mrow id=MJXp-Span-8592><span class=MJXp-mo id=MJXp-Span-8593 style=margin-left:0em;margin-right:0em>(</span><span class=MJXp-mrow id=MJXp-Span-8594><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8595>c</span><span class=MJXp-mo id=MJXp-Span-8596 style=margin-left:0.267em;margin-right:0.267em>+</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8597>v</span></span><span class=MJXp-mo id=MJXp-Span-8598 style=margin-left:0em;margin-right:0em>)</span></span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-8599 style=vertical-align:0.5em><span class=MJXp-mn id=MJXp-Span-8600>2</span></span></span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-8601 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-mfrac id=MJXp-Span-8602 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-8603><span class=MJXp-mn id=MJXp-Span-8604>2</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8605>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8606>γ</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8607>L</span><span class=MJXp-mrow id=MJXp-Span-8608><span class=MJXp-mo id=MJXp-Span-8609 style=margin-left:0em;margin-right:0em>(</span><span class=MJXp-mrow id=MJXp-Span-8610><span class=MJXp-mn id=MJXp-Span-8611>1</span><span class=MJXp-mo id=MJXp-Span-8612 style=margin-left:0.267em;margin-right:0.267em>−</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8613>v</span><span class=MJXp-mo id=MJXp-Span-8614 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8615>c</span></span><span class=MJXp-mo id=MJXp-Span-8616 style=margin-left:0em;margin-right:0em>)</span></span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-8617><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8618>c</span><span class=MJXp-mrow id=MJXp-Span-8619><span class=MJXp-mo id=MJXp-Span-8620 style=margin-left:0em;margin-right:0em>(</span><span class=MJXp-mrow id=MJXp-Span-8621><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8622>c</span><span class=MJXp-mo id=MJXp-Span-8623 style=margin-left:0.267em;margin-right:0.267em>+</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8624>v</span></span><span class=MJXp-mo id=MJXp-Span-8625 style=margin-left:0em;margin-right:0em>)</span></span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-8626 style=margin-left:0em;margin-right:0.222em>,</span></span></span><span class="mjx-chtml MJXc-display MJXc-processing sf-hidden"></span>
</span>
</div><p> as indicated in <a href=#j_phys-2023-0110_fig_007 class="link link-fig" data-bs-target=j_phys-2023-0110_fig_007>Figure A3</a>(d).</p>
<p>After reaching B on the upper track, the photon passes to the lower track and moves toward A, reaching it when <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-8627><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8628>L</span><span class=MJXp-mo id=MJXp-Span-8629 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8630>γ</span><span class=MJXp-mo id=MJXp-Span-8631 style=margin-left:0.267em;margin-right:0.267em>−</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8632>c</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8633>t</span><span class=MJXp-mo id=MJXp-Span-8634 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-mo id=MJXp-Span-8635 style=margin-left:0.267em;margin-right:0.267em>−</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8636>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8637>t</span></span></span><span id=MathJax-Element-613-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> at, <div class=formula id=j_phys-2023-0110_eq_041>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class="MJXp-math MJXp-display" id=MJXp-Span-8638><span class=MJXp-msub id=MJXp-Span-8639><span class=MJXp-mrow id=MJXp-Span-8640 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8641>t</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-8642 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-8643>3</span></span></span><span class=MJXp-mo id=MJXp-Span-8644 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-mfrac id=MJXp-Span-8645 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-8646><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8647>L</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-8648><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8649>γ</span><span class=MJXp-mrow id=MJXp-Span-8650><span class=MJXp-mo id=MJXp-Span-8651 style=margin-left:0em;margin-right:0em>(</span><span class=MJXp-mrow id=MJXp-Span-8652><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8653>c</span><span class=MJXp-mo id=MJXp-Span-8654 style=margin-left:0.267em;margin-right:0.267em>−</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8655>v</span></span><span class=MJXp-mo id=MJXp-Span-8656 style=margin-left:0em;margin-right:0em>)</span></span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-8657 style=margin-left:0em;margin-right:0.222em>,</span></span></span><span class="mjx-chtml MJXc-display MJXc-processing sf-hidden"></span>
</span>
</div><p> as in shown <a href=#j_phys-2023-0110_fig_007 class="link link-fig" data-bs-target=j_phys-2023-0110_fig_007>Figure A3</a>(e).</p>
<p>At this point, the photon at A goes to the upper track and starts moving toward <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-8658><span class=MJXp-msup id=MJXp-Span-8659><span class=MJXp-mrow id=MJXp-Span-8660 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-8661>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-8662 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-8663>*</span></span></span></span></span><span id=MathJax-Element-615-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>. However, in the interval <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-8664><span class=MJXp-msub id=MJXp-Span-8665><span class=MJXp-mrow id=MJXp-Span-8666 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8667>t</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-8668 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-8669>2</span></span></span><span class=MJXp-mo id=MJXp-Span-8670 style=margin-left:0.267em;margin-right:0.267em>+</span><span class=MJXp-msub id=MJXp-Span-8671><span class=MJXp-mrow id=MJXp-Span-8672 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8673>t</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-8674 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-8675>3</span></span></span></span></span><span id=MathJax-Element-616-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>, point A has moved to the distance <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-8676><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8677>v</span><span class=MJXp-mrow id=MJXp-Span-8678><span class=MJXp-mo id=MJXp-Span-8679 style=margin-left:0em;margin-right:0em;vertical-align:-0.244em><span style=font-size:1.978em;margin-left:-0.05em class="MJXp-right MJXp-scale7">(</span></span><span class=MJXp-mrow id=MJXp-Span-8680><span class=MJXp-msub id=MJXp-Span-8681><span class=MJXp-mrow id=MJXp-Span-8682 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8683>t</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-8684 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-8685>2</span></span></span><span class=MJXp-mo id=MJXp-Span-8686 style=margin-left:0.267em;margin-right:0.267em>+</span><span class=MJXp-msub id=MJXp-Span-8687><span class=MJXp-mrow id=MJXp-Span-8688 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8689>t</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-8690 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-8691>3</span></span></span></span><span class=MJXp-mo id=MJXp-Span-8692 style=margin-left:0em;margin-right:0em;vertical-align:-0.244em><span style=font-size:1.978em;margin-left:-0.05em class="MJXp-right MJXp-scale7">)</span></span></span></span></span><span id=MathJax-Element-617-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> to the left of <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-8693><span class=MJXp-msup id=MJXp-Span-8694><span class=MJXp-mrow id=MJXp-Span-8695 style=margin-right:0.05em><span class=MJXp-mi id=MJXp-Span-8696>C</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-8697 style=vertical-align:0.5em><span class=MJXp-mo id=MJXp-Span-8698>*</span></span></span></span></span><span id=MathJax-Element-618-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>. Then, from A, the photon reaches C* when <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-8699><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8700>c</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8701>t</span><span class=MJXp-mo id=MJXp-Span-8702 style=margin-left:0.333em;margin-right:0.333em>=</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8703>v</span><span class=MJXp-mrow id=MJXp-Span-8704><span class=MJXp-mo id=MJXp-Span-8705 style=margin-left:0em;margin-right:0em;vertical-align:-0.244em><span style=font-size:1.978em;margin-left:-0.05em class="MJXp-right MJXp-scale7">(</span></span><span class=MJXp-mrow id=MJXp-Span-8706><span class=MJXp-msub id=MJXp-Span-8707><span class=MJXp-mrow id=MJXp-Span-8708 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8709>t</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-8710 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-8711>2</span></span></span><span class=MJXp-mo id=MJXp-Span-8712 style=margin-left:0.267em;margin-right:0.267em>+</span><span class=MJXp-msub id=MJXp-Span-8713><span class=MJXp-mrow id=MJXp-Span-8714 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8715>t</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-8716 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-8717>3</span></span></span></span><span class=MJXp-mo id=MJXp-Span-8718 style=margin-left:0em;margin-right:0em;vertical-align:-0.244em><span style=font-size:1.978em;margin-left:-0.05em class="MJXp-right MJXp-scale7">)</span></span></span></span></span><span id=MathJax-Element-619-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> after the interval, <div class=formula id=j_phys-2023-0110_eq_042>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class="MJXp-math MJXp-display" id=MJXp-Span-8719><span class=MJXp-mtable id=MJXp-Span-8720><span><span class=MJXp-mtr id=MJXp-Span-8721 style=vertical-align:baseline><span class=MJXp-mtd id=MJXp-Span-8722 style=text-align:center><span class=MJXp-msub id=MJXp-Span-8723><span class=MJXp-mrow id=MJXp-Span-8724 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8725>t</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-8726 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-8727>4</span></span></span></span><span class=MJXp-mtd id=MJXp-Span-8728 style=padding-left:0.33em;text-align:center><span class=MJXp-mo id=MJXp-Span-8729 style=margin-left:0.333em;margin-right:0.333em>=</span></span><span class=MJXp-mtd id=MJXp-Span-8730 style=padding-left:0.33em;text-align:center><span class=MJXp-mfrac id=MJXp-Span-8731 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-8732><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8733>v</span><span class=MJXp-mrow id=MJXp-Span-8734><span class=MJXp-mo id=MJXp-Span-8735 style=margin-left:0em;margin-right:0em;vertical-align:-0.244em><span style=font-size:1.978em;margin-left:-0.05em class="MJXp-right MJXp-scale7">(</span></span><span class=MJXp-mrow id=MJXp-Span-8736><span class=MJXp-msub id=MJXp-Span-8737><span class=MJXp-mrow id=MJXp-Span-8738 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8739>t</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-8740 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-8741>2</span></span></span><span class=MJXp-mo id=MJXp-Span-8742 style=margin-left:0.267em;margin-right:0.267em>+</span><span class=MJXp-msub id=MJXp-Span-8743><span class=MJXp-mrow id=MJXp-Span-8744 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8745>t</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-8746 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-8747>3</span></span></span></span><span class=MJXp-mo id=MJXp-Span-8748 style=margin-left:0em;margin-right:0em;vertical-align:-0.244em><span style=font-size:1.978em;margin-left:-0.05em class="MJXp-right MJXp-scale7">)</span></span></span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-8749><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8750>c</span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-8751 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-mfrac id=MJXp-Span-8752 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-8753><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8754>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8755>L</span><span class=MJXp-mrow id=MJXp-Span-8756><span class=MJXp-mo id=MJXp-Span-8757 style=margin-left:0em;margin-right:0em;vertical-align:-0.289em><span style=font-size:2.156em;margin-left:-0.09em class="MJXp-right MJXp-scale6">(</span></span><span class=MJXp-mrow id=MJXp-Span-8758><span class=MJXp-mn id=MJXp-Span-8759>2</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8760>v</span><span class=MJXp-mrow id=MJXp-Span-8761><span class=MJXp-mo id=MJXp-Span-8762 style=margin-left:0em;margin-right:0em>(</span><span class=MJXp-mrow id=MJXp-Span-8763><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8764>c</span><span class=MJXp-mo id=MJXp-Span-8765 style=margin-left:0.267em;margin-right:0.267em>−</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8766>v</span></span><span class=MJXp-mo id=MJXp-Span-8767 style=margin-left:0em;margin-right:0em>)</span></span><span class=MJXp-mo id=MJXp-Span-8768 style=margin-left:0.267em;margin-right:0.267em>+</span><span class=MJXp-msup id=MJXp-Span-8769><span class=MJXp-mrow id=MJXp-Span-8770 style=margin-right:0.05em><span class=MJXp-mrow id=MJXp-Span-8771><span class=MJXp-mo id=MJXp-Span-8772 style=margin-left:0em;margin-right:0em>(</span><span class=MJXp-mrow id=MJXp-Span-8773><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8774>c</span><span class=MJXp-mo id=MJXp-Span-8775 style=margin-left:0.267em;margin-right:0.267em>+</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8776>v</span></span><span class=MJXp-mo id=MJXp-Span-8777 style=margin-left:0em;margin-right:0em>)</span></span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-8778 style=vertical-align:0.5em><span class=MJXp-mn id=MJXp-Span-8779>2</span></span></span></span><span class=MJXp-mo id=MJXp-Span-8780 style=margin-left:0em;margin-right:0em;vertical-align:-0.289em><span style=font-size:2.156em;margin-left:-0.09em class="MJXp-right MJXp-scale6">)</span></span></span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-8781><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8782>γ</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8783>c</span><span class=MJXp-msup id=MJXp-Span-8784><span class=MJXp-mrow id=MJXp-Span-8785 style=margin-right:0.05em><span class=MJXp-mrow id=MJXp-Span-8786><span class=MJXp-mo id=MJXp-Span-8787 style=margin-left:0em;margin-right:0em>(</span><span class=MJXp-mrow id=MJXp-Span-8788><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8789>c</span><span class=MJXp-mo id=MJXp-Span-8790 style=margin-left:0.267em;margin-right:0.267em>+</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8791>v</span></span><span class=MJXp-mo id=MJXp-Span-8792 style=margin-left:0em;margin-right:0em>)</span></span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-8793 style=vertical-align:0.5em><span class=MJXp-mn id=MJXp-Span-8794>2</span></span></span><span class=MJXp-mrow id=MJXp-Span-8795><span class=MJXp-mo id=MJXp-Span-8796 style=margin-left:0em;margin-right:0em>(</span><span class=MJXp-mrow id=MJXp-Span-8797><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8798>c</span><span class=MJXp-mo id=MJXp-Span-8799 style=margin-left:0.267em;margin-right:0.267em>−</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8800>v</span></span><span class=MJXp-mo id=MJXp-Span-8801 style=margin-left:0em;margin-right:0em>)</span></span></span></span></span></span></span></span></span></span><span class=MJXp-mtr id=MJXp-Span-8802 style=vertical-align:baseline><span class=MJXp-mtd id=MJXp-Span-8803 style=padding-top:0.431em;text-align:center></span><span class=MJXp-mtd id=MJXp-Span-8804 style=padding-left:0.33em;padding-top:0.431em;text-align:center><span class=MJXp-mo id=MJXp-Span-8805 style=margin-left:0.333em;margin-right:0.333em>=</span></span><span class=MJXp-mtd id=MJXp-Span-8806 style=padding-left:0.33em;padding-top:0.431em;text-align:center><span class=MJXp-mfrac id=MJXp-Span-8807 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-8808><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8809>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8810>γ</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8811>L</span><span class=MJXp-mrow id=MJXp-Span-8812><span class=MJXp-mo id=MJXp-Span-8813 style=margin-left:0em;margin-right:0em;vertical-align:-0.289em><span style=font-size:2.156em;margin-left:-0.09em class="MJXp-right MJXp-scale6">(</span></span><span class=MJXp-mrow id=MJXp-Span-8814><span class=MJXp-msup id=MJXp-Span-8815><span class=MJXp-mrow id=MJXp-Span-8816 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8817>c</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-8818 style=vertical-align:0.5em><span class=MJXp-mn id=MJXp-Span-8819>2</span></span></span><span class=MJXp-mo id=MJXp-Span-8820 style=margin-left:0.267em;margin-right:0.267em>+</span><span class=MJXp-mn id=MJXp-Span-8821>4</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8822>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8823>c</span><span class=MJXp-mo id=MJXp-Span-8824 style=margin-left:0.267em;margin-right:0.267em>−</span><span class=MJXp-msup id=MJXp-Span-8825><span class=MJXp-mrow id=MJXp-Span-8826 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8827>v</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-8828 style=vertical-align:0.5em><span class=MJXp-mn id=MJXp-Span-8829>2</span></span></span></span><span class=MJXp-mo id=MJXp-Span-8830 style=margin-left:0em;margin-right:0em;vertical-align:-0.289em><span style=font-size:2.156em;margin-left:-0.09em class="MJXp-right MJXp-scale6">)</span></span></span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-8831><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8832>c</span><span class=MJXp-mrow id=MJXp-Span-8833><span class=MJXp-mo id=MJXp-Span-8834 style=margin-left:0em;margin-right:0em>(</span><span class=MJXp-mrow id=MJXp-Span-8835><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8836>c</span><span class=MJXp-mo id=MJXp-Span-8837 style=margin-left:0.267em;margin-right:0.267em>+</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8838>v</span></span><span class=MJXp-mo id=MJXp-Span-8839 style=margin-left:0em;margin-right:0em>)</span></span><span class=MJXp-msup id=MJXp-Span-8840><span class=MJXp-mrow id=MJXp-Span-8841 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8842>c</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-8843 style=vertical-align:0.5em><span class=MJXp-mn id=MJXp-Span-8844>2</span></span></span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-8845 style=margin-left:0em;margin-right:0.222em>.</span></span></span></span></span></span></span><span class="mjx-chtml MJXc-display MJXc-processing sf-hidden"></span>
</span>
</div><p>
</p>
<p>After some algebra, the resulting round-trip time interval for the co-propagating photon is found to be, <div class=formula id=j_phys-2023-0110_eq_043>
<span class=label>(A16)</span>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class="MJXp-math MJXp-display" id=MJXp-Span-8846><span class=MJXp-mtable id=MJXp-Span-8847><span><span class=MJXp-mtr id=MJXp-Span-8848 style=vertical-align:baseline><span class=MJXp-mtd id=MJXp-Span-8849 style=text-align:center><span class=MJXp-msub id=MJXp-Span-8850><span class=MJXp-mrow id=MJXp-Span-8851 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8852>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-8853 style=vertical-align:-0.4em><span class=MJXp-mo id=MJXp-Span-8854>⇐</span></span></span></span><span class=MJXp-mtd id=MJXp-Span-8855 style=padding-left:0.33em;text-align:center><span class=MJXp-mo id=MJXp-Span-8856 style=margin-left:0.333em;margin-right:0.333em>=</span></span><span class=MJXp-mtd id=MJXp-Span-8857 style=padding-left:0.33em;text-align:center><span class=MJXp-msub id=MJXp-Span-8858><span class=MJXp-mrow id=MJXp-Span-8859 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8860>t</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-8861 style=vertical-align:-0.4em><span class=MJXp-mi id=MJXp-Span-8862>out</span></span></span><span class=MJXp-mo id=MJXp-Span-8863 style=margin-left:0.267em;margin-right:0.267em>+</span><span class=MJXp-msub id=MJXp-Span-8864><span class=MJXp-mrow id=MJXp-Span-8865 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8866>t</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-8867 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-8868>2</span></span></span><span class=MJXp-mo id=MJXp-Span-8869 style=margin-left:0.267em;margin-right:0.267em>+</span><span class=MJXp-msub id=MJXp-Span-8870><span class=MJXp-mrow id=MJXp-Span-8871 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8872>t</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-8873 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-8874>3</span></span></span><span class=MJXp-mo id=MJXp-Span-8875 style=margin-left:0.267em;margin-right:0.267em>+</span><span class=MJXp-msub id=MJXp-Span-8876><span class=MJXp-mrow id=MJXp-Span-8877 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8878>t</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-8879 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-8880>4</span></span></span></span></span><span class=MJXp-mtr id=MJXp-Span-8881 style=vertical-align:baseline><span class=MJXp-mtd id=MJXp-Span-8882 style=padding-top:0.431em;text-align:center></span><span class=MJXp-mtd id=MJXp-Span-8883 style=padding-left:0.33em;padding-top:0.431em;text-align:center><span class=MJXp-mo id=MJXp-Span-8884 style=margin-left:0.333em;margin-right:0.333em>=</span></span><span class=MJXp-mtd id=MJXp-Span-8885 style=padding-left:0.33em;padding-top:0.431em;text-align:center><span class=MJXp-mfrac id=MJXp-Span-8886 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-8887><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8888>L</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-8889><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8890>γ</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8891>c</span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-8892 style=margin-left:0.267em;margin-right:0.267em>+</span><span class=MJXp-mfrac id=MJXp-Span-8893 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-8894><span class=MJXp-mn id=MJXp-Span-8895>2</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8896>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8897>γ</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8898>L</span><span class=MJXp-mrow id=MJXp-Span-8899><span class=MJXp-mo id=MJXp-Span-8900 style=margin-left:0em;margin-right:0em>(</span><span class=MJXp-mrow id=MJXp-Span-8901><span class=MJXp-mn id=MJXp-Span-8902>1</span><span class=MJXp-mo id=MJXp-Span-8903 style=margin-left:0.267em;margin-right:0.267em>−</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8904>v</span><span class=MJXp-mo id=MJXp-Span-8905 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8906>c</span></span><span class=MJXp-mo id=MJXp-Span-8907 style=margin-left:0em;margin-right:0em>)</span></span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-8908><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8909>c</span><span class=MJXp-mrow id=MJXp-Span-8910><span class=MJXp-mo id=MJXp-Span-8911 style=margin-left:0em;margin-right:0em>(</span><span class=MJXp-mrow id=MJXp-Span-8912><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8913>c</span><span class=MJXp-mo id=MJXp-Span-8914 style=margin-left:0.267em;margin-right:0.267em>+</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8915>v</span></span><span class=MJXp-mo id=MJXp-Span-8916 style=margin-left:0em;margin-right:0em>)</span></span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-8917 style=margin-left:0.267em;margin-right:0.267em>+</span><span class=MJXp-mfrac id=MJXp-Span-8918 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-8919><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8920>L</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-8921><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8922>γ</span><span class=MJXp-mrow id=MJXp-Span-8923><span class=MJXp-mo id=MJXp-Span-8924 style=margin-left:0em;margin-right:0em>(</span><span class=MJXp-mrow id=MJXp-Span-8925><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8926>c</span><span class=MJXp-mo id=MJXp-Span-8927 style=margin-left:0.267em;margin-right:0.267em>−</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8928>v</span></span><span class=MJXp-mo id=MJXp-Span-8929 style=margin-left:0em;margin-right:0em>)</span></span></span></span></span></span></span></span></span></span><span class=MJXp-mtr id=MJXp-Span-8930 style=vertical-align:baseline><span class=MJXp-mtd id=MJXp-Span-8931 style=padding-top:0.431em;text-align:center></span><span class=MJXp-mtd id=MJXp-Span-8932 style=padding-left:0.33em;padding-top:0.431em;text-align:center></span><span class=MJXp-mtd id=MJXp-Span-8933 style=padding-left:0.33em;padding-top:0.431em;text-align:center><span class=MJXp-mo id=MJXp-Span-8934 style=margin-left:0em;margin-right:0.111em>+</span><span class=MJXp-mfrac id=MJXp-Span-8935 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-8936><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8937>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8938>γ</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8939>L</span><span class=MJXp-mrow id=MJXp-Span-8940><span class=MJXp-mo id=MJXp-Span-8941 style=margin-left:0em;margin-right:0em;vertical-align:-0.289em><span style=font-size:2.156em;margin-left:-0.09em class="MJXp-right MJXp-scale6">(</span></span><span class=MJXp-mrow id=MJXp-Span-8942><span class=MJXp-msup id=MJXp-Span-8943><span class=MJXp-mrow id=MJXp-Span-8944 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8945>c</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-8946 style=vertical-align:0.5em><span class=MJXp-mn id=MJXp-Span-8947>2</span></span></span><span class=MJXp-mo id=MJXp-Span-8948 style=margin-left:0.267em;margin-right:0.267em>+</span><span class=MJXp-mn id=MJXp-Span-8949>4</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8950>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8951>c</span><span class=MJXp-mo id=MJXp-Span-8952 style=margin-left:0.267em;margin-right:0.267em>−</span><span class=MJXp-msup id=MJXp-Span-8953><span class=MJXp-mrow id=MJXp-Span-8954 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8955>v</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-8956 style=vertical-align:0.5em><span class=MJXp-mn id=MJXp-Span-8957>2</span></span></span></span><span class=MJXp-mo id=MJXp-Span-8958 style=margin-left:0em;margin-right:0em;vertical-align:-0.289em><span style=font-size:2.156em;margin-left:-0.09em class="MJXp-right MJXp-scale6">)</span></span></span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-8959><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8960>c</span><span class=MJXp-mrow id=MJXp-Span-8961><span class=MJXp-mo id=MJXp-Span-8962 style=margin-left:0em;margin-right:0em>(</span><span class=MJXp-mrow id=MJXp-Span-8963><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8964>c</span><span class=MJXp-mo id=MJXp-Span-8965 style=margin-left:0.267em;margin-right:0.267em>+</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8966>v</span></span><span class=MJXp-mo id=MJXp-Span-8967 style=margin-left:0em;margin-right:0em>)</span></span><span class=MJXp-msup id=MJXp-Span-8968><span class=MJXp-mrow id=MJXp-Span-8969 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8970>c</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-8971 style=vertical-align:0.5em><span class=MJXp-mn id=MJXp-Span-8972>2</span></span></span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-8973 style=margin-left:0em;margin-right:0.222em>.</span></span></span></span></span></span></span><span class="mjx-chtml MJXc-display MJXc-processing sf-hidden"></span>
</span>
</div><p>
</p>
<p>The sum <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-8974><span class=MJXp-msub id=MJXp-Span-8975><span class=MJXp-mrow id=MJXp-Span-8976 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8977>t</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-8978 style=vertical-align:-0.4em><span class=MJXp-mi id=MJXp-Span-8979>out</span></span></span><span class=MJXp-mo id=MJXp-Span-8980 style=margin-left:0.267em;margin-right:0.267em>+</span><span class=MJXp-msub id=MJXp-Span-8981><span class=MJXp-mrow id=MJXp-Span-8982 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8983>t</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-8984 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-8985>3</span></span></span></span></span><span id=MathJax-Element-622-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span> can be expressed as follows: <div class=formula id=j_phys-2023-0110_eq_044>
<span class=label>(A17)</span>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class="MJXp-math MJXp-display" id=MJXp-Span-8986><span class=MJXp-mtable id=MJXp-Span-8987><span><span class=MJXp-mtr id=MJXp-Span-8988 style=vertical-align:baseline><span class=MJXp-mtd id=MJXp-Span-8989 style=text-align:center><span class=MJXp-msub id=MJXp-Span-8990><span class=MJXp-mrow id=MJXp-Span-8991 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8992>t</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-8993 style=vertical-align:-0.4em><span class=MJXp-mi id=MJXp-Span-8994>out</span></span></span><span class=MJXp-mo id=MJXp-Span-8995 style=margin-left:0.267em;margin-right:0.267em>+</span><span class=MJXp-msub id=MJXp-Span-8996><span class=MJXp-mrow id=MJXp-Span-8997 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-8998>t</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-8999 style=vertical-align:-0.4em><span class=MJXp-mn id=MJXp-Span-9000>3</span></span></span></span><span class=MJXp-mtd id=MJXp-Span-9001 style=padding-left:0.33em;text-align:center><span class=MJXp-mo id=MJXp-Span-9002 style=margin-left:0.333em;margin-right:0.333em>=</span></span><span class=MJXp-mtd id=MJXp-Span-9003 style=padding-left:0.33em;text-align:center><span class=MJXp-mfrac id=MJXp-Span-9004 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-9005><span class="MJXp-mi MJXp-italic" id=MJXp-Span-9006>L</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-9007><span class="MJXp-mi MJXp-italic" id=MJXp-Span-9008>γ</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-9009>c</span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-9010 style=margin-left:0.267em;margin-right:0.267em>+</span><span class=MJXp-mfrac id=MJXp-Span-9011 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-9012><span class="MJXp-mi MJXp-italic" id=MJXp-Span-9013>L</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-9014><span class="MJXp-mi MJXp-italic" id=MJXp-Span-9015>γ</span><span class=MJXp-mrow id=MJXp-Span-9016><span class=MJXp-mo id=MJXp-Span-9017 style=margin-left:0em;margin-right:0em>(</span><span class=MJXp-mrow id=MJXp-Span-9018><span class="MJXp-mi MJXp-italic" id=MJXp-Span-9019>c</span><span class=MJXp-mo id=MJXp-Span-9020 style=margin-left:0.267em;margin-right:0.267em>−</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-9021>v</span></span><span class=MJXp-mo id=MJXp-Span-9022 style=margin-left:0em;margin-right:0em>)</span></span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-9023 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-mfrac id=MJXp-Span-9024 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-9025><span class=MJXp-mn id=MJXp-Span-9026>2</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-9027>L</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-9028><span class="MJXp-mi MJXp-italic" id=MJXp-Span-9029>γ</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-9030>c</span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-9031 style=margin-left:0.267em;margin-right:0.267em>−</span><span class=MJXp-mfrac id=MJXp-Span-9032 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-9033><span class="MJXp-mi MJXp-italic" id=MJXp-Span-9034>L</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-9035><span class="MJXp-mi MJXp-italic" id=MJXp-Span-9036>γ</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-9037>c</span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-9038 style=margin-left:0.267em;margin-right:0.267em>+</span><span class=MJXp-mfrac id=MJXp-Span-9039 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-9040><span class="MJXp-mi MJXp-italic" id=MJXp-Span-9041>L</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-9042><span class="MJXp-mi MJXp-italic" id=MJXp-Span-9043>γ</span><span class=MJXp-mrow id=MJXp-Span-9044><span class=MJXp-mo id=MJXp-Span-9045 style=margin-left:0em;margin-right:0em>(</span><span class=MJXp-mrow id=MJXp-Span-9046><span class="MJXp-mi MJXp-italic" id=MJXp-Span-9047>c</span><span class=MJXp-mo id=MJXp-Span-9048 style=margin-left:0.267em;margin-right:0.267em>−</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-9049>v</span></span><span class=MJXp-mo id=MJXp-Span-9050 style=margin-left:0em;margin-right:0em>)</span></span></span></span></span></span></span></span></span></span><span class=MJXp-mtr id=MJXp-Span-9051 style=vertical-align:baseline><span class=MJXp-mtd id=MJXp-Span-9052 style=padding-top:0.431em;text-align:center></span><span class=MJXp-mtd id=MJXp-Span-9053 style=padding-left:0.33em;padding-top:0.431em;text-align:center><span class=MJXp-mo id=MJXp-Span-9054 style=margin-left:0.333em;margin-right:0.333em>=</span></span><span class=MJXp-mtd id=MJXp-Span-9055 style=padding-left:0.33em;padding-top:0.431em;text-align:center><span class=MJXp-mfrac id=MJXp-Span-9056 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-9057><span class=MJXp-mn id=MJXp-Span-9058>2</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-9059>L</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-9060><span class="MJXp-mi MJXp-italic" id=MJXp-Span-9061>γ</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-9062>c</span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-9063 style=margin-left:0.267em;margin-right:0.267em>+</span><span class=MJXp-mfrac id=MJXp-Span-9064 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-9065><span class="MJXp-mi MJXp-italic" id=MJXp-Span-9066>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-9067>L</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-9068><span class="MJXp-mi MJXp-italic" id=MJXp-Span-9069>γ</span><span class=MJXp-msup id=MJXp-Span-9070><span class=MJXp-mrow id=MJXp-Span-9071 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-9072>c</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-9073 style=vertical-align:0.5em><span class=MJXp-mn id=MJXp-Span-9074>2</span></span></span><span class=MJXp-mrow id=MJXp-Span-9075><span class=MJXp-mo id=MJXp-Span-9076 style=margin-left:0em;margin-right:0em>(</span><span class=MJXp-mrow id=MJXp-Span-9077><span class=MJXp-mn id=MJXp-Span-9078>1</span><span class=MJXp-mo id=MJXp-Span-9079 style=margin-left:0.267em;margin-right:0.267em>−</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-9080>v</span><span class=MJXp-mo id=MJXp-Span-9081 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-9082>c</span></span><span class=MJXp-mo id=MJXp-Span-9083 style=margin-left:0em;margin-right:0em>)</span></span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-9084 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-mfrac id=MJXp-Span-9085 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-9086><span class=MJXp-mn id=MJXp-Span-9087>2</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-9088>L</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-9089><span class="MJXp-mi MJXp-italic" id=MJXp-Span-9090>γ</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-9091>c</span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-9092 style=margin-left:0.267em;margin-right:0.267em>+</span><span class=MJXp-mfrac id=MJXp-Span-9093 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-9094><span class="MJXp-mi MJXp-italic" id=MJXp-Span-9095>γ</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-9096>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-9097>L</span><span class=MJXp-mrow id=MJXp-Span-9098><span class=MJXp-mo id=MJXp-Span-9099 style=margin-left:0em;margin-right:0em>(</span><span class=MJXp-mrow id=MJXp-Span-9100><span class=MJXp-mn id=MJXp-Span-9101>1</span><span class=MJXp-mo id=MJXp-Span-9102 style=margin-left:0.267em;margin-right:0.267em>+</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-9103>v</span><span class=MJXp-mo id=MJXp-Span-9104 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-9105>c</span></span><span class=MJXp-mo id=MJXp-Span-9106 style=margin-left:0em;margin-right:0em>)</span></span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-9107><span class=MJXp-msup id=MJXp-Span-9108><span class=MJXp-mrow id=MJXp-Span-9109 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-9110>c</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-9111 style=vertical-align:0.5em><span class=MJXp-mn id=MJXp-Span-9112>2</span></span></span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-9113 style=margin-left:0em;margin-right:0.222em>.</span></span></span></span></span></span></span><span class="mjx-chtml MJXc-display MJXc-processing sf-hidden"></span>
</span>
</div><p>
</p>
<p>By substituting Eq. (<a href=#j_phys-2023-0110_eq_044 class="link link-disp-formula" data-bs-target=j_phys-2023-0110_eq_044>A17</a>) in Eq. (<a href=#j_phys-2023-0110_eq_043 class="link link-disp-formula" data-bs-target=j_phys-2023-0110_eq_043>A16</a>), we find, <div class=formula id=j_phys-2023-0110_eq_045>
<span class=label>(A18)</span>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class="MJXp-math MJXp-display" id=MJXp-Span-9114><span class=MJXp-mtable id=MJXp-Span-9115><span><span class=MJXp-mtr id=MJXp-Span-9116 style=vertical-align:baseline><span class=MJXp-mtd id=MJXp-Span-9117 style=text-align:center><span class=MJXp-msub id=MJXp-Span-9118><span class=MJXp-mrow id=MJXp-Span-9119 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-9120>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-9121 style=vertical-align:-0.4em><span class=MJXp-mo id=MJXp-Span-9122>⇐</span></span></span></span><span class=MJXp-mtd id=MJXp-Span-9123 style=padding-left:0.33em;text-align:center><span class=MJXp-mo id=MJXp-Span-9124 style=margin-left:0.333em;margin-right:0.333em>=</span></span><span class=MJXp-mtd id=MJXp-Span-9125 style=padding-left:0.33em;text-align:center><span class=MJXp-mfrac id=MJXp-Span-9126 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-9127><span class=MJXp-mn id=MJXp-Span-9128>2</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-9129>L</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-9130><span class="MJXp-mi MJXp-italic" id=MJXp-Span-9131>γ</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-9132>c</span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-9133 style=margin-left:0.267em;margin-right:0.267em>+</span><span class=MJXp-mfrac id=MJXp-Span-9134 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-9135><span class="MJXp-mi MJXp-italic" id=MJXp-Span-9136>γ</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-9137>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-9138>L</span><span class=MJXp-mrow id=MJXp-Span-9139><span class=MJXp-mo id=MJXp-Span-9140 style=margin-left:0em;margin-right:0em>(</span><span class=MJXp-mrow id=MJXp-Span-9141><span class=MJXp-mn id=MJXp-Span-9142>1</span><span class=MJXp-mo id=MJXp-Span-9143 style=margin-left:0.267em;margin-right:0.267em>+</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-9144>v</span><span class=MJXp-mo id=MJXp-Span-9145 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-9146>c</span></span><span class=MJXp-mo id=MJXp-Span-9147 style=margin-left:0em;margin-right:0em>)</span></span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-9148><span class=MJXp-msup id=MJXp-Span-9149><span class=MJXp-mrow id=MJXp-Span-9150 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-9151>c</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-9152 style=vertical-align:0.5em><span class=MJXp-mn id=MJXp-Span-9153>2</span></span></span></span></span></span></span></span></span></span></span><span class=MJXp-mtr id=MJXp-Span-9154 style=vertical-align:baseline><span class=MJXp-mtd id=MJXp-Span-9155 style=padding-top:0.431em;text-align:center></span><span class=MJXp-mtd id=MJXp-Span-9156 style=padding-left:0.33em;padding-top:0.431em;text-align:center></span><span class=MJXp-mtd id=MJXp-Span-9157 style=padding-left:0.33em;padding-top:0.431em;text-align:center><span class=MJXp-mo id=MJXp-Span-9158 style=margin-left:0em;margin-right:0.111em>+</span><span class=MJXp-mfrac id=MJXp-Span-9159 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-9160><span class=MJXp-mn id=MJXp-Span-9161>2</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-9162>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-9163>γ</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-9164>L</span><span class=MJXp-mrow id=MJXp-Span-9165><span class=MJXp-mo id=MJXp-Span-9166 style=margin-left:0em;margin-right:0em>(</span><span class=MJXp-mrow id=MJXp-Span-9167><span class=MJXp-mn id=MJXp-Span-9168>1</span><span class=MJXp-mo id=MJXp-Span-9169 style=margin-left:0.267em;margin-right:0.267em>−</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-9170>v</span><span class=MJXp-mo id=MJXp-Span-9171 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-9172>c</span></span><span class=MJXp-mo id=MJXp-Span-9173 style=margin-left:0em;margin-right:0em>)</span></span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-9174><span class="MJXp-mi MJXp-italic" id=MJXp-Span-9175>c</span><span class=MJXp-mrow id=MJXp-Span-9176><span class=MJXp-mo id=MJXp-Span-9177 style=margin-left:0em;margin-right:0em>(</span><span class=MJXp-mrow id=MJXp-Span-9178><span class="MJXp-mi MJXp-italic" id=MJXp-Span-9179>c</span><span class=MJXp-mo id=MJXp-Span-9180 style=margin-left:0.267em;margin-right:0.267em>+</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-9181>v</span></span><span class=MJXp-mo id=MJXp-Span-9182 style=margin-left:0em;margin-right:0em>)</span></span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-9183 style=margin-left:0.267em;margin-right:0.267em>+</span><span class=MJXp-mfrac id=MJXp-Span-9184 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-9185><span class="MJXp-mi MJXp-italic" id=MJXp-Span-9186>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-9187>γ</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-9188>L</span><span class=MJXp-mrow id=MJXp-Span-9189><span class=MJXp-mo id=MJXp-Span-9190 style=margin-left:0em;margin-right:0em;vertical-align:-0.289em><span style=font-size:2.156em;margin-left:-0.09em class="MJXp-right MJXp-scale6">(</span></span><span class=MJXp-mrow id=MJXp-Span-9191><span class=MJXp-msup id=MJXp-Span-9192><span class=MJXp-mrow id=MJXp-Span-9193 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-9194>c</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-9195 style=vertical-align:0.5em><span class=MJXp-mn id=MJXp-Span-9196>2</span></span></span><span class=MJXp-mo id=MJXp-Span-9197 style=margin-left:0.267em;margin-right:0.267em>+</span><span class=MJXp-mn id=MJXp-Span-9198>4</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-9199>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-9200>c</span><span class=MJXp-mo id=MJXp-Span-9201 style=margin-left:0.267em;margin-right:0.267em>−</span><span class=MJXp-msup id=MJXp-Span-9202><span class=MJXp-mrow id=MJXp-Span-9203 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-9204>v</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-9205 style=vertical-align:0.5em><span class=MJXp-mn id=MJXp-Span-9206>2</span></span></span></span><span class=MJXp-mo id=MJXp-Span-9207 style=margin-left:0em;margin-right:0em;vertical-align:-0.289em><span style=font-size:2.156em;margin-left:-0.09em class="MJXp-right MJXp-scale6">)</span></span></span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-9208><span class="MJXp-mi MJXp-italic" id=MJXp-Span-9209>c</span><span class=MJXp-mrow id=MJXp-Span-9210><span class=MJXp-mo id=MJXp-Span-9211 style=margin-left:0em;margin-right:0em>(</span><span class=MJXp-mrow id=MJXp-Span-9212><span class="MJXp-mi MJXp-italic" id=MJXp-Span-9213>c</span><span class=MJXp-mo id=MJXp-Span-9214 style=margin-left:0.267em;margin-right:0.267em>+</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-9215>v</span></span><span class=MJXp-mo id=MJXp-Span-9216 style=margin-left:0em;margin-right:0em>)</span></span><span class=MJXp-msup id=MJXp-Span-9217><span class=MJXp-mrow id=MJXp-Span-9218 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-9219>c</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-9220 style=vertical-align:0.5em><span class=MJXp-mn id=MJXp-Span-9221>2</span></span></span></span></span></span></span></span></span></span></span><span class=MJXp-mtr id=MJXp-Span-9222 style=vertical-align:baseline><span class=MJXp-mtd id=MJXp-Span-9223 style=padding-top:0.431em;text-align:center></span><span class=MJXp-mtd id=MJXp-Span-9224 style=padding-left:0.33em;padding-top:0.431em;text-align:center><span class=MJXp-mo id=MJXp-Span-9225 style=margin-left:0.333em;margin-right:0.333em>=</span></span><span class=MJXp-mtd id=MJXp-Span-9226 style=padding-left:0.33em;padding-top:0.431em;text-align:center><span class=MJXp-mfrac id=MJXp-Span-9227 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-9228><span class=MJXp-mn id=MJXp-Span-9229>2</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-9230>L</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-9231><span class="MJXp-mi MJXp-italic" id=MJXp-Span-9232>γ</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-9233>c</span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-9234 style=margin-left:0.267em;margin-right:0.267em>+</span><span class=MJXp-mfrac id=MJXp-Span-9235 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-9236><span class="MJXp-mi MJXp-italic" id=MJXp-Span-9237>γ</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-9238>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-9239>L</span><span class=MJXp-mrow id=MJXp-Span-9240><span class=MJXp-mo id=MJXp-Span-9241 style=margin-left:0em;margin-right:0em;vertical-align:-0.289em><span style=font-size:2.156em;margin-left:-0.09em class="MJXp-right MJXp-scale6">(</span></span><span class=MJXp-mrow id=MJXp-Span-9242><span class=MJXp-mn id=MJXp-Span-9243>4</span><span class=MJXp-msup id=MJXp-Span-9244><span class=MJXp-mrow id=MJXp-Span-9245 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-9246>c</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-9247 style=vertical-align:0.5em><span class=MJXp-mn id=MJXp-Span-9248>2</span></span></span><span class=MJXp-mo id=MJXp-Span-9249 style=margin-left:0.267em;margin-right:0.267em>+</span><span class=MJXp-mn id=MJXp-Span-9250>4</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-9251>c</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-9252>v</span></span><span class=MJXp-mo id=MJXp-Span-9253 style=margin-left:0em;margin-right:0em;vertical-align:-0.289em><span style=font-size:2.156em;margin-left:-0.09em class="MJXp-right MJXp-scale6">)</span></span></span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-9254><span class="MJXp-mi MJXp-italic" id=MJXp-Span-9255>c</span><span class=MJXp-mrow id=MJXp-Span-9256><span class=MJXp-mo id=MJXp-Span-9257 style=margin-left:0em;margin-right:0em>(</span><span class=MJXp-mrow id=MJXp-Span-9258><span class="MJXp-mi MJXp-italic" id=MJXp-Span-9259>c</span><span class=MJXp-mo id=MJXp-Span-9260 style=margin-left:0.267em;margin-right:0.267em>+</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-9261>v</span></span><span class=MJXp-mo id=MJXp-Span-9262 style=margin-left:0em;margin-right:0em>)</span></span><span class=MJXp-msup id=MJXp-Span-9263><span class=MJXp-mrow id=MJXp-Span-9264 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-9265>c</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-9266 style=vertical-align:0.5em><span class=MJXp-mn id=MJXp-Span-9267>2</span></span></span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-9268 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-mfrac id=MJXp-Span-9269 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-9270><span class=MJXp-mn id=MJXp-Span-9271>2</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-9272>L</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-9273><span class="MJXp-mi MJXp-italic" id=MJXp-Span-9274>γ</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-9275>c</span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-9276 style=margin-left:0.267em;margin-right:0.267em>+</span><span class=MJXp-mfrac id=MJXp-Span-9277 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-9278><span class=MJXp-mn id=MJXp-Span-9279>4</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-9280>γ</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-9281>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-9282>L</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-9283><span class=MJXp-msup id=MJXp-Span-9284><span class=MJXp-mrow id=MJXp-Span-9285 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-9286>c</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-9287 style=vertical-align:0.5em><span class=MJXp-mn id=MJXp-Span-9288>2</span></span></span></span></span></span></span></span></span><span class=MJXp-mo id=MJXp-Span-9289 style=margin-left:0em;margin-right:0.222em>,</span></span></span></span></span></span></span><span class="mjx-chtml MJXc-display MJXc-processing sf-hidden"></span>
</span>
</div><p> and with <span class=inline-formula>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class=MJXp-math id=MJXp-Span-9290><span class=MJXp-msub id=MJXp-Span-9291><span class=MJXp-mrow id=MJXp-Span-9292 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-9293>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-9294 style=vertical-align:-0.4em><span class=MJXp-mo id=MJXp-Span-9295>⇒</span></span></span><span class=MJXp-mo id=MJXp-Span-9296 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-mn id=MJXp-Span-9297>2</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-9298>L</span><span class=MJXp-mo id=MJXp-Span-9299 style=margin-left:0.267em;margin-right:0.267em>⁄</span><span class=MJXp-mrow id=MJXp-Span-9300><span class=MJXp-mo id=MJXp-Span-9301 style=margin-left:0em;margin-right:0em>(</span><span class=MJXp-mrow id=MJXp-Span-9302><span class="MJXp-mi MJXp-italic" id=MJXp-Span-9303>γ</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-9304>c</span></span><span class=MJXp-mo id=MJXp-Span-9305 style=margin-left:0em;margin-right:0em>)</span></span></span></span><span id=MathJax-Element-625-Frame class="mjx-chtml MathJax_CHTML MJXc-processing sf-hidden" tabindex=0></span>
</span>
</span>, <div class=formula id=j_phys-2023-0110_eq_046>
<span class=alternatives>
<span class=MathJax_Preview style=color:inherit><span class="MJXp-math MJXp-display" id=MJXp-Span-9306><span class=MJXp-mi id=MJXp-Span-9307>Δ</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-9308>T</span><span class=MJXp-mo id=MJXp-Span-9309 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-msub id=MJXp-Span-9310><span class=MJXp-mrow id=MJXp-Span-9311 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-9312>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-9313 style=vertical-align:-0.4em><span class=MJXp-mo id=MJXp-Span-9314>⇐</span></span></span><span class=MJXp-mo id=MJXp-Span-9315 style=margin-left:0.267em;margin-right:0.267em>−</span><span class=MJXp-msub id=MJXp-Span-9316><span class=MJXp-mrow id=MJXp-Span-9317 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-9318>T</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-9319 style=vertical-align:-0.4em><span class=MJXp-mo id=MJXp-Span-9320>⇒</span></span></span><span class=MJXp-mo id=MJXp-Span-9321 style=margin-left:0.333em;margin-right:0.333em>=</span><span class=MJXp-mfrac id=MJXp-Span-9322 style=vertical-align:0.25em><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-9323><span class=MJXp-mn id=MJXp-Span-9324>4</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-9325>γ</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-9326>v</span><span class="MJXp-mi MJXp-italic" id=MJXp-Span-9327>L</span></span></span><span class=MJXp-box style=margin-top:-0.9em><span class=MJXp-denom><span><span class=MJXp-rule style="height:1em;border-top:medium none;border-bottom:1px solid;margin:0.1em 0px"></span></span><span><span class=MJXp-box><span class=MJXp-mrow id=MJXp-Span-9328><span class=MJXp-msup id=MJXp-Span-9329><span class=MJXp-mrow id=MJXp-Span-9330 style=margin-right:0.05em><span class="MJXp-mi MJXp-italic" id=MJXp-Span-9331>c</span></span><span class="MJXp-mrow MJXp-script" id=MJXp-Span-9332 style=vertical-align:0.5em><span class=MJXp-mn id=MJXp-Span-9333>2</span></span></span></span></span></span></span></span></span></span></span><span class="mjx-chtml MJXc-display MJXc-processing sf-hidden"></span>
</span>
</div><p> in agreement with the result of the standard linear Sagnac effect.</p>
</section>
</section>
</div>
</span>
<span class=ref-list>
<h2 class=subheading>References</h2>
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</div><div class="publicationDates mb-3"><div class=receivedDate><span class=label-received><span><strong>Received: </strong></span></span>2023-06-08</div><div class=revisedDate><span class=label-revised><span><strong>Revised: </strong></span></span>2023-08-21</div><div class=acceptedDate><span class=label-accepted><span><strong>Accepted: </strong></span></span>2023-08-23</div><div class=publishedOnlineDate><span class=label-publishedOnline><span><strong>Published Online: </strong></span></span>2023-09-16</div></div><div class=copyrightStatement><p>© 2023 the author(s), published by De Gruyter</p></div><div class=licenseStatement><p>This work is licensed under the Creative Commons Attribution 4.0 International License.</p></div></div></div>
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