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url: https://arxiv.org/abs/gr-qc/0403111
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saved date: Mon Feb 12 2024 01:33:59 GMT-0500 (Eastern Standard Time)
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<title>[gr-qc/0403111] Sagnac effect, twin paradox and space-time topology - Time and length in rotating systems and closed Minkowski space-times</title>
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<meta property=og:title content="Sagnac effect, twin paradox and space-time topology - Time and length in rotating systems and closed Minkowski space-times">
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<meta property=og:description content="We discuss the Sagnac effect in standard Minkowski coordinates and with an alternative synchronization convention. We find that both approaches lead to the same result without any contradictions. When applying standard coordinates to the complete rim of the rotating disk, a time-lag has to be taken into account which accounts for the global anisotropy. We propose a closed Minkowski space-time as an exact equivalent to the rim of a disk, both in the rotating and non-rotating case. In this way the Sagnac effect can be explained as being purely topological, neglecting the radial acceleration altogether. This proves that the rim of the disk can be treated as an inertial system. In the same context we discuss the twin paradox and find that the standard scenario is equivalent to an unaccelerated version in a closed space-time. The closed topology leads to preferred frame effects which can be detected only globally. The relation of synchronization conventions to the measurement of lengths is discussed in the context of Ehrenfest's paradox. This leads to a confirmation of the classical arguments by Ehrenfest and Einstein.">
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<meta name=twitter:title content="Sagnac effect, twin paradox and space-time topology - Time and...">
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<meta name=twitter:description content="We discuss the Sagnac effect in standard Minkowski coordinates and with an alternative synchronization convention. We find that both approaches lead to the same result without any contradictions....">
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<meta name=citation_title content="Sagnac effect, twin paradox and space-time topology - Time and length in rotating systems and closed Minkowski space-times"><meta name=citation_author content="Wucknitz, Olaf"><meta name=citation_date content=2004/03/29><meta name=citation_online_date content=2004/03/29><meta name=citation_pdf_url content=http://arxiv.org/pdf/gr-qc/0403111.pdf><meta name=citation_arxiv_id content=gr-qc/0403111><meta name=citation_abstract content=" We discuss the Sagnac effect in standard Minkowski coordinates and with an alternative synchronization convention. We find that both approaches lead to the same result without any contradictions. When applying standard coordinates to the complete rim of the rotating disk, a time-lag has to be taken into account which accounts for the global anisotropy. We propose a closed Minkowski space-time as an exact equivalent to the rim of a disk, both in the rotating and non-rotating case. In this way the Sagnac effect can be explained as being purely topological, neglecting the radial acceleration altogether. This proves that the rim of the disk can be treated as an inertial system. In the same context we discuss the twin paradox and find that the standard scenario is equivalent to an unaccelerated version in a closed space-time. The closed topology leads to preferred frame effects which can be detected only globally. The relation of synchronization conventions to the measurement of lengths is discussed in the context of Ehrenfest's paradox. This leads to a confirmation of the classical arguments by Ehrenfest and Einstein.">
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<h1>General Relativity and Quantum Cosmology</h1>
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(gr-qc)
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<style>#abs{font-family:"Lucida Grande",Helvetica,Arial,sans-serif!important}#abs h1.title{display:block;font-size:1.8em!important;font-weight:700;margin-block-end:12px;margin-block-start:12px;margin-bottom:12px;margin-inline-end:0px;margin-inline-start:20px;margin-left:20px;margin-right:0px;margin-top:12px}#abs div.authors{font-size:1.2em;line-height:24px;margin-bottom:8px;margin-left:20px;margin-right:0px;margin-top:8px}#abs div.dateline{font-size:0.9em;font-style:italic;margin-bottom:6.5px;margin-left:20px;margin-right:0px;margin-top:6.5px}#abs blockquote.abstract{font-size:1.05em;margin-block-end:21.6px;margin-block-start:14.4px;margin-bottom:21.6px;margin-inline-end:40px;margin-inline-start:40px;background-color:white;border-left:0px;padding:0px}#abs div.metatable{font-size:0.95em!important;margin-bottom:19px;margin-left:20px;margin-right:0px;margin-top:0px;border:0px;padding:0px}#abs div.metatable tbody{vertical-align:middle}#abs tr{margin-top:0px;margin-bottom:0px}#abs td.tablecell{padding-top:0px;padding-bottom:0px;padding-right:6.5px;padding-left:0px;vertical-align:top;font-size:0.95em!important;margin-top:0px;margin-bottom:0px;border:0px}#abs td.tablecell.label{font-weight:400!important}#abs span.primary-subject{font-weight:700}#abs span.arxivid{font-weight:700}</style>
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[Submitted on 29 Mar 2004]</div>
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<h1 class="title mathjax"><span class="descriptor sf-hidden">Title:</span>Sagnac effect, twin paradox and space-time topology - Time and length in rotating systems and closed Minkowski space-times</h1>
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<div class=authors><span class="descriptor sf-hidden">Authors:</span><a href="https://arxiv.org/search/gr-qc?searchtype=author&query=Wucknitz,+O">Olaf Wucknitz</a> (Universitaet Potsdam)</div> <div id=download-button-info class=sf-hidden hidden>Download a PDF of the paper titled Sagnac effect, twin paradox and space-time topology - Time and length in rotating systems and closed Minkowski space-times, by Olaf Wucknitz (Universitaet Potsdam)</div>
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<a class="mobile-submission-download sf-hidden" href=https://arxiv.org/pdf/gr-qc/0403111.pdf>Download PDF</a>
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<blockquote class="abstract mathjax">
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<span class="descriptor sf-hidden">Abstract:</span> We discuss the Sagnac effect in standard Minkowski coordinates and with an alternative synchronization convention. We find that both approaches lead to the same result without any contradictions. When applying standard coordinates to the complete rim of the rotating disk, a time-lag has to be taken into account which accounts for the global anisotropy. We propose a closed Minkowski space-time as an exact equivalent to the rim of a disk, both in the rotating and non-rotating case. In this way the Sagnac effect can be explained as being purely topological, neglecting the radial acceleration altogether. This proves that the rim of the disk can be treated as an inertial system. In the same context we discuss the twin paradox and find that the standard scenario is equivalent to an unaccelerated version in a closed space-time. The closed topology leads to preferred frame effects which can be detected only globally. The relation of synchronization conventions to the measurement of lengths is discussed in the context of Ehrenfest's paradox. This leads to a confirmation of the classical arguments by Ehrenfest and Einstein.
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<td class="tablecell label">Comments:</td>
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<td class="tablecell comments mathjax">31 pages, 10 (mostly color) figures included. revtex4. Submitted to Foundations of Physics</td>
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<td class="tablecell label">Subjects:</td>
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<span class=primary-subject>General Relativity and Quantum Cosmology (gr-qc)</span>; Astrophysics (astro-ph)</td>
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<tr>
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<td class="tablecell label">Cite as:</td>
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<td class="tablecell arxivid"><span class=arxivid><a href=https://arxiv.org/abs/gr-qc/0403111>arXiv:gr-qc/0403111</a></span></td>
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<td class="tablecell label"> </td>
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<td class="tablecell arxividv">(or <span class=arxivid>
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<a href=https://arxiv.org/abs/gr-qc/0403111v1>arXiv:gr-qc/0403111v1</a></span> for this version)
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<td class="tablecell arxivdoi">
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<a href=https://doi.org/10.48550/arXiv.gr-qc/0403111>https://doi.org/10.48550/arXiv.gr-qc/0403111</a>
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arXiv-issued DOI via DataCite
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<h2>Submission history</h2> From: Olaf Wucknitz [<a href=https://arxiv.org/show-email/b86874dc/gr-qc/0403111>view email</a>] <br> <strong>[v1]</strong>
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Mon, 29 Mar 2004 16:50:45 UTC (68 KB)<br>
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Download a PDF of the paper titled Sagnac effect, twin paradox and space-time topology - Time and length in rotating systems and closed Minkowski space-times, by Olaf Wucknitz (Universitaet Potsdam)</div><li><a href=https://arxiv.org/pdf/gr-qc/0403111.pdf aria-describedby=download-button-info accesskey=f class="abs-button download-pdf">Download PDF</a><li><a href=https://arxiv.org/format/gr-qc/0403111 class="abs-button download-format">Other Formats</a></ul>
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or <a class=is-link href=https://subscribe.sorryapp.com/24846f03/slack/new target=_blank><svg xmlns=http://www.w3.org/2000/svg viewBox="0 0 448 512" class="icon filter-black" role=presentation><path d="M94.12 315.1c0 25.9-21.16 47.06-47.06 47.06S0 341 0 315.1c0-25.9 21.16-47.06 47.06-47.06h47.06v47.06zm23.72 0c0-25.9 21.16-47.06 47.06-47.06s47.06 21.16 47.06 47.06v117.84c0 25.9-21.16 47.06-47.06 47.06s-47.06-21.16-47.06-47.06V315.1zm47.06-188.98c-25.9 0-47.06-21.16-47.06-47.06S139 32 164.9 32s47.06 21.16 47.06 47.06v47.06H164.9zm0 23.72c25.9 0 47.06 21.16 47.06 47.06s-21.16 47.06-47.06 47.06H47.06C21.16 243.96 0 222.8 0 196.9s21.16-47.06 47.06-47.06H164.9zm188.98 47.06c0-25.9 21.16-47.06 47.06-47.06 25.9 0 47.06 21.16 47.06 47.06s-21.16 47.06-47.06 47.06h-47.06V196.9zm-23.72 0c0 25.9-21.16 47.06-47.06 47.06-25.9 0-47.06-21.16-47.06-47.06V79.06c0-25.9 21.16-47.06 47.06-47.06 25.9 0 47.06 21.16 47.06 47.06V196.9zM283.1 385.88c25.9 0 47.06 21.16 47.06 47.06 0 25.9-21.16 47.06-47.06 47.06-25.9 0-47.06-21.16-47.06-47.06v-47.06h47.06zm0-23.72c-25.9 0-47.06-21.16-47.06-47.06 0-25.9 21.16-47.06 47.06-47.06h117.84c25.9 0 47.06 21.16 47.06 47.06 0 25.9-21.16 47.06-47.06 47.06H283.1z"></path></svg>slack</a>
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