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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: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=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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[Submitted on 29 Mar 2004]</div>
<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>
<div class=authors><span class="descriptor sf-hidden">Authors:</span><a href="https://arxiv.org/search/gr-qc?searchtype=author&amp;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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<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 comments mathjax">31 pages, 10 (mostly color) figures included. revtex4. Submitted to Foundations of Physics</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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<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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<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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<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>
Mon, 29 Mar 2004 16:50:45 UTC (68 KB)<br>
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