{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:10:42Z","timestamp":1760148642653,"version":"build-2065373602"},"reference-count":34,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2023,5,30]],"date-time":"2023-05-30T00:00:00Z","timestamp":1685404800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>The Sagnac effect and related twin paradox with a rotating disc are analyzed. It may seem that the special theory of relativity gives an easy and exhaustive treatment here. However, such consideration is deceptive since the principles of special relativity are originally established only for the inertial frames of reference, whereas the Sagnac experiment and the twin paradox exist in a noninertial one. We introduce an additional group of motions related to the rotation with uniform angular speed and show that these transformations leave the Minkowski metric invariant. Thus, we can give a firm mathematical ground to a usual easy consideration of the Sagnac effect. It should be noted that the presented result is true for a special case of motions; general coordinate transformations into accelerating frames of reference do not preserve the metric.<\/jats:p>","DOI":"10.3390\/axioms12060537","type":"journal-article","created":{"date-parts":[[2023,5,31]],"date-time":"2023-05-31T02:57:10Z","timestamp":1685501830000},"page":"537","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Noninertial Proper Motions of the Minkowski Metric, the Sagnac Effect, and the Twin Paradox"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5680-4225","authenticated-orcid":false,"given":"Nikolay","family":"Popov","sequence":"first","affiliation":[{"name":"Federal Research Center \u201cComputer Science and Control\u201d of the Russian Academy of Sciences, Vavilov Str., 44\/2, 119333 Moscow, Russia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2005-9467","authenticated-orcid":false,"given":"Ivan","family":"Matveev","sequence":"additional","affiliation":[{"name":"Federal Research Center \u201cComputer Science and Control\u201d of the Russian Academy of Sciences, Vavilov Str., 44\/2, 119333 Moscow, Russia"}]}],"member":"1968","published-online":{"date-parts":[[2023,5,30]]},"reference":[{"key":"ref_1","first-page":"1410","article-title":"On the proof of the reality of the luminiferous aether by the experiment with a rotating interferometer","volume":"157","author":"Sagnac","year":"1913","journal-title":"Comptes Rendus"},{"key":"ref_2","first-page":"635","article-title":"Sagnac\u2019s Experiment with Radiowaves","volume":"75","author":"Bershtein","year":"1950","journal-title":"Dokl. 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