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A Common Origin for the Sagnac Effect and Einstein’s Train-Embankment Thought Experiment

Stefano Quattrini

Published May 5, 2025• 0 citations
Publisher

Abstract

The Sagnac effect and the Einstein Train-Embankment thought experiment deal with the simultaneous emission of light and its non-simultaneous absorption. The original Einstein’s thought experiment arrangement is slightly modified, also for pedagogical purposes, becoming a rectilinear version of Sagnac’s interferometer. It is shown that at the base of the effect lies the solution of the famous Achilles and the tortoise paradox, a problem of pursuit. An account is given of the failure of simultaneity at a distance, forming the basis of what Einstein called the relativity of simultaneity. The effect experienced by the moving observer, which relies also on time dilation, is also discussed.

DOI
10.32388/wtulik

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The Sagnac effect and the Einstein Train-Embankment thought experiment deal with the simultaneous emission of light and its non-simultaneous absorption. The original Einstein’s thought experiment arrangement is slightly modified, also for pedagogical purposes, becoming a rectilinear version of Sagnac’s interferometer. It is shown that at the base of the effect lies the solution of the famous Achilles and the tortoise paradox, a problem of pursuit. An account is given of the failure of simultaneity at a distance, forming the basis of what Einstein called the relativity of simultaneity. The effect experienced by the moving observer, which relies also on time dilation, is also discussed.
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In this paper, we examine the thought (gedanken) experiment referred to by the title, by utilizing the two principles (hypotheses) of the Theory of Special Relativity and adhering to Heisenberg’s and the School of Copenhagen’s philosophical line. In other words, we introduce to the theater of events the Observer who measures them in both Space and Time and request that the propositions of Physical Science are derived from those very measurements. By doing so, we arrive to the conclusion that events measured as simultaneous from one system of reference, are also measured as simultaneous from any other system of reference moving in a linear uniform translatory motion relative to it, contrary to Einstein’s thesis. Resume Dans ce traite, nous examinons l’experience de pensee (Gedankenexperiment) evoquee par le titre, en utilisant les deux principes (hypotheses) de la Theorie de la Relativite Restreinte et suivant la ligne philosophique de Heisenberg et de l'Ecole de Copenhague. En d'autres termes, nous introduisons dans le theâtre des evenements l'Observateur qui les mesure a la fois dans l'espace et le temps, en exigeant que les propositions de la science physique soient derivees de ces memes mesures. Ce faisant, nous arrivons a la conclusion que les evenements consideres comme simultanes par la mesure selon un premier systeme de reference, sont egalement mesures comme simultanes selon tout autre systeme de reference, se deplacant dans un mouvement lineaire de translation uniforme par rapport au premier, contrairement a la these d'Einstein.
More than a century ago, M. Sagnac realized an experiment with light rays, whose results according to him invalidated the theory of Relativity and validated the hypothesis of the Aether. This hypothesis of the ether was not retained by the scientific community, and relativistic explanations were given to the results of the Sagnac experiment. But these relativistic explanations remain open to criticism because they are various and because the prediction may differ depending on whether the observer’s frame of reference is at rest or in motion. The neo-Newtonian mechanics proposes a new explanation which leads to demonstrate the formula with P the light path. In order to verify this new interpretation, it is proposed to do again the Sagnac experiment with a slightly different light path, a square-shaped path. The results should be at least 30% lower than those predicted by the theory of Relativity. In which case, the relativistic explanation would be questioned.
It is understandable that in 1916 Einstein was unable to explain his postulate c=const, that in the case of the lightning and the train that moves on the railway embankment he still tacitly implied that the inertial coordinate system which is at rest has advantage over the one in motion. In serious scientific journals, there are no tries of explanations of this postulate, but it is strange that even today, at popular lectures, Einstein's explanation is taken as valid. It isn't difficult to show that his explanation is not valid; it is difficult to find the right explanation without trying to form an alternative theory. The article is dedicated to this goal. The found explanation will also serve to explain, for example, the EPR-paradox without any “spooky action at a distance” or “hidden variables” (Einstein’s expressions). And this is not the only example where it can serve.
Abstract We use a quantum variant of the Sagnac interferometer to argue for the quantum nature of gravity assuming the equivalence principle, which we formulate in its quantum version. We first present an original derivation of the phase acquired in the conventional Sagnac matter-wave interferometer, within the Hamiltonian formalism. Then we modify the interferometer in two crucial respects. The interfering matter wave is interfered along two different distances from the centre and the interferometer is prepared in a superposition of two different angular velocities. We argue that if the radial and angular degrees of freedom of the matter wave become entangled through this experiment, then, via the equivalence principle, the gravitational field must be non-classical.