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Qeios

The Sagnac-Wang Interferometers and Absolute vs. Relative Simultaneity

Justo Pastor Lambare

Published Jan 16, 2024• 0 citations
Publisher

Abstract

Gianfranco Spavieri, George T. Gillies & Espen Gaarder Haug (The Sagnac effect and the role of simultaneity in relativity theory, Journal of Modern Optics (2021)), claim that the Sagnac effect reveals the theory of relativity is incorrect and inconsistent. We prove that when standard relativity is appropriately interpreted, it is observationally correct and logically sound.

DOI
10.32388/6c4wdr

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Gianfranco Spavieri, George T. Gillies & Espen Gaarder Haug (The Sagnac effect and the role of simultaneity in relativity theory, Journal of Modern Optics (2021)), claim that the Sagnac effect reveals the theory of relativity is incorrect and inconsistent. We prove that when standard relativity is appropriately interpreted, it is observationally correct and logically sound.
We thoroughly examine the role of absolute and relative simultaneity in the interpretation of the Sagnac effect, using an approach that allows for determining the local speed along the light path. If the local speed of light is assumed to be c over the whole closed contour, there is no agreement with the observed result. There is agreement if the local speed is c along an open section of the contour only. Thus a rigorous and coherent interpretation of the Sagnac effect favours absolute over relative simultaneity. The implications for the Lorentz transformations and synchronization by means of the Global Positioning System are considered.
A rotating interferometer with paths that enclose a physical area exhibits a phase shift proportional to this area and to the rotation rate of the frame. Understanding the origin of this so-called Sagnac effect has played a key role in the establishment of the theory of relativity and has pushed for the development of precision optical interferometers. The fundamental importance of the Sagnac effect motivated the realization of experiments to test its validity for waves beyond optical, but precision measurements remained a challenge. Here, we report the accurate test of the Sagnac effect for matter waves, by using a Cesium atom interferometer featuring a geometrical area of 11 cm 2 and two sensitive axes of measurements. We measure the phase shift induced by Earth’s rotation and find agreement with the theoretical prediction at an accuracy level of 25 parts per million. Beyond the importance for fundamental physics, our work opens practical applications in seismology and geodesy.
This paper builds on no-go theorems to the effect that quantum theory is inconsistent with observations being absolute; that is, unique and non-relative. Unlike the existing no-go results, the one introduced here is based on a theory-independent absoluteness assumption, and there is no need to assume the validity of standard probability theory or of modal logic. The contradiction is derived by assuming that quantum theory applies in any inertial reference frame; accordingly, the result also illuminates a tension between special relativity and absoluteness.
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.
The Sagnac effect, manifest in the phase shift of a rotating interferometer proportional to its physical area and to the rotation rate of the frame, plays a crucial role in modern physics being generalized to any kind of interferometer. However, as compared to light, the accurate experimental validation of the Sagnac effect for matter-waves remains challenging. We report the accurate measurement of the Sagnac phase shift, induced by the Earth’s rotation, using a large-area cold atom interferometer. We probe the atomic Sagnac phase shift along the two orthogonal horizontal axes in various orientation of the sensor with respect to geographic north and obtain an agreement with the theoretical prediction at the 20 ppm level, improving by twenty five-fold over the previous achievements for matter waves. Our results underline the universality of the Sagnac effect and open new horizons for testing other fundamental theories, as well as for a number of technological applications in seismology, geodesy and inertial navigation systems.
A Sagnac interferometer has been a powerful tool for gyroscope, spectroscopy, and navigation based on the Sagnac effects between counterpropagating twin fields in a closed loop, whose difference phase is caused by Einstein’s special relativity. Here, a nonclassical version of a Sagnac interferometer is presented using completely different physics of coherence de Broglie waves (CBW) in a cavity, where CBW is a nonclassical feature overcoming the standard quantum limit governed by classical physics.