A note on the Sagnac effect and current terrestrial experiments

Abstract

We focus on the Sagnac effect for light beams in order to evaluate if the higher order relativistic corrections of kinematic origin could be relevant for actual terrestrial experiments. Moreover, we discuss to what extent the analogy with the Aharonov-Bohm effect holds true in a fully relativistic framework. We show that the analogy with the Aharonov-Bohm is not true in general, but is recovered in a suitable low order approximation, and that even though the Sagnac effect is influenced by both the position of the interferometer in the rotating frame and its extension, these effects are negligible for current terrestrial experiments. * Electronic address: matteo.ruggiero@polito.it † Electronic address: angelo.tartaglia@polito.it

A Novel Covariant Approach to Gravito-Electromagnetism

“…These relationships were observed and reported during the second half of the nineteenth century, and we recommend [1,2] for historical review and references. Various approaches to GEM have recently been proposed, and we quote a non-exhaustive list of papers concerning, by way of example, gravitomagnetic effects [3][4][5][6], the relation of GEM to special relativity [2,7], tidal tensors [8,9], weak-field approximation [10][11][12], the Lorentz violation [13,14], teleparallel gravity [15,16], the Mashhoon-Theiss effect [17], quantum gravity [18,19], gravitational waves [20,21], the relation of GEM to electro-dynamics in curved spacetime [22,23], gravitational field of astrophysical objects [24,25], the Sagnac effect [26,27], torsion gravity [28], the Schrödinger-Newton equation [29], non-commutative geometry [30], spin-gravity coupling [31], gravity and thermodynamics [32], the Casimir effect [33], gauge transformations [34] and, quantum field gravity [35,36]. It is commonly known that GEM is a source of new ideas and a guide for research into new physics.…”

Sagnac Effect, Ring Lasers and Terrestrial Tests of Gravity

“…Actually, this is not the case: the Sagnac Effect can be completely explained in relativistic framework both in flat and curved space time (see e.g. [32], [33], [34], [35], [36], [45], [46]), as we are going to show.…”

“…where L is the linear size of the interferometer, that is a factor L/R smaller than the leading gravitational contribution (see below). Eventually, since A = −Ω 2 ⊕ R sin θ, where θ is the laboratory colatitude, it is possible to show [45] that the kinematics corrections non linear in Ω ⊕ , can be safely neglected, since…”

“…In this paper, we aim at reviewing the conceptual bases of the use of ring lasers to probe the space-time structure. We start, in Section II, by studying the Sagnac Effect, in arbitrary stationary space-time [45]. In particular, we show that the Sagnac Effect does not depend on the physical nature of the propagating beams, provided that suitable kinematic conditions are fulfilled; thus, it can be interpreted as a property of the space-time structure itself [46].…”

Test of gravitomagnetism with satellites around the Earth

“…It is possible to apply the Stokes theorem to the line integral (6); to this end, we define the vector field h such that h i = g0i g00 (see e.g. [21]). The Stokes theorem states that…”