The Sagnac Phase Shift Suggested by the Aharonov-Bohm Effect for Relativistic Matter Beams

Abstract

The phase shift due to the Sagnac Effect, for relativistic matter beams counter-propagating in a rotating interferometer, is deduced on the bases of a a formal analogy with the the Aharonov-Bohm effect. A procedure outlined by Sakurai, in which non relativistic quantum mechanics and newtonian physics appear together with some intrinsically relativistic elements, is generalized to a fully relativistic context, using the Cattaneo's splitting technique. This approach leads to an exact derivation, in a self-consistently relativistic way, of the Sagnac effect. Sakurai's result is recovered in the first order approximation.

Null paths on a toroidal topological black hole in conformal Weyl gravity

“…In this section we describe the Sagnac effect [42] by applying the formalism developed by Sakurai [43], Tartaglia [44], Rizzi & Ruggiero [45][46][47][48], among others, to the exterior space-time of the topoloical toroidal black hole. This approach was used to calculate this effect in the exterior spacetime to an uncharged spherical symmetric black hole in Conformal Weyl gravity [49].…”

“…As was shown in [45], it is possible to express the phase shift and time delay between light beams detected by a comoving observer on the interferometer in terms of the gravitomagnetic induction field, B G = ∇ × A G , by means of the expressions…”

General relativistic Sagnac formula revised

“…Their correct evaluation is important in planing future experiments and from the theoretical point of view however. On the theoretical side the effect is involved in the synchronization procedure of remote clocks [20,21], provides a gravitational analogue of the Aharonov-Bohm effect [22,23,24,25,26] and a general characterization of rotations in general relativity [22]. Up to now its description within the framework of general relativity is given as follows: in a stationary space-time with coordinates x = (ct, x) and line element ds 2 = g µν (x)dx µ dx ν , the coordinate-time shift ∆t is given by the formula…”

Sagnac Effect, Ring Lasers and Terrestrial Tests of Gravity

“…this leads to the analogy with the Aharonov-Bohm effect (see e.g. [34]). In order to write the time delay (17) in terms of area enclosed by the path of the beams, we proceed as follows.…”

“…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.…”