Detection of the gravitomagnetic clock effect

Abstract

The essence of the gravitomagnetic clock effect is properly defined showing that its origin is in the topology of world lines with closed space projections. It is shown that, in weak field approximation and for a spherically symmetric central body, the loss of synchrony between two clocks counter-rotating along a circular geodesic is proportional to the angular momentum of the source of the gravitational field. Numerical estimates are presented for objects within the solar system. The less unfavorable situation is found around Jupiter.

Gravitomagnetism and relative observer clock effects

“…Finally, the observer-independent two-clock clock effect results from specializing these equations to the geodesic meeting point observer, recovering the results of Tartaglia [9,10] for the Kerr and van Stockum spacetimes. The proper periods between three successive crossings corresponding to each geodesic making a complete revolution (with respect to such an observer) are…”

“…The latter result must be halved to compare with the result of Tartaglia [9,10] for Kerr, since he considers two successive crossings of the geodesics. Note also that the first meeting point after the pair of geodesics leave φ = 0 will be at π plus half the amount of angle through which the geodesic meeting point observers have moved in one full revolution…”

“…However, there are experimental difficulties that must be overcome before there is any hope of measuring this effect [9,10,35,36]. Note that the gravitomagnetic clock effect may be extended to general orbits based on the idea of 'azimuthal closure' [4,5,30,34].…”

TELEPENSOUTH Project: Measurement of the Earth Gravitomagnetic Field in a Terrestrial Laboratory

“…Moreover, different possibilities connected both with the clock effect and the gravitational Sagnac effect have been considered [5], [6].…”

Angular Momentum Effects in Michelson–Morley Type Experiments

“…The only positive result at the moment concerns the precession of the nodes of the orbit of the LAGEOS satellite [4] (Lense-Thirring effect [5]). In the next few years the space mission Gravity Probe B (GPB) is planned to fly carrying gyroscopes which should in turn verify the Lense-Thirring effect too [6]; finally a series of different possibilities connected both with the Sagnac effect and the gravitomagnetic clock effect have been considered [8] [7].…”