Relativity and Cosmology


A Derivation of the Geodetic Effect Without Space Curvature

Authors: J. M. Kerr

The ‘curvature component’ is 2/3 of the geodetic effect. This part of the angle through which an orbiting gyroscope moves is thought to be due to space curvature, as in general relativity (GR). There are different interpretations for the other 1/3, some of which apply whether space is curved or flat. Here it is shown that the curvature component 2/3 can alternatively be derived from flat space, if one simply assumes that matter near a mass is slowed by (1 - (2GM/rc^2))^1/2. In Planck scale gravity (PSG), a theory that closely mimics GR, for an orbiting spherical object minor corrections are made to local speeds within the object, at different heights in the field. This leads to a slight turning of the object as it orbits. The result can be generalised as an equation for a single orbit around any spherical mass, which gives the same numbers as GR to many decimal places, but is mathematically different. In the case of one of the gyroscopes on Gravity Probe B, it gives an angle change in the plane of the orbit, in the same direction as the geodetic precession, of 4.4 arcsecs/yr. That is 2/3 of the total geodetic effect, the value of the curvature component. The GR geodetic effect and this equivalent effect are at present indistinguishable by experiment, but PSG can be tested in other ways, such as by interferometer experiments [4].

Comments: 3 Pages.

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Submission history

[v1] 24 Jan 2008
[v2] 2012-07-21 10:20:38

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