Mansouri-Sexl Test for Light Speed Anisotropy via Cosmic Aberration~!2010-02-11~!2010-02-26~!2010-06-30~!

Abstract

The Mansouri-Sexl theory is a well known test theory of relativity. In the current paper we will derive the Man- souri-Sexl formalism for the light aberration and we will show how to improve on the theoretical and experimental basis by constraining both the Mansouri-Sexl parameter a(!) and the parameter b(!) . In the process of constraining the Man- souri parameters we devise a novel experiment for measuring and constraining light speed anisotropy as well. An over- whelming number of experiments dealing with light speed anisotropy are laboratory-bound and they are limited to con- straining only parameter a(!) ; we will also take the approach of setting up an astronomical experiment instead of a lab- based one as it befits the relativistic aberration effect. Our paper is organized as follows: in the first section we give a new and more complete derivation of the Mansouri-Sexl aberration effect. In the second part, we apply the newly expanded Mansouri-Sexl aberration formalism in order to devise an astronomical experiment used for constraining both the parame- ter a(!) and the parameter b(!) . This turns the Mansouri-Sexl aberration experiment into a very powerful tool for con- straining light speed anisotropy. 1. THE ROBERTSON-MANSOURI-SEXL TEST THEORY The test theories of special relativity differ in their as- sumptions about the form of the Lorentz transforms. The main test theories of special relativity (SR) are named after their authors, Robertson (1), Mansouri and Sexl (2-4) (RMS). These test theories can also be used to examine po- tential alternate theories to SR - such alternate theories pre- dict particular values of the parameters of the test theory, which can easily be compared to values determined by ex- periments analyzed with the test theory (5-20). The existing experiments put rather strong experimental constraints on any alternative theory. RMS starts by admitting by reduction to absurd that there is a preferential inertial frame Σ in which the light propagates isotropically with the speed c 0 . All other frames in motion with respect to Σ are considered non- preferential and the light speed is anisotropic. The light speed in the non-preferential frames can be deduced via sim- ple calculations described in (3). We start with the Mansouri- Sexl transforms: x=b(v)(X!vT) y=d(v)Y z=d(v)Z t=a(v)T+(v)x=(a!bv)T+bX