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3.2 Robertson-Mansouri-Sexl framework

The Robertson-Mansouri-Sexl framework [246211277Jump To The Next Citation Point] is a well known kinematic test theory for parameterizing deviations from Lorentz invariance. In the RMS framework, there is assumed to be a preferred frame S where the speed of light is isotropic. The ordinary Lorentz transformations to other frames are generalized to
' - 1 t = a (t - e .x), ' - 1 -1 -1 v(v .x) -1 (16) x = d x - (d - b )--v2---+ a vt,
where the coefficients a,b,d are functions of the magnitude v of the relative velocity between frames. This transformation is the most general one-to-one transformation that preserves rectilinear motion in the absence of forces. In the case of special relativity, with Einstein clock synchronization, these coefficients reduce to a = b-1 = V~ 1---v2,d = 1. The vector e depends on the particular synchronization used and is arbitrary. Many experiments, such as those that measure the isotropy of the one way speed of light [275] or propagation of light around closed loops, have observables that depend on a,b,d but not on the synchronization procedure. Hence the synchronization is largely irrelevant and we assume Einstein synchronization.

The RMS framework is incomplete, as it says nothing about dynamics or how given clocks and rods relate to fundamental particles. In particular, the coordinate transformation of Equation (16View Equation) only has meaning if we identify the coordinates with the measurements made by a particular set of clocks and rods. If we chose a different set of clocks and rods, the transformation laws may be completely different. Hence it is not possible to compare the RMS parameters of two experiments that use physically different clocks and rods (for example, an experiment that uses a cesium atomic clock versus an experiment that uses a hydrogen one). However, for experiments involving a single type of clock/rod and light, the RMS formalism is applicable and can be used to search for violations of Lorentz invariance in that experiment. The RMS formalism can be made less ambiguous by placing it into a complete dynamical framework, such as the standard model extension of Section 4.1.1. In fact, it was shown in [179Jump To The Next Citation Point] that the RMS framework can be incorporated into the standard model extension.

Most often, the RMS framework is used in situations where the velocity v is small compared to c. We therefore expand a,b,d in a power series in v,

( 1 ) a = 1 + aRMS - -- v2 + ..., (17) ( 2 ) 1 2 b = 1 + bRMS + 2- v + ..., (18) d = 1 + dRMSv2 + ..., (19)
and will give constraints on the parameters a RMS, b RMS, and d RMS instead.
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