### 3.2 Robertson-Mansouri-Sexl framework

The Robertson-Mansouri-Sexl framework [246, 211, 277] 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 where the speed of light is isotropic. The ordinary Lorentz transformations to other
frames are generalized to
where the coefficients are functions of the magnitude 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 . The vector 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 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 (16) 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 [179] that the RMS framework can be incorporated into the standard model
extension.

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

and will give constraints on the parameters , , and instead.