### 5.3 Cavity experiments

From the Michelson-Morley experiments onward, interferometry has been an excellent method of testing relativity. Modern cavity experiments extend on the ideas of interferometry and provide very precise tests on the bounds of certain photon parameters. The main technique of a cavity experiment is to detect the variation of the resonance frequency of the cavity as its orientation changes with respect to a stationary frequency standard. In this sense, it is similar to a clock comparison experiment. However, since one of the clocks involves photons, cavity experiments constrain the electromagnetic sector of the mSME as well.

The analysis of cavity experiments is much easier if we make a field redefinition of the electromagnetic sector of the mSME [179]. In analogy to the theory of dielectrics, we define two new fields and by

The coefficients are related to the mSME coefficients by
With this choice of fields, the modified Maxwell equations from the mSME take the suggestive form
This redefinition shows that the Lorentz violating background tensor can be thought of as a dielectric medium with no charge or current density. Hence we can apply much of our intuition about the behavior of fields inside a dielectric to construct tests of Lorentz violation. Note that since and depend on the components of , the properties of the dielectric are orientation dependent.

Constraints from cavity experiments are not on the parameters themselves, but rather on the linear combinations

, , and are all parity even, while and are parity odd. The usefulness of this parameterization can be seen if we rewrite the Lagrangian in these parameters [179],
From this expression it is easy to see that corresponds to a rotationally invariant shift in the speed of light. It can be shown that and also yield a shift in the speed of light, although in a direction dependent manner. The coefficients and control birefringence. Cavity experiments yield limits on and , while birefringence (see Section 6.3) bounds and .

The most straightforward way to constrain Lorentz violation with cavity resonators is to study the resonant frequency of a cavity. Since we have a cavity filled with an orientation dependent dielectric, the resonant frequency will also vary with orientation. The resonant frequency of a cavity is

where is the mode number, is the speed of light, is the index of refraction (including Lorentz violation) of any medium in the cavity, and is the length of the cavity. can be sensitive to Lorentz violating effects through , , and . Depending on the construction of the cavity some effects can dominate over others. For example, in sapphire cavities the change in due to Lorentz violation is negligible compared to the change in . This allows one to isolate the electromagnetic sector.

In general, all cavities are sensitive to the photon parameters. In contrast to sapphire, for certain materials the strain induced on the cavity by Lorentz violation is large. This allows sensitivity to the electron parameters at a level equivalent to the photon parameters. Furthermore, by using a cavity with a medium, the dependence of on gives additional electron sensitivity [226].

The complete bounds on the mSME coefficients for cavity experiments are given in [236722722628020732261]. The strongest bounds are displayed in Table 1. Roughly, the components of and are bounded at while is bounded at . The difference arises as enters constraints suppressed by the boost factor of the earth relative to the solar “rest” frame where the coefficients are taken to be constant.

 Parameter Value ()

 Table 1: Cavity limits on , , and (taken from [23, 226, 32, 261]). Components are in a sun centered equatorial frame. Error bars are . The non-zero value of is argued by the authors to be due to systematics in the experiment [32].