Resonant Frequencies of an Electromagnetic Cavity in an Accelerated System of Reference

The resonant frequencies of an electromagnetic cavity in a nonpermanent gravitational field such as that provided by rotation is considered. The constitutive equations for accelerated macroscopic matter are developed and it is shown that the electromagnetic-field tensors are related by $H_{\mathrm{xt}}=K_e{F}_{\mathrm{xt}}$ and, $K_m{H}^{\mathrm{xy}}=F^{\mathrm{xy}}$, etc. For the special case of angular rotation about the $z$ axis the constitutive equations are given in terms of noncovariant field vectors B, H, D, E. Using these constitutive equations Maxwell's equations are solved, and it is shown that the degeneracy between the axially degenerate modes, i.e., clockwise and counter-clockwise traveling waves, is removed by the rotation. In vacuum due to the similarity between energy flux and momentum a shift in frequency of $\Omega ·\frac{\mathrm{J}}{h}$ or a splitting between traveling wave modes of $2\Omega ·\frac{\mathrm{J}}{h}$ is predicted. This led to a suggestion of the "Coriolis-Zeeman" effect for photons. Using either the above development or the energy density it is shown that the effect depends on the moment of the energy flux and is only proportional to the angular momentum. In the geometrical-optics region an index of refraction valid for accelerated macroscopic matter is developed and is applied to the square Fabry-Perot cavity rate gyroscope to yield the same result as either of the above methods. An experiment to show the validity of Minkowski's decomposition of the energy-momentum tensor is discussed.