Testing for Anisotropy of Space via an Extension of Special Relativity

In special relativity, testing for spatial anisotropy usually means testing for anisotropic propagation of light. This paper explores a different possibility, in which light is still assumed to propagate isotropically in all frames with an invariant speed, yet other physical effects exhibit a direction dependence. If spatial isotropy is not assumed in the derivation of the coordinates transformations, the resulting equations differ from the Lorentz relations by an additional factor $(\dfrac{c - v}{c + v})^{\kappa}$, where $\kappa$ is the anisotropy exponent, which depends on the direction chosen as the x-axis. Time dilation and length contractions become direction dependent. The anisotropy exponent is frame-independent, so no preferred isotropic frame exists if $\kappa$ is non-vanishing. The Doppler shift can be used to measure this exponent and determine experimentally the degree of anisotropy our universe actually possesses.