Such a choice of reference frames is allowed in many theories, particularly theories involving a medium for light, but no such arbitrary preferences are allowed in the observer-based special theory of relativity.
On further inspection, it becomes clear that the positing of an ether that revolves with the earth in its orbit around the sun, but does not spin with the earth as it rotates on its axis leads to correct predictions for all electromagnetic and time dilation experiments. This theory would also point toward the likelihood of a whirling ether in the vast expanses between the galaxies, which in turn, would be consistent with the recent "surprising Nodland / Ralston results of the "corkscrew" effect on the polarization of light from distant galaxies.
