Some Dynamical Aspects of a Test Theory of Special Relativity

Kinematically viable space-time theories admitting a velocity-dependent dilatation factor in addition to the Lorentz transformation between the inertial systems are considered. It is shown that these theories are very unsatisfactory, in the sense of leading neither to a unique definition of time nor to a unique formulation of a dynamics. As an example, the relativistic theory of anisotropic spacetime proposed by Bogoslovsky is shown to differ discretely from the special theory of relativity. First-order rotor experiments restrict the free parameter r in this theory to values smaller than 10-10