Some Dynamical Aspects of a Test Theory of Special Relativity

Kinemat ica l ly viable space-t ime theories a d m i t t i n g a ve loc i ty-dependent d i la ta t ion fac tor in addi t ion to t h e Loren tz t r ans fo rma t ion between the inertial sys tems a re considered. I t is shown t h a t these theories a re very unsa t i s fac tory , in the sense of leading nei ther to a un ique defini t ion of t ime nor to a unique fo rmula t ion of a dynamics . As a n example , t h e relat ivist ic theory of anisotropic spacet i m e proposed by Bogoslovsky is shown to differ discretely f r o m t h e special theory of re la t iv i ty . F i rs t -order ro to r expe r imen t s restr ict t he free pa r ame te r r in th is t heo ry t o va lues smaller t h a n 10 1 0 .