Relativity principles in 1+1 dimensions and differential aging reversal

Abstract

We study the behavior of clocks in 1+1 spacetime assuming the relativity principle, the principle of constancy of the speed of light and the clock hypothesis. These requirements are satisfied by a class of Finslerian theories parametrized by a real coefficient $β$, special relativity being recovered for $β=0$. The effect of differential aging is studied for the different values of $β$. Below the critical values $|β| =1/c$ the differential aging has the usual direction - after a round trip the accelerated observer returns younger than the twin at rest in the inertial frame - while above the critical values the differential aging changes sign. The non-relativistic case is treated by introducing a formal analogy with thermodynamics.

12 pages, no figures. Previous title "Parity violating terms in clocks' behavior and differential aging reversal". v2: shortened introduction, some sections removed, pointed out the relation with Finsler metrics. Submitted to Found. Phys. Lett