The Time Coordinate in Einstein’s Restricted Theory of Relativity

Summary

After drawing some preliminary divisions between different conceptions of time, distinguished as “proper time”, “Kantian time”, “psychological time”, “physical time”, and “mathematical time”, there follows a discussion of time dilatation and the clock paradoxes of Einstein’s restricted theory of relativity. Beginning with Lorentz’s time transformations, and some remarks on the different attitudes of Lorentz, Poincaré, and Einstein to the transformation equations generally, we turn to the clock paradox, often held to involve Einstein in inconsistency. A new notation is introduced, which not only simplifies the manipulation of the Lorentz transformation equations, but which makes it natural to preserve certain terms which are commonly suppressed unknowingly. The notation makes clear what has long been appreciated by some, but denied by others, namely, that the time dilatation equations, correctly expressed, are consistent under a suitable interpretation (and not merely mathematically consistent). Different attempts to engender contradiction within Einstein’s theory are considered, in particular by taking more than two observers, moving uniformly. Necessarily we introduce the notion of an aggregate proper time of two observers, which may not satisfy those looking for a solution to the problem of actual space travellers. There are also difficult problems of specifying what is to count as a journey, under this interpretation. Nevertheless, there is here no sign of the inconsistency in the interpretation of Einstein’s theory for which some writers have argued. Where there is an asymmetry in the aggregate times experienced, there is also an asymmetry in the observers.