An exposition of special relativity without appeal to "constancy of speed of light" hypotheses

Abstract

We present the theory of special relativity here through the lens of differential geometry. In particular, we explicitly avoid any reference to hypotheses of the form "The laws of physics take the same form in all inertial reference frames" and "The speed of light is constant in all inertial reference frames", or to any other electrodynamic phenomenon. For the author, the clearest understanding of relativity comes about when developing the theory out of just the primitive concept of time (which is also a concept inherent in any standard exposition) and the basic tenets of differential geometry. Perhaps surprisingly, once the theory is framed in this way, one can predict existence of a "universal velocity" which stays the same in all "inertial reference frames". This prediction can be made by performing much more basic time measurement physical experiments that we outline in these notes, rather than experiments of an electrodynamic nature. Thus, had these physical experiments been performed prior to Michelson-Morley type experiments (which, in principle, could have been done in any period with precise enough time keeping instruments), the Michelson-Morley experiments would simply give us an example of a physical entity, i.e., light, which enjoys this special "universal" status.