1 The Clock Riddle and Einstein’s Third Postulate of Special Relativity

The present work calls attention to an undeclared assumption made by Einstein in his landmark paper [Ann. Physik 17, 891 (1905)] in which he introduced the special theory of relativity (SR). The emphasis in textbooks and periodicals is always on his two postulates of relativity (the relativity principle and the constancy of the speed of light in free space), but the well-known results of his theory such as Fitzgerald-Lorentz length contraction and the symmetry of time dilation (two clocks in motion each running slower than the other) are based just as directly on the former assumption as they are on the original postulates. It is shown that an alternative assumption of clock-rate proportionality is also consistent with the first two postulates and also with Einstein’s velocity addition theorem (VT), but that it leads to an alternative version of the Lorentz transformation (ALT) whose predictions regarding length and time measurements by moving observers are significantly different from those of the original space-time transformation (LT). A “clock riddle, ” as opposed to the well-known “clock paradox, ” is presented to underscore the differences between these two versions of the Lorentz transformation. Finally, it is shown that the ALT is consistent with 2 remote simultaneity and the impossibility of time inversion, and therefore does not rule out the existence of faster-than-c particles as long as they have null proper mass