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

Abstract

The present work calls attention to an undeclared assumption made by Einstein in his landmark paper [Ann. Physik 322 (10), 891 (1905)] in which he introduced the Special Theory of Relativity (STR). The emphasis in textbooks and periodicals is always on his two postulates of relativity [the Relativity Principle (RP) and the constancy of the speed of light in free space]. Yet, the well-known results of his theory such as Fitzgerald-Lorentz length contraction (FLC) and the symmetry of time dilation (two clocks in motion each running slower than the other) are based exclusively on this third postulate. It is shown that an alternative assumption of clock-rate proportionality (Newtonian Simultaneity) is also consistent with Einstein’s first two postulates and with the Relativistic Velocity Transformation (RVT), but that it leads to a fundamentally different space-time transformation than the Lorentz Transformation (LT) of STR. It is referred to as the Newton-Voigt Transformation (NVT). Its predictions regarding length and time measurements by moving observers differ sharply from those of the LT. A “clock riddle,” distinct from the well-known “clock paradox,” is presented to underscore the differences between these two versions of the relativistic space-time transformation. It is shown that the NVT is consistent with remote simultaneity and the impossibility of time inversion, and therefore does not rule out the existence of faster-than-c particles under the condition that they have null proper mass