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 spacetime
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
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



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