Inadequacies in the Current Definition of the Meter and Ramifications Affecting Einstein’s Second Postulate of Relativity

Abstract

The current definition of the meter as based on the time of light transmission and the postulated universal constant light speed is ill-defined and inadequate. The definition fails to identify which second is required, whether to use coordinate or proper time, or which method to construct an exact meter, besides ignoring gravity’s effect. In Einstein’s 1905 paper that defined special relativity, Einstein stipulated correctly that light traversing the ends of a resting rod takes equal time transmissions in either direction. If that rod is oriented parallel to a constant velocity, a photon from one end of the moving rod takes a longer time span with a universal constant light speed to overtake the receding end and takes a shorter time span to intercept the approaching end of the rod when transmitted in the opposite direction, resulting in a longer roundtrip distance of photons traversing the moving rod versus the resting rod. Length contraction undercompensates this difference. Einstein did not address this issue. However, Einstein claimed the unequal time intervals over the moving rod versus equal intervals over the resting rod are because simultaneous states for the resting observer and resting rod are nonsimultaneous for the constant moving observer. This contradicts his first postulate of relativity: any state of a physical system (e.g., equal timed traverses of photons moving over a rod) is unaffected by a constant translational velocity between inertial reference frames. An in-depth analysis examines Einstein’s thought experiment for an adequate redefinition. The analysis reveals one-way photon velocities obey vector velocity addition involving moving photon sources, but it proves by induction that roundtrip photon traverses have an average speed that is identical to the standard light speed c. Thus, Einstein’s second postulate of relativity is not general, but is valid for roundtrip traverses of photon transmissions. This may change many physical concepts, since one-way velocities for photons and particles are not limited by the second postulate. A suggested redefinition of the meter is submitted.