The Principle of Physical Identity of Units of Measure in Einstein's Special Relativity

Abstract

Einstein's principle of special relativity (SR) implies the existence of physical processes giving identical lengths and times within all inertial frames. This theory of measurement of length and duration, that occupies an essential place in Einstein's SR, can only be wholly justified in quantum theory. Einstein's principle of identity of units is not necessary to establish a complete theory of SR. Indeed Poincaré established in 1905 another SR, without Einstein's measurement theory, based on the principle of relativity (group structure of Lorentz's transformations, LT) and on the Lorentz principle of real contraction of units of lengths. Each SR is based on its own system of two principles. Poincaré's classical SR supposes a specific use of LT and a specific definition of units not only of space but also of time. In particular the contrast between 1905 Poincaré's relativistic use of classical astronomical clocks and Einstein's 1905 relativistic use of identical quantum atoms clocks meets questions which have a certain importance today in physics. In the next few years indeed several experiments will measure the relativistic effects with cold-atoms clocks in space. So the clear separation of the “standard mixture” SR into its two components (Einstein's SR and Poincaré's SR) may help to solve the delicate problems which still persist at the interface between quantum theory and general relativity.