On the empirical foundations of special relativity

Abstract

It is known that the Lorentz transformation can be derived from purely topological and kinematical axioms, without reference to the velocity of light or to electrodynamics. The major consequences of this approach are discussed, and some deeply ingrained ideas are found wanting. The value of the kinematical limiting velocity c0 must be determined empirically; the usual assumption, here called the « signal postulate », identifies it with the light velocityc, but the evidence is fragmentary. The weakest link is the « second postulate » stating the independence ofc from the state of motion of the source; further work is desirable under circumstances where nonelectrodynamical forces, radiative reactions and changes of source acceleration play prominent roles. The signal postulate holds if and only ifc does not depend on frequency. Eecent observations on the Crab Nebula pulsar, an effectively stationary flash source, have established a constancy ofc in the visible region which can plausibly be interpreted as implying a photon rest mass of less than 2 MHz. However, a smaller limit may be surmised from the consistency of quantum electrodynamics as known at present; thus the pulsar work should be extended. It is also possible to determine c0 directly; the best way seems to be a calculation from combined nuclear transmutation energies and accuratem/e values. The kinematical approach also calls for sharper verifications of the direct consequences of the Lorentz transformation, such as Doppler effect, time dilatation and Einstein addition law; any observed violation would mean a failure of the underlying assumptions about the topological nature of space and time.