Physical consequences of a co-ordinate transformation to a uniformly accelerating frame

Abstract

The classical equations of particle motion and of classical electrodynamics are known to be covariant with respect to conformai co-ordinate transformations. This paper deals with a simple conformai co-ordinate transformation from an inertial frame to one which accelerates uniformly; it examines the physical consequences predicted by the covariant theory and the transformation. Expressions are derived for various effects of the conformai invariance on mass, length, and time measurements; the predictions of the theory are shown to be the same as the corresponding predictions derived from the general theory of relativity for the transformation being studied. The predictions of the conformai theory depend on the particular co-ordinate system chosen (with an explicit dependence on the origin). The corresponding situation prevails in general relativity with the components of the metric tensor being a function of space and time. An example of the « twin paradox » is studied. Finally, after considering the behavior of four-momentum conservation under conformai transformations, the frequency shift of radiation emitted by an excited atom falling freely in a uniform field is calculated to first order in acceleration. Identical results are obtained from the conformai and general relativistic points of view. The frequency shifts are what one would expect to obtain by properly combining the Doppler shifts and the shift arising as a consequence of the equivalence of inertial mass to gravitational mass.