We consider the possibility that particle rest masses may vary in spacetime. According to arguments originated by Dicke, if this is the case various null experiments indicate that all masses vary in the same way. Their variation relative to the Planck-Wheeler mass defines a universal scalar rest-mass field. We construct the relativistic dynamics for this field based on very general assumptions. In addition, we assume Einstein's equations to be valid in Planck-Wheeler units. A special case of the theory coincides with Dicke's reformulation of Brans-Dicke theory as general relativity with variable rest masses. In the general case the rest-mass field is some power $r$ of a scalar field which obeys an ordinary scalar equation with coupling to the curvature of strength $q$. The $r$ and $q$ are the only parameters of the theory. Comparison with experiment is facilitated by recasting the theory into units in which rest masses are constant, the Planck-Wheeler mass varies, and the metric satisfies the equations of a small subset of the scalar-tensor theories of gravitation. The results of solar system experiments, usually used to test general relativity, are here used to delimit the acceptable values of $r$ and $q$. We conclude that if cosmological considerations are not invoked, then the solar-system experiments do not rule out the possibility of rest-mass variability. That is, there are theories which agree with all null and solar-system experiments, and yet contradict the strong equivalence principle by allowing rest masses to vary relative to the Planck-Wheeler mass. We show that the field theory of the rest-mass field can be quantized and interpreted in terms of massless scalar quanta which interact very weakly with matter. This explains why they have not turned up in high-energy experiments. In future reports we shall investigate the implications of various cosmological and astrophysical data for the theory of variable rest masses. The ultimate goal is a firm decision on whether rest masses vary or not.

• Received 16 August 1976

DOI:https://doi.org/10.1103/PhysRevD.15.1458