Comments on the scalar-tensor theory

Scalar-tensor theories are discussed as encompassing three classical long-range fields, including the electromagnetic field. In order to shed additional light on the restrictive assumptions made by Dicke concerning the coupling of the scalar field with matter, the ponderomotive laws of a scalar-tensor theory are constructed free of approximations in the form of integral laws. The integrals are extended over two- and three-dimensional domains that lie entirely in empty space but surround the regions containing matter; as for the latter, the vacuum field equations are not required to hold, but no further assumptions are made. It turns out that the gradient of the incident scalar field will contribute to the rate of change of the mass and linear momentum of a particle an amount proportional to that particle's scalar-field source strength, which in turn is an arbitrary function of time, unless Dicke's special restriction is imposed. To this extent the motion of a test particle is indeterminate, contrary to experience.A preliminary version of this paper was presented at the colloquium on relativistic fluids and fields under the auspices of the Centre National de la Recherche Scientifique in Paris in June 1967. Support by Aerospace Research Laboratories and by the Air Force Office of Scientific Research, both agencies of the United States Air Force, is gratefully acknowledged, as is a travel grant by the CNRS.