Phenomenological linear theory of gravitation: Part II. Interaction with the maxwell field

Abstract

The theory of Part I is applied to the interaction of gravity, matter, and electromagnetism. Maxwell's equations are valid with an apparent electric and magnetic susceptibility of space due to the gravitational field. One effect of this susceptibility is a refraction of light rays by a gravitational field, from which the bending of light rays passing the sun can be derived. The result is the same as found in Part I for the deviation of particles traveling at the speed of light. The equivalence principle is shown to be valid in our linear theory as in Einstein's theory, notwithstanding the velocity dependence of the gravitational acceleration of free particles. For bound particles, the dependence of the gravitational forces on the relative velocities of parts of a system with respect to the system's center of gravity is neutralized by gravitational effects on the binding forces. We have shown this only for a special case, and the calculation is performed only in electrostatic approximation. As the errors thus introduced cancel in Einstein's theory, it is assumed that they cancel also here. The parallelism with the corresponding derivations in Einstein's theory are apparent at each step of the calculation, and remains, with altered numerical coefficients in the formulas, for any values assigned to the constants of our linear theory of gravitation. It is, however, possible that in higher approximations our linear theory would violate the equivalence principle. This question is worth further theoretical investigation, and, if such effects theoretically would follow from our theory, Eötvös's experiments on the equivalence principle should be pushed from 10 −8 to 10 −11 in order to discover such effects and to make an experimental decision between the linear and the general-relativistic theories of gravitation.