On a wavefunction picture for the direct particle theory of gravitation and electromagnetism

Abstract The paper is in three parts. The direct particle theory developed in previous papers is reviewed in the introductory first part. A new result is obtained, that while long-range gravitational forces are necessarily attractive very short-range forces must be repulsive. The theory for strong gravitational fields differs radically therefore from general relativity. In general relativity a finite particle collapses into a singularity. Here a singularity explodes into a finite particle. The concept of a finite particle is explored in the second and third parts. In the second part, the particle is treated as a classical world tube. A further new result emerges, that the inertial mass of such a particle must be very small. The gravitational mass is the same as in the line singularity case, but it turns out that a particle represented by a world tube shields its inertial mass through its own influence on the metric tensor. It is suggested that the very small ratio of gravitational to electrical forces may be due, not to the weakness of gravitation but to the smallness of the inertial mass. The advantage of this suggestion is that no very large dimensionless number need appear in the action formula. In the third part we pass to a wavefunction picture for the particles. An action principle is used that leads to the Dirac equation for the particles. The field equations are the same as in the line singularity case, except that the energy-momentum tensor associated with matter is changed from the form used in general relativity to the form that is usual for a Dirac ‘field’. The wave-function picture, as developed here, contains the simpler ideas of the quantum theory—the superposition principle, stationary states, the quasi-classical theory of radiative transitions. No attempt is made in this paper to extend the theory to include effects that are particular to quantum electrodynamics.