Particles of finite size in the gravitational field

Abstract

I should like to speak briefly about some work that I am engaged on, although it is not yet complete. The object of this work is to set up a theory of the gravitational field interacting with particles. I want this theory to be in agreement with Einstein’s theory of gravitation, and also I insist that it shall follow from an action principle. I do insist on this because I believe that Nature works according to an action principle, and if we have an action principle, we certainly have a first step towards quantization. Now in considering a particle interacting with the gravitational field, the first thing one would think of would be a point particle, but here one runs into a difficulty, because if one keeps to physically acceptable ideas, one cannot have a particle smaller than the Schwarzschild radius, which provides a sort of natural boundary to space. The mathematicians can go beyond this Schwarzschild radius, and get inside, but I would maintain that this inside region is not physical space, because to send a signal inside and get it out again would take an infinite time, so I feel that the space inside the Schwarzschild radius must belong to a different universe and should not be taken into account in any physical theory. So from the physical point of view, the possibility of having a point singularity in the Einstein field is ruled out. Each particle must have a finite size no smaller than the Schwarzschild radius.