Inertia as a manifestation of the reality of spacetime

Vesselin Petkov

An attempt is made to pursue more rigorously Minkowski's program - "physical laws might find their most perfect expression as reciprocal relations between world-lines" - by addressing the open question of inertia. This question has become even more urgent in view of the fact that in general relativity the so-called gravitational force is considered to be inertial [1] which explains why "there is no such thing as the force of gravity" in general relativity [2]. If the physical objects are not the ordinary three-dimensional bodies but are rather four-dimensional "worldlines" (as the theory of relativity implies), then inertial and gravitational forces can be regarded as originating from a four-dimensional stress in a body's worldline which arises when the worldline is deformed due to its being deviated from its geodesic state (when the body accelerates or is at rest in a gravitational field). It is shown that the deformation of a classical electron's worldline does give rise to a self-force which has the form of the inertial force. Semi-classical calculations of the self-force acting on a non-inertial charge (whose worldline is deformed) in quantum electrodynamics also show that the same type of acceleration-dependent self-interaction effects that give rise to the inertia and mass of the classical electron appear in quantum field theory as well when the general relativistic frequency shift of the virtual quanta, mediating the electromagnetic, weak, and strong interactions, is taken into account.

1. W. Rindler, Essential Relativity, 2nd ed. (Springer-Verlag, New York, 1977), p. 244.
2. J. L. Synge, Relativity: the general theory, (Nord-Holand, Amsterdam, 1960), p. 109.