Action at a Distance and Cosmology: A Historical Perspective

The first law of theoretical physics, the Newtonian law of gravitation, relies on the concept of action at a distance. The success of this law led to the concept being applied to electricity and magnetism, which were next to be explored in depth. Here the action at a distance had a limited success and ultimately had to be abandoned in favor of the increasingly more popular field theory. Nevertheless, in the 1940s, an attempt was made to revive the concept of action at a distance in a relativistically invariant way by Wheeler & Feynman (1945, 1949). It inspired a series of investigations in both electrodynamics and gravity in which the field concept was not used but the interaction was described as taking place directly between particles. As it impinged very intimately on cosmology, Hoyle was keenly interested in it. This review discusses the work by Hoyle, the author, and others on the development of electrodynamics and gravitation as direct particle theories. In this review, the author discusses how the work was started and went through stages of increasing sophistication, e.g., extending the Wheeler-Feynman electrodynamics to curved spacetime, its consequences in different cosmologies, and the issues arising from its quantization. The resolution of ultraviolet divergences in quantum electrodynamics is also briefly discussed. The parallel development of a Machian theory of gravitation followed the lead from electrodynamics. In both theories one sees a strong link between the large-scale structure of the universe and local physics, as might be expected from an action-at-a-distance framework.