Particles, fields, and rigid bodies in the formulation of relativity theories

Abstract

The particle theories of Heeler and Feynman (electrodynamics) and Whitehead (gravitation) are studied, and the relationships to their field counterparts are examined. An invariant distance and suitable covariant potentials are defined in Riemannian space-time, and by this means the theories are generalized, in particular to the de Sitter space-time of constant curvature. It is shown that the generalization has an interesting significance with respect to the steady-state theory of cosmology. The electrodynamic generalization consists of finding a covariant vector potential in de Sitter space from which Maxwell's equations can be derived. It is shown that in the flat-space theory of Wheeler and Feynman radiation damping is indeterminate, but that in de Sitter space and in conjunction with steady-state cosmology the irreversibility of radiation is closely related to the phenomenon of the creation of matter. In de Sitter space Whitehead's theory is shown to yield the Schwarzschild solution of the general theory of relativity with a cosmological constant. A close relationship between Whitehead's theory and the general theory of relativity in suggested. Whitehead's theory is shown to be compatible with steady state cosmology.