Wheeler–Feynman absorber theory

The Wheeler–Feynman absorber theory (also called the Wheeler–Feynman time-symmetric theory), named after its originators, the physicists Richard Feynman and John Archibald Wheeler, is an interpretation of electrodynamics derived from the assumption that the solutions of the electromagnetic field equations must be invariant under time-reversal transformation, as are the field equations themselves. Indeed, there is no apparent reason for the time-reversal symmetry breaking, which singles out a preferential time direction and thus makes a distinction between past and future. A time-reversal invariant theory is more logical and elegant. Another key principle, resulting from this interpretation and reminiscent of Mach's principle due to Tetrode, is that elementary particles are not self-interacting. This immediately removes the problem of self-energies.

The requirement of time-reversal symmetry, in general, is difficult to conjugate with the principle of causality. Maxwell's equations and the equations for electromagnetic waves have, in general, two possible solutions: a delayed solution and an advanced one. Accordingly, any charged particle generates waves, say at time ${\displaystyle t_{0}=0}$ and point ${\displaystyle x_{0}=0}$, which will arrive at point ${\displaystyle x_{1}}$ at the instant ${\displaystyle t_{1}=x_{1}/c}$ (here ${\displaystyle c}$ is the speed of light), after the emission (retarded solution), and other waves, which will arrive at the same place at the instant ${\displaystyle t_{2}=-x_{1}/c}$, before the emission (advanced solution). The latter, however, violates the causality principle: advanced waves could be detected before their emission. Thus the advanced solutions are usually discarded in the interpretation of electromagnetic waves. In the absorber theory, instead charged particles are considered as both emitters and absorbers, and the emission process is connected with the absorption process as follows: Both the retarded waves from emitter to absorber and the advanced waves from absorber to emitter are considered. The sum of the two, however, results in causal waves, although the anti-causal (advanced) solutions are not discarded a priori.

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