Causality of relativistic many-particle classical dynamics theories

Abstract

At the present time, the relativistic many-particle classical dynamics theory of the Fokker–Wheeler–Feynman type for isolated systems admits to two contradictory and mutually exclusive interpretations, noncausal versus causal. This work resolves this contradiction by demonstrating definitively that the mathematical structure of this theory is inconsistent with the assumption of noncausality. The demonstration is effected by identifying the fundamental difference in the input assumptions responsible for the two interpretations, by presenting general arguments proving the deterministic nature of the equations of motion, and by giving explicit examples that not only display the deterministic nature of the equations of motion but also their causal character, namely, being solvable by a stepwise forward in time integration using solely past information. One concludes, first, that the assumption of noncausality, and related deductions, is invalid and must be rejected and, second, that one has, at last, the relativistic generalization of many-particle nonrelativistic classical dynamics based on a Hamilton's principle and with a Lagrangian structure. Thus, one can sensibly proceed to examine the physical implications.