Space-time orbits for interacting relativistic particles: Syntactic versus semantic observables

Abstract

Recent work establishing a violation of the so-called "no-interaction theorem" for interacting relativistic particles was directed primarily toward the development of the quantum theory of such systems. In that work the classical trajectories for two-particle systems span a two-dimensional region in phase space. The present paper addresses itself more directly to the intended classical content of the "no-interaction" theorem, namely, the determination of orbits in space-time for the pair of particles under consideration. The problem is nontrivial in the sense that its treatment requires the recognition of the conceptual distinction between syntactically defined observables and semantically defined observables. The latter betray Machian features in so far as they make reference to the open character of the system vis-a-vis the other matter of the universe. It is noteworthy and curious that such considerations were not required for the proper treatment of the quantized system. A critique of the essential features of the "no-interaction" theorem, including certain unstated (and hard to justify) assumptions, is presented.