Interaction contra Classical Relativistic Hamiltonian Particle Mechanics

Abstract

The relativistic Hamiltonian formalism is outlined and discussed for classical particles. The implications of the requirement that the coordinates of an event transform according to the Lorentz transformation law are discussed and expressed in a form, called the world‐line conditions, which may be considered in the relativistic Hamiltonian formalism. It is then shown that the world‐line conditions imply that there is no interaction in the relativistic Hamiltonian formalism; that is, the motion of any pair of particles described by the relativistic Hamiltonian formalism consists of straightline motion. In other words, if the events which compose the world lines of the particles transform according to the Lorentz transformation law, and the path of the particle is not a straight line, then this phenomena cannot be described in terms of a relativistic two‐particle Hamiltonian formalism. The experimental basis for a determination of the transformation properties of an event is considered, and the relationship of the experiment to the applicability of such a formalism is discussed.