On inert properties of particles in classical theory

TL;DR

This paper critically reviews inert properties of classical relativistic particles, classifying them as Galilean or non-Galilean, and discusses their motions, inert characteristics, and implications for classical electrodynamics in higher dimensions.

Contribution

It introduces a detailed classification of particles based on inert properties and explores the necessity of rigid mechanics for consistent classical electrodynamics in higher-dimensional spacetimes.

Findings

Non-Galilean particles can exhibit complex motions including Zitterbewegung and self-accelerations.

A free non-Galilean particle's inert properties are characterized by two invariants, not one.

Rigid mechanics is essential for constructing consistent classical electrodynamics in dimensions greater than four.

Abstract

This is a critical review of inert properties of classical relativistic point objects. The objects are classified as Galilean and non-Galilean. Three types of non-Galilean objects are considered: spinning, rigid, and dressed particles. In the absence of external forces, such particles are capable of executing not only uniform motions along straight lines but also Zitterbewegungs, self-accelerations, self-decelerations, and uniformly accelerated motions. A free non-Galilean object possesses the four-velocity and the four-momentum which are in general not collinear, therefore, its inert properties are specified by two, rather than one, invariant quantities. It is shown that a spinning particle need not be a non-Galilean object. The necessity of a rigid mechanics for the construction of a consistent classical electrodynamics in spacetimes of dimension D+1 is justified for D+1>4. The problem of how much the form of fundamental laws of physics orders four dimensions of our world is revised together with its solution suggested by Ehrenfest. The present analysis made it apparent that the notion of the ``back-reaction'' does not reflect the heart of the matter in classical field theories with point-like sources, the notion of ``dressed'' particles proves more appropriate.