Subtleties of the clock retardation

TL;DR

This paper provides an exact electromagnetic analysis of a simple clock model to clarify how its rate changes under uniform motion, revealing that some standard relativistic assumptions about clock retardation need correction.

Contribution

It offers a precise dynamical calculation of clock retardation using electromagnetic theory, challenging and refining existing relativistic generalizations.

Findings

Exact change in clock rate derived for a charged particle model

Standard relativistic clock retardation assumptions are partially incorrect

Electromagnetic dynamics influence the interpretation of relativistic effects

Abstract

For a simple electromagnetic model of a clock introduced by Jefimenko (clock $\#$ 1 in 1996 {\it Am. J. Phys.} {\bf 64} 812), a change of the rate of the clock when it is set in uniform motion is calculated exactly, employing the correct equation of motion of a charged particle in the electromagnetic field and the universal boostability assumption. Thus, for the clock under consideration, a dynamical content of the clock retardation is demonstrated. Somewhat surprisingly, the analysis presented discloses that some familiar relativistic generalisations concerning the retardation of clocks have to be amended.