The fallacy of Schott energy-momentum

TL;DR

This paper critically examines the concept of Schott energy-momentum in electromagnetic radiation, demonstrating through a specific case that it does not physically exist in the fields, challenging longstanding assumptions.

Contribution

The study provides a rigorous analysis showing the non-existence of Schott energy-momentum in electromagnetic fields, refuting its proposed role in radiation reaction.

Findings

No evidence of Schott energy-momentum in electromagnetic fields

Challenges the validity of the Schott energy concept in radiation theory

Supports abandoning the Schott term in electromagnetic radiation formulations

Abstract

The incompatibility between Larmor's formula for radiation losses (at a rate proportional to square of the acceleration of the electric charge) and the radiation reaction (the rate of loss of momentum of the accelerated charge proportional to its rate of change of acceleration) was recently shown to arise because a proper distinction is not kept between radiation losses calculated in terms of a retarded time and those expressed in terms of a "real time". However, the occurrence of this disparity between two formulations is usually reconciled in literature by proposing an acceleration-dependent Schott energy lying somewhere in the nearby electromagnetic fields of an accelerated charge. But nobody has yet unambiguously demonstrated where the Schott energy actually lies in the fields. By scrutinizing electromagnetic fields of a uniformly accelerated charge, a mathematically tractable case, we show that contrary to the ideas prevalent in the literature, there is no evidence of any acceleration-dependent Schott energy-momentum in the electromagnetic fields, anywhere in the near vicinity of the charge or elsewhere. Accordingly, we expose the fallacy of the Schott energy-momentum term, which should henceforth be abandoned, in the electromagnetic radiation formulation.