Relativity and Synchrotron Radiation: Critical Reexamination of Existing Theory

TL;DR

This paper critically reexamines the traditional synchrotron radiation theory, emphasizing the importance of covariant relativistic kinematics and Lorentz transformations, which have been overlooked in conventional non-covariant treatments.

Contribution

It highlights the necessity of incorporating covariant relativistic effects and Lorentz transformations into synchrotron radiation theory, challenging the conventional non-covariant approach.

Findings

Non-covariant trajectories omit relativistic kinematics effects.

Differences between covariant and non-covariant trajectories are due to Lorentz boost non-commutativity.

A correction to the conventional radiation theory is proposed.

Abstract

Maxwell's equations are valid only in Lorentz frame i.e. in inertial frame where the Einstein synchronization procedure is used to assign values of the time coordinate. Einstein time order must be applied and kept in consistent way in both dynamics and electrodynamics. However, the usual for accelerator engineering non-covariant treatment of relativistic particle dynamics in a constant magnetic field looks precisely the same as in non-relativistic Newtonian dynamics. According to both treatments, the magnetic field is only capable of altering the direction of motion, but not the speed of an electron. However, the non-covariant trajectory does not include relativistic kinematics effects. The covariant electron trajectory is viewed from the Lorentz lab frame as a result of successive infinitesimal Lorentz transformations. One of the consequences of non-commutativity of non-collinear Lorentz boosts is a difference between covariant and non-covariant single particle trajectories in a constant magnetic field. One can see that this essential point has never received attention in the physical community. As a result a correction of the conventional radiation theory is required. In this paper we present a critical reexamination of existing synchrotron radiation theory. The main emphasis of this paper is on spontaneous synchrotron radiation from bending magnets and undulators.