Comment on "Trouble with the Lorentz Law of Force: Incompatibility with Special Relativity and Momentum Conservation"

TL;DR

This paper clarifies that the presence of torque in a relativistic system with magnetic dipoles and charges aligns with special relativity and conservation laws, countering claims of incompatibility in prior work.

Contribution

It demonstrates that torque observed in certain frames is consistent with relativity when total momentum, including fields and particles, is considered.

Findings

Torque is compatible with special relativity when total momentum is conserved.

Conservation laws require contributions from both fields and particles.

Classical electrodynamics needs a coupled dynamical description of particles and fields.

Abstract

In a recent Letter [arXiv:1205.0096], Mansuripur considers a magnetic dipole positioned at a fixed location from a point charge. Performing a Lorentz transformation to a laboratory frame where the charge distribution moves he finds that `a net torque acts on the dipole pair'. He then argues that `this torque in the (lab) frame in the absence of a corresponding torque in the (rest) frame is sufficient proof of the inadequacy of the Lorentz (force) law'. In this comment we demonstrate that the presence of a torque is not incompatible with special relativity: it is required by the conservation laws that apply to the total momentum of the system (including the particles). We furthermore stress that classical electrodynamics needs a consistent dynamical description of the particles that involves coupled equations for the electromagnetic fields and the trajectories [M. Brachet and E. Tirapegui, Nuovo Cimento Soc. Ital. Fis. A 47, 210 (1978)] and any conserved quantity will then contain contributions from both the field and the particles.