Relativity matters: Two opposing views of the magnetic force reconciled

Moreover, our understanding of how a point-particle carrying a charge moves in presence of an inhomogenous magnetic field relied until now on two theories that were believed to differ. The first stems from William Gilbert's study of elementary magnetism in 16th century, while the second relies on André-Marie Ampère electric currents. In a new study just published in EPJ C, the authors Johann Rafelski and colleagues from the University of Arizona, USA, succeeded in resolving this ambiguity between Ameperian and Gilbertian forms of magnetic force. Their solution makes it possible to characterise the interaction of particles whose speed is close to the speed of light in the presence of inhomogeneous electromagnetic fields.

In the new study, the authors present, for the first time, an important insight into how magnetic field non-homogeneity impacts particle spin dynamics, called spin precession. No prior work has recognised the need to make the form of magnetic torque consistent with the form of magnetic force -- the torque was made consistent only with the Lorentz-Maxwell force.

This advance allows the impact of field non-homogeneity on precision experiment to be quantified. It seeks to resolve a discrepancy in the understanding of quantum field corrections to the magnetic moment of the muon, an elementary particle often referred to as a "heavy electron."

These findings can be applied to the study of neutrinos, opening the door to realms beyond the standard model of particle physics. Rafelski and colleagues show that the magnetic force can be large for particles whose speed is very close to the speed of light.