World-line geometry probed by fast spinning particle

TL;DR

This paper explores how the interaction of spin with electromagnetic and gravitational fields modifies the effective geometry along a particle's world line, affecting the critical speed and the definitions of time and distance.

Contribution

It introduces a framework using an effective metric to reconcile spin interactions with special relativity's definitions of time and distance.

Findings

Critical speed differs from light speed when using standard definitions.

Adopting a general-relativity approach aligns critical speed with light speed.

Effective metric arises from spin interactions with electromagnetic and gravitational fields.

Abstract

Interaction of spin with electromagnetic field yields an effective metric along the world line of spinning particle. If we insist to preserve the usual special-relativity definitions of time and distance, critical speed which spinning particle can not overcome during its evolution in external field differs from the speed of light. Instead, we can follow the general-relativity prescription to define physical time and distance in the presence of electromagnetic field. With these definitions, critical speed coincides with the speed of light. Effective metric arises also when spin interacts with gravitational field.