World-line geometry probed by fast spinning particle
  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. 
Alexei A. Deriglazov and Walberto Guzm\'an Ram\'irez
physics.gen-ph