Variation of physical constants and electron–positron oscillations: Zitterbewegung in a plane wave

The space and time dependence of physical constants is currently a debated issue for experimental findings, and theoretical reasons seem to indicate that this is not a mere speculative possibility. The paper provides a relativistic description of a free fermion evolving under the assumption of temporal variation of the physical constants. The assumed generalisation of the Dirac equation is particularly simple and permits a grouping of the constants in one single parameter and a consequent agile treatment of the problem. The form of the equations suggests a rescaling of the temporal coordinate x= ct which allows a plane wave solution. Two are the main results of the treatment. First, the effects of the variation of the constants are better seen in the weak relativistic regime which indicates that experiments can be carried out without having to resort to super accelerators and, second, that a slow particle–antiparticle oscillation occurs in the evolution of a plane wave. This prediction of charge non-conserving oscillation is the analytical outcome of the generalised Dirac equation and appears to be a necessary consequence of the variation of the physical constants.