Eur. Phys. J. C (2012) 72: 1944
https://doi.org/10.1140/epjc/s10052-012-1944-y

Letter

Superluminality and the equivalence postulate of quantum mechanics

Department of Mathematical Sciences, University of Liverpool, Liverpool, L69 7ZL, UK

^* e-mail: faraggi@amtp.liv.ac.uk

Received: 17 January 2012
Revised: 21 February 2012
Published online: 21 March 2012

Abstract

An interpretation of the recent results reported by the OPERA collaboration is that neutrinos propagation in vacuum exceeds the speed of light. It has been further been suggested that this interpretation can be attributed to the variation of the particle average speed arising from the Relativistic Quantum Hamilton–Jacobi Equation. I derive an expression for the quantum correction to the instantaneous relativistic velocity in the framework of the relativistic quantum Hamilton–Jacobi equation, which is derived from the equivalence postulate of quantum mechanics. While the quantum correction does indicate deviations from the classical energy–momentum relation, it does not necessarily lead to superluminal speeds. The quantum correction found herein has a non-trivial dependence on the energy and mass of the particle, as well as on distance travelled. I speculate on other possible observational consequences of the equivalence postulate approach.