OPERA data and The Equivalence Postulate of Quantum Mechanics

TL;DR

This paper analyzes the OPERA neutrino results within the framework of the equivalence postulate of quantum mechanics, deriving quantum velocity corrections that do not imply superluminal speeds, and discusses potential observational implications.

Contribution

It derives a quantum correction to relativistic velocity from the equivalence postulate, clarifying that such corrections do not necessarily imply faster-than-light neutrino propagation.

Findings

Quantum correction depends on energy, mass, and distance.

Corrections do not necessarily lead to superluminal speeds.

Potential observational consequences are discussed.

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 speed arising from the Relativistic Quantum Hamilton Jacobi Equation. I show that this is in general not the case. 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.