Superluminal Neutrinos and a Curious Phenomenon in the Relativistic Quantum Hamilton-Jacobi Equation

Details Superluminal Neutrinos and a Curious Phenomenon in the Relativistic Quantum Hamilton-Jacobi Equation Superluminal Neutrinos and a Curious Phenomenon in the Relativistic Quantum Hamilton-Jacobi Equation

2011-09-29

arxiv.org/abs/1109.6631v2

Physics

High Energy Physics

High Energy Physics - Phenomenology

4 pages. Extended version, details and ackn. added

Scientific paper

OPERA's results, if confirmed, pose the question of superluminal neutrinos. We investigate the kinematics defined by the quantum version of the relativistic Hamilton-Jacobi equation, i.e. E^2=p^2c^2+m^2c^4+2mQc^2, with Q the quantum potential of the free particle. The key point is that the quantum version of the Hamilton-Jacobi equation is a third-order differential equation, so that it has integration constants which are missing in the Schroedinger and Klein-Gordon equations. In particular, averaging the velocity on a period leads, depending on the value of an integration constant, to superluminal solutions in agreement with OPERA's results. This also suggests formulating the relativistic quantum Hamilton-Jacobi equation on a discrete space-time.

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