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.
Highlights
The OPERA collaboration reported evidence for superluminal neutrino propagation from CERN to the Gran Sasso laboratory [1]
The arrival time of the muon neutrinos with average energy of 17 GeV is earlier by δ ≡ (v2 − 1) = 5 × 10−5 as compared to the speed of light in vacuum, and is reported with significance level of 6σ
It has further been suggested that superluminal speeds are obtained from a quantum version of the relativistic quantum
Summary
The OPERA collaboration reported evidence for superluminal neutrino propagation from CERN to the Gran Sasso laboratory [1]. The quantum versions of the non-relativistic and relativistic Hamilton–Jacobi equations have been derived from the equivalence postulate of quantum mechanics [24–30]. While the quantum correction does indicate deviations from the classical energy–momentum relation, it does not necessarily lead to superluminal speeds.
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