Causality violation in e⁺e⁻ pair production by superluminal neutrinos

Department of Physics, Hiroshima University - 1-3-1 Kagami-yama, Higashi-Hiroshima 739-8526, Japan

^a tom@geminga.org

Received: 6 February 2012
Accepted: 12 March 2012

Abstract

Pair emission by superluminal neutrinos is shown to be causality violating in the 10–50 GeV range covered by the OPERA experiment. Thus, the energy density of a freely propagating superluminal neutrino current is not affected by energy loss due to e⁺ e⁻ pair creation, in accordance with the unperturbed energy profile observed by ICARUS. Interaction processes involving sub- and superluminal particles give rise to time inversions in the rest frames of the subluminal constituents, resulting in causality violating predetermination. Therefore, kinematic causality constraints in addition to energy-momentum conservation are necessary to exclude causality violation outside the lightcone. Electron-positron pair production by superluminal muon neutrinos is forbidden in the OPERA energy range, as the kinematic constraints on the neutrino frequencies and wave vectors required by causality and energy-momentum conservation cannot simultaneously be satisfied.