Collapse of Neutrino Wave Functions under Penrose Gravitational Reduction

TL;DR

This paper investigates how Penrose's gravitational collapse model affects neutrino oscillations, reinterpreting experimental data to constrain the model's parameters and identifying observable signatures of gravitationally induced decoherence.

Contribution

It applies Penrose's gravitational collapse model to neutrino oscillations and derives experimental constraints on the model's parameters from IceCube data.

Findings

Momentum diffusion effects are ruled out by IceCube data for certain neutrino wave packet widths.

Constraints on the neutrino wave packet width at production are established.

Reinterpretation of neutrino decoherence limits within the Penrose collapse framework.

Abstract

Models of spontaneous wave function collapse have been postulated to address the measurement problem in quantum mechanics. Their primary function is to convert coherent quantum superpositions into incoherent ones, with the result that macroscopic objects cannot be placed into widely separated superpositions for observably prolonged times. Many of these processes will also lead to loss of coherence in neutrino oscillations, producing observable signatures in the flavor profile of neutrinos at long travel distances. The majority of studies of neutrino oscillation coherence to date have focused on variants of the continuous state localization model, whereby an effective decoherence strength parameter is used to model the rate of coherence loss with an assumed energy dependence. Another class of collapse models that have been proposed posit connections to the configuration of gravitational field accompanying the mass distribution associated with each wave function that is in the superposition. A particularly interesting and prescriptive model is Penrose's description of gravitational collapse which proposes a decoherence time $\tau$ determined through $E_{g}\tau\sim\hbar$, where $E_{g}$ is a calculable function of the Newtonian gravitational potential. Here we explore application of the Penrose collapse model to neutrino oscillations, reinterpreting previous experimental limits on neutrino decoherence in terms of this model. We identify effects associated with both spatial collapse and momentum diffusion, finding that the latter is ruled out in data from the IceCube South Pole Neutrino Observatory so long as the neutrino wave packet width at production is $\sigma_{\nu,x}\leq2\times10^{-12}$ m.