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arXiv:2410.21850 · Qeios

Quantum Coherence Between Mass Eigenstates of a Neutrino Can Be Destroyed by Its Mass-Momentum Entanglement

Shi‐Biao Zheng

Published Dec 13, 2024• 0 citations
arXivHTMLPDF

Abstract

If a neutrino or antineutrino produced in the decay of an unstable particle is not entangled to its accompanying particles, its mass is necessarily correlated with its momentum. In this manuscript, I illustrate that this entanglement would destroy the quantum coherence between the neutrino’s mass eigenstates in both the momentum and position representations, which was overlooked by other authors in previous investigations of entanglement and coherence associated with neutrino oscillations. I further point out that the states of a neutrino and an electron become nonseparable after their charged-current interaction. This nonseparability leads to decoherence for neutrinos propagating in matter, but was not taken into consideration in previous investigations of the matter effect.

DOI
10.32388/59ije9

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Comment on "Quantum coherence between mass eigenstates of a neutrino cannot be destroyed by its mass-momentum entanglement"

Shi-Biao Zheng

In arXiv:2410.21850, I proved that the quantum coherence between the mass eigenstates of a neutrino will be destroyed if they are correlated with different momenta. In arXiv:2411.01190, James M. Cline claimed that I had made the unrealistic assumption that the neutrino is always in a nearly exact energy eigenstate, and ignored the spatial dependence of the wavefunction in my paper. However, I did not assume that the neutrino is in a nearly exact eigenstate of energy anywhere in my paper, and the wavefunction I wrote in the position representation has a spatial dependence. The argumentation of arXiv:2411.01190 is based on misinterpreting my claim, and on ignoring the critical fact that the neutrino's wavepacket has a finite size and the detector has a large volume.

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Quantum coherence between mass eigenstates of a neutrino cannot be destroyed by its mass-momentum entanglement

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In the latest of a series of papers (arXiv:2410.21850), it has been claimed that neutrinos cannot oscillate as a consequence of their mass mixing. I clarify that this arises from the unrealistic assumption that neutrinos will always be in nearly exact eigenstates of energy, and ignoring the spatial dependence of the neutrino wave function. Taking into account the latter, neutrinos will be observed to oscillate in precisely the expected manner.

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If a neutrino or antineutrino produced in the decay of an unstable particle is not entangled to its accompanying particles, its mass is necessarily correlated with its momentum. In this manuscript, I illustrate that this entanglement would destroy the quantum coherence between the neutrino’s mass eigenstates in both the momentum and position representations, which was overlooked by other authors in previous investigations of entanglement and coherence associated with neutrino oscillations. I further point out that the states of a neutrino and an electron become nonseparable after their charged-current interaction. This nonseparability leads to decoherence for neutrinos propagating in matter, but was not taken into consideration in previous investigations of the matter effect.
Abstract Although neutrino–antineutrino states originating from neutral-current interactions are blind concerning the flavor state, an oscillation pattern is predicted provided that both neutrino and antineutrino are detected. This issue arises from both the coherence and entanglement of the neutrino–antineutrino states. Based on quantum resource theory, we use the l1l_1l1​ l 1 -norm and concurrence to quantify quantum coherence and entanglement, respectively. Considering the localization properties by the wave packet approach and a matter potential which appears when neutrino and antineutrino propagate in a material medium, we obtain the l1l_1l1​ l 1 -norm and concurrence. We see that the neutrino and antineutrino remain entangled for larger baseline lengths when they propagate in a material medium. In the case of the coherence property, the l1l_1l1​ l 1 -norm decreases in comparison to the corresponding one in vacuum. However, its damping occurs for larger distances.
In arXiv:2410.21850, I proved that the quantum coherence between the mass eigenstates of a neutrino will be destroyed if they are correlated with different momenta. In arXiv:2411.01190, James M. Cline claimed that I had made the unrealistic assumption that the neutrino is always in a nearly exact energy eigenstate, and ignored the spatial dependence of the wavefunction in my paper. However, I did not assume that the neutrino is in a nearly exact eigenstate of energy anywhere in my paper, and the wavefunction I wrote in the position representation has a spatial dependence. The argumentation of arXiv:2411.01190 is based on misinterpreting my claim, and on ignoring the critical fact that the neutrino's wavepacket has a finite size and the detector has a large volume.
In charged current weak interaction processes, neutrinos are produced in an entangled state with the charged lepton. This correlated state is disentangled by the measurement of the charged lepton in a detector at the production site. We study the dynamical aspects of disentanglement, propagation, and detection, in particular, the conditions under which the disentangled state is a coherent superposition of mass eigenstates. The appearance and disappearance far-detection processes are described from the time evolution of this disentangled ``collapsed'' state. The familiar quantum mechanical interpretation and factorization of the detection rate emerges when the quantum state is disentangled on time scales much shorter than the inverse oscillation frequency, in which case the final detection rate factorizes in terms of the usual quantum mechanical transition probability provided the final density of states is insensitive to the neutrino energy difference. We suggest possible corrections for short-baseline experiments. If the charged lepton is unobserved, neutrino oscillations and coherence are described in terms of a reduced density matrix obtained by tracing out an unobserved charged lepton. The diagonal elements in the mass basis describe the production of mass eigenstates whereas the off-diagonal ones provide a measure of coherence. It is shown that coherences are of the same order of the diagonal terms on time scales up to the inverse oscillation frequency, beyond which the coherences oscillate as a result of the interference between mass eigenstates.
Simple rigorous quantum mechanics with no hand waving nor loopholes clarifies the confusion between three contradictory descriptions of the coherence between different neutrino mass eigenstates that can give rise to oscillations: (1) The standard textbook description of oscillations in time produced by coherence between states with different masses and different energies. (2) Stodolsky's proof that interference between states having different energies cannot be observed in realistic experiments. (3) The description of a pion decay at rest into an observed muon and unobserved neutrino as a “missing mass” experiment where coherence between different neutrino mass eigenstates is not observable. The known position in space of all realistic detectors is rigorously shown to provide the quantum-mechanical ignorance of the neutrino momentum needed to produce coherence between amplitudes from neutrino states with the same energy and different masses. Conditions are precisely formulated for the loss of coherence when mass eigenstate wave packets moving with different velocities separate. The example of Bragg scattering shows how quantum-mechanically imposed ignorance produces coherence.
Abstract Recently, several studies of neutrino oscillations in the vacuum have not found the decoherence long expected from the separation of wave packets of neutrinos in different mass eigenstates. We show that such decoherence will, on the other hand, be present in a treatment including any mechanism which leads to a dependence of the final state on both the neutrino’s emission and absorption time. Using a simplified model in 1+11+11+1 1 + 1 d, we show that if the positions of the final state particles are measured, or equivalently entangled with the environment, then decoherence will damp neutrino oscillations. We also show that wave packet spreading can cause the decoherence to eventually saturate, without completely suppressing the oscillations. These results are not an artifact of the approximation used: we show that, considering the V−AV-AV−A V - A model in 3+13+13+1 3 + 1 d, the difference would be simply a total multiplicative factor that would not affect the oscillation probability nor the decoherence.