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arXiv:hep-ph/9802387 · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields

When the wavepacket is unnecessary

Leo Stodolsky

Published Jul 9, 1998• 95 citations
arXivHTMLPDF

Abstract

We point out that many wavepacket discussions for the coherence properties of particle beams are unnecessary since they deal with stationary sources; and when the problem is stationary, essentially all information is in the energy spectrum. This recognition allows a simple answer to a number of long-debated points, usually framed in terms of the``length of the wavepacket.'' In particular we discuss neutrino oscillations, and some issues in neutron physics. The question as to whether two simple beams with the same energy spectrum are distinguishable is answered negatively for stationary situations. The question as to whether neutrino oscillations should be thought of as taking place between states of the same energy or the same momentum is answered in favor of energy for stationary situations. The consequences for proposals involving the ${}^{7}\mathrm{Be}$ neutrino line of the Sun, the observation of oscillations in supernova neutrinos, and wavepacket studies with neutrons are briefly discussed, as well as the connection with the coherence notions of quantum optics.

DOI
10.1103/physrevd.58.036006

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We point out that many wavepacket discussions for the coherence properties of particle beams are unnecessary since they deal with stationary sources; and when the problem is stationary, essentially all information is in the energy spectrum. This recognition allows a simple answer to a number of long-debated points, usually framed in terms of the``length of the wavepacket.'' In particular we discuss neutrino oscillations, and some issues in neutron physics. The question as to whether two simple beams with the same energy spectrum are distinguishable is answered negatively for stationary situations. The question as to whether neutrino oscillations should be thought of as taking place between states of the same energy or the same momentum is answered in favor of energy for stationary situations. The consequences for proposals involving the 7Be{}^{7}\mathrm{Be}7Be neutrino line of the Sun, the observation of oscillations in supernova neutrinos, and wavepacket studies with neutrons are briefly discussed, as well as the connection with the coherence notions of quantum optics.
The role of simple quantum mechanics in understanding neutrino oscillation experiments is pointed out by comparison with two-slit and Bragg scattering experiments. The importance of considering the beam and the detector as a correlated quantum system is emphasized. Quantum mechanics alone shows that the difference observed in the same neutrino detector at Super-Kamiokande between upward and downward going neutrinos requires the existence of a neutrino mass difference. The localization of the source and detector in space in the laboratory system for long times leads to an uncertainty in the momentum but not of the energy of the neutrino and to coherence between states having different momenta and the same energy and not between states with different energies.
We point out three apparent inconsistencies in the treatment of oscillation coherence from reactor neutrino and source neutrino experiments in recent paper "Damping of neutrino oscillations, decoherence and the lengths of neutrino wave packets''. First, that the dependence of the oscillation probability upon the subsequent interactions of entangled recoil particles implies causality violations and in some situations superluminal signaling; second, that integrating over a non-orthogonal basis for the entangled recoil leads to unphysical effects; and third, that the question of what interactions serve to measure the position of the initial state particle remains ambiguous. These points taken together appear to undermine the claim made therein that the effects of wave packet separation must be strictly unobservable in reactor and radioactive source based neutrino experiments.
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I will present some of the results obtained regarding the emergence of decoherence in neutrino oscillations. In our model all the particles, including the source and detector, are treated dynamically and evolved consistently with Quantum Field Theory; decoherence can emerge naturally given the time evolution of the initial state and the final state considered. We have shown that some of the assumptions commonly used in the literature, such as the covariance of the wavepackets, are inconsistent. We found that a crucial ingredient for decoherence is the localization in space-time of the neutrino creation and detection: in Nature, such a measurement is usually carried out by environmental interactions, however it could also be approximated by considering localized wavefunctions in the final state. On the other hand, if the environmental interactions are not present (for example, if the decay happens in vacuum), the final position of the daughter particles will not be measured, i.e. they will be described by plane waves instead: in this case the neutrino is not localized either, and we don't have decoherence. A consequence of the time-evolution is that a Gaussian wavepacket will gradually spread: I will show that such an effect could in principle affect decoherence; moreover it would depend on the absolute mass scale of the neutrino, not on the Δm2\Delta m^2Δm2, which could offer a possible way to probe such a parameter by studying the neutrino oscillations.
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