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Scientific Reports

Mass oscillations and matter wave’s phase and amplitude modulations of relativistic quantum particles induced by Heisenberg’s uncertainty principle

Jau Tang, Qiang Tang, Zhibin Hu

Published Sep 1, 2022• 0 citations
Publisher

Abstract

We present a flip-flop dual-component model to treat quantum dynamics of relativistic particles with a rest mass and investigate the matter waves' phase and amplitude modulations due to Heisenberg's uncertainty principle. Their matter waves behave like a traveling Gaussian-shaped wave packet accompanied by a guiding pilot wave, and the phase modulations result in mass oscillations. These effects are more prominent for light-weighted elementary particles, such as neutrinos and electrons. This mechanism is solely due to the uncertainty principle and has nothing to do with the flavor-mixing of neutrinos. Simulations using neutrinos and electrons are presented, which indicate an oscillation period on the order of ps. This study primarily focuses on the predicted mass oscillations induced by the uncertainty principle. A slit-type interference experiment using neutrinos and electrons from reactors is proposed to test the predicted behaviors.

DOI
10.1038/s41598-022-19344-9

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We present a flip-flop dual-component model to treat quantum dynamics of relativistic particles with a rest mass and investigate the matter waves' phase and amplitude modulations due to Heisenberg's uncertainty principle. Their matter waves behave like a traveling Gaussian-shaped wave packet accompanied by a guiding pilot wave, and the phase modulations result in mass oscillations. These effects are more prominent for light-weighted elementary particles, such as neutrinos and electrons. This mechanism is solely due to the uncertainty principle and has nothing to do with the flavor-mixing of neutrinos. Simulations using neutrinos and electrons are presented, which indicate an oscillation period on the order of ps. This study primarily focuses on the predicted mass oscillations induced by the uncertainty principle. A slit-type interference experiment using neutrinos and electrons from reactors is proposed to test the predicted behaviors.
When neutrinos propagate over long distances, the mass eigenstate components of a flavor eigenstate will become spatially separated due to their different group velocities. This can happen over terrestrial distance scales if the neutrino energy is of order MeV and if the neutrino is localized (in a quantum mechanical sense) to subatomic scales. For example, if the Heisenberg uncertainty in the neutrino position is below 0.01 Angstrom, neutrino decoherence can be observed in reactor neutrinos using a large liquid scintillator detector.
The problem of particle oscillation is considered in a pedagogical and comprehensive way. Examples from K, B and neutrino physics are given. Conceptual difficulties of the traditional approach to particle oscillation are discussed. It is shown how the probability current density and the wave packet treatments of particle oscillations resolve some problems. It is also shown that only full field theoretical approach is free from conceptual difficulties. The possibility of oscillation of particles produced together with kaons or neutrinos is considered in full wave packet quantum mechanics language. Precise definition of the oscillation of particles which recoil against mixed states is given. The general amplitude which describes the oscillation of two particles in the final states is found. Using this EPR-type amplitude the problem of oscillation of particles recoiling against kaons or neutrinos is resolved. The relativistic EPR correlations on distances of the order of coherence lengths are considered.
The phase velocity is discussed using de Broglie relations and Schrödinger equation. We argue that in non-relativistic quantum mechanics the Hamiltonian should be added by a rest-energy term when Schrödinger equation is used to study the interference between particles of different masses. From neutrino oscillation experiments, we find that the phase velocity can be related to a measurable quantity (the flavor transition probability), therefore, the phase factor originated from the rest energy can’t be omitted. Correspondingly, the energy in de Broglie relations should always be total energy rather than kinetic energy, contrary to some textbooks of quantum mechanics.
The deterministic origin of quantum mechanics remains one of the most enduring challenges in modern physics. While standard quantum theory provides a probabilistic framework for elementary particles, its underlying physical mechanism is often considered non-classical. Here we show that central features of quantum phenomena can emerge from a classical electrodynamic model where particles are treated as tightly bound composites of oscillating charge distributions. These internal oscillations transform the particle into a Hertzian dipole that emits high-frequency, coherent, classical electromagnetic waves. We demonstrate that these waves, when reflected by surrounding matter, generate ponderomotive fields that act back on the particle’s trajectory. Our simulations of electron trajectories in atomic configurations reproduce the interference and diffraction patterns characteristic of double-slit experiments, realizing a pilot-wave-like dynamics reminiscent of de Broglie’s double-solution theory. These findings suggest that wave-particle duality, the measurement problem, and the uncertainty principle may not be irreducible quantum axioms, but rather emergent properties of deterministic, classical interactions between matter and high-frequency electromagnetic fields.
Until Heisenberg proposed the uncertainty principle in 1927, it was an open question whether models for the structure of matter reflected actual reality or were useful fictions for operational purposes. There wasn’t any sense in either case that there might be parameters it was impossible to determine. The uncertainty principle says that it is impossible to determine simultaneously the location and momentum of an electron. While it applies to a specific situation, ‘uncertainty’ is a good description for the entire approach of quantum theory. Schrödinger’s equations show that electrons behave simultaneously as waves and particles. The double-slit experiment, when a beam of light or electrons passes through two parallel slits, shows that the act of observation influences the behavior of the wave–particle duality. The ability of a pair of ‘entangled’ electrons (or other particles) to influence each other instantaneously appears to exceed the speed limit of light. Paradoxes of quantum behavior may even extend to biological situations. Intuition or common sense are no guide to quantum behavior.
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.