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arXiv:quant-ph/0505104

Equations of Motion with Multiple Proper Time: A New Interpretation of Basic Quantum Physics

xiaodong Chen

Published May 15, 2005• 0 citations
arXivHTMLPDF

Abstract

Equations of motion for single particle under two proper time model and three proper time model have been proposed and analyzed. The motions of particle are derived from pure classical method but they exhibit the same properties of quantum physics: the quantum wave equation, de Broglie equations, uncertainty relation, statistical result of quantum wave-function. This shows us a possible new way to interpret quantum physics. We will also prove that physics with multiple proper time does not cause causality problem.

DOI
10.48550/arxiv.quant-ph/0505104

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Equations of motion for single particle under two proper time model and three proper time model have been proposed and analyzed. The motions of particle are derived from pure classical method but they exhibit the same properties of quantum physics: the quantum wave equation, de Broglie equations, uncertainty relation, statistical result of quantum wave-function. This shows us a possible new way to interpret quantum physics. We will also prove that physics with multiple proper time does not cause causality problem.
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An attempt is made to show that it is possible to constnuct a theory of particle systems in accord with the basic ideas of the causal interpretation of wave mechanics by the theory of the double solution. After a discussion of the theory of the individual particle, the de Broglie and Vigier theories on the causal interpretation of the theory of systems are examined. It is then shown that it is possible to reframe the analytical mechanics of systems and, in particular, the Hamilton-Jacobi theory in a space with three dimensions. The question of the form of the basic equations in physical space is discussed in detail. The statistical theory of systems of particles of different nature is explained. (J.S.R.)
Following de Broglie, Bohm, and others, it is assumed that quantum mechanics may be interpreted causally and that the $\ensuremath{\psi}$ function plays the role of a generating function for particle trajectories. By arguing that the $\ensuremath{\psi}$ function should not be interpreted as a probability amplitude, a new method for generating particle trajectories is postulated. The four-momentum of a scalar particle is assumed to be given as the gradient of an unspecified function $F(\ensuremath{\psi})$, where $\ensuremath{\psi}$ is a pure real solution of the Klein-Gordon equation. Since the location of a particle is determined solely by its trajectory, the probability distribution differs from $\ensuremath{\psi}{\ensuremath{\psi}}^{*}$; and therefore, ordinary experimental results differing from the traditional theory may, in principle, be predicted. Particle motion and trajectories are discussed for three examples: a free particle, a particle in a box, and the double slit.
Time-dependent Schroedinger equation represents the basis of any quantum-theoretical approach. The question concerning its proper content in comparison to the classical physics has not been, however, fully answered until now. It will be shown that there is one-to-one physical correspondence between basic solutions (represented always by one Hamiltonian eigenfunction only) and classical ones, as the non-zero quantum potential has not any physical sense, representing only the "numerical" difference between Hamilton principal function and the phase of corresponding wave function in the case of non-inertial motion. Possible interpretation of superposition solutions will be then discussed in the light of this fact. And also different interpretation alternatives of the quantum-mechanical model will be newly analyzed and new attitude to them will be reasoned.
In the de Broglie–Bohm interpretation of quantum mechanics, the momentum of a particle in a box of perfectly reflecting walls is vanishing. On the contrary, the classical physics predicts an oscillatory motion between the walls. The resulting difference between the behavior of a body in classical and quantum regime is unsatisfactory for Einstein and many other scientists. In order to solve the problem, we show that it is possible to obtain a motion of the body using the rules of quantum mechanics. The result holds for the quantum systems described by solutions of the time independent Schrödinger equation that are real functions.