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How virtual particles generate quantum dynamics

de la Torre, Carlos Alberto

Published May 16, 2015• 1 citation
OpenAlex

Abstract

In support of the quantum field theory interpretation of quantum mechanics, stochastic processes with virtual particles whose mean field equations describe quantum dynamics are presented. Two type of virtual particles $A$ and $B$ with an asymmetric interaction such that $A$ rejects (hates) $B$ and $B$ attracts (loves) $A$ have a combined distribution that satisfies Schr\odinger equation. It is also shown how four virtual particles drifting, creating and destroying themselves have a combined distribution that satisfies Dirac equation. Finally, a non-markovian process that generates Klein-Gordon equation is given. However, markovian property is recovered if we postulate reversed causality.

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In support of the quantum field theory interpretation of quantum mechanics, stochastic processes with virtual particles whose mean field equations describe quantum dynamics are presented. Two type of virtual particles AAA and BBB with an asymmetric interaction such that AAA rejects (hates) BBB and BBB attracts (loves) AAA have a combined distribution that satisfies Schr\odinger equation. It is also shown how four virtual particles drifting, creating and destroying themselves have a combined distribution that satisfies Dirac equation. Finally, a non-markovian process that generates Klein-Gordon equation is given. However, markovian property is recovered if we postulate reversed causality.
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.
This paper proposes an interpretation of quantum mechanics, relying on the time-symmetric stochastic dynamics of quantum particles and on non-classical probability theory. Our main purpose is to demonstrate that the wave function and its complex conjugate can be interpreted as complex probability distributions in two complex diffusion equations related to non-real forward and backward in time stochastic motions respectively. We say non-real because Schroedinger forward and backward diffusions describe both reversible (real trajectories) and irreversible trajectories (non-real trajectories). The reversible trajectories are the only real trajectories and are given by the intersection of those forward and backward processes. It turns out that if we translate this intersection using set-theoretic language, we are led to a reversible diffusion described by Born rule probabilities. This proposal is useful also for explaining more about the role of complex numbers in quantum mechanics that produces this so-called "wave-like" nature of quantum reality. Our perspective also challenges the notion of physical superposition and aims at a derivation of superposition principle not based on the linearity of Schroedinger's equation but relying on pure probability theory. Moreover, it is suggested that, embracing the idea of stochastic processes in quantum theory, explains the reasons for the appearance of classical behavior in large objects, in contrast to the quantum behavior of small ones. In other words, we claim that a combination of a probabilistic and no-ontic view (neither epistemic though) of the wave function with a stochastic hidden-variables approach, may provide some insight into the quantum physical reality and potentially establish the groundwork for a novel interpretation of quantum mechanics.
Tracking a real trajectory of a quantum particle still has been treated as the interpretation problem. It shall be expressed by a Brownian (stochastic) motion suggested by E. Nelson, however, the well-defined mechanism of field generation from a stochastic particle hasn't been proposed yet. For the improvement of this, I propose the extension of Nelson's quantum dynamics, for describing a relativistic scalar electron with its radiation equivalent to the Klein-Gordon particle and field system.