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arXiv:2502.06859 · Foundations

Stochastic Interpretation of Quantum Mechanics Assuming That Vacuum Fields Are Real

Emilio Santos

Published May 4, 2022• 10 citations
arXivHTMLPDF

Abstract

We characterize the electromagnetic vacuum as a stochastic field. Some consequences, like the particle behaviour of light, are studied. The stochastic approach is connected with the standard Hilbert space formalism via the Weyl transform. Several experiments involving spontaneous parametric down conversion are studied comparing Hilbert space and Weyl–Wigner formalisms. This allows an intuitive picture of entanglement to be obtained as a correlation between field fluctuations in distant places, involving the vacuum fields. The analysis shows that the Bell definition of local realism is not general enough, whence the reported violation of Bell inequalities does not refute local realism.

DOI
10.3390/foundations2020028

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We characterize the electromagnetic vacuum as a stochastic field. Some consequences, like the particle behaviour of light, are studied. The stochastic approach is connected with the standard Hilbert space formalism via the Weyl transform. Several experiments involving spontaneous parametric down conversion are studied comparing Hilbert space and Weyl–Wigner formalisms. This allows an intuitive picture of entanglement to be obtained as a correlation between field fluctuations in distant places, involving the vacuum fields. The analysis shows that the Bell definition of local realism is not general enough, whence the reported violation of Bell inequalities does not refute local realism.
Abstract I revisit the Wigner (or Weyl–Wigner, WW) representation of the quantum electromagnetic field. I show that, assuming that Fock states are just mathematical concepts devoid of physical reality, WW suggests a realistic interpretation which turns out to be (classical) Maxwell theory with the assumption that there is a random radiation filling space, the vacuum field. I elucidate why, in sharp contrast, non-relativistic quantum mechanics of particles does not admit a realistic interpretation via WW. I interpret experiments involving entangled light beams within WW, in particular optical tests of Bell inequalities. I show that WW provides clues in order to construct local models for those experiments. I give arguments why Bell definition of local realism is not general enough.
The quantum electromagnetic (EM) field is formulated in the Weyl–Wigner representation (WW), which is equivalent to the standard Hilbert space one (HS). In principle, it is possible to interpret within WW all experiments involving the EM field interacting with macroscopic bodies, the latter treated classically. In the WW formalism, the essential difference between classical electrodynamics and the quantum theory of the EM field is just the assumption that there is a random EM field-filling space, i.e., the existence of a zero-point field with a Gaussian distribution for the field amplitudes. I analyze a typical optical test of a Bell inequality. The model admits an interpretation compatible with local realism, modulo a number of assumptions assumed plausible.
I contend that physics should provide a coherent account of reality, in addition to being an efficient algorithm for the prediction of empirical results. This article offers pictures of reality derived from theories of modern physics. In particular, it is shown that Bose quantum fields may be interpreted as pure wave fields via the Weyl–Wigner representation, the most relevant result being the existence of a stochastic vacuum field corresponding to the quantum vacuum fluctuations of the standard, canonical, formulation of field theory. That field provides explanations for the particle (photons) behavior of the electromagnetic field. Also, a realistic interpretation is offered for interference experiments with actual particles, like atoms. The interpretation of classical general relativity is standard but emphasis is given to the principle of equivalence. Problems like spacetime singularities (black holes) and the empirical violation of Bell inequalities are touched on but slightly. Asides from these problems, the main incompleteness of the article is the absence of a realistic interpretation of Fermi fields.
Stochastic optics may be considered as simply a local realistic interpretation of quantum optics and, in this sense, it is a first step in the reinterpretation of the whole of quantum theory. However, as it is not possible to interpret all the details of quantum theory in a local realistic manner, as shown by Bell's theorem, minor changes are introduced in the formalism with the consequence that the new theory makes different predictions in some special cases. In stochastic optics, the quantum-operator formalism is simply considered a formal way of dealing with stochastic fields. In particular, the quantum zero point is taken as a real random electromagnetic radiation filling the whole of space. This radiation noise has the same nature as light signals, the only difference being the greater intensity of the latter. We assume that photon detectors have an intensity threshold just above the level of the noise, thus detecting only signals. Transmission of radiation through polarizers follows Malus's law, but the interplay of signal and noise leads quite naturally to the prediction that the detection probability of some signals is enhanced, which is known to be a necessary condition for the violation of the empirically tested Bell inequalities. In our view, correlated photon pairs are pairs of light signals supercorrelated in polarization, in the sense that, as well as the signal, the accompanying noise is also correlated. Thus stochastic optics allows predictions for the empirical correlations very close, but not identical, to the quantum ones. The theory is applied to the analysis of all experiments designed to test the Bell inequalities by measuring polarization correlations of photon pairs. The predictions agree with quantum optics and experiments within statistical errors, except for the Holt-Pipkin experiment. In this case, the experimental results agree with stochastic optical predictions within two standard deviations while violating quantum optics by four.