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arXiv:quant-ph/0108141

Numerical simulation of Einstein-Podolsky-Rosen experiments in a local hidden variables model

Werner A. Hofer

Published Aug 31, 2001• 2 citations
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Abstract

We simulate correlation measurements of entangled photons numerically. The model employed is strictly local. In our model correlations arise from a phase, connecting the electromagnetic fields of the two photons at their separate points of measurement. We sum up coincidences for each pair individually and model the operation of a polarizer beam splitter numerically. The results thus obtained differ substantially from the classical results. In addition, we analyze the effects of decoherence and non-ideal beam splitters. It is shown that under realistic experimental conditions the Bell inequalities are violated by more than 30 standard deviations.

DOI
10.48550/arxiv.quant-ph/0108141

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We simulate correlation measurements of entangled photons numerically. The model employed is strictly local. In our model correlations arise from a phase, connecting the electromagnetic fields of the two photons at their separate points of measurement. We sum up coincidences for each pair individually and model the operation of a polarizer beam splitter numerically. The results thus obtained differ substantially from the classical results. In addition, we analyze the effects of decoherence and non-ideal beam splitters. It is shown that under realistic experimental conditions the Bell inequalities are violated by more than 30 standard deviations.
We simulate correlation measurements of entangled photons numerically. The model employed is strictly local. The correlation is determined by its classical expression with one decisive difference: we sum up coincidences for each pair individually. We analyze the effects of decoherence, detector efficiency and polarizer thresholds in detail. The Bell inequalities are violated in these simulations. The violation depends crucially on the threshold of the polarizer switches and can reach a value of 2.0 in the limiting case. Existing experiments can be fully accounted for by limited coherence and non-ideal detector switches. It seems thus safe to conclude that the Bell inequalities are no suitable criterium to decide on the nonlocality issue.
The violation of Bell's inequalities in Einstein-Podolsky-Rosen experiments has been demonstrated for photons and ions. In all experiments of this kind the relation between visibility, efficiency, and Bell violation is generally unknown. In this paper we show that simulations based on a local hidden variables models for entangled photons provide this information. It is established that these properties are closely related by the way, in which photons are detected after a polarizer beam splitter. On this basis we suggest controlled experiments which, for the first time, subject the superposition principle to experimental tests.
Conventionally, one interprets the correlations observed in Einstein-Podolsky-Rosen experiments by Bell's inequalities and quantum nonlocality. We show, in this paper, that identical correlations arise, if the phase relations of electromagnetic fields are considered. In particular, we proceed from an analysis of a one-photon model. The correlation probability in this case contains a phase relation cos(b - a) between the two settings. In the two photon model the phases of the photon's electromagnetic fields are related at the origin. It is shown that this relation can be translated into a linearity requirement for electromagnetic fields between the two polarizers. Along these lines we compute the correlation integral with an expression conserving linearity. This expression, as shown, correctly describes the measured values. It seems thus that quantum nonlocality can be seen as a combination of boundary conditions on possible electromagnetic fields between the polarizers and a relation of the electromagnetic fields of the two photons via a phase. We expect the same feature to arise in every experiment, where joint probabilities of separate polarization measurements are determined.
The purpose of this article is to show that the introduction of hidden variables to describe individual events is fully consistent with the statistical predictions of quantum theory. We illustrate the validity of this assertion by discussing two fundamental experiments on correlated photons which are believed to behave ``violently non-classical''. Our considerations carry over to correlated pairs of neutral particles of spin one-half in a singlet state. Much in the spirit of Einstein's conviction we come to the conclusion that the state vector of a system does not provide an exhaustive description of the individual physical system. We also briefly discuss an experiment on ``quantum teleportation'' and demonstrate that our completely local approach leads to a full understanding of the experiment indicating the absence of any teleportation phenomenon. We caution that the indiscriminated use of the term ``Quantum Theory'' tends to obscure distinct differences between the quantum mechanics of massive particles and the propagation of photons. It is emphasized that the properties of polarizers, beam splitters, halfwave plates etc. used in photon-correlation experiments are defined by the laws of classical optics. Hence, understanding the outcome of those experiments requires a well-founded interconnection between classical and quantum electrodynamics free from unnecessary hypotheses.
In a series of experiments performed by Mandel and co-workers, nonclassical effects have been demonstrated in the interference of two photons generated in a process of parametric down-conversion. The nonclassical effects in the two-photon interference effects can be discussed in the framework of two different descriptions. In the first description, a stochastic theory of electromagnetic field fluctuations can be used in order to calculate the interference pattern. In the second description, a theory of hidden-variable fluctuations can be applied in order to calculate correlations of the interference pattern. A stochastic theory leads to statistical inequalities for the light intensities, while a local hidden-variable theory leads to Bell's inequalities. Using the Schwinger-boson representation of the angular momentum, we show that the two-photon interference effects can be described in terms of spin-correlated states. In particular, we show that the action of a beam splitter on the photons in a parametric down-conversion is equivalent to the production of an entangled state that is very similar to the well-known Einstein, Podolsky, and Rosen spin-singlet state. We show that the stochastic theory of two-photon fluctuations is not equivalent to a hidden-variable theory of photon correlations. We establish a range for which the stochastic theory fails but the hidden-variable theory is still possible. We compare our theoretical predictions with the experimental results and conclude that a violation of the stochastic theory has been clearly observed, while the violation of the hidden-variable theory is less pronounced.
This work develops a deterministic, field-based reformulation of quantum mechanics in which entanglement arises naturally from correlated hidden variables, directly realizing Einstein’s prediction. Fermions are modeled as coupled real fields whose internal oscillatory phases provide a physical ontology for spin, interference, and charge. The model yields the standard −cosθ correlation law in the uniform-phase limit, while predicting a small deterministic correction C( θ )=−cosθ+ε sin 2 θ with ε≈0.06 . This deviation is benchmarked against historic and modern Bell tests, showing it is not excluded but lies within the sensitivity of angle-resolved experiments. Thus, the work provides a realist, experimentally testable account of entanglement, aligning with Einstein’s vision of hidden variables. Experimental deviation between the quantum mechanics model to our real coupled-fields model is expected to be of order ε=0.06 . The model provides unique experimental predictions—a finite offset at symmetry points (e.g. Δ = 45˚) not explained by noise or reduced visibility. This work examines the violation of Bell’s inequality through the lens of the Coupled-Fields model. While standard quantum mechanics attributes these results to nonlocal entanglement, the Coupled-Fields framework reproduces the same correlations through deterministic, local interactions between the internal variables of the coupled strings. Each fermion pair shares an intrinsic phase relationship established at creation, which governs measurement outcomes without requiring instantaneous influence. Statistical violation of Bell’s inequality thus reflects the geometry of internal field orientations rather than true nonlocality. This analysis reconciles experimental data with physical realism, demonstrating that local hidden variables—when properly defined within the coupled-fields structure—can reproduce the full quantum correlation pattern. Our conclusion is that Einstein (EPR) [1] was right. Internal phase is the hidden variable.