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arXiv:quant-ph/0006005

Information transfer via the phase: A local model of Einstein-Podolksy-Rosen experiments

Werner A. Hofer

Published Jun 1, 2000• 1 citation
arXivHTMLPDF

Abstract

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.

DOI
10.48550/arxiv.quant-ph/0006005

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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 conventional interpretation of EPR-type experiments is based on Bell's inequalities and quantum nonlocality. In contrast, the model presented is strictly local. It is based on the analysis of consecutive polarization measurements. We show that the mathematical representation of these experiments contains a phase relation cos(b - a), connecting the two separate events conceptually. This feature of consecutive measurements, related to the phase of the photon's electromagnetic field, is at the bottom of the commonly assumed quantum nonlocality. We expect it to arise in every experiment, where joint probabilities of polarization measurements are determined.
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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 examine the properties and behavior of the original Einstein-Podolsky-Rosen (EPR) wave function [Phys. Rev. 47, 777 (1935)] and related Gaussian-correlated wave functions. We assess the degree of entanglement of these wave functions and consider an argument of Bell [Ann. (N.Y.) Acad. Sci. 480, 263 (1986)] based on the Wigner phase-space distribution [Phys. Rev. 40, 749 (1932)], which implies that the original EPR correlations can accommodate a local hidden-variable description. We extend Bell's analysis to the related Gaussian wave functions. We then show that it is possible to identify definite nonlocal aspects for the original EPR state and related states. We describe possible experiments that would demonstrate these nonlocal features through violations of Bell inequalities. The implications of our results, and in particular their relevance for the causal interpretation of quantum mechanics, are considered.
So far no mechanism is known, which could connect the two measurements in a Bell-type experiment with a speed beyond the speed of light, commonly considered the ultimate limit of propagation of any field-like interaction. Here, we suggest such a mechanism, based on the phase of a photon field during its propagation. We show that two measurements, corresponding to two independent rotations of the fields, are connected, even if no signal passes from one point of measurement to the other. The non-local connection of a photon pair is the result of its origin at a common source, where the two fields acquire a well defined phase difference. Therefore, it is not actually a non-local effect in any conventional sense.
Recent experiments on the classic Einstein-Podolsky-Rosen (EPR) setting claim to test the compatibility between nonlocal quantum entanglement and the (special) theory of relativity. Confirmation of quantum theory has led to the interpretation that Einstein's image of physical reality for each photon in the EPR pair cannot be maintained. A detailed critique on two representative experiments is presented following the original EPR notion of local realism. It is argued that relativity does not enter into the picture, however for the Bell-Bohm version of local realism in terms of hidden variables such experiments are significant. Of the two alternatives, namely incompleteness of quantum theory for describing an individual quantum system, and the ensemble view, it is only the former that has been ruled out by the experiments. An alternative approach gives a statistical ensemble interpretation of the observed data, and the significant conclusion that these experiments do not deny physical reality of the photon is obtained. After discussing the need for a photon model, a vortex structure is proposed based on the space-time invariant property-spin, and pure gauge fields. To test the prime role of spin for photons and the angular-momentum interpretation of electromagnetic fields, experimental schemes feasible in modern laboratories are suggested.