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arXiv:quant-ph/0609062

Hidden variables or hidden theories?

A. Feoli

Published Sep 8, 2006• 0 citations
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Abstract

We show that a modified Relativity Principle could explain in a "classical" way the strange correlations of entangled photons. We propose a gedanken experiment with balls and boxes that predicts the same distribution of probability of the Quantum Mechanics in the case of the EPR experiment with a pair of entangled photons meeting a pair of polarizers. In the light of this gedanken experiment, we find an alternative description of the real EPR experiment postulating the existence of two observers (one for each polarizer) embedded in two locally anisotropic spacetimes. In our model there is no need to invoke quantum non separability or instantaneous action at distance.

DOI
10.48550/arxiv.quant-ph/0609062

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We show that a modified Relativity Principle could explain in a "classical" way the strange correlations of entangled photons. We propose a gedanken experiment with balls and boxes that predicts the same distribution of probability of the Quantum Mechanics in the case of the EPR experiment with a pair of entangled photons meeting a pair of polarizers. In the light of this gedanken experiment, we find an alternative description of the real EPR experiment postulating the existence of two observers (one for each polarizer) embedded in two locally anisotropic spacetimes. In our model there is no need to invoke quantum non separability or instantaneous action at distance.
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A critical reconsideration of the EPR (Einstein-Podolsky-Rosen) paper shows that the EPR argument can be developed without using the concept of `element of physical reality', thus eliminating any philosophical element in the logical chains of the paper. Deprived of its philosophical ornament, the EPR argument plainly reduces to require what quantum mechanics can not do: to assign definite values to two incompatible physical quantities. Hidden variables theories built up according to Bell - type theorems are formulated on the basis of the assumption that the locality condition implies the statistical independence between two measurements space - like separated. This assumption is valid only with the additional one that statistical dependence between two measurements requires a causal connection between them. This additional assumption rules out the possibility that statistical dependence may due to an intrinsic property of the physical system under study. Therefore, hidden variables theories are built up with a restriction which leads them to be disproved by experiment. Quantum mechanical non - locality, invoked for describing EPR - type experiments, is strictly connected to the hypothesis (NDV hypothesis) according to which the twin photons of entangled pairs do not have a definite polarization before measurements. Both hypotheses are used only for describing EPR experiments and not for making predictions. Therefore, they can be dropped without reducing the predictive power of quantum mechanics concerning entangled photons pairs. Furthermore, both hypotheses can be experimentally tested by a modification of a standard experimental apparatus designed for studying entangled photons pairs.
In derivating of Bell’s inequalities, the probability distribution is supposed to be a function only of a hidden variable. We point out that the true implication of the probability distribution of Bell’s correlation function is the distribution of joint measurement outcomes on the two sides. It is therefore a function of both the hidden variable and the settings. In this case, Bell’s inequalities fail. Our further analysis shows that Bell’s locality holds neither for dependent events nor for independent events. We think that the measurements of EPR pairs are dependent events, and hence violation of Bell’s inequalities cannot rule out the existence of local hidden variable. To explain the results of EPR-type experiments, we suppose that a polarization-entangled photon pair can be composed of two circularly or linearly polarized photons with correlated hidden variables, and a couple of experiments of quantum measurement are proposed. The first uses delayed measurement on one photon of the EPR pair to demonstrate directly whether measurement on the other could have any nonlocal influence on it. Then several experiments are suggested to reveal the components of the polarization-entangled photon pair. The last one uses successive polarization measurements on a pair of EPR photons to show that two photons with the same quantum state behave the same under the same measuring conditions.
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.
The EPR-Bohm experiment is studied in a classical model with hidden variables. The main hypothesis of Bell about this experiment must be modified in a non-trivial way to allow for the fact that our model is non-linear and so non fully deterministic. With our classical model, we then arrive at the same angular behaviour than the one that is predicted by Quantum Mechanics for the correlated measurement of spin projections on the polarizer axis. If the spin-spin interaction predicted by our particle model, or more precisely in the present case, the spin-polarizer field axis interaction, is not able to align the spin axis with the polarizer axis, then our classical result differs by a factor 3 from the quantum mechanical result. It is surprising to find that the angular behaviour is easier to reproduce by a classical model than the amount of probability. Naively, one would have expected the reverse.
EPR correlations exist and can be observed independently of any a priori given frame of reference. We can even construct a frame of reference that is based on these correlations. This observation-based frame of reference is equivalent to the customary a priori given frame of reference of the laboratory when describing real EPR experiments. J.S. Bell has argued that local hidden parameter theories that reproduce the predictions of Quantum Mechanics cannot exist, but the counterfactual reasoning leading to Bell's conclusion is physically meaningless if the frame of reference that is based on EPR-correlations is accepted as the backdrop for EPR-type experiments. The refutal of Bell's proof opens up for the construction of a viable hidden parameter theory. A model of a spin h/2 particle in terms of a non-flat metric of space-time is shown to be able to reproduce the predictions of quantum mechanics in the Bohm-Aharonov version of the EPR experiment, without introducing non-locality.