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Physical Review A

Locally real states of photons and particles

Stuart Mirell

Published Jan 30, 2002• 4 citations
Publisher

Abstract

A locally real representation is derived from projections in Hilbert space without arbitrary constants. The inherent enhancement property of the resultant states removes restriction by Bell's theorem. Exact agreement with quantum mechanics is demonstrated by explicit calculations of photon transmission in Malus's law, joint detection probability for correlated photons, spin $\frac{1}{2}$ particle transmission through successive Stern-Gerlach analyzers, and joint detection probability for correlated spin $\frac{1}{2}$ particles. The representation is experimentally testable with respect to quantum mechanics.

DOI
10.1103/physreva.65.032102

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Physical Review A•Jun 1, 1989•33 citations
A locally real representation is derived from projections in Hilbert space without arbitrary constants. The inherent enhancement property of the resultant states removes restriction by Bell's theorem. Exact agreement with quantum mechanics is demonstrated by explicit calculations of photon transmission in Malus's law, joint detection probability for correlated photons, spin 12\frac{1}{2}21​ particle transmission through successive Stern-Gerlach analyzers, and joint detection probability for correlated spin 12\frac{1}{2}21​ particles. The representation is experimentally testable with respect to quantum mechanics.
A locally real representation of quantum mechanics deduced from the underlying quantum formalism is presented here. The representation is based upon Mirell's local hidden variable theory, an LHVT, [doi: 10.1103/PhysRevA.65.032102] that provides correlations in agreement with reported Bell experiments. Conversely, the non-local phenomenon of entanglement is necessarily invoked by the Copenhagen Interpretation of that formalism for those reported experiments by maintaining that the formalism is complete. Although a broad class of LHVT's has been disproven by Bell's inequality, Mirell's LHVT is identifiable as a special exempted case by its inherent inclusion of the property of enhancement. Clauser and Horne [doi: 10.1103/PhysRevD.10526] showed that LHVT's with the property of enhancement are not testable by Bell's inequality. In order to address that lack of testability, the representation presented here substantially expands on Mirell's earlier LHVT by self-consistently demonstrating locally real photon state transits of common loop configurations, transits that necessarily invoke non-local superposition under the Copenhagen Interpretation of the quantum formalism. We then analyze those locally real transits and deduce methods to re-engineer the loop configurations to achieve selected output state distributions and show that these re-engineered configurations are predicted by the present representation to yield novel distributions of locally real states. Conversely, the Copenhagen Interpretation predicts corresponding output distributions for these re-engineered configurations that are unremarkable. Those mutually disparate output distributions provide the experimentally testable basis for definitively falsifying either the present locally real representation or the completeness of the original quantum formalism as postulated under the Copenhagen Interpretation.
Agreement with quantum theory and experiment exists for locally real models violating the apparently plausible additional assumptions of Bell inequalities subject to the use of low-efficiency detectors. A locally real optical hidden-variable model of this class is constructed here with asymmetric correlated photon pairs from the physical basis of Malus's law. The model introduces no arbitrary constants, naturally violates factorization and no enhancement, predicts a 1/3cos2{3\mathrm{c}\mathrm{o}\mathrm{s}}^{2}3cos2\ensuremath{\theta} joint probability for high-efficiency detectors, and is testable with currently available low-efficiency detectors.
Published experimental results and analytic developments indicate the possibility of achieving stronger correlations of physical events with independent photons rather than with entangled ones. The probability of coincident detections of quantum events should not be confused with the correlation of mixed states. The theoretical requirements for implementing the quantum nonlocality theory are not present in the experimental configurations purporting to prove Bohr’s or Bell’s nonlocality because of the quantum Rayleigh scattering of single photons. By means of a normalization factor corresponding to the total number of initiated events, the detection probabilities obtained experimentally are too small to enable any violation of a Bell inequality. Correlations between independent states of qubits can easily outperform those calculated with entangled photons. Additionally, the quantum joint probability for a Bell state can be factorized enabling a local detection of the alleged quantum nonlocality, if it existed
This paper aims at reproducing quantum mechanical (QM) spin and spin entanglement results using a realist, stochastic, and local approach, without the standard QM mathematical formulation. The concrete model proposed includes the description of Stern–Gerlach apparatuses and of Bell test experiments. Single particle trajectories are explicitly evaluated as a function of a few stochastic variables that they assumedly carry on. QM predictions are retrieved as probability distributions of similarly-prepared ensembles of particles. Notably, it is shown that the proposed model, despite being both local and realist, is able to violate the Bell–CHSH inequalities by exploiting the coincidence loophole and thus intrinsically renouncing to one of the Bell’s assumptions.
Published experimental results and analytic developments indicate the possibility of achieving stronger correlations of physical events with independent photons rather than with entangled ones. The probability of coincident detections of quantum events should not be confused with the correlation of mixed states. The theoretical requirements for implementing the quantum nonlocality theory are not present in the experimental configurations purporting to prove Bohr's or Bell's nonlocality because of the quantum Rayleigh scattering of single photons. By means of a normalization factor corresponding to the total number of initiated events, the detection probabilities obtained experimentally are too small to enable any violation of a Bell inequality. Correlations between independent states of qubits can easily outperform those calculated with entangled photons. Additionally, the quantum joint probability for a Bell state can be factorized enabling a local detection of the alleged quantum nonlocality, if it existed.
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.