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A Testable Locally Real Representation of Quantum Mechanics in Agreement with Performed Experiments

Stuart Mirell, Daniel Mirell

Published Aug 24, 2025• 0 citations

Abstract

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.

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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.

Locally real states of electromagnetic radiation derived from the underlying quantum mechanical formalism are shown to provide an alternative basis for definite polarized states of the widely accepted probabilistic interpretation. The locally real states traverse common loop configurations without invoking non-local superposition. Correlated photon pairs represented by the locally real states are consistent with the underlying quantum mechanical formalism independent of Bell's inequality and without invoking entanglement. Replacement of interdependent non-local probabilistic states with the locally real states yields independence of those states. A novel loop configuration provides differential testability of the representation of the locally real states relative to the probabilistic interpretation with the prediction of a unique polarization state.

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.

Bell's inequalities(1964) provides a quantitative criterion to test the local hidden variable theory(LHVT) versus quantum mechanics(QM).For the first time,it leads to the possibility to experimentally distinguish LHVT and QM.So far,there have been tens of experiments ever since the first experiment by Clauser et al(1972).An overwhelming majority of these experiments are in good agreement with the predictions of QM yet violate those of LHVT.Some loopholes in these experiments are discussed in Section I,followed by a respective summary to 12 experiments between 1972 to 1982 and 31 experiments from 1985 and on in Sections II and III.It is finally pointed out that so far there is not a single experiment to close both the locality loophole and the detection loophole at the same time,but the experimental outcomes are irreversible.Accordingly,theoretical physicists must admit that the present physics foundation is broken,i.e.quantum mechanics is contradiction with special relativity.

Recent experiments of Gröblacher et al proved the violation of a Leggett-type inequality that was claimed to be valid for a broad class of non-local hidden-variable theories. The impossibility of constructing a non-local and realistic theory, unless it entails highly counterintuitive features, seems thus to have been experimentally proved. This would bring us close to a definite refutation of realism. Indeed, realism was proved to be also incompatible with locality, according to a series of experiments testing Bell inequalities. The present paper addresses the said experiments of Gröblacher et al and presents an explicit, contextual and realistic, model that reproduces the predictions of quantum mechanics. It thus violates the Leggett-type inequality that was established with the aim of ruling out a supposedly broad class of non-local models. We can thus conclude that plausible contextual, realistic, models are still tenable. This restates the possibility of a future completion of quantum mechanics by a realistic and contextual theory which is not in a class containing only highly counterintuitive models. The class that was ruled out by the experiments of Gröblacher et al is thus proved to be a limited one, arbitrarily separating models that physically belong in the same class.

Bell's theorem, and inequalities that stem from it, address the conflict between the explanation of key experimental observations by quantum mechanics (QM) and by models expressing Locally Realistic (LR) properties, regardless of their inclusion or exclusion of hidden variables. To demonstrate the conflict between experimental results described by QM and LR models, a physical realization of the quantum state must be chosen. Entangled photons or electrons provide the most viable choices. In this work we consider a simplified version of a Bell inequality (BI) that focuses entirely on the physical state properties of photons in order to demonstrate the difference between QM and LR correlations. While the experiment we propose is in principle similar in intent to prior Bell inequality experiments, our version requires fewer measurements, and is more advantageous in its conceptual clarity.

EPR showed that two particles emitted from a source can be entangled by a shared wavefunction where two non-commuting observables (position, momentum) can be simultaneously real, leading to a contradiction with quantum mechanics (two non-commuting variables can not be simultaneously real). John Bell derived an inequality where any local hidden variables prediction is bounded and quantum mechanics can violate the inequality. Bell tests on correlated photon pairs showed a clear violation of the Bell inequality and agreement with quantum mechanics. This study revealed that the Bell inequality holds at any individual instances in a given system but it does not hold over the entire population. The Bell inequality is not an incompatibility criterion for local hidden variables vs quantum mechanics rather it is a criterion for an individual nature vs population dynamics. The nonlocality prediction given by wavefunction is a system approximation and local causality (photon polarization) provides a complete description of the Bell tests. The paper concludes with great satisfaction that the measurement of two correlated photons at a distance was a local cause (photon-filter interaction did not violate the special theory of relativity).