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Quantum Entangled Photons are Synchronized Waves

Michael Macdonald

Published Oct 12, 2026• 0 citations
Publisher

Abstract

This letter challenges the standard interpretation of Bell test results, which has been used to argue for the abandonment of local realism. We demonstrate that the quantum-mechanical correlation Pc (θ) = cos2 (θ) and the classical Malus' Law result Pc (θ) = 1/2 cos2 (θ) + 1/4 are not contradictory but are complementary descriptions of two distinct source preparations. By modeling light as a real transverse electromagnetic wave, we identify the initial phase orientation of the wavefront as a local hidden variable. Stochastic (randomly prepared) photon sources produce four equally likely phase combinations, yielding the full Malus' Law distribution. Correlated sources, however, are physically constrained to produce only the synchronized subset of these combinations, yielding the cos2 (θ) correlation. We argue that standard Bell test analysis conflates these distinct populations and violates the Fair Sampling Assumption, rendering Bell's inequality inapplicable to the aggregated data. The observed "quantum" correlation is therefore the signature of a correlated source producing pre-synchronized wavefronts, not evidence of non-local communication. We conclude that local realism remains a viable, classical framework for describing these phenomena.

DOI
10.5281/zenodo.23322387

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This letter challenges the standard interpretation of Bell test results, which has been used to argue for the abandonment of local realism. We demonstrate that the quantum-mechanical correlation Pc (θ) = cos2 (θ) and the classical Malus' Law result Pc (θ) = 1/2 cos2 (θ) + 1/4 are not contradictory but are complementary descriptions of two distinct source preparations. By modeling light as a real transverse electromagnetic wave, we identify the initial phase orientation of the wavefront as a local hidden variable. Stochastic (randomly prepared) photon sources produce four equally likely phase combinations, yielding the full Malus' Law distribution. Correlated sources, however, are physically constrained to produce only the synchronized subset of these combinations, yielding the cos2 (θ) correlation. We argue that standard Bell test analysis conflates these distinct populations and violates the Fair Sampling Assumption, rendering Bell's inequality inapplicable to the aggregated data. The observed "quantum" correlation is therefore the signature of a correlated source producing pre-synchronized wavefronts, not evidence of non-local communication. We conclude that local realism remains a viable, classical framework for describing these phenomena.
Conventional tests of Bell’s inequality rely on entangled photon pairs. Here, we replace entangled pairs with two independent photons of orthogonal polarization, and demonstrate that Bell’s inequality is still violated. Given the inherent local realism of independent photons, this experiment proves that Bell’s inequality cannot falsify the local realism of photons. We thus conjecture that the violation of Bell’s inequality by entangled photon pairs originates from their orthogonal polarizations, rather than the breakdown of local realism. To interpret this unexpected violation with independent photons, we further substitute the two photons with two monochromatic light beams, and calculate the transmittance correlation through polarizers via Malus’s law and Karl Pearson’s correlation formula. We show that this correlation also defies Bell’s inequality. Retracing the derivation of Bell’s inequality reveals its validity is restricted to binary events, which accounts for the observed violation with light beams. Finally, we propose a thought experiment involving gradual attenuation of light intensity down to the single-photon regime, and hypothesize that single-photon transmission through a polarizer does not constitute a binary event. This hypothesis provides a unified interpretation for both our experimental findings and all canonical Bell inequality tests reported to date.
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.
Since John Bell has established his famous inequality and several independent experiments have confirmed the distinct polarization correlation of entangled photons predicted by quantum mechanics it is evident that quantum mechanics cannot be explained by local realistic theories. Actually, the observed polarization correlation can be deduced from wave optical considerations. The correlation has its origin in the phase coupling of the two circularly polarized wave packets leaving the photon source simultaneously. The experimental results violate Bell's inequality although no non-local interactions have to be assumed. In consequence the principle of locality remains valid in the scope of quantum mechanics. However, the principle of realism has to be replaced by the less stringent principle of contextuality.
Abstract This paper proposes a local-deterministic completion of quantum entanglement by identifying the instantaneous phase of rotating electric field vectors as the primary hidden variable. We demonstrate that the observed violation of the Bell-CHSH inequality is not a signature of non-locality, but a natural consequence of the Intensity-Phase doubling mechanism inherent in Maxwellian electrodynamics. Through analytical derivation and discrete-time numerical integration, it proves that the correlation of synchronized transverse waves—governed by the quadratic nature of Malus’s Law \(\:\left(\varvec{I}\:\propto\:\:{\varvec{E}}^{2}\right)\)—generates the exact quantum correlation function  E(Δ θ )=  Cos(2Δ θ )\:E\left(\varDelta\:\theta\:\right)=\:\:Cos(2\varDelta\:\theta\:)E(Δθ)=Cos(2Δθ). We resolve the long-standing discrepancy regarding measurement angles by showing that the maximum violation of the CHSH inequality  (S=22)\:(S=2\sqrt{2})(S=22​) occurs at a physical polarizer setting of  22.5∘ \:22.5^\circ\:22.5∘, which corresponds to a  45∘ \:45^\circ\:45∘, shift in the internal field phase . By distinguishing between mechanical rotation and field-space geometry, this model saturates the Tsirelson bound while strictly maintaining Einsteinian locality and causality. This framework suggests that the "spooky action" of entanglement is a manifestation of temporal phase-locking between the source and the detector, providing a fully realistic and Maxwellian interpretation of Bell-type statistics.
This work proposes a new perspective on quantum correlations by showing that Bell inequality violations can emerge from a probabilistic equilibrium principle. The framework demonstrates that quantum-like correlations arise from two basic conditions: balanced marginals (P(A=+) = P(B=+) = 0.5) and statistical identity (identical particle responses to measurements). offering a local realistic interpretation of phenomena like EPR correlations and double-slit interference. Key aspects of this work: • New derivation: We derive the quantum correlation E(θ) = cos(2θ) from classical probabilistic foundations, showing how Malus' law naturally leads to Bell violations under probabilistic equilibrium. • Theoretical framework: We propose that Bell violations indicate statistical identity between particles rather than non-locality, offering an alternative to conventional interpretations. • Experimental alignment: The theoretical predictions show consistency with recent experiments and suggest new testable configurations through marginal bias studies. • Broader implications: This approach provides a geometric-probabilistic foundation for quantum phenomena while maintaining locality and realism. The manuscript presents what I believe is a meaningful contribution to understanding quantum foundations, with specific testable predictions .
Malus’s law and the correlations of Bell-type experiments yield the same curve, the squared cosine of the angular offset between two polarizers. We propose a reinterpretation of both phenomena through a single mechanism: the correlation of responses at two points a and b, in series for Malus on a single photon, in parallel for Bell on two identical photons. No other situation is analyzed. The proposed resolution is strictly local, and reassigns cos²(a−b), observed in both cases, as the universal angular ratio of photons. The two experiments thus bring this correlation to light not because paired or polarized photons carry it, but because they make an otherwise invisible correlation testable. Bell’s theorem does not apply to this proposal, because cos²(a−b) is no longer read as the statistics of the responses at a and at b taken separately, but as the statistics of the responses at a and b taken jointly, independently of every other point. In other words, the cos² distribution of responses around an angle a holds only in association with the considered response at a, and does not constrain what the individual statistics of the response at b must be when the response at a is unknown. The article concludes that a strictly local explanation of Bell is possible again, and offers a falsifiable prediction: if identity sharing exists, understanding what it consists of will make it possible to produce identical photons without a common source.