Malus's law and the correlations of Bell-type experiments yield the same curve, the squared cosine of the angular gap between two polarizers. We show that they are the same phenomenon. A polarizer is a pair of orthogonal planes: its response is binary, exact on the axis and on the orthogonal, and the reading of a radial quantity by a plane is a projection, a cosine. A correlation between two polarizers is a double event: one projection factor per verdict, hence the square. The photon contributes only one property, x, defined by a single clause: two photons sharing x respond identically at equal angles. Malus tests x in series, on one photon that conserves it. Bell tests it in parallel, on a pair that shares it. No further hypothesis is required. The squared cosine thus belongs to the polarizer, and the correlation of Bell-type experiments receives a purely mechanical explanation. preprint submitted for peer review additional analysis : https://doi.org/10.5281/zenodo.23630357
Malus's law and the correlations of Bell-type experiments yield the same curve, the squared cosine of the angular gap between two polarizers. We show that they are the same phenomenon. A polarizer is a pair of orthogonal planes: its response is binary, exact on the axis and on the orthogonal, and the reading of a radial quantity by a plane is a projection, a cosine. A correlation between two polarizers is a double event: one projection factor per verdict, hence the square. The photon contributes only one property, x, defined by a single clause: two photons sharing x respond identically at equal angles. Malus tests x in series, on one photon that conserves it. Bell tests it in parallel, on a pair that shares it. No further hypothesis is required. The squared cosine thus belongs to the polarizer, and the correlation of Bell-type experiments receives a purely mechanical explanation. preprint submitted for peer review additional analysis : https://doi.org/10.5281/zenodo.23630357
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.
FINDING: Malus's Law — both classical (light polarization) and quantum (spin-1/2) — reduces to a cosine-squared intensity law, with the quantum case requiring a quasi-probability distribution that can go negative, revealing a deep algebraic identity between SU(2) spin projections and classical polarization geometry. | MATH: Classical: I(θ)=I0cos2θ (Malus, 1809). Quantum spin-1/2: for a spin state ∣+⟩n measured along axis m, probability P=cos2(θ/2), where θ is the angle between axes n and m. Equivalently, P=21(1+cosθ)=21(1+n⋅m). The quantum Malus law is formally identical to classical if one uses a Wigner-like quasi-distribution W(θ) that can be negative; the classical case has W(θ)=δ(θ−θ0) (positive). Generalization to spin-j: Pj(θ)=[cos2j(θ/2)] for extreme eigenstates, with intermediate proj Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
This paper examines a local deterministic model of an experiment involving correlated photons. The experimental setup involves a source that emits two linearly polarized photons in each act, two two-channel analyzers, and detectors included in the coincidence scheme. The orientation angle of the photon polarization plane is a random variable with a uniform distribution, and it is the same for simultaneously emitted photons. The model presented here is a generalization of the “naive example of hidden variable theory” described in A. Aspect's article ‘Bell's Theorem: The Naive View of an Experimentalist. In our model, the outcome of the photon interaction with the analyzer (hit in one of the two channels) is uniquely determined by the angle between the photon polarization plane and the analyzer axis and is described by a step function. The difference in our model is that the step function contains a large number of segments of different lengths. The location and lengths of the segments are set so that the probability of a photon hitting a specific channel of an ideal analyzer, determined by averaging the outcomes over small neighborhoods of angles, approaches the Malus law when the maximum length of a segment decreases. This ensures that the classical model is self-consistent. When ideal analyzers are used, the absolute value of the correlation coefficient of detector readings mainly does not exceed the values from Aspect's ‘naive example’. However, when analyzers with absorption are used, the calculated correlations for some orientations of the analyzers exceed the quantum mechanical values. Key words: linear polarization of photons, Malus law, entangled photons, correlations, hidden parameters.
The paper considers a local deterministic phenomenological model of an experiment with correlated photons. A source emits two same-state photons simultaneously in each act. Then each photon enters its own two-channel analyzer. There are two parameters that characterize the photon state in this model. The first one is the polarization plane orientation angle. The second parameter is an “additional” one that takes values within the [0,l] range. When the photon interacts with the analyzer, it either gets into the “+” or “-” channel or is absorbed in the analyzer. Such an outcome is determined by the angle between the photon polarization plane and the axis of the analyzer along with the value of the “additional” parameter. The probability of a photon entering the "+" channel P{A= l} obeys the Malus law when considering a single-particle experiment with polarized photons and no photon absorption. And for a two-particle experiment, the dependence of the correlation coefficient of detectors readings on the angles between the analyzers’ axes follows the classic linear law. However, the correlation coefficient is described by a polyline that satisfactorily approximates the exact function when absorption is considered, and the probability P{A=l} for individual polarized photons is quite close to the Malus law.
For polarization experiments involving photon counting we introduce a quasi-deterministic eigenstate transition model of the analyzer process. Distributions accumulated one photon at a time, provide a deterministic explanation for the law of Malus. We combine this analyzer model with causal polarization coupling to calculate photon-photon correlations, one photon pair at a time. The calculated correlations exceed the Bell limits and show excellent agreement with the measured correlations of [ A. Aspect, P. Grangier and G. Rogers, Phys. Rev. Lett. 49 91 (1982)]. We discuss why this model exceeds the Bell type limits.
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.