ABSTRACT This work presents a revised analysis and corresponding perspective of Bell‐type inequalities and their connection to entanglement in polarization experiments with single‐photon resolution. It is argued that standard derivations of Bell‐type inequalities implicitly rely on additional assumptions beyond those originally stated, specifically concerning the cardinalities of the sets of measurements and the sets of photon‐pair properties (Einstein's elements of physical reality, Bell's ). Any model‐based averages must depend on these cardinalities and violations of Bell‐type inequalities become possible for certain ranges of them. In addition, we argue that for Aspect‐type experiments, the statistical properties associated with Bell's (hidden variable) λ can be different before and after actual photon‐transmission through the polarizers. This distinction is particularly necessary for the actual equipment used in the Aspect‐type experiments. Building on these observations, we construct a model based on a consistent evaluation of the measurement events relative to each other. The model reproduces all quantum‐mechanical expectation values for polarization correlations without invoking instantaneous influences at a distance, and additionally yields explicit outcomes for individual photon‐pair measurements. Within this framework, our Einstein‐type Global Space‐Time Model (GSTM) accounts also for polarization correlations in Malus‐type experiments and addresses all commonly discussed paradoxes associated with single‐photon measurements.
ABSTRACT This work presents a revised analysis and corresponding perspective of Bell‐type inequalities and their connection to entanglement in polarization experiments with single‐photon resolution. It is argued that standard derivations of Bell‐type inequalities implicitly rely on additional assumptions beyond those originally stated, specifically concerning the cardinalities of the sets of measurements and the sets of photon‐pair properties (Einstein's elements of physical reality, Bell's ). Any model‐based averages must depend on these cardinalities and violations of Bell‐type inequalities become possible for certain ranges of them. In addition, we argue that for Aspect‐type experiments, the statistical properties associated with Bell's (hidden variable) λ can be different before and after actual photon‐transmission through the polarizers. This distinction is particularly necessary for the actual equipment used in the Aspect‐type experiments. Building on these observations, we construct a model based on a consistent evaluation of the measurement events relative to each other. The model reproduces all quantum‐mechanical expectation values for polarization correlations without invoking instantaneous influences at a distance, and additionally yields explicit outcomes for individual photon‐pair measurements. Within this framework, our Einstein‐type Global Space‐Time Model (GSTM) accounts also for polarization correlations in Malus‐type experiments and addresses all commonly discussed paradoxes associated with single‐photon measurements.
We present mathematical models that also may be formulated as computer models for experiments that feature single photon resolution and multiple pairs of polarizers to determine the sorting into ordinary and extraordinary channels. The models are based on Einstein’s hypothesis of elements of physical reality that determine the photon properties and are at first developed for Malus-type experiments. It is then shown that analogous models apply to the well-known Clauser-Aspect-Zeilinger experiments and violate all Bell-type inequalities without violating Einstein’s separation principle. The Bell-type inequalities do not apply to the actual experiments, because they cannot obey the physically necessary symmetry with respect to polarizer-pair rotations. We believe that these findings suggest a change of current interpretations of quantum entanglement away from instantaneous influences at a distance, as promoted in the physics Nobel-lectures 2022, and back toward Einstein’s ideas as well as the more recent ideas of Gerard ‘t Hooft.
Bell's inequality is widely regarded as the death knell of local hidden variable theories. However, this paper points out that Bell's argument implicitly relies on an overly narrow assumption about what constitutes a "local hidden variable"—namely, that hidden variables must assign measurement outcomes to each particle independently at the moment of measurement. This paper proposes that the deterministic correspondence established between entangled particles at the moment of their creation, and determined by initial conditions, can itself serve as a local hidden variable. As long as the polarization direction of the photons is not altered, this correspondence persists indefinitely. It is independent of whether a measurement is performed, and requires no superluminal communication to sustain. From this perspective, quantum entanglement experiments do not violate special relativity; the violation of Bell's inequality merely rules out a specific class of hidden variable models, not all forms of local realism.
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.
Bell inequalities have long served as the standard criterion to verify local hidden variable theories. Experimental violations of these inequalities are commonly interpreted as fundamental quantum nonlocality at the microscopic scale. This paper proves rigorously that Bell inequalities hold only under three prerequisites: countable discrete variables, countably additive probability measures, and classical absolute simultaneity. The state space of entangled quantum systems forms an uncountable infinite continuum. By the property of Vitali non-measurable sets in measure theory, the integral deduction of the CHSH inequality collapses naturally over continuous state spaces. Furthermore, special relativity excludes universal global time synchronization, so the absolute time embedded in Bell’s theory is an artificial assumption inconsistent with physical reality. Inspired by the framework dependence of probability revealed in Bertrand’s paradox, we demonstrate that the excess correlation observed in experiments is an apparent effect caused by the mismatch between classical measurement frameworks and the intrinsic continuum property of quantum systems, rather than evidence against local hidden variables. Statistical correlation between entangled particles originates from their shared evolutionary sequence defined at pair generation, with no superluminal interaction, fully complying with relativistic causality. This paper does not explore the ultimate origin of entanglement, but treats it as a given primitive physical law. Two falsifiable predictions are proposed to distinguish the continuum model from standard quantum mechanics. The conclusion is that hidden variable theories have never been falsified by experiments; they only need to be extended from discrete forms to continuum models compatible with relativity.
The Bell's inequality is thought to be a common constraint shared by all models of local hidden variables that aim to describe the entangled states of two qubits. Since the inequality is violated by the quantum mechanical description of these states, it purportedly allows distinguishing in an experimentally testable way the predictions of quantum mechanics from those of models of local hidden variables and, ultimately, ruling the latter out. In this paper, we show, however, that the models of local hidden variables constrained by the Bell's inequality all share a subtle, though crucial, feature that is not required by fundamental physical principles and, hence, it might not be fulfilled in the actual experimental setup that tests the inequality. Indeed, the disputed feature neither can be properly implemented within the standard framework of quantum mechanics and it is even at odds with the fundamental principle of relativity. Namely, the proof of the inequality requires the existence of a preferred absolute frame of reference (supposedly provided by the lab) with respect to which the hidden properties of the entangled particles and the orientations of each one of the measurement devices that test them can be independently defined through a long sequence of realizations of the experiment. We notice, however, that while the relative orientation between the two measurement devices is a properly defined physical magnitude in every single realization of the experiment, their global rigid orientation with respect to a lab frame is a spurious gauge degree of freedom. Following this observation, we were able to explicitly build a model of local hidden variables that does not share the disputed feature and, hence, it is able to reproduce the predictions of quantum mechanics for the entangled states of two qubits.
This paper presents a conceptually simple account of the EPR argument and Bell’s theorem using entangled photon polarization experiments. It clarifies how quantum correlations arise from conditioning outcomes through fundamental properties of quantum entanglement that result in conditional probability structures rather than from superluminal influences or pre-existing particle properties. Building on this analysis, the paper explores the informational and philosophical consequences of Bell violations. Hidden-variable theories are shown to entail severe informational overhead by requiring microscopic labeling of otherwise indistinguishable particles, whereas quantum mechanics encodes structure economically through relational constraints on joint outcomes. A striking but rarely-emphasized feature of Bell-type experiments is that while traditionally the geometery of the apparatus used to carry out these experiments are aligned with each other, according to quantum mechanics the physical orientations of the apparatus have no physical meaning with respect to one another at the time of measurement. The geometry is defined only locally, relative to the laboratory in which the tests is set. The essay further argues that Bell’s theorem motivates a shift from object-centered classical realism toward a form of realism referred to as “Relational Realism” wherein correlations and informational structure are ontologically primary, while objects having individual properties are contextual and derivative. This perspective dissolves the traditional realism-versus-idealism dichotomy and situates quantum mechanics as a fundamentally relational theory of physical reality rather than an incomplete classical one.