This preprint presents an independent investigation of Bell-type correlations and the physical assumptions underlying Bell/CHSH analyses. It develops a phase-based model intended to examine whether observed quantum correlations can be reproduced through a different underlying physical mechanism than is usually assumed in standard interpretations. The manuscript focuses on the mathematical structure of the proposed model, its relationship to Bell-type inequalities, and the conditions under which its predictions may differ from standard quantum-mechanical expectations. This is version 1.2 of the preprint and has not yet undergone formal peer review.
This preprint presents an independent investigation of Bell-type correlations and the physical assumptions underlying Bell/CHSH analyses. It develops a phase-based model intended to examine whether observed quantum correlations can be reproduced through a different underlying physical mechanism than is usually assumed in standard interpretations. The manuscript focuses on the mathematical structure of the proposed model, its relationship to Bell-type inequalities, and the conditions under which its predictions may differ from standard quantum-mechanical expectations. This is version 1.2 of the preprint and has not yet undergone formal peer review.
This paper investigates whether Bell-like and CHSH-type correlations can arise within a fully classical stochastic framework. The study develops an event-based model using competing Poisson processes, exponential waiting-time races, intensity-to-probability mappings, and Monte Carlo simulation to generate binary measurement outcomes and joint correlations. The model examines how contextual measurement settings, classical interference, and sinusoidal intensity relationships can produce correlation structures commonly associated with quantum-mechanical experiments. Particular attention is given to singlet-like cosine correlations, joint probability distributions, and the statistical conditions under which CHSH correlations emerge. Rather than assuming quantum probability rules at the outset, the analysis constructs the correlations from underlying stochastic events and evaluates the resulting synthetic data statistically. The work is intended as an exploratory contribution to the foundations of quantum mechanics, especially the interpretation of Bell inequalities, contextuality, and the distinction between quantum and classical stochastic descriptions.
SuperTimePosition (STP) and Gravitational Phase-Lock (GPL) are developed as a conditional model program for Bell-type correlations. The proposal retains local response functions and asks whether a hidden phase can become statistically dependent on detector settings through a physical phase-lock process. This changes the measurement-independence premise used in standard Bell arguments; it does not refute Bell's theorem and is not validated merely because Bell inequalities are experimentally violated. This revision adds an exact, bounded finite-lock benchmark. A phase on the circle follows a setting-conditioned diffusion whose stationary density is an equal mixture of two shifted hyperbolic-cosine components. With explicit local binary response laws, the construction yields exactly unbiased marginals, a closed joint probability law, and a cosine correlation with a Bessel-function visibility. It also admits a deterministic local completion. The mathematical closure comes at a measurable cost: Hall's measurement-dependence fraction falls below one half at the onset of CHSH violation and approaches zero as the singlet visibility is approached. A causal-timing proposition further shows that a strictly retarded detector-to-source mechanism cannot produce a setting-conditioned emission state when the settings are selected outside the emission event's past light cone without an additional common-past, retrocausal, nonlocal, or late-update premise. The result is therefore two-sided. Version 8 closes the stationary-density, full binary-joint, and binary-marginal obligations for one explicit family, but it does not derive the lock strength from gravity, establish a physical value of the phase-diffusion rate, explain all experimental records, or prove the wider Super Information Theory framework. STP/GPL remains a falsifier-first research program whose next decisive requirement is an independently calibrated map from apparatus and gravitational variables to the model parameters.
The Bell inequality constrains the outcomes of measurements on pairs of distant entangled particles. The Bell contradiction states that the Bell inequality is inconsistent with the calculated outcomes of these quantum experiments. This contradiction led many to question the underlying assumptions, viz. so-called realism and locality. The probability model underlying the Bell inequality is generally left implicit. We propose an explicit probability model for the CHSH version of the Bell experiment. This model has only two simultaneously observable detector settings per measurement, and therefore does not assume realism. The quantum expectation now becomes a conditional expectation, given the two detector settings. This probability model is in full agreement with both quantum mechanics and experiments. As a result, the model satisfies the Bell inequality; there are no so-called violations. We extend this model to include a hidden variable. This extended model is not Bell-separable. This non-separability implies that the model is non-deterministic or non-local (or both).
Abstract. Bell's inequality established that no local hidden-variable theory can exceed a CHSH value of 2, andexperiment has repeatedly confirmed the quantum-mechanical prediction 2√2. Without modifying any measuredfact, this paper presents one structural picture of the origin of entanglement correlations — within a frameworkin which a particle is a bound triple of three wavons at mutual 120° phase: the two entangled systems do notcarry locally predetermined values, but share a single phase relation, and a measurement projects that sharedphase onto a direction angle. Within this picture the correlation function E(a,b) = ±cos 2(a−b) and CHSH = 2√2are reproduced, and no-signalling holds as a result rather than an assumption. For contrast, the value-sharinglocal translation is shown to fail, confined to CHSH ≤ 2, making explicit the criterion that separates the twopictures. At the present stage the picture is a restatement mathematically equivalent to the quantum formalism;no new prediction is claimed. Two forcing problems that must be proved before the restatement can be promotedto a derivation, and four points at which the picture is exposed to test and refutation, are stated explicitly.Keywords: Bell inequality · CHSH · quantum entanglement · no-signalling theorem · interpretation · phasesuperposition · wavon
We present a Leggett-type model that reproduces quantum correlations for the Bell states. It cannot be falsified through known tests based on Bell-type, Leggett-type, or so-called chained Bell inequalities. The model entails partial suppression of measurement independence (free will) to a fraction of 1/4, as quantified by a recently proposed measure that varies between 0 and 1. This is a consequence of assuming a possible nonlocal relationship between an entangler and one of two measuring stations, thereby differing from the usual nonlocal, Leggett-type models. Furthermore, the model admits arbitrary time ordering for events occurring at two spacelike separated measuring stations. The predicted correlations reproduce the quantum-mechanical ones. Thus, the model is not falsified by so-called before-before tests.
The empirical evidence tends to confirm the quantum - mechanically (QM) predicted violation of Bell's - type inequalities. The latter are widely accepted to be correct representation of the objective reality (OR) underlying EPR's gedankenexperiment. Contrariwise, we argue here that the starting premises leading to Bell's and CHSH's inequalities are not appropriate formulations of OR in the EPR context. Indeed, the essence of EPR argument is the correlation between pair of particles travelling with some well defined orientations. To measure such correlation, one requires detectors with high resolution, and some appropriately defined relative orientations. On the contrary, experimental tests of Bell's inequalities typically involve counting the number of particles with some value of spin (or polarisation) using low-resolution detectors and completely arbitrary orientations. Depending upon the relative orientation of good-resolution detectors, we obtain two families of CHSH-type inequalities. One of these families is the most often used version of CHSH inequality, that was derived by Clauser and Horne with the supplementary no - enhancement assumption: here, it is obtained without special provisions. The other family is completely new and refers to coincidence counts from multiple events. Experimental test to distinguish between the QM and OR descriptions of nature should take into account these new constraints.