This paper introduces a new tool for analyzing quantum mechanics, adding new insight into the nature of spin and amplitudes. Instead of restricting states to discrete spin, we model the physical state of an individual particle using a continuous, phase-coherent directional amplitude. We have successfully derived a mathematical distribution for the vector sum of these individual amplitudes. By keeping this enriched amplitude information intact and tracking its geometric phase, the framework naturally reproduces Malus’ law for single photons. More importantly, when we apply this tool to entangled photon pairs, we demonstrate that preserving the information about the local state of the photons exactly saturates the Tsirelson Bound (). Ultimately, this proves that the complex correlations usually attributed to "non-local" entanglement can be fully generated by strictly local interactions, provided we do not prematurely discard the system's underlying amplitude information. We demonstrate that the rules of quantum mechanics must incorporate such underlying properties, and therefore we arrive at the same endpoint. But the method of QM hides some of the underlying dynamical principles, while our framework utilize these principles openly for reaching the same end goal. We benchmark our discovery by testing it on entangled photons proving that we can preserve the information from their common origine, and by calculating probabilities from amplitudes before analyzers, we achieve the same results as CHSH tests without any non-local influences.
This paper introduces a new tool for analyzing quantum mechanics, adding new insight into the nature of spin and amplitudes. Instead of restricting states to discrete spin, we model the physical state of an individual particle using a continuous, phase-coherent directional amplitude. We have successfully derived a mathematical distribution for the vector sum of these individual amplitudes. By keeping this enriched amplitude information intact and tracking its geometric phase, the framework naturally reproduces Malus’ law for single photons. More importantly, when we apply this tool to entangled photon pairs, we demonstrate that preserving the information about the local state of the photons exactly saturates the Tsirelson Bound (). Ultimately, this proves that the complex correlations usually attributed to "non-local" entanglement can be fully generated by strictly local interactions, provided we do not prematurely discard the system's underlying amplitude information. We demonstrate that the rules of quantum mechanics must incorporate such underlying properties, and therefore we arrive at the same endpoint. But the method of QM hides some of the underlying dynamical principles, while our framework utilize these principles openly for reaching the same end goal. We benchmark our discovery by testing it on entangled photons proving that we can preserve the information from their common origine, and by calculating probabilities from amplitudes before analyzers, we achieve the same results as CHSH tests without any non-local influences.
Abstract. In a recent work, we established a phase-coherent directional amplitude framework that natively reproduces the full spectrum of bipartite quantum correlations, exactly saturating the Tsirelson bound . While that work demonstrated the predictive power of retaining continuous geometric phase information, the structural origin and uniqueness of the underlying signed amplitude distributions remained implicit. In the present paper we show that these distributions are uniquely determined by symmetry and measurement geometry. We propose a geometric interpretation of quantum measurement in which state reduction arises from marginalization over operationally inaccessible degrees of freedom. An arriving particle and a measurement apparatus uniquely determine a plane of relevance, while orthogonal degrees of freedom are physically filtered and marginalized from the effective description. Using harmonic analysis on the sphere, we prove that this geometric marginalization—together with rotational covariance and normalization—uniquely fixes the post-selection amplitude distributions. For spin-½ systems, rotational symmetry restricts the Legendre expansion to its lowest harmonics, forcing the exact signed distribution previously employed. Extended to bipartite product spaces , global rotational invariance uniquely determines the joint amplitude structure that reproduces the standard singlet correlation law. These results provide a kinematic explanation of the amplitude distributions underlying quantum spin correlations and offer a geometric account of quantum state reduction as marginalization over degrees of freedom that are operationally inaccessible to the measurement interaction.
We introduce a local phase-field framework for describing spin entanglement in which measurement correlations arise from an internal scalar phase associated with each fermion. The phase is defined by two underlying real fields and evolves according to local relativistic dynamics. When particle pairs are produced at a common spacetime event, a phase-locking constraint is established at creation, after which the internal phases evolve independently without any nonlocal interaction.Spin measurements performed by Stern–Gerlach analyzers are modeled as local filtering operations that depend only on the internal phase and the analyzer orientation. Using this deterministic local response, we derive the exact quantum correlation function; when inserted into the CHSH expression, it attains the standard Tsirelson bound.The framework preserves locality, parameter independence, and no-signaling, while providing a concrete physical ontology for spin correlations based on internal phase structure. We compare the model with earlier phase-based approaches and outline experimental configurations—such as time-resolved and multi-stage Stern–Gerlach measurements—that could probe the dynamical evolution of the internal phase. The results demonstrate that exact quantum entanglement correlations can emerge from a strictly local phase-field description.Bell’s theorem constrains models in which measurement outcomes are functions of pre-assigned discrete values. The present framework instead employs a continuous internal phase field as the relevant physical variable. Measurement outcomes are deterministic functions of the local phase and analyzer orientation. The model preserves locality, parameter independence, and no-signaling, while allowing outcome dependence, which is permitted within Bell’s framework.
For nearly a century, quantum mechanics (QM) has established itself as an incredibly effective tool for predicting the collective movements and statistical distributions of particles. However, its predictive success comes with a major conceptual cost: the apparent abandonment of local realism. When one attempts to apply the quantum formalism at the scale of an individual particle, paradoxes inevitably arise, such as non-locality, state superposition, or wave-particle duality. The central thesis of this document is that these paradoxes are not intrinsic properties of nature, but rather result from an ontological category error. The current formalism applies ensemble statistical laws designed to describe the average behavior of a large number of particles to the scale of the individual, where they are not intended to apply. This undue promotion of statistics to the rank of instantaneous reality leads to a ``magical'' interpretation of statistically balanced phenomena. This article propose a reconsideration of three pillars of the standard quantum interpretation: Firstly, we demonstrate that the violation of Bell’s inequalities can be reinterpreted locally through the principle of Statistical Identity (shared initial orientation), which establishes an equivalence between parallel and sequential measurements, allowing the application of Malus’s law to reproduce the correlations without requiring any non-local influence. second, we show that interferometry does not reveal a superposition of states, but rather involves a deterministic geometric transformation of probability distributions via polarization rotation. Finally, we challenge the standard postulate of simultaneity in the Young's slits. We introduce an ``event-by-event'' formulation where interference fringes emerge from temporal correlations preserved by the non-commutativity of averaging, rather than from the interaction of simultaneous fields. By restoring the distinction between statistical law and individual reality, this work aims to end ``quantum geocentrism'' and lay the foundations for a coherent, local, and realistic Sub-Quantique and Infra-Particules physics.
For nearly a century, quantum mechanics (QM) has established itself as an exceptionally effective framework for predicting the collective movements and statistical distributions of particles. However, its predictive success comes with a significant conceptual cost: the apparent abandonment of local realism. When one attempts to apply the standard quantum formalism at the scale of an individual particle, paradoxes inevitably arise. This article argues that these contradictions are not intrinsic properties of nature, but rather stem from a fundamental category error: the misapplication of ensemble statistical laws to individual events, which unrightfully promotes statistical averages to instantaneous physical realities. To address the root cause of this conceptual deviation, we must establish a foundational axiom: the Principle of Particle Reality. This principle posits that if a particle exists as a real entity, it must inherently possess definite physical properties—such as a precise polarization, velocity, and trajectory—independent of our capacity to detect them. Ignoring this ontology has led the standard model to treat physical realities as abstract paradoxes. To resolve them, this work proposes a unified reconsideration of three main pillars of quantum interpretation. First, regarding locality, we demonstrate that the passage probabilities through two polarizers for a particle within an unpolarized beam remain identical regardless of their order. Governed by Malus's law and the strict mathematical symmetry \cos^2(a-b) = \cos^2(b-a), this establishes that polarizers can be arranged in any sequential order or even in parallel for statistically identical pairs without altering the total passage probabilities. By establishing a physical equivalence, we show that exact quantum correlations emerge directly from a particle-by-particle application of the strictly positive classical Malus's law (0 \le p \le 1). This successfully explains the violation of Bell’s inequalities within a strictly local framework, bypassing the non-physical negative quasi-probabilities encountered in previous angular hidden-variable models. Secondly, on the illusion of state superposition, we show that failing to recognize that an interferometer physically and deterministically alters the polarization orientation of a particle led to an abstract formulation; in reality, this involves a deterministic geometric transformation of probability distributions. Finally, addressing wave-particle duality, we challenge the standard postulate of artificial simultaneity in the double-slit configuration, which caused a deep confusion between the collective behavior of a group and the sequential passage of an individual entity. We introduce an ``event-by-event'' formulation where interference fringes emerge instead from temporal correlations preserved by the non-commutativity of averaging. By restoring the strict distinction between statistical ensemble laws and individual reality through the Principle of Particle Reality, this work aims to definitively end ``quantum geocentrism'' and to lay the foundations for a coherent, local, and realistic sub-quantum physics.
This paper introduces the Geometric Phase Support (GPS) framework, a mathematically rigorous local-realistic alternative to standard quantum foundational assumptions. Historically, proofs of Bell's theorem rely on a flat-circle topology where local hidden variables are treated as one-dimensional directional vectors, an architectural assumption that systematically dilutes correlation amplitudes by half and forces an artificial ceiling of. We demonstrate that by replacing directional flat averaging with a continuous, rotational axial phase manifold ( ) operating under a sharp boundary condition, the standard quantum mechanical CHSH expectation value ( ) is directly derived via explicit, term-by-term calculus integration. Because the integration boundaries track the hidden variable dynamically ( to ), destructive cross-terms cancel symmetrically during global spatial averaging, allowing the full doubled-angle correlation to survive intact. By successfully reproducing real-world experimental violations up to the Tsirelson bound ( ), this framework validates Albert Einstein's original intuition regarding the completeness and local-realistic nature of physical reality, proving that non-local state updates and faster-than-light signaling are mathematical artifacts of an inadequate geometric choice rather than genuine features of nature.
For nearly a century, quantum mechanics (QM) has established itself as an exceptionally effective framework for predicting the collective movements and statistical distributions of particles. However, its predictive success comes with a significant conceptual cost: the apparent abandonment of local realism. When one attempts to apply the standard quantum formalism at the scale of an individual particle, paradoxes inevitably arise. This article argues that these contradictions are not intrinsic properties of nature, but rather stem from a fundamental category error: the misapplication of ensemble statistical laws to individual events, which unrightfully promotes statistical averages to instantaneous physical realities. To address the root cause of this conceptual deviation, we must establish a foundational axiom: the Principle of Particle Reality. This principle posits that if a particle exists as a real entity, it must inherently possess definite physical properties—such as a precise polarization, velocity, and trajectory—independent of our capacity to detect them. Ignoring this ontology has led the standard model to treat physical realities as abstract paradoxes. To resolve them, this work proposes a unified reconsideration of three main pillars of quantum interpretation. First, regarding locality, we demonstrate that a polarizer does not create a state but merely reveals a pre-existing polarization. The concrete proof lies in the reduction of a beam’s intensity, which is fundamentally a physical drop in the number of transmitted particles. By establishing a physical equivalence between parallel and sequential measurements via the principle of Statistical Identity, we show that exact quantum correlations emerge directly from a particle-by-particle application of the strictly positive classical Malus’s law (0 ≤ p ≤ 1). This successfully explains the violation of Bell’s inequalities within a strictly local framework, bypassing the non-physical negative quasi-probabilities encountered in previous angular hidden-variable models. Secondly, on the illusion of state superposition, we show that failing to recognize that an interferometer physically and deterministically alters the polarization orientation of a particle led to an abstract formulation; in reality, this involves a deterministic geometric transformation of probability distributions. Finally, addressing wave-particle duality, we challenge the standard postulate of artificial simultaneity in the double-slit configuration, which caused a deep confusion between the collective behavior of a group and the sequential passage of an individual entity. We introduce an “event-by-event” formulation where interference fringes emerge instead from temporal correlations preserved by the non-commutativity of averaging. By restoring the strict distinction between statistical ensemble laws and individual reality through the Principle of Particle Reality, this work aims to definitively end “quantum geocentrism” and to lay the foundations for a coherent, local, and realistic sub-quantum physics.