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A Mathematical Foundation for Locality

Peter Bierhorst

Published Jan 1, 2014• 1 citation
OpenAlex

Related papers

Title: Geometric Proofs of Non-Local Interactions in Physics

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This paper explores the concept of geometric proofs of non-local interactions within physics, aiming to establish a rigorous mathematical framework for demonstrating these phenomena. The core claim is to develop a formal mathematical model that explicitly visualizes and analyzes the influence of particles through geometric transformations, enabling the verification of non-locality. Current approaches often rely on approximations, and this research proposes a fundamental shift towards a stronger, more precise mathematical foundation. The paper details the proposed geometric representation, its properties, and the rigorous mathematical steps involved in establishing a proof of non-locality through geometric analysis. The focus is on constructing a model that allows for the unambiguous demonstration of interactions that transcend spatial locality.

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Quantum entanglement has been misinterpreted for a century. The Standard Model describes it as non-local, non-separable, and fundamentally probabilistic. This interpretation was not derived from physics. It was derived from pure mathematics — from the algebra of Hilbert spaces, the linearity of operators, and the symmetry of equations. This deposit contains two complementary theses that together form a complete correction of this error. Volume 148 — The Quantum Misstep:This thesis argues that the mathematical interpretation of entanglement is wrong at its foundation. The symmetry of an equation is not a property of nature. The linearity of an operator is not a property of the real. The non-locality of a correlation is not a mechanism. From this initial error, everything else follows: the qubit was built on a mathematical abstraction, not a physical structure; the quantum computer was built on the qubit; the entire field of quantum computing is built on a misinterpretation. Volume 149 — Phase Locking:This thesis presents what replaces the misinterpretation. Entanglement is not a non-local mystery. It is a phase locking through a continuous physical medium. This mechanism has two outcomes: when the phase locks, the effective coupling is established and information flows; when the phase does not lock, the coupling fails and erroneous information is rejected at the source. The true quantum computer is not a collection of fragile qubits. It is a system of phase modes in a physical medium, operating at ambient temperature, without error correction, and scalable naturally. Together, these two volumes provide:- A refutation of the mathematical misinterpretation of entanglement.- A mechanical theory of quantum coupling in a physical medium.- A new foundation for quantum computing based on phase modes, not qubits.- A bilingual edition (English / French) for international accessibility. Key ideas:1. Entanglement is not a non-local mystery. It is a local phase coupling.2. The qubit is a mathematical abstraction, not a physical object.3. The quantum computer is not a collection of qubits. It is a system of phase modes in a physical medium.4. The quantum computer is not a qubit. It is an ocean.

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Locality in coding theory

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本文建立了元公理(Yuan-Axiom, YA)与原初局域性公理(Primordial Locality Axiom, PLA)的统一数学基础 ,并严格区分了两个不同层次的基本原理

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This paper explores the concept of geometric proofs of non-local interactions within physics, aiming to establish a rigorous mathematical framework for demonstrating these phenomena. The core claim is to develop a formal mathematical model that explicitly visualizes and analyzes the influence of particles through geometric transformations, enabling the verification of non-locality. Current approaches often rely on approximations, and this research proposes a fundamental shift towards a stronger, more precise mathematical foundation. The paper details the proposed geometric representation, its properties, and the rigorous mathematical steps involved in establishing a proof of non-locality through geometric analysis. The focus is on constructing a model that allows for the unambiguous demonstration of interactions that transcend spatial locality.
Quantum entanglement has been misinterpreted for a century. The Standard Model describes it as non-local, non-separable, and fundamentally probabilistic. This interpretation was not derived from physics. It was derived from pure mathematics — from the algebra of Hilbert spaces, the linearity of operators, and the symmetry of equations. This deposit contains two complementary theses that together form a complete correction of this error. Volume 148 — The Quantum Misstep:This thesis argues that the mathematical interpretation of entanglement is wrong at its foundation. The symmetry of an equation is not a property of nature. The linearity of an operator is not a property of the real. The non-locality of a correlation is not a mechanism. From this initial error, everything else follows: the qubit was built on a mathematical abstraction, not a physical structure; the quantum computer was built on the qubit; the entire field of quantum computing is built on a misinterpretation. Volume 149 — Phase Locking:This thesis presents what replaces the misinterpretation. Entanglement is not a non-local mystery. It is a phase locking through a continuous physical medium. This mechanism has two outcomes: when the phase locks, the effective coupling is established and information flows; when the phase does not lock, the coupling fails and erroneous information is rejected at the source. The true quantum computer is not a collection of fragile qubits. It is a system of phase modes in a physical medium, operating at ambient temperature, without error correction, and scalable naturally. Together, these two volumes provide:- A refutation of the mathematical misinterpretation of entanglement.- A mechanical theory of quantum coupling in a physical medium.- A new foundation for quantum computing based on phase modes, not qubits.- A bilingual edition (English / French) for international accessibility. Key ideas:1. Entanglement is not a non-local mystery. It is a local phase coupling.2. The qubit is a mathematical abstraction, not a physical object.3. The quantum computer is not a collection of qubits. It is a system of phase modes in a physical medium.4. The quantum computer is not a qubit. It is an ocean.