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Gauge Probability Charge Theory

Ren Matsuoka

Published Sep 10, 2026• 0 citations
Publisher

Abstract

Gauge Probability Charge Theory (GPCT) proposes a physical framework in which quantum probability is treated as physically meaningful and capable of participating in gauge interactions. The central idea of GPCT is that probability density is not merely a mathematical tool for predicting measurement outcomes, but can play an active physical role in interactions. In this framework, the probability density associated with a quantum state is interpreted as a probability charge density, while corresponding probability fields describe its interaction with the gauge sectors of physics. GPCT develops this idea within a field-theoretical framework. It introduces probability-field dynamics, interaction Lagrangians, Hamiltonian formulations, Green's functions, propagators, and gauge-covariant descriptions. The framework is examined in relation to electromagnetic, strong, weak, and gravitational interactions, with the aim of describing these interactions through a common probability-charge coupling principle. A central application of the theory is quantum measurement. GPCT interprets measurement as a physical interaction that compresses and localizes probability density rather than as an instantaneous mathematical projection. The theory proposes a dynamical description of this compression and considers the apparent instantaneous nature of quantum measurement as a limiting behavior of the underlying interaction process. The theory also investigates the relationship between probability-field interactions and quantum uncertainty. It proposes a unified perspective in which uncertainty relations arise from the interaction between physical quantities and their corresponding probability fields. For electromagnetism, GPCT reinterprets electric charge as the coupling strength associated with the interaction between particle probability density and the electromagnetic probability field. Analogous probability-charge descriptions are developed for color and weak interactions, while gravity is considered through a gravitational probability field coupled to matter. The framework further discusses probability-field excitations, probability virtual particles, gauge symmetry, quantum corrections, renormalization-group behavior, and possible connections to established quantum field theory. GPCT proposes several possible experimental avenues for testing deviations or additional effects associated with probability-field interactions. These include precision electromagnetic measurements, atomic spectroscopy, anomalous magnetic moments, collider physics, jet structure, weak-interaction measurements, neutrino physics, and gravitational-wave observations. The purpose of this work is to present a unified theoretical framework in which quantum probability and gauge interactions can be considered from a common physical perspective. The theory is intended as a foundation for further mathematical development, theoretical consistency checks, and experimental investigation.

DOI
10.5281/zenodo.22686565

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Gauge Probability Charge Theory (GPCT) proposes a physical framework in which quantum probability is treated as physically meaningful and capable of participating in gauge interactions. The central idea of GPCT is that probability density is not merely a mathematical tool for predicting measurement outcomes, but can play an active physical role in interactions. In this framework, the probability density associated with a quantum state is interpreted as a probability charge density, while corresponding probability fields describe its interaction with the gauge sectors of physics. GPCT develops this idea within a field-theoretical framework. It introduces probability-field dynamics, interaction Lagrangians, Hamiltonian formulations, Green's functions, propagators, and gauge-covariant descriptions. The framework is examined in relation to electromagnetic, strong, weak, and gravitational interactions, with the aim of describing these interactions through a common probability-charge coupling principle. A central application of the theory is quantum measurement. GPCT interprets measurement as a physical interaction that compresses and localizes probability density rather than as an instantaneous mathematical projection. The theory proposes a dynamical description of this compression and considers the apparent instantaneous nature of quantum measurement as a limiting behavior of the underlying interaction process. The theory also investigates the relationship between probability-field interactions and quantum uncertainty. It proposes a unified perspective in which uncertainty relations arise from the interaction between physical quantities and their corresponding probability fields. For electromagnetism, GPCT reinterprets electric charge as the coupling strength associated with the interaction between particle probability density and the electromagnetic probability field. Analogous probability-charge descriptions are developed for color and weak interactions, while gravity is considered through a gravitational probability field coupled to matter. The framework further discusses probability-field excitations, probability virtual particles, gauge symmetry, quantum corrections, renormalization-group behavior, and possible connections to established quantum field theory. GPCT proposes several possible experimental avenues for testing deviations or additional effects associated with probability-field interactions. These include precision electromagnetic measurements, atomic spectroscopy, anomalous magnetic moments, collider physics, jet structure, weak-interaction measurements, neutrino physics, and gravitational-wave observations. The purpose of this work is to present a unified theoretical framework in which quantum probability and gauge interactions can be considered from a common physical perspective. The theory is intended as a foundation for further mathematical development, theoretical consistency checks, and experimental investigation.
Quantum Light Theory (QLT) is the development in Quantum Field Theory (QFT). In Quantum Field Theory, the fundamental interaction fields are replacing the concept of elementary particles in Classical Quantum Mechanics. In Quantum Light Theory the fundamental interaction fields are being replaced by One Single Field. The Electromagnetic Field, generally well known as Light. To realize this theoretical concept, the fundamental theory has to go back in time 300 years, the time of Isaac Newton to follow a different path in development. Nowadays experiments question more and more the fundamental concepts in Quantum Field Theory and Classical Quantum Mechanics. The publication “Operational Resource Theory of Imaginarity“ in “Physical Review Letters” in 2021 (Ref. [2]) presenting the first experimental evidence for the measurability of “Quantum Mechanical Imaginarity” directly leads to the fundamental question in this experiment: How is it possible to measure the imaginary part of “Quantum Physical Probability Waves”? This publication provides an unambiguously answer to this fundamental question in Physics, based on the fundamental “Gravitational Electromagnetic Interaction” force densities. The “Quantum Light Theory” presents a new “Gravitational-Electromagnetic Equation” describing Electromagnetic Field Configurations which are simultaneously the Mathematical Solutions for the Quantum Mechanical “Schrodinger Wave Equation” and more exactly the Mathematical Solutions for the “Relativistic Quantum Mechanical Dirac Equation”. The Mathematical Solutions for the “Gravitational-Electromagnetic Equation” carry Mass, Electric Charge and Magnetic Spin at discrete values.
Quantum Light Theory (QLT) is the development in Quantum Field Theory (QFT). In Quantum Field Theory, the fundamental interaction fields are replacing the concept of elementary particles in Classical Quantum Mechanics. In Quantum Light Theory the fundamental interaction fields are being replaced by One Single Field. The Electromagnetic Field, generally well known as Light. To realize this theoretical concept, the fundamental theory has to go back in time 300 years, the time of Isaac Newton to follow a different path in development. Nowadays experiments question more and more the fundamental concepts in Quantum Field Theory and Classical Quantum Mechanics. The publication “Operational Resource Theory of Imaginarity“ in “Physical Review Letters” in 2021 (Ref. [2]) presenting the first experimental evidence for the measurability of “Quantum Mechanical Imaginarity” directly leads to the fundamental question in this experiment: How is it possible to measure the imaginary part of “Quantum Physical Probability Waves”? This publication provides an unambiguously answer to this fundamental question in Physics, based on the fundamental “Gravitational Electromagnetic Interaction” force densities. The “Quantum Light Theory” presents a new “Gravitational-Electromagnetic Equation” describing Electromagnetic Field Configurations which are simultaneously the Mathematical Solutions for the Quantum Mechanical “Schrodinger Wave Equation” and more exactly the Mathematical Solutions for the “Relativistic Quantum Mechanical Dirac Equation”. The Mathematical Solutions for the “Gravitational-Electromagnetic Equation” carry Mass, Electric Charge and Magnetic Spin at discrete values.
Quantum Gravity Field-Based Probability explores the potential of utilizing quantum entanglement to refine probability calculations within complex quantum systems. The core claim posits the development of a novel framework – the 'Quantum Entanglement Probability Field' – that quantifies the probability of event outcomes by encoding these probabilities within a dynamically evolving field. This represents a departure from classical probability models, offering a potential pathway to improved prediction and a deeper understanding of quantum phenomena. The paper introduces the concept, details the design of the entanglement probability field, and outlines the theoretical and potential experimental implications of this research.
This work proposes a phenomenological framework linking quantum localization to weak-field gravitational response through informational load functionals. The central idea is that the degree of spatial localization of a quantum state may be associated with an effective participation factor governing how strongly that state contributes to inertial and gravitational phenomena. Localization is quantified using standard measures such as the inverse participation ratio (IPR), combined with reference scales that render localization dimensionless. A monotonic substrate response function is introduced to map localization load to observable effects. In the weak-field regime, a linear response approximation recovers familiar gravitational scaling relations. The framework does not modify Schrödinger dynamics, introduce new particles, or attempt a full theory of quantum gravity. Instead, it explores whether aspects of gravity normally described geometrically can be reinterpreted as state-dependent informational load. Illustrative empirical connections are discussed using known atomic ionization data to show how varying localization regimes may correspond to different participation factors. These examples are intended as phenomenological consistency checks rather than precision derivations. Scope and Status: This work is exploratory and interpretational. It is intended as a conceptual bridge between quantum and gravitational descriptions, not as a completed fundamental theory. Predictions are restricted to weak-field regimes, and strong-field behavior is left open. Key Points: Treats mass-like behavior as state-dependent participation Uses established localization measures (IPR) Introduces substrate response only phenomenologically Does not invoke gravitons or modify QM equations Suggests testable scaling relations in principle Purpose: The goal is to stimulate discussion on whether gravitational response might be expressible in informational or localization terms, providing an alternative viewpoint on the QM–GR interface.Update in this version: Reference to the Effective Mass Theory.Reference to the Objective Collapse Theory
This work proposes a phenomenological framework linking quantum localization to weak-field gravitational response through informational load functionals. The central idea is that the degree of spatial localization of a quantum state may be associated with an effective participation factor governing how strongly that state contributes to inertial and gravitational phenomena. Localization is quantified using standard measures such as the inverse participation ratio (IPR), combined with reference scales that render localization dimensionless. A monotonic substrate response function is introduced to map localization load to observable effects. In the weak-field regime, a linear response approximation recovers familiar gravitational scaling relations. The framework does not modify Schrödinger dynamics, introduce new particles, or attempt a full theory of quantum gravity. Instead, it explores whether aspects of gravity normally described geometrically can be reinterpreted as state-dependent informational load. Illustrative empirical connections are discussed using known atomic ionization data to show how varying localization regimes may correspond to different participation factors. These examples are intended as phenomenological consistency checks rather than precision derivations. Scope and Status: This work is exploratory and interpretational. It is intended as a conceptual bridge between quantum and gravitational descriptions, not as a completed fundamental theory. Predictions are restricted to weak-field regimes, and strong-field behavior is left open. Key Points: Treats mass-like behavior as state-dependent participation Uses established localization measures (IPR) Introduces substrate response only phenomenologically Does not invoke gravitons or modify QM equations Suggests testable scaling relations in principle Purpose: The goal is to stimulate discussion on whether gravitational response might be expressible in informational or localization terms, providing an alternative viewpoint on the QM–GR interface.Update in this version: Reference of Effective Mass Theory. Noticed there exist the effe
General relativity is a deterministic theory with non-fixed causal structure. Quantum theory is a probabilistic theory with fixed causal structure. In this paper, we build a framework for probabilistic theories with non-fixed causal structure. This combines the radical elements of general relativity and quantum theory. We adopt an operational methodology for the purposes of theory construction (though without committing to operationalism as a fundamental philosophy). The key idea in the construction is physical compression . A physical theory relates quantities. Thus, if we specify a sufficiently large set of quantities (this is the compressed set), we can calculate all the others. We apply three levels of physical compression. First, we apply it locally to quantities (actually probabilities) that might be measured in a particular region of spacetime. Then we consider composite regions. We find that there is a second level of physical compression for a composite region over and above the first level physical compression for the component regions. Each application of first and second level physical compression is quantified by a matrix. We find that these matrices themselves are related by the physical theory and can therefore be subject to compression. This is the third level of physical compression. The third level of physical compression gives rise to a new mathematical object which we call the causaloid. From the causaloid for a particular physical theory we can calculate everything the physical theory can calculate. This approach allows us to set up a framework for calculating probabilistic correlations in data without imposing a fixed causal structure (such as a background time). We show how to put quantum theory in this framework (thus providing a new formulation of this theory). We indicate how general relativity might be put into this framework and how the framework might be used to construct a theory of quantum gravity.