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Visualization of Quantum Motion Using a Stochastic Geometry Approach and Integration with General Relativity

Ryusho Nemoto

Published Jul 28, 2025• 0 citations
OpenAlex

Abstract

This preprint presents an accessible visualization-based exploration of quantum motion using stochastic geometry. It models quantum behavior via probabilistic processes and illustrates how 3D and 4D graphs can represent particle dynamics and entanglement. The paper further extends this approach to gauge fields, the Higgs mechanism, and general relativity, offering a pathway toward unifying quantum and gravitational theories through stochastic structures.

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This preprint presents an accessible visualization-based exploration of quantum motion using stochastic geometry. It models quantum behavior via probabilistic processes and illustrates how 3D and 4D graphs can represent particle dynamics and entanglement. The paper further extends this approach to gauge fields, the Higgs mechanism, and general relativity, offering a pathway toward unifying quantum and gravitational theories through stochastic structures.
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This paper explores the application of high-order quantum geometry to the analysis of complex systems. We propose a novel approach that integrates the probabilistic structure of quantum geometry with the dynamics of a probability field, offering a more precise framework for understanding system evolution. The core mechanism involves modeling the topological structure as a probability field and subsequently simulating the evolution of the probability field through changes in the topological structure. This methodology aims to provide a deeper, more quantitative understanding of complex systems by capturing the underlying probabilistic nature of their behavior. The work demonstrates the potential for a significant advancement in the representation and analysis of topological phenomena within complex systems.
We unify Brownian motion and quantum mechanics in a single mathematical framework. In particular, we show that non-relativistic quantum mechanics of a single spinless particle on a flat space can be described by a Wiener process that is rotated in the complex plane. We then extend this theory to relativistic stochastic theories on manifolds using the framework of second order geometry. As a byproduct, our results suggest that a consistent path integral based formulation of a quantum theory on a Lorentzian (Riemannian) manifold requires an Ito deformation of the Poincare (Galilean) symmetry, arising due to the coupling of the quadratic variation to the affine connection.
This preprint introduces a new probabilistic framework for quantum theory by applying stochastic geometry to the interpretation of quantum state transitions. It redefines time as a series of probabilistically generated "tensions"—discrete time units—that govern the evolution of quantum states. This approach allows for the discretization of the Schrödinger equation and provides a new foundation for understanding quantum uncertainty, time, and the structure of spacetime, contributing to the broader pursuit of a quantum gravity theory and Grand Unified Theory.
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