Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

A New Mathematical Framework for Integrating Tension with Quantum Mechanics and General Relativity

Ryusho Nemoto

Published Jul 28, 2025• 0 citations
OpenAlex

Abstract

This paper introduces a new mathematical framework that incorporates the concept of “tension” as a probabilistically generated particle of time. It proposes a novel approach to unify quantum mechanics and general relativity through stochastic processes and noncommutative geometry, offering a probabilistic structure for understanding the evolution of time and spacetime.

Related papers

New Connections Between Stochastic Geometry and Quantum Theory: Redefining the Probabilistic Nature of Quantum States

Ryusho Nemoto

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.

•Jul 28, 2025•0 citations

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

Ryusho Nemoto

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.

•Jul 28, 2025•0 citations

Unification of Quantum Mechanics and General Relativity from the Stability of Matter

Pushpendra Singh

The persistent challenge of unifying quantum mechanics with general relativity is often traced to a series of apparent structural tensions: complex versus real ontology, probabilistic versus deterministic dynamics, linear versus nonlinear evolution, and spectral discreteness versus geometric continuity. We argue that these tensions do not signal a fundamental incompatibility between the theories, but rather originate from surplus structure in the conventional formulation of quantum mechanics. Beginning from the physically indispensable requirement of matter stability, we prove that the Hamiltonian spectrum can always be shifted to become non-negative. The consequent positivity of energy enforces one-sided temporal frequency support for all physical states, selecting the Hardy space of analytic signals as the admissible solution space. In this space, the real and imaginary parts of the wave function are not independent; they are linked uniquely via the temporal Hilbert transform. Hence, the complex structure of quantum mechanics emerges as a representational artifact of an underlying real operator algebra. Building on our earlier work on Unified Quantum Mechanics and the Unified Real Wave Equation, we establish a rigorous proof of exact equivalence between the real-field evolution and the Schrödinger equation on the physical subspace. Probabilistic quantities arise naturally as quadratic invariants of analytic signals, rather than as independent postulates. The resulting framework provides a realfield formulation of quantum mechanics and gravitation, with stability and causality implemented as foundational principles, and demonstrates that the Einstein field equations are compatible with a unified field-theoretic description of spacetime and matter. Extending the same analyticity principle to spacetime geometry, we propose an analytic formulation of the Einstein field equations, from which classical general relativity is recovered exactly as the real projection.

•Feb 2, 2026•0 citations

Probabilistic Geometry and the Relativistic Structure of Quantum Motion

Nemoto, Ryusho

We present a probabilistic-geometric formulation of quantum motion that establishes a direct geometric correspondence between statistical uncertainty and relativistic curvature. Quantum states are represented as probability distributions on a statistical manifold equipped with the Fisher–Rao metric, whose geodesic flow reproduces the dynamical evolution of quantum motion in probabilistic form. Embedding this manifold into a Lorentzian spacetime yields a unified metric structure in which stochastic fluctuations generate microscopic deformations of spacetime geometry. This framework enables the visualization and prediction of quantum motion as probabilistic geodesics, and provides a foundation for connecting information geometry, stochastic mechanics, and general relativity within a single coherent formulation.

•Nov 7, 2025•0 citations

New Relationship Between Tension and Quantum Uncertainty: Introducing Tension as the Quantum Fluctuation of Time

Ryusho Nemoto

This preprint redefines the nature of time in quantum theory by introducing "tension"—a probabilistically generated particle representing the minimal unit of time. It proposes that time is not continuous but composed of discrete quantum events, each fluctuating probabilistically. This leads to a new interpretation of quantum uncertainty, where time itself exhibits quantum fluctuation. The approach challenges traditional views of time and offers a new foundation for integrating time into quantum gravity frameworks.

•Jul 28, 2025•0 citations

State vector reduction as a shadow of a noncommutative dynamics

Michael C. Heller, Wiesław Sasin, Zdzisław Odrzygóźdź

A model, based on a noncommutative geometry, unifying general relativity and quantum mechanics, is developed. It is shown that the dynamics in this model can be described in terms of one-parameter groups of random operators, and that the noncommutative counterparts of the concept of state and that of probability measure coincide. We also demonstrate that the equation describing noncommutative dynamics in the quantum mechanical approximation gives the standard unitary evolution of observables, and in the “space–time limit” it leads to the state vector reduction. The cases of the spin and position operators are discussed.

arXiv:hep-th/9906132•Journal of Mathematical Physics•Aug 1, 2000•10 citations
This paper introduces a new mathematical framework that incorporates the concept of “tension” as a probabilistically generated particle of time. It proposes a novel approach to unify quantum mechanics and general relativity through stochastic processes and noncommutative geometry, offering a probabilistic structure for understanding the evolution of time and spacetime.
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.
The persistent challenge of unifying quantum mechanics with general relativity is often traced to a series of apparent structural tensions: complex versus real ontology, probabilistic versus deterministic dynamics, linear versus nonlinear evolution, and spectral discreteness versus geometric continuity. We argue that these tensions do not signal a fundamental incompatibility between the theories, but rather originate from surplus structure in the conventional formulation of quantum mechanics. Beginning from the physically indispensable requirement of matter stability, we prove that the Hamiltonian spectrum can always be shifted to become non-negative. The consequent positivity of energy enforces one-sided temporal frequency support for all physical states, selecting the Hardy space of analytic signals as the admissible solution space. In this space, the real and imaginary parts of the wave function are not independent; they are linked uniquely via the temporal Hilbert transform. Hence, the complex structure of quantum mechanics emerges as a representational artifact of an underlying real operator algebra. Building on our earlier work on Unified Quantum Mechanics and the Unified Real Wave Equation, we establish a rigorous proof of exact equivalence between the real-field evolution and the Schrödinger equation on the physical subspace. Probabilistic quantities arise naturally as quadratic invariants of analytic signals, rather than as independent postulates. The resulting framework provides a realfield formulation of quantum mechanics and gravitation, with stability and causality implemented as foundational principles, and demonstrates that the Einstein field equations are compatible with a unified field-theoretic description of spacetime and matter. Extending the same analyticity principle to spacetime geometry, we propose an analytic formulation of the Einstein field equations, from which classical general relativity is recovered exactly as the real projection.
We present a probabilistic-geometric formulation of quantum motion that establishes a direct geometric correspondence between statistical uncertainty and relativistic curvature. Quantum states are represented as probability distributions on a statistical manifold equipped with the Fisher–Rao metric, whose geodesic flow reproduces the dynamical evolution of quantum motion in probabilistic form. Embedding this manifold into a Lorentzian spacetime yields a unified metric structure in which stochastic fluctuations generate microscopic deformations of spacetime geometry. This framework enables the visualization and prediction of quantum motion as probabilistic geodesics, and provides a foundation for connecting information geometry, stochastic mechanics, and general relativity within a single coherent formulation.
This preprint redefines the nature of time in quantum theory by introducing "tension"—a probabilistically generated particle representing the minimal unit of time. It proposes that time is not continuous but composed of discrete quantum events, each fluctuating probabilistically. This leads to a new interpretation of quantum uncertainty, where time itself exhibits quantum fluctuation. The approach challenges traditional views of time and offers a new foundation for integrating time into quantum gravity frameworks.
A model, based on a noncommutative geometry, unifying general relativity and quantum mechanics, is developed. It is shown that the dynamics in this model can be described in terms of one-parameter groups of random operators, and that the noncommutative counterparts of the concept of state and that of probability measure coincide. We also demonstrate that the equation describing noncommutative dynamics in the quantum mechanical approximation gives the standard unitary evolution of observables, and in the “space–time limit” it leads to the state vector reduction. The cases of the spin and position operators are discussed.