Probabilistic Spacetime and Integration with General Relativity

Ryusho Nemoto

Frank Blume

Ryusho Nemoto

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.

VS Morales-Salgado

This work reflects on mechanics as an epistemological framework on the state of a physical system to regard dynamics as the distribution of mechanical properties over spacetime coordinates. The resulting distribution is taken to be the partition function of the relevant physical quantities over a spacetime parametrized by coordinates. The partition yields a probabilistic interpretation that, based on Feynman's path integral formulation, leads to a dynamical law that generalizes the Schrödinger equation. A variety of systems can be put into the form proposed here, including particles in potentials, as well as matter and interaction fields. The main advantage of the proposed framework is that it presents the space of properties separately from that of the space of coordinates, whereas the dynamical law can be interpreted as the equation of two differential structures, one from each of these spaces. The resulting framework shows possibilities to further study physical quantities that relate directly to the spacetime coordinates, whose dynamics is best described in thermodynamical, rather than Hamiltonian, terms. A notable example is the theory of general relativity, in which the case of a scalar field in a Robertson-Walker metric is explored.

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.

Ernst Schmützer