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The Ninth Marcel Grossmann Meeting

Constructing relational statistical spacetime in the theory of gravitation and in quantum mechanics

Vladimir V. Aristov

Published Nov 16, 2017• 2 citations
Publisher
DOI
10.1142/9789813226609_0326

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The past century after the creation of quantum mechanics forces us to turn to the fundamentals of physical theory at a different level. In the relational approach, statistical spacetime is constructed, which correlates with the probabilistic notions of quantum mechanics. Mach’s principle in its generalized formulation also turns out to be important. The present paper shows how, by moving to a graph formalism for expressing spatial dimensions, coupled with the statistical dimension of time, quantum relationships are derived. Combined with a description of gravitational effects, a general physical apparatus can be created. The global nature of Mach’s principle allows us to connect the microand macroscales of description.

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The past century after the creation of quantum mechanics forces us to turn to the fundamentals of physical theory at a different level. In the relational approach, statistical spacetime is constructed, which correlates with the probabilistic notions of quantum mechanics. Mach’s principle in its generalized formulation also turns out to be important. The present paper shows how, by moving to a graph formalism for expressing spatial dimensions, coupled with the statistical dimension of time, quantum relationships are derived. Combined with a description of gravitational effects, a general physical apparatus can be created. The global nature of Mach’s principle allows us to connect the microand macroscales of description.
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We develop a pregeometric framework in which quantum mechanics, gauge structure, gravitation, matter, and spacetime emerge from the stability dynamics of coherent relational transport organization. Rather than assuming spacetime manifolds, Hilbert spaces, or gauge symmetries as fundamental, the theory begins from a primitive causal-relational substrate consisting only of composable transport relations. A generalized spectral transport operator is introduced to represent coherent relational dynamics. Stable eigensectors of generate effective particles, locality, gauge structure, and geometry. Physical organization is governed by a generalized relational stability functional whose extrema define dynamically persistent coherent structures. Quantum mechanics emerges from coherent compositional consistency, gauge symmetry emerges as redundancy of transport representation, and spacetime geometry emerges statistically through spectral localization, thermodynamic projection, and relational distinguishability stabilization. The framework therefore proposes that physical reality is fundamentally not a collection of objects evolving inside spacetime, but a self-stabilizing process of coherent relational spectral organization from which matter, fields, and spacetime itself emerge