Quantum Gravity from the Composition of Spacetime Constructed through Generalised Proper Time

TL;DR

This paper proposes a novel theory unifying quantum mechanics and general relativity by constructing spacetime from a generalized proper time, leading to a geometric framework that inherently includes quantum indeterminacy.

Contribution

It introduces a new approach to quantum gravity based on spacetime composition from proper time, without presupposing matter fields or geometric structures, aligning with Einstein's equations and quantum indeterminacy.

Findings

Spacetime constructed from generalized proper time exhibits quantum properties.

The geometric structure aligns with Einstein's field equations.

Inherent indeterminacy captures quantum phenomena.

Abstract

We describe a theory amalgamating quantum theory and general relativity through the identification of a continuous 4-dimensional spacetime arena constructed from the substructures of a generalised multi-dimensional form for proper time. In beginning with neither a matter field content nor the geometric structure of an extended 4-dimensional spacetime the properties of these entities, together with their mutual correspondence, are derived through the constraints implied in founding the theory upon the general form of proper time alone. The geometric structure of the spacetime identified exhibits a locally degenerate description in terms of an inherent ambiguity in the apparent matter field content, in a manner consistent with the Einstein field equation of general relativity while also incorporating an intrinsic indeterminacy that is characteristic of quantum phenomena. Here the quantum properties of all non-gravitational fields arise from this composition of spacetime, rather than via a postulated set of rules applied in spacetime to be extended and applied to the gravitational field or spacetime itself. The contrast with several other approaches to quantum gravity and the manner in which this framework can incorporate the essential properties of general relativity and quantum theory, both individually and in combination, will be elaborated. While emphasis will be upon providing a unifying conceptual basis the development of the associated mathematical framework will also be described.