Bell's Theorem, Non-Computability and Conformal Cyclic Cosmology: A Top-Down Approach to Quantum Gravity

TL;DR

This paper proposes Invariant Set Theory, a novel approach to quantum gravity that explains Bell Inequality violations without abandoning determinism or local causality, by linking fractal geometry with the universe's phase space.

Contribution

It introduces Invariant Set Theory, connecting fractal phase space geometry with quantum mechanics and gravity, offering a new perspective on quantum gravity and Bell Inequality violations.

Findings

IST explains Bell Inequality violations without abandoning determinism.

Quantum mechanics emerges as a limit of finite complex Hilbert states.

A modified field equation aligns general relativity with IST.

Abstract

This paper draws on a number of Roger Penrose's ideas - including the non-Hamiltonian phase-space flow of the Hawking Box, Conformal Cyclic Cosmology, non-computability and gravitationally induced quantum state reduction - in order to propose a radically unconventional approach to quantum gravity: Invariant Set Theory (IST). In IST, the fundamental laws of physics describe the geometry of the phase portrait of the universe as a whole: "quantum" process are associated with fine-scale fractal geometry, "gravitational" process with larger-scale heterogeneous geometry. With this, it becomes possible to explain the experimental violation of Bell Inequalities without having to abandon key ingredients of general relativity: determinism and local causality. Ensembles in IST can be described by complex Hilbert states over a finite set $\mathbb C_p$ of complex numbers, where $p$ is a large finite integer. The quantum mechanics of finite-dimensional Hilbert spaces is emergent as a singular limit when $p \rightarrow \infty$. A small modification to the field equations of general relativity is proposed to make it consistent with IST.