[Paper Review] Quantum mechanics and gravity as preclusion principles of four dimensional geometries

Roman Sverdlov|ArXiv.org|Oct 1, 2008

Relativity and Gravitational Theory11 references3 citations

TL;DR

This paper proposes a relativistically covariant model of quantum mechanics and gravity by treating spacetime as a static four-dimensional geometry where 'unwanted' field behaviors are precluded based on quantum and classical consistency. Using a frame-independent preclusion principle, it shows how quantum correlations and Einstein's equation can emerge without dynamical laws, offering a unified framework that accommodates both quantum gravity and classical gravity as equally valid, precluded geometries.

ABSTRACT

The goal of this paper is to employ a "preclusion principle" originally suggested by Rafael Sorkin in order to come up with a relativistically covariant model of quantum mechanics and gravity. Space-time is viewed as geometry as opposed to dynamics, and "unwanted" histories in that geometry are precluded.

Motivation & Objective

• To develop a relativistically covariant model of quantum mechanics and gravity by replacing dynamical evolution with a preclusion principle.
• To resolve the tension between quantum mechanics and general relativity by treating spacetime as a static geometric structure where only consistent field behaviors are allowed.
• To show that quantum correlations and classical gravity can both emerge from the same preclusion mechanism, without requiring dynamical laws or field fluctuations.
• To support intellectual pluralism by simultaneously accommodating both quantum gravity and classical gravity as precluded geometries.
• To provide a framework where the third law of thermodynamics emerges naturally from a lower bound on entropy density.

Proposed method

• Apply Rafael Sorkin’s preclusion principle to four-dimensional spacetime geometry, where all non-precluded field behaviors are equally allowed and precluded ones are forbidden regardless of probability.
• Define preclusion constraints that enforce quantum mechanical correlations on field boundaries, ensuring consistency across all reference frames.
• Introduce an approximate Einstein equation with a tolerance for macroscopic validity, precluding only large-scale violations of general relativity.
• Use path integral correlations over imagined fluctuations to preclude non-quantum behaviors in gravity, without requiring actual field fluctuations.
• Impose a lower bound on entropy density to ensure decoherence occurs at large scales, enabling consistent macroscopic predictions.
• Distinguish between 'easier' and 'harder' versions of preclusion constraints to explore frame selection and potential observational signatures.

Experimental results

Research questions

• RQ1 Can quantum mechanics and gravity emerge as preclusion principles in a static, four-dimensional spacetime geometry without dynamical evolution?
• RQ2 How can preclusion be made relativistically covariant while still enforcing quantum correlations and classical gravity?
• RQ3 What is the role of entropy density in ensuring decoherence and consistency of macroscopic predictions in the preclusion framework?
• RQ4 Can both quantum gravity and classical gravity coexist as precluded geometries within the same theoretical framework?
• RQ5 How does the preclusion principle avoid introducing a preferred reference frame, and what distinguishes it from a hidden ether?

Key findings

• The preclusion principle allows all non-precluded field behaviors to be equally valid, while all precluded ones are forbidden, enabling a frame-independent selection of consistent physical behaviors.
• Quantum correlations emerge not from dynamics but from the preclusion of field configurations that do not match quantum predictions on spatial boundaries.
• Classical gravity is not dynamically generated but is enforced by precluding macroscopic violations of the approximate Einstein equation with a defined tolerance.
• Quantum gravity is accommodated by precluding field configurations that do not match path integral predictions for imagined fluctuations, without requiring actual field quantization.
• The model naturally implies the third law of thermodynamics through a lower bound on entropy density, ensuring decoherence at large scales.
• The framework avoids postulating a preferred frame by using 'there exists' statements in a relativistically invariant way, though this raises philosophical questions about relativity and the nature of physical laws.