Conformal Invariance, Anomalous Gravitational Coupling and Derivation of a Particle Concept

TL;DR

This paper explores a conformally invariant gravitational model with anomalous matter coupling, deriving a particle concept linked to variable gravitational strength and quantum-like potential effects, relevant to quantum mechanics interpretations.

Contribution

It introduces a novel conformal gravitational framework that relates anomalous matter coupling to a quantum-like particle concept, bridging gravity and quantum interpretations.

Findings

Derivation of a relativistic particle concept from conformal invariance.

Identification of a quantum potential-like term from gravitational coupling.

Discussion of pilot wave characteristics in the model.

Abstract

We study a gravitational model whose vacuum sector is invariant under conformal transformations. In this model we investigate the anomalous gravitational coupling of the large-scale matter. In this kind of coupling the large-sale matter is taken to couple to a metric which is different but conformally related to the metric appearing explicitly in the vacuum sector. The effect of the conformal symmetry breaking of the large-scale matter would lead in general to a variable strength of the anomalous gravitational coupling. This feature is used to derive a relativistic particle concept which shares the essential dynamical characteristics of the particle concept used in the causal interpretation of quantum mechanics with respect to the form of the Hamilton-Jacobi equation. The basic aspect of this result is that it relates the variable strength of the anomalous gravitational coupling of the large-scale matter to the appearance of a term similar to a quantum potential term. Some of the general characteristics of the corresponding pilot wave are discussed.