A possible correspondence between Ricci identities and Dirac equations in the Newman-Penrose formalism: towards an understanding of gravity induced collapse of the wave-function?

TL;DR

This paper explores a potential link between Ricci identities and Dirac equations within the Newman-Penrose formalism, aiming to understand gravity-induced wave-function collapse in quantum measurement.

Contribution

It proposes that Dirac equations can be viewed as a special case of Ricci identities with torsion, suggesting a new approach to quantum gravity and wave-function collapse.

Findings

Identifies a possible correspondence between Dirac equations and Ricci identities with torsion.

Suggests a framework for gravity-induced wave-function collapse during quantum measurement.

Draws parallels with Einstein-Cartan-Sciama-Kibble theory.

Abstract

It is well-known that in the Newman-Penrose formalism the Riemann tensor can be expressed as a set of eighteen complex first-order equations, in terms of the twelve spin coefficients, known as Ricci identities. The Ricci tensor herein is determined via the Einstein equations. It is also known that the Dirac equation in a curved spacetime can be written in the Newman-Penrose formalism as a set of four first-order coupled equations for the spinor components of the wave-function. In the present article we suggest that it might be possible to think of the Dirac equations in the N-P formalism as a special case of the Ricci identities, after an appropriate identification of the four Dirac spinor components with four of the spin coefficients, provided torsion is included in the connection, and after a suitable generalization of the energy-momentum tensor. We briefly comment on similarities with the Einstein-Cartan-Sciama-Kibble theory. The motivation for this study is to take some very preliminary steps towards developing a rigorous description of the hypothesis that dynamical collapse of the wave-function during a quantum measurement is caused by gravity.