Spin and Entanglement in General Relativity

TL;DR

This paper explores how relativistic quantum spin and entanglement can be embedded within general relativity, revealing complex spin structures in gravitational fields and extending prior theoretical frameworks.

Contribution

It introduces a method to embed the quantum theory of relativistic spin into general relativity using a local induced representation, connecting spin, entanglement, and gravity.

Findings

Complex spin structures exist in gravitational fields.

Spin entanglement behavior is analyzed in a relativistic gravitational context.

The embedding of relativistic spin theory into GR is explicitly constructed.

Abstract

In a previous paper, we have shown that the classical and quantum relativistic dynamics of the Stueckelberg-Horwitz-Piron [SHP] theory can be embedded in general relativity (GR). We briefly review the SHP theory here, and, in particular, the formulation of the theory of spin in the framework of relativistic quantum theory. We show here how the quantum theory of relativistic spin can be embedded, using a theorem of Abraham, Marsden and Ratiu, and also explicit derivation, into the framework of GR by constructing a local induced representation. The relation to the work of Fock and Ivanenko is also discussed. We show that in a gravitational field there is s highly complex structure for the spin distribution in the support of the wave function. We then discuss entanglement for the spins of a two body system.