Quantum of area from gravitation on complex octonions

TL;DR

This paper proposes that a quantized area element emerges from a complex octonion-based quantum gravity model, supported by scattering results indicating a minimum interaction area, bridging quantum and classical gravity.

Contribution

It introduces a novel operator formulation of Euclidean quantum gravity using non-associative complex octonions, linking quantized charges to a minimum area element.

Findings

Minimum scattering cross section from spin contribution.

Finite charges imply a quantized minimum area.

Model suggests a connection to Loop Quantum Gravity.

Abstract

Using spin 1/2 particle elastic scattering on a fixed target, in a 1/|x| potential on Euclidean metric, a minimum scattering cross section appears from the spin contribution. Interpreted as semi-classical limit of an earlier proposed operator formulation of four dimensional Euclidean quantum gravity, using non-associative complex octonion algebra, this is understood as an area quantum for the observation: Existence of finite (quantized) charges yields a minimum area element of interaction. This suggests that models built on the fundamental assumption of a quantized area element (namely as in Loop Quantum Gravity) may in principle approximate General Relativity in the non-quantum limit.