A Non-Classical Linear Xenomorph as a Model for Quantum Causal Space

TL;DR

This paper introduces a quantum model of Minkowski space's causal structure using a non-classical topos based on real quaternion algebras, highlighting key differences from classical models and aligning with algebraically quantized causal sets.

Contribution

It presents a novel quantum topos framework for modeling spacetime causal structure, extending classical quaternion algebra models into a non-classical quantum domain.

Findings

Quantum topos properties differ from classical counterparts

Model aligns with algebraically quantized causal set features

Highlights key properties of quantum causal structure

Abstract

A quantum picture of the causal structure of Minkowski space M is presented. The mathematical model employed to this end is a non-classical version of the classical topos {H} of real quaternion algebras used elsewhere to organize the perceptions of spacetime events of a Boolean observer into M. Certain key properties of this new quantum topos are highlighted by contrast against the corresponding ones of its classical counterpart {H} modelling M and are seen to accord with some key features of the algebraically quantized causal set structure.