Geometrical modification of quaternionic quantum mechanics

TL;DR

This paper proposes a geometrical modification to quaternionic quantum mechanics that incorporates a possible-worlds semantics, enabling the prediction of fundamental spacetime features such as dimensionality, topology, and metric signature.

Contribution

It introduces a novel axiomatic framework for quaternionic quantum mechanics with a possible-worlds interpretation, linking quantum theory to spacetime geometry and topology.

Findings

Predicts spacetime dimensionality and topology

Determines metric signature and distinguished directions

Links quantum mechanics with spacetime geometry

Abstract

We present an axiomatic modification of quaternionic quantum mechanics with a possible-worlds semantics capable of predicting essential "nonquantum" features of an observable universe model - the dimensionality and topology of spacetime, the existence, the signature and a specific form of a metric on it, and certain naturally distinguished directions (vistas) in spacetime unrelated to its metric properties.