Six-dimensional space-time from quaternionic quantum mechanics

TL;DR

This paper explores how quaternionic quantum mechanics implies a five-dimensional space for spin particles, but a natural reduction to three dimensions occurs, with potential experimental implications for detecting extra dimensions.

Contribution

It demonstrates a canonical reduction from five to three dimensions in quaternionic quantum mechanics and analyzes the behavior of dynamical variables in this framework.

Findings

Existence of a reduction from five to three dimensions in quaternionic quantum mechanics.

Dynamical variables oscillate around a cylinder, showing quasi one-dimensional behavior.

Potential experimental tests for extra dimensions at low energies.

Abstract

Quaternionic quantum Hamiltonians describing nonrelativistic spin particles require the ambient physical space to have five dimensions. The quantum dynamics of a spin-1/2 particle system characterised by a generic such Hamiltonian is worked out in detail. It is shown that there exists, within the structure of quaternionic quantum mechanics, a canonical reduction to three spatial dimensions upon which standard quantum theory is retrieved. In this dimensional reduction, three of the five dynamical variables are shown to oscillate around a cylinder, thus behaving in a quasi one-dimensional manner at large distances. An analogous mechanism is shown to exist in the case of octavic Hamiltonians, where the ambient physical space has nine dimensions. Possible experimental tests in search for the signature of extra dimensions at low energies are briefly discussed.