A Novel Approach to Extra Dimensions

TL;DR

This paper introduces a new mathematical framework linking one-dimensional time structures to higher-dimensional spacetime, offering insights into symmetry breaking and properties of the Standard Model of particle physics.

Contribution

It presents a novel approach connecting arithmetic structures of time to the emergence of spacetime dimensions and symmetries relevant to particle physics.

Findings

Derivation of four-dimensional spacetime from time-based arithmetic structures

A natural symmetry breaking mechanism leading to Standard Model properties

Mathematical development linking higher-dimensional forms to physical symmetries

Abstract

Four-dimensional spacetime, together with a natural generalisation to extra dimensions, is obtained through an analysis of the structures and symmetries deriving from possible arithmetic expressions for one-dimensional time. On taking the infinitesimal limit this simple one-dimensional structure can be consistently equated with a homogeneous form of arbitrary dimension possessing both spacetime and more general symmetries. An extended 4-dimensional manifold, with the associated spacetime symmetry, provides a natural breaking mechanism for a higher-dimensional form and symmetry of time. It will be described how this symmetry breaking leads to a series of distinct properties of the Standard Model of particle physics, deriving directly from the natural mathematical development of the theory.