Matter in Space

TL;DR

The paper proposes a novel linear mapping of octonions to coordinate space-time, addressing foundational issues in orthogonality and symmetry, and extending four-dimensional space-time with connections to historical ideas.

Contribution

It introduces a new linear mapping of octonions for space-time coordinate systems, clarifying pre-metric concepts and extending the tangent space of 4D space-time.

Findings

Explicit mapping of octonions to space-time coordinates

Resolution of pre-metric orthogonality issues

Extension of 4D space-time tangent space

Abstract

A new linear mapping of the linear vector space (LVS) of the octonions is suggested as an approach to the co-ordinatization of space-time. This approach resolves some perplexing issues concerning the validity of certain pre-metric notions of orthogonality and mirror symmetry. It makes explicit the tangent space extension of four-dimensional space-time that was alluded to earlier by the author [3] and shows that the null space component of the extended space can be related to ideas that were set out many years ago by H J S Smith.