Scaffolding of Spacetime

TL;DR

This paper explores the geometric Clifford algebra with signature (2,3) as a foundational framework for relativistic quantum mechanics, offering a new algebraic perspective on Pauli and Dirac matrices.

Contribution

It introduces the use of Clifford algebra with signature (2,3) to factor Pauli and Dirac vectors into complex bivectors, providing a deeper algebraic foundation.

Findings

Clifford algebra (2,3) underpins relativistic quantum mechanics.

Pauli and Dirac vectors are factored into complex bivectors.

Provides a new algebraic perspective on spacetime structures.

Abstract

The mathematical foundations of relativistic quantum mechanics is largely based upon the discovery of the Pauli and Dirac matrices. An algebra which lies at an even more fundamental level is the geometric Clifford algebra with metric signature (2,3)=(++---). In this geometric algebra both the fundamental Pauli vectors of space and the Dirac vectors of spacetime are factored into complex bivectors.