Overview of the structural unification of quantum mechanics and relativity using the algebra of quantions

TL;DR

This paper introduces the algebra of quantions as a unified mathematical framework for combining quantum mechanics and relativity, emphasizing its structural advantages over traditional division algebras.

Contribution

It provides an overview of quantions, a non-division algebra that unifies quantum mechanics and relativity, and discusses its implications for electroweak theory and wave function interpretation.

Findings

Quantions unify quantum mechanics and relativity within a single algebraic structure.

Lack of division in quantions allows compatibility with relativistic space-time.

Implications for the interpretation of wave functions in quantum theory.

Abstract

The purpose of this contribution is to provide an introduction for a general physics audience to the recent results of Emile Grgin that unifies quantum mechanics and relativity into the same mathematical structure. This structure is the algebra of quantions, a non-division algebra that is the natural framework for electroweak theory on curved space-time. Similar with quaternions, quantions preserve the core features of associativity and complex conjugation while giving up the unnecessarily historically biased property of division. Lack of division makes possible structural unification with relativity (one cannot upgrade the linear Minkowski space to a division algebra due to null light-cone vectors) and demands an adjustment from Born's standard interpretation of the wave function in terms of probability currents. This paper is an overview to the theory of quantions, followed by discussions.