Real wave equations, spin origin of charge, and outlook on particle physics

TL;DR

This paper proposes a novel framework for particle physics that links real wave equations, topology, and the origin of charge to a topological interpretation of spin, suggesting particles are knotted vortex structures.

Contribution

It introduces a new conceptual model where space and time's topology underpins particle properties, connecting spin, charge, and fundamental interactions through topological and geometric structures.

Findings

Reinterprets wave equations with real matrices and topological significance.

Proposes spin origin of charge (SOC) based on topological vortex structures.

Links coupling strengths of fundamental interactions to spin angular momentum.

Abstract

Radical revision on the conventional spacetime picture, illusion or emergent phenomenon, has been the focus of the speculations on the unified frameworks for fundamental interactions in nature. Compared to strong experimental credence to the standard model of particle physics there is practically no relation of these speculations with the world of real particles. In this paper we present a new conceptual framework for particle physics in which nontrivial geometry and topology of space and time have fundamental reality. To develop this model we proceed with the analysis of the standard wave equations and make them real using the transformation rule $i=\sqrt{-1} \rightarrow C=\begin{bmatrix} 0 & 1 \\ -1 & 0 \end{bmatrix}$. Topological significance is attached to $i$ in terms of a point defect in 1D directed line. New interpretation of Schroedinger wave equation and $Z_2$ vortex throw light on the nature of spin. A new meaning is also obtained on U(1) gauge symmetry and charge. Novel properties of C-matrix and known applications are presented. Topological origin of spin is inferred from the interpretation of Pauli algebra that they signify 2D directed area in phase space as topological obstruction. Electron magnetic moment decomposition in QED serves the basis for the proposition: spin origin of charge (SOC). A dynamical logarithmic spiral geometric structure comprising of 2+1D braids, 3 vortices with associated three 2-spinors is envisaged based on SOC. It is termed as meta-electron; meta-neutrino has 2-vortex structure. These are the only building blocks of all particles having the knotted vortex structures in our model. Coupling strengths of the three fundamental interactions are related with the magnitudes of the spin angular momentum of constituent spinors of the meta-electron.