Why is matter electrically neutral?

When some symmetry breaking mechanism in the early universe separated matter from anti-matter, particles were segregated from their anti-particles. And yet, the sign of the electric charge was not the criterion for deciding who went where. Matter has the positively charged up quark (2/3) and the negatively charged down quark (-1/3) and the electron (-1). Anti-matter has their anti-particles. If sign of electric charge was the deciding criterion for separating matter from anti-matter, all particles in our universe ought to have had the same sign of charge. That is not the case, and yet matter is electrically neutral! How could that have come about?

Even the algebraic proof based on the octonions, which shows quantisation of electric charge, naturally clubs positively charged particles together, when their states are made from a Clifford algebra:

Particles and charge Anti-particles and charge

Neutrino 0 Anti-neutrino 0

Anti-down quark 1/3 down quark -1/3

Up quark 2/3 anti-up -2/3

Positron 1 electron -1

What picks the up quark from the left, and down and electron from the right, and club them as matter, and yet maintain electrical neutrality?

We have proposed that the criterion distinguishing matter from anti-matter is square-root of mass, not electric charge. One can make a new Clifford algebra afresh from the octonions, and show that square-root of mass is quantised:

Matter and square-root mass Anti-matter and sqrt mass

Neutrino 0 Anti-neutrino

Electron 1/3 Positron -1/3

Up quark 2/3 Anti-up -2/3

Down quark 1 anti-down -1

Let us now calculate the net electric charge of matter, remembering that there are three down quarks (color) and three up quarks (color):

0 + (-1x1) + (3 x 2/3) + (3 x -1/3) = 0

It seems remarkable that the sum of the electric charges of matter (particles with +ve sqrt mass) comes out to be zero. It need not have been so. This demonstration might help understand how matter-antimatter separation preserved electrical neutrality.

Before this separation, the net square-root mass of matter and anti-matter was zero, even though individual sqrt masses were non-zero. In this we differ from the standard gauge-theoretic picture of EW symmetry breaking and mass acquisition. In EW, particles are massless before symmetry breaking, because a mass term in the Lagrangian breaks gauge invariance. However, for us sqrt mass is not zero before the symmetry breaking - its non-zero value was already set at the Planck scale (and cosmological expansion scaled down actual mass values while preserving mass ratios). Indeed it is rather peculiar if prior to the symmetry breaking particles have electric charge but no mass. For us, QFT on a spacetime background (and hence gauge theories) are not valid before the left-right symmetry breaking. In fact spacetime itself, along with gravitation, emerge after this symmetry breaking, as a result of the quantum to classical transition. Spacetime emerges iff classical matter emerges.

Prior to the symmetry breaking, dynamics is described by trace dynamics, there is no spacetime, and we have `atoms' of space-time-matter. The concepts of electric charge and mass are not defined separately....there is only a charge-square-root mass [a hypercharge can also be defined, as for EW] and this is the source for a unified force in octonionic space.