Comment by adrian_b

The fact that the proton has the same charge in absolute value as the electron is just a consequence of the fact that the 8 elementary particles at the lowest energy level, i.e. electron and its neutrino, the 3 up quarks and the 3 down quarks have charges that sum to zero in a 3-dimensional charge space.

These 8 particles and their 8 antiparticles are located in the corners of 2 cubes of unit edge in that 3-dimensional charge space. One cube is in the first octant of the coordinates, with 1 corner in the origin, while the other cube is in the opposite octant, also with 1 corner in the origin.

The neutrino and the antineutrino are in the origin, while the electron and the positron are in the opposite corners of the cubes, in the points (-1,-1,-1) and (1,1,1), and the quarks and the antiquarks are in the 12 off-diagonal corners of the 2 cubes.

As functions of the position vector of a particle in this 3-dimensional charge space, the electric charge is the component of the position vector that is parallel to the cube diagonal that passes through origin and the corners of the electron and positron, while the corresponding component that is orthogonal to the diagonal is the so-called color charge (hence chromodynamics; while the electric forces attempt to make null the 1-dimensional electric charge, the strong forces attempt to make null the 2-dimensional color charge), which is non-null only for the quarks and antiquarks, which are off-diagonal, and it is null for electron, neutrino and their antiparticles.

The projections of the off-diagonal corners of the cubes on the diagonal are at one third and two thirds distances from origin, which is why the electric charges of the quarks are 1/3 and 2/3 in absolute value (where the unit of electric charge is the electron charge, i.e. the diagonal of one unit cube), even if in the charge space all the particles have coordinates that are either 1 or 0 in absolute value.

While this symmetry of the charges is interesting, it is not known why it is so.

In any case, if this symmetry had not existed, the Universe as we know it could not exist, because this symmetry ensures that in the nucleons the total color charge of the quarks is null, so they no longer interact through strong forces (except at very short distances, where the residual forces bind the nucleons into nuclei) and at the next level the total electric charge of the atoms is null, so they no longer interact through electric forces (except at very short distances, where the residual forces bind the atoms into molecules).

The same symmetry exists for the other 2 groups of 8 particles and 2 groups of 8 antiparticles, where the muon and the tauon correspond to the electron, because those particles have greater masses but identical charges with the first groups.

In the initial state of the Big Bang, this symmetry of the charges ensures that even if there were only particles in equal numbers and without any antiparticles, the total electric charge and the total color charge of all matter was null.

While the neutrinos do not contribute to any of the charges, their presence ensures that the total spin, i.e. the total angular momentum, was also null.