The hint from quantum field theory (and things like lattice gauge theory) is that charge emerges from interesting topological states/defects of the underlying field (by "interesting topological shapes" I mean - imagine a vortex in the shape of a ring/doughnut). It's kind of a topological property of a state of the photonic field, if you will - something like a winding number (which has to be an integer). Electric charge is a kind of "defect" or "kink" in the photonic field, while color charge (quarks) are defects in the strong-force field, etc.
When an electron-positron pair is formed from a vacuum, we get all sorts of interesting geometry which I struggle to grasp or picture clearly. I understand the fact that these are fermions with spin-1/2 can similarly be explained as localized defects in a field of particles with integer spin (possibly a feature of the exact same "defect" as the charge itself, in the photonic field, which is what defines an electron as an electron).
EDIT:
> However, there are no theories why this is -- they are simply measured and that is it.
My take is that there _are_ accepted hypotheses for this, but solving the equations (of e.g. the standard model, in full 3D space) to a precision suitable to compare to experimental data is currently entirely impractical (at least for some things like absolute masses - though I think there are predictions of ratios etc that work out between theory and measurement - sorry not a specialist in high-energy physics, had more exposure to low-energy quantum topological defects).
> something like a winding number (which has to be an integer). Electric charge is a kind of "defect" or "kink" in the photonic field, while color charge (quarks) are defects in the strong-force field, etc.
Right, but then you have the questions of 1) why do leptons have (a multiple of) the same fundamental unit as quarks, and 2) why does that multiple equal the number of quarks in a baryon, so that protons have a charge of exactly the same magnitude as electrons?
I mean, I guess you could say that charge comes from (or is) the coupling of the quark/lepton field to the electromagnetic field, and therefore if it's something that's quantized on the electromagnetic side of that, then quarks and leptons would have the same scale. I'm not sure that's the real answer, much less that it's proven. (But it might be - it's a long time since my physics degree...)
When an electron-positron pair is formed from a vacuum, we get all sorts of interesting geometry which I struggle to grasp or picture clearly. I understand the fact that these are fermions with spin-1/2 can similarly be explained as localized defects in a field of particles with integer spin (possibly a feature of the exact same "defect" as the charge itself, in the photonic field, which is what defines an electron as an electron).
EDIT:
> However, there are no theories why this is -- they are simply measured and that is it.
My take is that there _are_ accepted hypotheses for this, but solving the equations (of e.g. the standard model, in full 3D space) to a precision suitable to compare to experimental data is currently entirely impractical (at least for some things like absolute masses - though I think there are predictions of ratios etc that work out between theory and measurement - sorry not a specialist in high-energy physics, had more exposure to low-energy quantum topological defects).