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).

Technically, the charge of a proton can be derived from its constituent 2 up quarks and 1 down quark, which have charges 2/3 and -1/3 respectively. I'm not aware of any deeper reason why these should be simple fractional ratios of the charge of the electron, however, I'm not sure there needs to be one. If you believe the stack of turtles ends somewhere, you have to accept there will eventually be (hopefully simple) coincidences between certain fundamental values, no?

I'm convinced there are some semi-classical explanations that just haven't been figured out.

Electrons are helically moving photons: https://www.researchgate.net/publication/281322004_The_elect...

That's some interesting/wacky stuff, but there has been more research to improve those calculations - like deriving the electron charge and magnetic moment.

Personally I like the idea that a proton is somehow literally an electron and 3 up quarks (a neutron gets 2 electrons and 3 up quarks). I am not a physicist though, so I'm sure there are reasons they "know" this is not the case.

I find it fascinating that some physicists say wave functions are somehow "real" and then we've got Jacob Barandes saying you don't even need wave functions to do the computations of QM: https://www.youtube.com/watch?v=7oWip00iXbo

IMHO there is a lot of exploration to be done without particle accelerators.

As soon as charge is quantized, this will happen. In any quantization scheme you will have some smallest charge. There are particles with charge +2 (the Delta++, for example), but ... anything that can decay while preserving quantum numbers will decay, so you end up with protons in the end. (ok, the quarks have fractional charge but that's not really relevant at scales we care about QED)

If the question is, why is quantum mechanics the correct theory? Well, I guess that's how our universe works...

One argument (while unsatisfying) is there are trillions of possible configurations, but ours is the one that happened to work which is why we're here to observe it. Changing any of them even a little bit would result in an empty universe.

If it wasn't the case then matter wouldn't be stable.

For a given calculation on given hardware, the 100th digit of a floating point decimal can be replicated every time. But that digit is basically just noise, and has no influence on the 1st digit.

In other words: There can be multiple "layers" of linked states, but that doesn't necessarily mean the lower layers "create" the higher layers, or vice versa.

Aren’t things like this usually explained by being the only viable configuration, or is that not the case here?

Or why the quarks that make up protons and neutrons have fractional charges, with +1 protons mixing two +2/3 up quarks and one -1/3 down quark, and the neutral neutron is one up quark and two down quarks. And where are all the other Quarks in all of this, busy tending bar?

This is "expected" from theory, because all particles seem to be just various aspects of the "same things" that obey a fairly simple algebra.

For example, pair production is:

    photon + photon = electron + (-)electron

   electron + photon = electron - photon

   proton = neutron + electron + (-)neutrino

The precise why of this algebra is the big question! People are chipping away at it, and there's been slow but steady progress.

One of the "best" approaches I've seen is "The Harari-Shupe preon model and nonrelativistic quantum phase space"[1] by Piotr Zenczykowski which makes the claim that just like how Schrodinger "solved" the quantum wave equation in 3D space by using complex numbers, it's possible to solve a slightly extended version of the same equation in 6D phase space, yielding matrices that have properties that match the Harari-Shupe preon model. The preon model claims that fundamental particles are further subdivided into preons, the "charges" of which neatly add up to the observed zoo of particle charges, and a simple additive algebra over these charges match Feyman diagrams. The preon model has issues with particle masses and binding energies, but Piotr's work neatly sidesteps that issue by claiming that the preons aren't "particles" as such, but just mathematical properties of these matrices.

I put "best" in quotes above because there isn't anything remotely like a widely accepted theory for this yet, just a few clever people throwing ideas at the wall to see what sticks.

[1] https://arxiv.org/abs/0803.0223

There are layers science can not access.