Is the electromagnetic charge of a single electon exactly the same* as that of a proton? Or is there perhaps some small difference between them? If they are exactly the same,* why? It just seems unlikely that it would just happen to turn out that way for no reason, I guess.
*I know that electrons are negatively and protons are positively charged. I guess I’m asking about the absolute values of the charges of electrons and protons, except that I don’t think you can take the absolute value of a physical phenomenon. Or maybe you can. The important thing is that I’m learning. 
Take a look at Elementary Charge - quarks have a charge that is an integer multiple of 1/3e, but cannot exist as stable entities on their own. Protons and electrons have charge of +/- e because the quarks charge combine that way, and all stable quark combinations are integer multiples of e.
Si
Electrons are not made of quarks. They are considered elementary. This in fact makes the issue of why protons and electrons have the same charge even harder to explain.
At some point the explanation is: that’s just the way it is. Along the way one can mention that:
Charge is a conserved quantity. You can’t remove a positive charge from the universe without also removing a negative charge, and the same applies to adding charge. For example a neutron decays into a proton and an electron.
The charges of the electron and proton are measured to have the same magnitude to within one part in 10[sup]21[/sup]. That is, the proton’s charge must be between -0.999999999999999999999 and -1.000000000000000000001 times that of an electron, according to measurements. Why are these charges apparently equal and opposite?
We don’t know. The Standard Model of particle physics provides no reason for why electric charges should appear in integer multiples of a single elementary value. This is one of the (several) strong motivations for seeking a so-called “grand unified theory” (GUT), in which all fundamental forces derive from a deeper “simple” framework.
The problem of electric charge quantization is an active area of theoretical research (through work on GUTs) and experimental research (through ever more precise charge measurements and through searches for fractionally charged particles).
Note that, if there exists such a thing as a magnetic charge (we’ve never repeatably observed one, but there’s no reason to believe they can’t exist, just that if they do they’re very rare), then you can derive the quantization of electric charge from quantum mechanics.
Do we know if the universe is has neutral charge as whole, i.e. same amount of positive and negative charge?
This is what motivated me to ask the question. It’s like protons and electrons are two totally different things that just happen to link up nicely, seemingly coincidentally.
Anyway, if charge is to be conserved and neutrons break down into protons and electrons, that would seem to imply that they are really, really close in value.
Does anyone have any ideas on what would happen if the magnitude of the charges of electrons and protons varied by more than they do? That is, if instead of being off by, say one part in 10[SUP]-21[/SUP], it was more like 10[SUP]-12[/SUP]? I guess what I’m asking is how much could they vary before the universe starts behaving much differently?
Thanks for the replies so far.
Except they aren’t totally different. In order for the Standard Model to work as a consistent quantum field theory, there’s the issue of anomalies. Basically, the whole thing only works if there are certain cancellations between the charges of the (apparently) fundamental particles involved. So the charge of the electron winds up closely related to that of the quarks.
Yet current theory doesn’t quite imply an exact relationship that would require an exact cancellation requiring an exactly opposite charge for electrons and protons. But that the charges are exactly equal does at least plausibly fall out naturally from the Standard Model. Anything additional required is probably minimal.
Even a small variation would cause real problems in molecules and macromolecular structures. If the electrons that would fit into stable orbits around an atom caused a net positive or negative charge, then atoms would repel each other by default. Molecular bonds would probably still form, but they’d have to be strong enough to overcome that repulsion. But bigger complexes would have even more trouble. The structure of ice is due to very weak bonding molecules (the oxygen is weakly negative and the hydrogens are weakly positive). It wouldn’t take much to disrupt those kinds of forces. At an even bigger scale, many enzymes in the body depend on very precise fits and weak electrical attraction to work. To get large objects to be neutral, you’d have to have ionized atoms with incomplete electrical shells, and those aren’t very stable. It might be that big molecules like DNA or enzymes would be impossible, and there goes any chance of life.
What might work better is a scenario where electrons are exactly 1/2 or 1/3 the charge of a proton - you’d still wind up with atoms that are neutral. But you’d certainly change the fundamental rules of molecular bonding. Things might still work, but not anything like what we know.
Of course, this is just one example. Most radioactive/nuclear interactions involve protons being able to turn into neutrons (and vice versa). For example, stars fuse four hydrogen into one helium, but the reaction requires that you turn four protons into two protons and two neutrons because a four-proton nucleus isn’t stable. So… if the charges don’t match, you either need other charged particles with fractional charges, or you shut down the ability to make a large variety of atoms. Maybe these fractionally charged particles can solve some of the molecule problems I mentioned, but once again we wind up with something that doesn’t look much like what we know today.
I believe we’re fairly sure it has a neutral charge, but I’m no nuclear physicist.
What makes a Universe turn neutral … Lust for gold? Power? Or were you just born with a heart full of neutrality?
A mole of neutral hydrogen (2 X 1.2 X 10^24 atoms) would need an extra 1.4 X 10^13 (or so) electrons to make it charge neutral. I expect that’d make the bulk material a heck of a good conductor. You’d have to have all these free electrons floating around just to get any atoms to condense into a solid state.
I think you multiplied by two twice, there.
And I wouldn’t expect that to be a particularly good conductor. A typical metal has one or two free electrons per atom, while the substance you’re talking about only has one free electron per 10[sup]12[/sup] atoms.