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?
There does appear to be a deeper reason, but it's really not well understood.
Consistent quantum field theories involving chiral fermions (such as the Standard Model) are relatively rare: the charges have to satisfy a set of polynomial relationships with the inspiring name "gauge anomaly cancellation conditions". If these conditions aren't satisfied, the mathematical model will fail pretty spectacularly. It won't be unitary, can't couple consistently to gravity, won't allow high and low energy behavior to decouple,..
For the Standard Model, the anomaly cancellation conditions imply that the sum of electric charges within a generation must vanish, which they do:
3 colors of quark * ( up charge 2/3 - down charge 1/3) + electron charge -1 + neutrino charge 0 = 0.
So, there's something quite special about the charge assignments in the Standard Model. They're nowhere near as arbitrary as they could be a priori.
Historically, this has been taken as a hint that the standard model should come from a simpler "grand unified" model. Particle accelerators and cosmology hace turned up at best circumstantial evidence for these so far. To me, it's one of the great mysteries.
So they have to cancel, or we don't have a universe? ("Have to" not because we need electrical neutrality for large-scale matter - though we do need that - but because you can't build a quantum field that doesn't explode in various ways without it.)
There's always some risk of confusing the model with the reality, but yeah, if you have chiral fermions interacting through gauge fields and gravity, the charges have to say satisfy all of the anomaly cancellation conditions (there's about half a dozen) or the model will be inconsistent.
I'm aware of the charge coming from quarks, but my point remains.
> you have to accept there will eventually be (hopefully simple) coincidences between certain fundamental values, no?
When the probability of coincidence is epsilon, then, no. Right now they are the same to 12 digits, but that undersells it, because that is just the trailing digits. There is nothing which says the leading digits must be the same, eg, one could be 10^30 times bigger than the other. Are you still going to just shrug and say "coincidence?"
That there are 26 fundamental constants and this one is just exactly the same is untenable.
I think I agree with you. It could be just a matter of static bias or some other fairly simple mechanism to explain why these numbers are the same.
Imagine an object made of only red marbles as the 'base state'. Now you somehow manage to remove one red marble: you're at -1. You add a red marble and you're at +1. It doesn't require any other marbles. Then you go and measure the charge of a marble and you and up at some 12 digit number. The one state will show negative that 12 digit number the other will show positive that 12 digit number.
Assigning charge as being the property of a proton or an electron rather than one of their equivalent constituent components is probably a mistake.
If you imagine the universe is made of random real fundamental constants rather than random integer fundamental constants, then indeed there's no reason to expect such collisions. But if our universe starts from discrete foundations, then there may be no more satisfying explanation to this than there is to the question of, say, why the survival threshold and the reproduction threshold in Conway's Game of Life both involve the number 3. That's just how that universe is defined.
Why do you assume the two have to be small integers? There is nothing currently in physics which would disallow the electron to be -1 and the proton to be +1234567891011213141516171819. The fact they are both of magnitude 1 is a huge coincidence.
I'm not assuming they have to be small integers—I'm saying that if the universe is built on discrete rather than continuous foundations, then small integers and coincidences at the bottom-turtle theory-of-everything become much less surprising. You're treating the space of possible charge values as if it's the reals, or at least some enormous range, but I consider that unlikely.
Consider: in every known case where we have found a deeper layer of explanation for a "coincidence" in physics, the explanation involved some symmetry or conservation law that constrained the values to a small discrete set. The quark model took seemingly arbitrary coincidences and revealed them as consequences of a restrictive structure. auntienomen's point about anomaly cancellation is also exactly this kind of thing. The smallness of the set in question isn't forced, but it is plausible.
But I actually think we're agreeing more than you realize. You're saying "this can't be a coincidence, there must be a deeper reason." I'm saying the deeper reason might bottom out at "the consistent discrete structures are sparse and this is one of them," which is a real explanation, but it might not have the form of yet another dynamical layer underneath.
It's simple to say "Ah well, it's sparse" that doesn't mean anything and doesn't explain anything.
Symmetries are equivalent to a conserved quantity. They exist because something else is invariant with respect to some transformation and vice versa. We didn't discover arbitrary constraints we found a conserved quantity & the implied symmetry.
"There are integers", "the numbers should be small" all of these are nothing like what works normally. They aren't symmetries. At most they're from some anthropic argument about collections of universes being more or less likely, which is its own rabbit hole that most people stay away from.
Perhaps only visible matter is made up of particles with these exactly matching charges? If they did not match, they would not stay in equilibrium, and would not be so easily found.
You seem to be contradicting yourself, having already said:
>I'm aware of the charge coming from quark
So it's not +huge_number because the number of quarks involved is small. Sure we still don't understand the exact reason, but it's hardly as surprising that, uh, charge is quantized...
Well yes, but the coincidence that Quarks have charges of multiples of another particle, that is not made up of quarks, should rise your brow, shouldn't it?
Like we could accept coincidences if at the bottom is all turtles, but here we see a stack of turtles and a stack of crocodiles and we are asking why they have similar characteristics even if they are so different.
Whence your confidence? As they say in math, "There aren't enough small numbers to meet the many demands made of them." If we assume the turtle stack ends, and it ends simply (i.e. with small numbers), some of those numbers may wind up looking alike. Even more so if you find anthropic arguments convincing, or if you consider sampling bias (which may be what you mean by, "in stable particles that like to hang out together").
Which makes every constant fair game. Currently, we don’t have a good process for explaining multiple universes beyond divine preference. Hence the notion that a random number settled on mirror whole sums.
