alt Hacker NewsTechnically, 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?
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> you have to accept there will eventually be (hopefully simple) coincidences between certain fundamental values, no?
No. It’s almost certainly not a coïncidence that these charges are symmetric like that (in stable particles that like to hang out together).
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.
Shrugging and calling it a coincidence is generally not an end state when figuring out how something works.
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.