Comment by ajkjk
2 years ago
I don't know the actual answer, but from my understanding of QFT the answer is going to be roughly this shape:
Charge is not actually a quantity on the real number line; it's more of a "count" of something. Not sure what exactly. The "topological defect" model of charges in 2d is a decent analogy though, in which a charge can be e.g. a count of how many vortices there are in a field which are oriented in a certain direction (picture a bathtub with a bunch of drains, and ask, how many tornado-like vortices, if we count clockwise vortices as +1 and counterclockwise as -1, are there? The number can vary but obviously it has to be an integer because what would half a vortex even mean?)
But that model is too simple for charge, since quarks have +-1/3 or 2/3 but the result always adds up to an integer in a hadron. Maybe it's something like a type of winding number or linking number? I don't know. Whatever it is, when the "correct" explanation is found, it will be obvious why it is always an integer and why its constituents are always 1/3 or 2/3, and it will no longer seem interesting to ask why it can't be any old fraction, because that misunderstands the "type" of object that it is counting.
Is there a reason why we say quarks have fractional charge instead of having just +-1 or +-2? And Then electron and proton would have -3 and +3?
That's purely by convention. It's just that we fist discovered electrons and protons and quarks with their fractional charges came in much later.
To be clear, we say that an electron has -1e charge: that "e" is the absolute value of the charge of an electron. The charge of an electron is approximately −1.602176634×10^−19 Coulombs. Quarks have either +-2(1.602176634×10^−19)/3 or +-(1.602176634×10^−19)/3 coulombs charge.
It's a fraction because we simply decided it was easier to describe an electron's charge as "e" and quark charges as being a fraction of that. It's entirely by convention.
We could've just as easily have described, like you mentioned, a quark to have either +-q or +-2q charge and electrons have -3q (where q=(1.602176634×10^−19)/3 C). We just happened to find electrons significantly before. It's also convenient as we don't see free quarks so every charge we see in the universe is a multiple of e, there's no advantage to going smaller than that.