Electron/Proton Charge and Quarks Charge

Question

So.. I´ve been investigating a bit on the subject of sub atomic particle charges and how they were defined, and basically what I´ve found out is that the defenition of the charge of an Electron or a Proton is totally arbitrary.

But then I remembered about the up quarks and down quarks and I got a bit confused because we say that a proton is positive due to the fact that it has 2 up quarks and 1 down quark, and that the up quark has a positive charge and the down quark has a negative charge.

My question is, is the charge of the up quark and down quark also arbitrary ?

Answer 1

We can define electrons as positively charged and protons as negatively charged and nothing fundamental about nature will change. We can say that the sign of the charge is arbitrary. But the amount of charge is not. And in the convention that we already use (electron as a negatively charged particle and proton as a positively charged particle) the up quark has $q=+\tfrac{2}{3}e$ and the down quark has $q=-\tfrac{1}{3}e$. If we change the sign of the proton's charge, of course we must also change the sign of the electric charge of the quarks and everything accordingly.

Further you can read about C-symmetry , CPT Invariance .

Answer 2

The answer for the sign of charge is given by the answer of Andrei. I will reply to

My question is, is the charge of the up quark and down quark also arbitrary ?

No the charges of the hadrons were and are measured in the lab. Pions, Kaons ,and all the plethora of resonances in the particle data tables have a definite charge a multiple of the charge of the electron, its negatives or zero.

Back in the sixties it was observed that other quantum numbers assigned to all these particles and resonances allowed them to be grouped in an SU(3) representations, now called the eightfold way.

An example of such a representation:

The hadronic decouplet , which predicted the Ω- from the symmetry of the representation, it had to exist and it was found.

Now SU(3) is the special unitary group of 3 states, this led to the proposal of the existence of a subset of 3 quarks with various quantum number combinations to add up to the charges of the observed particles . The proposed quarks, up and down, got the assigned charges so that they could add up to 1 for the proton and 0 for the neutron, and so on for consistency with other quantum numbers.

So the up and down charges are not arbitrary, once the electron charge is defined, they are constrained by the symmetries of the flavor SU(3) group, all observed hadronic particles and resonances fill a niche in one of its representations.