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I have read these questions:
My question is different. We live in a world, where quarks can have a real fraction of the elementary charge (-1/3 or 2/3). I do understand that the experimental data fit the models and that Baryons are made up of three quarks, and that those quarks can have -1/3 or 2/3 the elementary charge. This way, the quarks can combine so that the Baryon will have an integer of the elementary charge. This way, the nucleus and the electron can be in a stable atomic state, where their electric charges cancel (attract) exactly. Any other way, the atom would not be stable.
So electron says: hey quarks, let's team up, let's make an atom.
Quarks: Hey, great idea, how much electric charge do you have? Let's call it e. OK so we will team up of three of us, so we will just take each of us -1/3 or 2/3 of your charge.
Electron says: Great!, I feel it, this way we can have a stable atom.
I mean come on! I do understand the respect that the experimental data tells us that electrons and quarks are both elementary particles.
It seems that the quarks teamed up exactly so three of them in Baryons so they can cancel out (attract) exactly the electron's electric charge. Now I do understand that there could be Baryons made up of four quarks, and they could have then -1/4 and 3/4 charge of the electron's elementary charge. This would work too, and the neutron and proton would have the same way an integer of the electron's charge. So the atom would be stable.
We could do this with any integer number of quarks. But, come on, my question is, what if the quarks' charge could only be -1/sqrt(3) and 2/sqrt(3)? How many quarks would we then need to make up the nucleus - to make it match the electron's charge? Is it mathematically possible to have any kind of electric charge for the quark? We could simply put as many valence quarks in a Baryon to make a stable atom?
Is it a coincidence that quarks have -1/3 and 2/3 the electron's charge and there are three quarks in a Baryon? Could we have quarks with any kind of electric charge, like Sqrt(3)*elementary charge? Could we make a stable atom this way too? How many quarks would we put in this case into a Baryon to make atoms stable?
I accept and respect that currently, electrons are elementary particles. Is it impossible as of today's view that both electrons and quarks are made up of the same something smaller (strings)?