# Are the charges of electrons necessarily integer values?

It seems as if the charge we have labelled the electron with has simply been inferred by comparing it to the proton, in which case it is pretty much exactly the opposite, so we give the proton and electron charges of +1 and -1 respectively.

This is fine, but when we get to the standard model and we see electrons in the matter chart alongside up and down quarks with fractional charges, how do we know the charges they have been given are correct???

Color confinement says that standalone quarks can not been observed, so how can we know that, for example, a down quark has a third the charge of an electron?

Thanks!

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This is titled "charge of an electron", but it seems you are mostly interested in the charge of the quarks.

We know that the sum of the quark charges in a proton is 1 and for a neutron it's 0. We also know that the sum of the squares of the quark charges in the proton is 1 and for a neutron it's 2/3. Solve.

I think that, really, I'm interested in the actual relationship between the charges of the electron and quarks. So how do we know that the sum of the quark charges is actually 1? Is this in relationship to the charge we have given to the electron? Why is it not, for example 6 thirds, and the electron negative 6 thirds, where have we assumed the charges of the quarks from to make up the charge of the proton?
This is interesting about the sum of the squares, but I don't know why that's important...? Sorry, I'm quite a physics newbie!
Anyway, if all the charges we have given to the elementary particles (electrons included) are relative to biproducts of their resultant particles, how can we know if we have the right understanding?!

Meir Achuz
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The charges they have been given are correct!!!

Staff Emeritus
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We define a "unit" of charge to be a certain number of Coulombs, so that an electron has one unit of charge. We observe that all free objects have only integral charge.

We could have defined it to be half as big, and then made the observation that all free objects have only even integral charge. Or we ould have defined it to be twice as big, and then made the observation that all free objects have only half-integral charge. But why?

We know now that this observation is because net charge is caused by an imbalance in electrons, so must occur in integer multiples of an electron's charge.

Ok thanks, this is great, and of course I understand why we have called the charges of protons and electrons +1 and -1 :) it was really for the sake of argument.

The main purpose of this thread though is to ascertain whether a quark's charge is exactly as the standard model states in relation to an electron. Really, how could we possibly know if 3 down quarks possess the same charge as an electron?

Staff Emeritus
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We know that the sum of the quark charges in a proton is 1 and for a neutron it's 0. We also know that the sum of the squares of the quark charges in the proton is 1 and for a neutron it's 2/3. Solve.

Sorry I don't know why you are squaring and summing the charges of the quarks, so I don't know what exactly to solve! You are turning decreasing the magnitudes of each charge and turning negative values into positives. I don't know what this achieves though.... I am intrigued! Could you elaborate??!

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We know, from measurements, what the total charge and total charge squared is for the constituents of the proton and the neutron. From that, we can infer the charges of the constituents.

Bill_K
The quark content of a proton is uud ⇒ 2 Qup + Qdown = 1
The quark content of a neutron is udd ⇒ Qup + 2 Qdown = 0

The solution of these two equations is Qup = 2/3, Qdown = -1/3

Vanadium 50, please elaborate on this!!!! I don't know why you're talking about squaring the charges of the quarks.

How can we measure the squared total charge? I don't understand the physical experiment of measuring the squared charge of something, especially when the contents are inseparable - surely all you can measure is the net charge of a neutron, and zero squared doesn't give 2/3!!!

If you are asking why, fundamentally, should the electron charge be the opposite of the proton charge, I don't think there is an answer. Of course the proton charge comes from the charges of the quarks, but why the quark should have the charges that they do is also unknown. They come from some nice group theory, but really there is no known reason they couldn't have been any number of other things. Those other things would not give rise to the world we see around us, so they are experimentally excluded, but there is no deeper explanation than that at this stage.

Vanadium 50, please elaborate on this!!!! I don't know why you're talking about squaring the charges of the quarks.

How can we measure the squared total charge? I don't understand the physical experiment of measuring the squared charge of something, especially when the contents are inseparable - surely all you can measure is the net charge of a neutron, and zero squared doesn't give 2/3!!!

You measure the charge and then square it. The charge happens to be a number that if we take the sum of the squares, it happens to be the values that Vanadium 50 said, as well as taking the sums.

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Staff Emeritus
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Vanadium 50, please elaborate on this!!!! I don't know why you're talking about squaring the charges of the quarks.

How can we measure the squared total charge? I don't understand the physical experiment of measuring the squared charge of something, especially when the contents are inseparable - surely all you can measure is the net charge of a neutron, and zero squared doesn't give 2/3!!!

The experiment is called http://en.wikipedia.org/wiki/Deeply_Inelastic_Scattering" [Broken].

Bill_K showed that with the quark assignment p = uud and n = ddu there is one solution. By adding the additional information from DIS, one can show that this assignment works when others do not.

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Great thank you all! So am I right in thinking that these values have been extrapolated using some method like simultaneous equations? Had something in my head that I couldn't quite explain and am finding it difficult to remember what it was now, I'll be back if I remember!

Bill_K
If you are asking why, fundamentally, should the electron charge be the opposite of the proton charge, I don't think there is an answer.
Consistency of the standard model demands it. Leptons and quarks occur in three "generations", and there's a requirement that the sum of the charges in each generation must be zero. Quarks come in three colors and you have to count each color as a separate particle, so the condition is:

Qelectron + Qneutrino + 3 Qupquark + 3 Qdownquark = 0

That's -1 + 0 + 3(2/3) + 3(-1/3) = 0

Consistency of the standard model demands it. Leptons and quarks occur in three "generations", and there's a requirement that the sum of the charges in each generation must be zero. Quarks come in three colors and you have to count each color as a separate particle, so the condition is:

Hmm, interesting, what is the origin of this condition?