# How can we get the mass of an uncharged proton?

How can we get the mass of an uncharged proton, i.e. how varies the mass of the charged proton if i remove the electric charge?

For the isotopic spin theory neutron and proton have the same mass and it is possible to distinguish that particles only for the different values of the third component of the isotopic spin.

This is an approximated symmetry because the masses are different and the charges too. In a ideal world we can remove the electric charge from the proton and we get a "uncharged" proton. The question is how the mass changes.

You can interpret that question as what it is the contribution to the mass due the charge, not only for proton but for all particles.

• Uncharged protons don't exist. – Brandon Enright Feb 21 '14 at 20:09
• This question doesn't make sense. What would a proton be without its electric charge? – Hunter Feb 21 '14 at 20:09
• The question makes sense but it is underspecified. It's like saying, what would history be like if there were three sexes rather than two; there would be many possible biologies and "possible worlds" with three sexes, and the effect on human society would surely be very different depending on the details. Analogously, any answer to this question has to start by selecting a particular scenario for the "neutral proton". e.g. It could be like the standard model, but the individual quarks are all electrically neutral. – Mitchell Porter Feb 21 '14 at 20:49
• It's been too long for me to venture and answer, but I agree with @MitchellPorter, you need to say a little more. That said, I think the electroweak contribution to the nucleon mass is quite small, so you shouldn't expect a large effect. – dmckee Feb 22 '14 at 0:21
• Matteo, there is a reason I'm an experimenter and not a theorists; questions like that feed into it. But a zeroth order reasoning would be to note that the nucleons are mostly binding energy and then look at the coupling constants for the strong and electroweek interactions. – dmckee Feb 22 '14 at 15:49

The charge of a particle is completely independent of its mass. If you had some technique (and there isn't one) to just remove charge but keep the proton exactly the same it would not change its mass.

Particle masses arise from a combination of the mass of its constituents and their interactions (the potential energy of particle interactions give it mass through $E = m c ^2$). For the case of the proton it is made up of 2 up quarks and 1 down quark. Its mass is a combination of the masses of each of these quarks and the energy binding them together.

I should further say since you mentioned the proton that a neutron is very similar to a proton only it has slightly different constituents and is neutral. You can in principle change a proton into a neutron by giving it some energy (the neutron is slightly more massive). But its important to remember that excluding charges, the two particles are still not identical.

• Also interesting: if an electron were a black hole it would be super-extremal. – Brandon Enright Feb 21 '14 at 20:11
• Well, the charges have something to do in defining the overall potential for the binding of the quarks into a proton: up and down repel, after all, so the binding energies would change if there existed no electromagnetic interaction. – anna v Mar 24 '14 at 13:15
• @annav: True, I guess at that point it depends how you interpret the question. – JeffDror Mar 24 '14 at 13:34

Suppose that there existed no charge , i.e. up and down quarks were neutral with respect to charge but had the mass they have.

up 2.3 MeV/c^2

down 4.8 MeV/c^2

The neutron is udd , so the mass contribution is 11.9 MeV/c^2 mass of neutron 939.6 Mev?c^2

the proton uud has a mass contribution________9.4 MeV/c^2 the mass of proton 938.3

difference of sum of constituent masses : 1.5MeV/c^2

difference of neutron and proton masses :1.3 MeV/c^2

As far as the strong interactions go it is the color charges that play a role in how many sea quarks and gluons are swirling around generating the almost a hundred times extra mass.

There is 0.2 MeV/c^2 difference in proton and neutron masses. The extra charges in the proton diminish the effect of the sum of the constituent masses, i.e. create 0.2 MeV/c^2 extra mass for the proton.

[handwaving ]

Let me suppose that this 0.2 MeV/c^2 excess difference between a neutron,which has two down quarks swirling around one up quark, and a proton which has two down quarks swirling around one up, is due to more quark gluon sea energy for the proton because the repulsion of the charges will be more, ( larger charges are involved). Then one could take this 0.2 MeV/c^2 excess of the proton mass with respect to the neutron as the effect of the charges. This would give an upper limit for how smaller the mass of a chargeless proton could be .

It seems reasonable to expect that the existence of charges will introduce more energy into a system's binding energy in the case of the proton, since it is a repulsion of like charges of uu whereas the like charges in the neutron dd are of smaller value. In addition the ballpark of the magnitude, 0.2MeV/c is about 10^-4 of the proton mass, compatible with the 5*10^- 5 coupling-constant-squared of the electromagnetic interaction, which would give the relative strength of the electromagnetic contribution versus the strong force.

[/handwaving]