Why so much kinetic energy inside a proton?

Question

I'm reading 'Waves in an impossible sea' by Matt Strassler - a very good, popular science book, by the way - and he explains that the rest mass of a proton mostly comes from the kinetic energy of the quarks and gluons whizzing around. But I don't understand why there is quite so much energy in there - and why it is exactly what it is.

Intuitively, one could imagine that once everything was a quark-gluon soup, and when the universe cooled a bit, everything started coagulating into protons, neutrons etc, and if the kinetic energy inside one of those was too high, it would fall apart, so the only ones that 'survived' were the ones whose internal energy was low enough.

I'm sure the word 'quantum' will begin to show up around here, but the question that bugs me is, would it be possible, theoretically, to take the components of a proton, and very carefully place them together, so they don't start racing around? And why not?

Answer 1

The simplistic answer is that a proton is very small. The quarks are not free, but are confined to a small region. By the uncertainty principle a small uncertainty in the position of the quarks implies a large uncertainty in their momentum. The expectation of the momentum is zero, but the uncertainty is large. To calculate the energy you square the momentum, so the energy has a non-zero expectation that is relatively large.

Answer 2

I'm sure the word 'quantum' will begin to show up around here, but the question that bugs me is, would it be possible, theoretically, to take the components of a proton, and very carefully place them together, so they don't start racing around? And why not?

The impossibility of doing that is why everybody in the know emphasises that our world is quantum in nature. You are thinking of the stuff inside a proton as classical objects. They are not. They obey quantum theory, and we are very much forced to accept their crazy behaviour because experiments ruled out all the classical theories that we very much wished to be true.

The mathematically correct fundamental idea here is actually just the fact in Fourier transforms that waves with a sharp localisation in position is necessarily spread out in momentum, and vice versa (as Dale's answer emphasises), and there is really not that much more to it. However, the difficulty in accepting this is really just that we have to give up classical particles conception of things, and instead accept that these things are waves. They are quantum waves, but the quantum part, important as it is, is not the part that directly causes this behaviour. You have to accept that they are waves, and it is not clear as of your current understanding why they must be so.

But it is not a cover-up. Physicists are more than eager to tell you all the experiments that forced us to accept that reality is quantum.

Answer 3

"First, it gets some mass from the masses of its quarks, and some more from their movements. Next, it gets mass from the strong force energy that glues those quarks together, with this force manifesting as ‘gluons.’ Lastly, it gets mass from the dynamic interactions of the proton’s quarks and gluons." from https://www.jlab.org/news/releases/charming-experiment-finds-gluon-mass-proton

The kinetic energy of the quarks is not the whole mass of the proton. I interpret the energy from the gluons as 'potential energy', just like the virtual photons which bind electrons to atomic nuclei.

Original answer below:

The other two answers are very good, but I always thought of this in a different way.

Rather than large kinetic energy or large uncertainty in momentum, the reason the mass of the proton is large is that the potential energy is large. The potential energy is due to the binding of quarks together by the strong force which is carried by gluons. (I'm not saying Strassler is wrong, but that this is essentially an equally valid explanation.)

The rest mass of the up and down quarks in the proton is very small, roughly 0.1% of the rest mass of the proton. However, the strong force is called the strong force for a reason. If we try to knock the quarks out of the proton, the gluons try to claw it back, and they do so with a lot of energy. This is analogous to a rocket taking off without enough energy to leave earth's orbit: it simply falls back down. The energy required by the rocket to leave orbit is the potential energy at the launch site. The energy required to break apart the proton is the proton's mass, since that mass is due to potential energy. That is also called the binding energy, like the protons and neutrons bound in atomic nuclei.

But there is another wrinkle due to the way the strong force works. Unlike free electrons, there are no free quarks except for extremely brief intervals. In those intervals, virtual quarks are created out of the vacuum so that the particles observed after some brief time are either mesons (quark pairs) or baryons (quark triplets like the proton). So in order to break up the proton, you also need to create these particles, which is really just part of the binding energy of the proton. That is why the potential energy is so large.

Also see:

https://en.wikipedia.org/wiki/Strong_interaction

https://en.wikipedia.org/wiki/Mass%E2%80%93energy_equivalence