Here is a quote from Susskind's the Cosmic Landscape:

I'm having a very difficult time wrapping my head around this. I'm pessimistic that it can be explained how gluon's hold quarks together because in order to explain x you need to break x down into parts and as of yet we do not know of anything smaller than a gluon and a quark. How did they even discover this? Did they literally observe the gluons occupying space between quarks? Is it proven through equations? Further, is it simply an assumption that if bosons are occupying space between gluons, then they must be that which prevents the quarks from escaping from the nucleus, or is there more rigor involved?

Also regarding the fact that bosons can occupy the same space. I'm having trouble understanding that. How can you observe two bosons in the same space? It seems true by definition that there is one thing per one unit of space. Did they discover this through equations or observations?

I think the gluons are virtual gluons. We cannot directly observe things at this scale because they are so very very very small. It is derived from observations using particle colliders and a lot of complex math.

Both actually. Quantum Mechanics was developed about 90 years ago and describes particles using a wavefunction, which is a mathematical formula that describes the state a particle is in and how it behaves. Fermions, which are particles with spin 1/2, have a wavefunction that has to be rotated twice in order to get back to the original state. If you try to force two fermions together, the wavefunctions overlap in such a way as to destructively interfere with each other, which means that they CANNOT be in the same place and the same state at the same time.

Bosons, which are spin 1 particles, have a wavefunction that needs to be rotated around only once before coming back to it's original state. If you force two bosons together their wavefunctions CONSTRUCTIVELY interfere instead! This means that they CAN occupy the same state and the same place at the same time.

Be aware that we are talking about wavefunctions, not whether we will find a particle at a specific location. The wavefunction describes the probable location of a particle within an area of space. We can find the particle anywhere within the area described by the wavefunction, with certain areas being more or less likely.

It may seem like this should be true, however there is no such thing as a "unit of space". IF we develop a theory of quantized spacetime in the future this may be true, but for now we can't say that it is.

great answer. i also like the quote: it's not about what is possible it's about what is probable. i encounter that fallacy all the time in philosophical debates.

First decide whether you're satisfied with your understanding of how the electric field holds atoms together. The strong force isn't that different.

Yes, at this level our explanations tend to explain what things do and not necessarily why they do those things.

Using a variety of clues, we guessed the correct equations describing the strong force, and then we verified that those equations predicted all the phenomena we had already observed, and then some. The equations describe the behavior of quarks and gluons. However, they predict that you can never actually isolate quarks and gluons to look at them individually--this is "confinement". So we can't literally observe quarks and gluons directly, but we can infer that they're there, because we understand the behavior of composite particles like protons and neutrons through the behavior of the quarks and gluons they are composed of.

I'm not sure what you're asking here. Perhaps you are imagining that we looked really closely at the space between quarks, found some things we called "gluons," and concluded that they must be responsible for holding quarks together? No, QCD is on much stronger footing than that. QCD makes many quantitative predictions that we've verified to be correct.

Be careful about arguing "by definition," as if by defining terms in a certain way you could actually force the universe to behave differently.

A Bose-Einstein condensate is one well-studied instance of many bosons occupying the same space. But the fact that many bosons can occupy the same state is related to a fundamental aspect of quantum mechanics that is at play in *any* system involving bosons. This is a well-understood phenomenon both mathematically and experimentally.

As far as I'm concerned there is no explanation why the positive electric charge is attracted to the negative electric charge. You cannot break charge down into smaller parts therefore you cannot explain why + is attracted to -. Charge is just a property that atoms have and that's the end of it.

Yes, that's the way Ben Franklin et al thought about it 250 years ago. Little +'s and -'s that attracted and repelled each other for no apparent reason. Very simple picture. But sometimes, in trying to understand things at a more fundamental level it's necessary to introduce concepts that are rather more complicated.

The key to better understanding in this case was to focus on the field rather than the charges. A hundred years after Franklin, behavior of the electromagnetic field was summarized by Maxwell. And fifty years after that, special relativity showed us that the E and B fields in Maxwell's Equations were just different components of one field. And subsequently we realized that this field arose from the quantum field theory of a massless spin zero particle.

Franklin would have shaken his head in bewilderment and gone back to his original idea of little +'s and -'s because they were so much simpler!

The canonical formulation of QCD uses a so-called Hamiltonian with a kind of "potential" between color-charges to explain this "binding force". It first glance the potential term looks similar to QED with a Coulomb-like potential but the QCD potential is much more complicated and still purely understood. One can use this formulation to extract physics numerically, but of course one wants to understand especially the confinement issue analytically, which does not only say that there is a attractive "color-Coulomb force, but that there is a (linear rising potential) which ALWAYS holds quarks together. It is exactly this question where an answer (a mathematical proof) is still missing.