The Higgs boson gives elementary particles their mass, but 98% of the visible mass in the Universe (not dark matter) comes from a less famous mechanism: chiral symmetry breaking. This is why protons and neutrons are so much heavier than their quarks!

Briefly, protons and neutrons act like bags full of a soup of virtual quark-antiquark pairs, which give them most of their mass. This soup, called a 'quark condensate', breaks a certain symmetry that exists outside the bag: 'chiral symmetry', where you change the phase of the clockwise and counterclockwise rotating quarks separately. In the quark condensate, the clockwise spinning virtual quarks are entangled with counterclockwise spinning virtual antiquarks.

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

Chiral symmetry breaking - Wikipedia

@johncarlosbaez I know this is google-able, but I want to ask someone who knows more than me- what about bonding energy? I thought bonding energy accounted for a large amount of mass.

@cpkimber - if something has binding energy, it has *less* energy and thus *less* mass than it would otherwise have, because binding energy is the energy it would take to pull it apart. For example, when a hydrogen bomb goes off, the hydrogen nuclei fuse into something that has less energy and thus less mass, releasing a lot energy in the process.

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

Binding energy - Wikipedia

@johncarlosbaez @cpkimber It has less energy than when it is separated. But does it have less energy compared to if you turned off the force? Then to zeroth order I'd think it depends on the exponent?
@Quantensalat @cpkimber - it's a subtle counterfactual question, but I'd say a bound system has less energy than if you turned off the force that binds it.

@johncarlosbaez @cpkimber

If it's e.g. an r^2 potential then the virial theorem would suggest that all contributions are positive. In that case wouldn't I have an attractive potential that lifts the energy of the system above the free case?

(Adiabatically switching off might yield different results, i.d.k. if the virial theorem then keeps holding in each instant cooling off the system. I should find out....)