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The mass of a single proton, often said to be made of three quarks, is almost 1 GeV/c². To be more precise, a proton’s mass is 0.938 GeV/c², while that of a neutron is 0.939 GeV/c².

But the masses of up and down quarks, found in protons and neutrons, are each much less than 0.01 GeV/c². In short, the mass of each quark is less than one percent of a proton’s or neutron’s mass. If a proton were really made from three quarks, then there would seem to be a huge mismatch.

(Here and below, by “mass” I mean “rest mass” — an object’s intrinsic mass, which does not change with speed. It is sometimes called “invariant mass”. [Particle physicists usually just call it “mass”, though.])

Part of the explanation for the apparent discrepancy is that a proton or neutron is, in fact, made from far more than just three quarks. In its interior, one would find many gluons and a variety of quarks and anti-quarks. However, that doesn’t resolve the issue.

• Gluons, like photons, have zero rest mass, so they don’t help at all, naively speaking.
• The typical number of quarks and anti-quarks inside a proton, while more than three, is too small to add up to the proton’s full mass;

And thus one cannot explain the proton or neutron’s large mass as simply the sum of the masses of the objects inside it. The discrepancy remains.

Moreover, as can be verified using either strong theoretical arguments in analogous systems or direct numerical simulations, protons and neutrons would still have a substantial mass even if the quarks and anti-quarks they contain had none at all! Mass — from no mass.

Clearly, then, the solution to the puzzle lies elsewhere.