Atoms are made from electrons and atomic nuclei. Since the nucleus accounts for more than 99.9% of the atom’s mass, we can focus on the nucleus, or on the protons and neutrons it is made of. Protons and neutrons are made from quarks (each particle contains three quarks) and gluons. Therefore, most of the mass of ordinary matter comes from quarks and gluons. But how can that be possible when gluons are massless and the up and down quarks which compose neutrons and protons are nearly massless?

The answer emerged 50 years ago (1973) and resulted in a Nobel Prize in Physics 2004 to Gross, Politzer and Wilczek “for the discovery of asymptotic freedom in the theory of the strong interaction.” In his Nobel prize lecture, Wilczek recounts that Einstein in his 1905 paper stated his most famous equation as m = E/c². Another indication that Einstein considered the possibility that energy is the source of mass is that the title of the paper was a question, “Does the Inertia of a Body Depend Upon its Energy Content?”

In the early 1970s, a new quantum field theory called QCD (Quantum Chromodynamics) was developed to describe the “strong force” between quarks and gluons (each up and down quark has a unit color charge. Color gluons interact with color charges or change one into another). In Wilczek’s own words:

“Modern QCD answers Einstein’s question with a resounding ‘Yes!’ Indeed, the mass of ordinary matter derives almost entirely from energy – the energy of massless gluons and nearly massless quarks, which are the ingredients from which protons, neutrons, and atomic nuclei are made.”

Although on its face this statement brings to mind creation of matter out of nothing, that is not the case.  Empty space is not really empty!!!   It is permeated with constantly changing quantum fields and their evanescent excitations, also called virtual particles. The color charge of a single quark or gluon is small, but even in “empty” space, a cloud of virtual particles builds up around the actual quark. The explanation of how the cloud enhances the strength of the color charge is very technical. Here it suffices to say that this process also requires a growing amount of energy. Since energy cannot be created from nothing, free quarks are not found in nature.

For a particle like a proton, energetically the most favorable scenario would be that the color charge of its three quarks would cancel out. For the color charges to cancel out completely, the quarks must exactly overlay each other. However, the uncertainty principle imposes limitations on how well the quarks could be localized: precise localization would require huge momentum, i.e. enormous investment of energy. Optimally, a particle will have the lowest possible energy.

“Thus, in seeking to minimize the energy, there are two conflicting considerations: to minimize the field energy, you want to cancel the sources accurately; but to minimize the wave-function localization energy, you want to keep the sources fuzzy. The stable configurations will be based on different ways of compromising between those two considerations. In each such configuration, there will be both field energy and localization energy. This gives rise to mass, according to m = E/c², even if the gluons and quarks started out without any non-zero mass of their own. So the different stable compromises will be associated with particles that we can observe, with different masses…”

The citations are taken from Wilczek’s Nobel lecture. I recommend both to watch the video (it’s about half an hour) and to read the transcript. In 2009, Wilczek published a popular-science book, titled The Lightness of Being: Mass, Ether, and the Unification of Forces, which elaborates about the origin of mass. The book also addresses the feebleness of the gravitational force compared to the three other fundamental forces in nature (the strong, electromagnetic and the weak forces), and concludes with mathematically inspired speculations about a possible unification of the forces at ultrashort distances (i.e. huge energies inaccessible to any man-made machine). It also briefly discusses possible implications for understanding the cosmological puzzle of the dark matter. For me, the first part of the book that described in non-mathematical terms the “playground” where the creation of mass takes place was the most interesting (it is longer than the two other parts combined).

In the beginning of the chapter The Grid (Persistence of Ether), Wilczek states:

For natural philosophy, the most important lesson we learn with QCD is that what we perceive as empty space is in reality a powerful medium whose activity molds the world. Other developments in modern physics reinforce and enrich that lesson.

Another very interesting, and somewhat sobering part to read was the epilogue. Whereas the relation m = E/c² explains how 95% of ordinary matter emerges from massless building blocks, modern physics cannot account for the mass of the electron. I conclude with Wilczek’s words:

“The mass of the electron, although it contributes much less than 1% of the total mass of normal matter, is indispensable. The value of that mass determines the size of atoms… And yet we have no good idea (yet) about why electrons weigh what they do.
…It’s a similar story for the masses of our friends the up and down quarks, u and d. They make a quantitatively small but qualitatively crucial contribution to the masses of protons and neutrons, and hence of normal matter. If their values were significantly different, life might become difficult or impossible. Yet we can’t explain why they have the value they do.”

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The question does not refer to the “dark matter” found in galaxies nor to exotic particles that flicker into brief existence (for a very tiny fraction of a second) in high-energy experiments, but to ordinary matter made of atoms.