Mass: What is Stuff Made of?

It used to seem so simple.

We learned that matter is not continuous, but discrete. As a few of the philosophers of ancient Greece once speculated, nearly two and a half thousand years ago, matter comes in ‘lumps’. Centuries of scientific effort served to sharpen this basic insight. We learned that matter is built from molecules and molecules are, in their turn, constructed from atoms. And, just as we were beginning to accept the reality of atoms at the beginning of the twentieth century, a few physicists were already busy working out how to split them apart. We learned that an atom is mostly empty space, with a small, positively-charged nucleus of protons and neutrons orbited by negatively-charged electrons.

Okay, so things turned out to be a little more complicated than the ancient Greeks could have fathomed. But they were still right about one thing. They endowed their atoms with weight and, despite the subtleties of the new nuclear physics, we could still expect to find all the mass of the atoms concentrated in the protons and neutrons of their nuclei.

And then it all started to go horribly wrong.

We learned that the foundations of our universe are not as solid or as certain and dependable as we might have once imagined. They are instead built from ghosts and phantoms, of a peculiar quantum kind.

Einstein argued in 1905 that light waves are particles, which today we call photons. In 1923 Prince Louis, fifth duc de Broglie, argued that particles such as electrons are also waves. We would later watch as a single electron passes like a phantom at once through two closely-spaced holes or slits, to be recorded as a single spot on a far detector. Wait patiently as more and more electrons pass through the slits, one at a time, and we will be rewarded with a wave inference pattern. Try to find out which slit each electron really goes through and the pattern is lost. We get wave interference only if we don’t look to see how it happens. And, if the electron really is an extended wave, what then happens to its mass?

It got steadily worse. Instead of a small handful of elementary particles that could be used to construct everything in the universe, physicists were confronted by a veritable ‘zoo’ of different kinds of particles, many with seemingly absurd properties. Out of the fog of confusion emerged what we now call the ‘standard model’ of particle physics, in which particles are described by quantum fields. But our understanding of the nature of matter and the property of mass now became more confused than ever.

According to the standard model, protons and neutrons are not the last word. These particles are composites, assembled from different kinds of quark, held together by gluons. The standard model also demands something called a Higgs field (named for English theorist Peter Higgs), which fills all of space and acts as a background with which all particles interact. Such interactions are necessary in order for these particles to acquire mass.

This might cause us to pause for a minute or two to think about what this really means. But don’t take too long. The mass acquired in this way by the quarks that constitute a proton, for example, still only accounts for about one percent of the mass of a proton. The gluons that bind the quarks together are massless (like the photon), so where do we look to find the other 99 percent of the proton’s mass?

Solving the equations of the quantum field theory that describes quarks and gluons requires the world’s largest supercomputers. But recent calculations are unequivocal. We think of Einstein’s most famous equation as E = mc2, but in fact this expression does not make an appearance in his original 1905 paper. Instead, Einstein’s great insight was m = E/c2, ‘the mass of a body is a measure of its energy content’.

And this is the answer. The other 99 percent of the mass of a proton comes from the energy of the interactions of the gluon fields trapped inside it. This is ‘mass without mass’. It turns out that mass is not, as we had always supposed, an inherent or primary property of matter. It is not something that matter has. It is rather a behaviour. It is something that quantum fields do.

Whichever way you look at it, this is not the answer we might have anticipated to our seemingly simple and innocent question: ‘what is stuff made of?’