It has always been the dream of philosophers to have all matter built up from one fundamental kind of particle …
Paul Dirac1
It seems so simple.
You’re sitting here, reading this book. Maybe it’s a hardback copy, or a paperback, or an e-book on a tablet computer or e-reader. It doesn’t matter. Whatever you’re holding in your hands, we can be reasonably sure it’s made of some kind of stuff: paper, card, plastic, perhaps containing tiny metal electronic things on printed circuit boards. Whatever it is, we call it matter or material substance. It has a characteristic property that we call solidity. It has mass.
But what is matter, exactly? We learn in school science class 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’. If we dig around online we learn that we make paper by pressing together moist fibres derived from pulp. The pulp has an internal structure built from molecules (such as cellulose), and molecules are in turn constructed from atoms (carbon, oxygen, hydrogen). We further learn that atoms are mostly empty space, with a small, central nucleus of protons and neutrons orbited by electrons.
You might have also learned that protons and neutrons are not the last word on this subject. Particles thought to be the ultimate building blocks of matter or (more likely) whose internal structures are presently simply unknown are referred to by scientists as ‘elementary’. According to this definition protons and neutrons are not elementary particles. They are composites, assembled from different kinds of quark, held together by gluons.
Okay, so things are a little more complicated than we might have supposed. But surely all we’re really seeing here is successive generations of scientific discovery peeling away the layers of material substance. Paper, card, plastic; molecules; atoms; protons and neutrons; quarks and electrons. As we descend through each layer of matter we find smaller and smaller constituents. This is surely hardly surprising.
But then, just as surely, we can’t keep doing this indefinitely. Just as the ancient Greek philosophers once speculated, we imagine that we should eventually run up against some kind of ultimately fundamental, indivisible type of stuff, the building blocks from which everything in the universe is made.
And it doesn’t seem to require a particularly bold leap of imagination to suppose that, whatever it might be, there can be only one fundamental type of stuff. Or, at least, one fundamental type of stuff would seem simpler, or neater. The rest—electric charge, something called colour charge, flavour, spin, and many other things besides—would then just be ‘dressing’.
In 1930, the English physicist Paul Dirac called this ‘the dream of philosophers’. These were simpler times. The neutron hadn’t yet been discovered (it was discovered by James Chadwick in 1932) and, so far as physicists of the time understood, all matter was composed of just two kinds of elementary particle—positively charged protons and negatively charged electrons. For a time, Dirac thought he had found a way to reconcile these, and the quote that I used to open this Preface continues: ‘There are, however, reasons for believing that the electron and proton are really not independent, but are just two manifestations of one elementary kind of particle.’
Alas, Dirac was wrong. What he had stumbled across in the mathematical equations of his new quantum theory of the electron was not, after all, a fundamental relationship between the proton and the electron. He had deduced the existence of an altogether different kind of matter, which become known as anti-matter. The positively charged entity that his theory predicted was not the proton. It was the anti-electron (or positron), discovered in studies of cosmic rays just a couple of years later.
After 1930 things just went from bad to worse. The dream became something of a nightmare. Instead of two elementary particles that might somehow be related, physicists were confronted by a veritable ‘zoo’ of different kinds of particles, many with seemingly absurd properties. It is a simple truth that modern science has undermined all our comfortable preconceptions about the physical universe, and especially the nature of material substance.
What we have discovered is 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. And, at some point on this exciting journey of discovery, we lost our grip on the reassuringly familiar concept of mass, the ubiquitous m that appears in all the equations of physics, chemistry, and biology.
To the ancient Greek atomists, atoms had to possess weight. To Isaac Newton, mass was simply quantitas materiae, the amount or quantity of matter an object contains. On the surface, there seem no grounds for arguing with these perfectly logical conclusions. Mass is surely an ‘everyday’ property, and hardly mysterious. When we stand on the bathroom scales in the morning, or lift heavy weights in the gym, or stumble against an immovable object, we pay our respects to Newton’s classical conception of mass.
But when 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, what happens to the mass of this supposedly ‘indivisible’ elementary particle in between? Einstein’s most celebrated equation, E = mc2, is utterly familiar, but what does it really mean for mass and energy to be equivalent and interchangeable?
The so-called ‘standard model’ of particle physics is the most successful theoretical description of elementary particles and forces ever devised. In this model, particles are replaced by quantum fields. Now, how can a quantum field that is distributed through space and time have mass, and what is a quantum field anyway? What does it really mean to say that elementary particles gain their mass through interactions with the recently discovered Higgs field? If we add up the masses of the three quarks that are believed to form a proton, we get only one per cent of the proton mass. So, where’s the rest of it?
And then we learn from the standard model of inflationary big bang cosmology that this stuff that we tend to get rather obsessed about—so-called ‘baryonic’ matter formed from protons and neutrons—accounts for less than five per cent of the total mass-energy of the universe. About twenty-six per cent is dark matter, a ubiquitous but completely invisible and unknown form of matter that is responsible for shaping the large-scale structure of visible galaxies, galaxy clusters, and the voids in between. The rest (a mere sixty-nine per cent) is believed to be dark energy, the energy of ‘empty’ space, responsible for accelerating the expansion of spacetime.
How did this happen? How did the answers to our oh-so-simple questions become so complicated and so difficult to comprehend?
In Mass, I will try to explain how we come to find ourselves here, confronted by a very different understanding of the nature of matter, the origin of mass and its implications for our understanding of the material world.
One word of warning. The authors of works with pretentions to present popular interpretations of the conclusions of modern science tend to duck the difficult challenge of dealing with its mathematical complexity. There’s the famous quote in Stephen Hawking’s A Brief History of Time: ‘Someone told me that each equation I included in the book would halve the sales.’2 In previous books, I’ve tended to follow this rubric, limiting myself to a very small number of very familiar equations (see E = mc2, above).
But the language of mathematics has proved to be enormously powerful in describing the laws of nature and the properties of matter. It’s important to recognize that theorists will most often pursue a mathematical line of reasoning to see where it takes them, without worrying overmuch about how the mathematical terms that appear in their equations and the resulting conclusions should then be physically interpreted.
In the early years of the development of quantum mechanics, for example, the Austrian theorist Erwin Schrödinger bemoaned a general loss of what he called anschaulichkeit, of visualizability or perceptibility, as the mathematics became ever denser and more abstract. Theorists, supported by experiment or observation, may be able to prove that this mathematical equation represents some aspect of our physical reality. But there’s absolutely no guarantee that we’ll be able to interpret its concepts in a way that aids comprehension.
So, I’ve chosen in this book to reveal a little more of the mathematics than usual, simply so that interested readers can get some sense of what these concepts are, how physicists use them, and how they sometimes struggle to make sense of them. In doing this I’m only going to scratch the surface, hopefully to give you enough pause for thought without getting too distracted by the detail.*
If you can’t always follow the logic or don’t understand the physical meaning of this or that symbol, please don’t be too hard on yourself.
There’s a good chance nobody else really understands it, either.
It’s a real pleasure to acknowledge the efforts of Carlo Rovelli, who made some helpful and encouraging comments on the draft manuscript. Now I’ve never really expected family or friends to read my stuff, although it’s always nice when they do (especially when they then say nice things about it). Obviously, I’m thankful to my mother for lots of things, but on this occasion I’m especially grateful, as she took it upon herself to read every word and provide helpful suggestions on how I might make these words simpler and more accessible. Now my mum has had no formal scientific education (she graduated with a degree in history from Warwick University in England when she was seventy-four), but she has boundless curiosity and enthusiasm for knowledge about the world. My hope is that if my mum can follow it …
I must also acknowledge my debts to Latha Menon, my editor at Oxford University Press, and to Jenny Nugee, who helped to turn my ramblings into a book that is hopefully coherent, no matter what it’s made of.
Jim Baggott
October 2016