The Theory of Almost Everything: The Standard Model, the Unsung Triumph of Modern Physics - Robert Oerter (2006)
People are always asking for the latest developments in the unification of this theory with that theory, and they don’t give us a chance to tell them anything about one of the theories that we know pretty well... What I’d like to talk about is a part of physics that is known, rather than a part that is unknown.
—Richard Feynman, QED: The Strange Theory of Light and Matter
There is a theory in physics that explains, at the deepest level, nearly all of the phenomena that rule our daily lives. It summarizes everything we know about the fundamental structure of matter and energy. It provides a detailed picture of the basic building blocks from which everything is made. It describes the reactions that power the sun and the interactions that cause fluorescent lights to glow. It explains the behavior of light, radio waves, and X rays. It has implications for our understanding of the very first moments of the universe’s existence, and for how matter itself came into being. It surpasses in precision, in universality, in its range of applicability from the very small to the astronomically large, every scientific theory that has ever existed. This theory bears the unassuming name “The Standard Model of Elementary Particles,” or the “Standard Model,” for short. It deserves to be better known, and it deserves a better name. I call it “The Theory of Almost Everything.”
The Standard Model has a surprisingly low profile for such a fundamental and successful theory. It has deeper implications for the nature of the universe than chaos theory, and unlike string theory, which is purely speculative in nature, it has a strong experimental basis—but it is not as widely known as either. In physics news items, the Standard Model usually plays the whipping boy. Reports of successful experimental tests of the theory have an air of disappointment, and every hint of the theory’s inadequacy is greeted with glee. It is the Rodney Dangerfield of physical theories, it “don’t get no respect.” But it is, perhaps, the pinnacle of human intellectual achievement to date.
Some of the Standard Model’s architects are perhaps more visible than the theory itself: the clownish iconoclast Richard Feynman and the egotistical polymath Murray Gell-Mann have both written and been the subject of books. Many other names, though, are practically unknown outside specialist circles: Sin-Itiro Tomonaga, Julian Schwinger, George Zweig, Abdus Salam, Steven Weinberg, Yuval Ne‘eman, Sheldon Glashow, Martin Veltman, Gerard t’Hooft. Perhaps part of the reason for the Standard Model’s neglect is the sheer number of people involved. There is no solitary, rejected genius—no Einstein working alone in the patent office, no theory springing full-blown into existence overnight. Instead, the Standard Model was cobbled together by many brilliant minds over the course of nearly the whole of the twentieth century, sometimes driven forward by new experimental discoveries, sometimes by theoretical advances. It was a collaborative effort in the largest sense, spanning continents and decades.
The Standard Model is truly “a tapestry woven by many hands,” as Sheldon Glashow put it.1 It is, in this, a much better paradigm for how science is actually done than is the myth of the lone genius. But it conflicts with our prejudices about science and with the way popular physics is usually presented.
News reports and general-interest books about the Standard Model often emphasize the particles in the theory: the discovery of quarks, finding the W and Z bosons, looking for neutrino mass, the search for the Higgs particle. This emphasis misses the underlying structure of the theory. It is as if you were asked to describe a Christmas tree and you talked entirely about the ornaments and the lights, and never mentioned the tree itself: the piney smell, the color of the needles and the bark, the feathering of the branches, the symmetrical shape.
To a theoretical physicist, the quarks, electrons, and neutrinos are like the ornaments on the tree. Pretty, yes, but not what’s fundamentally important. The structure of the theory itself is what’s really fascinating. The Standard Model belongs to a class of theories called relativistic quantum field theories. Dream up any set of particles you like and you can write a relativistic quantum field theory to describe it. (I’ll show you how to do this in Chapter 9.) All such theories incorporate the strangeness both of special relativity, with its paradoxes of time and motion, and of quantum mechanics, with its fields that are neither wave nor particle. The framework of relativistic quantum field theory adds some weirdness of its own: particles that pop into existence out of pure energy, and disappear again, literally in a flash of light. This structure encodes the rather bizarre worldview of the physicist. It tells what can be known about the universe, and what must remain forever mysterious. This structure, the deep symmetries of the universe that are hidden within this structure, and its implications for our understanding of the physical world, are what I want to tell you about in this book.
There is symmetry all around us: the shape of a snowflake or a daffodil, the crystal symmetry of a perfectly cut diamond, the volcanic beauty of Mount Kilimanjaro. We desire symmetry. Architects, artists, and composers incorporate symmetry into their creations. We judge faces with symmetric features more beautiful. When selecting a Christmas tree, the buyer walks all around it to see if it is attractive from all sides. And yet, too much symmetry is boring. A well-proportioned house is beautiful, but an endless row of identical houses is repellant. A musical phrase repeated over and over becomes monotonous, loses our interest, and soon becomes annoying. In a Jackson Pollock painting, one section of the canvas looks much like any other section, but no two areas are identical. Symmetry need not be perfect, it must not be perfect, to achieve beauty. As Francis Bacon said, “There is no excellent beauty that hath not some strangeness in the proportion”.23
A tree, for example, displays many kinds of symmetry, not all of them obvious at first glance. Draw an imaginary vertical line through the center of the tree and you split it into two halves, each of which is a mirror image of the other, albeit an imperfect one. Symmetry of another kind can be found in the branching structure of the tree limbs. This structure is repeated for smaller branches, then for twigs, creating a kind of symmetry of scale. Select a small portion of a photograph of the tree and blow it up, then select a portion of the enlargement and blow that up. Each time the new photograph looks very similar to the previous one. This branching structure is repeated underground in the tree’s roots, making the bottom half of the tree a distorted mirror image of the top half.
Symmetry can be destroyed. A building collapses in an earthquake; a wine glass shatters when dropped. A tree, buffeted by wind, falls over. When you walk around the fallen tree, it no longer looks the same from every side. Its crown is crushed by the ground: now, when you draw a line through the trunk, the two sides are no longer mirror images.
The story of fundamental physics in the twentieth century is a story of symmetry: symmetry perfect and imperfect, symmetry discovered and symmetry destroyed. The symmetries involved are not ones that can be seen with the naked eye, however. To discover them we must dive into the tree’s inner structure. Its wood, viewed under a microscope, is made of cells, the cells built up of chains of molecules. The molecules in turn consist of atoms, which are constructed from still smaller particles. In a process of discovery that lasted the entire twentieth century, physicists learned that these smallest constituents of matter have symmetries of their own. If we could reach into the atom and give each of the particles a certain kind of twist, and if we could simultaneously give the same twist to every other particle in the universe, the world would go on exactly as if we had done nothing.
With a perfectly symmetrical face, you can’t tell if you are looking at a photograph or a mirror image. The deep symmetries of the fundamental particles are exact—there is no way to tell if the twist has been made or not. Beyond these exact symmetries, not visible even in the fundamental particles but hidden in physicists’ theories, lies yet another symmetry, one that existed in the first moments of the universe’s existence, but has since been shattered. This symmetry and its downfall is the reason that matter as we know it exists, the reason for stars, planets, daffodils, and you and me.
The Standard Model is a theory of almost everything. Specifically, it is a theory of everything except gravity. Gravity may seem to be a major omission; in everyday life, gravity is certainly the force we feel most strongly. Without magnetism, the photos of your niece would fall off the refrigerator; without electricity, you could walk across a rug on a dry day and not get shocked when you touch the doorknob; but without gravity, you would go floating up off the Earth into space and asphyxiate.
Paradoxically, gravity is more noticeable to us because it is the weakest force. A proton, for example, has the smallest electric charge that it’s possible to isolate in nature, yet the electric force between two protons is immensely larger (by a factor of 1036!) than the gravitational force between them. Because the electric force is so strong, matter tends to hang out in neutral clumps, with equal amounts of positive and negative charges. The positive and negative charges cancel each other, and the resulting neutral clump doesn’t feel any electric force from other neutral clumps. This is why we never see, for instance, an apple flying up out of a tree due to electrical repulsion from the Earth. The Earth is nearly neutral, apples are nearly neutral, so the net electric force is small compared to the gravitational force. Whenever an imbalance of charge is created, as when you shuffle across a rug, picking up extra negatively charged electrons from the rug, the imbalance will correct itself at the first opportunity. When you touch the doorknob, the extra electrons try to escape your body, repelled not by your personality, but by their mutual electric force and attracted toward any extra positive charges in the doorknob. The same thing happens in lightning strikes, when a large amount of charge flows back to the Earth from an electrically charged cloud, restoring electric neutrality.
Electric and magnetic forces, however, are much more important in everyday life than refrigerator magnets and static cling. The electric engine that runs the refrigerator contains magnets and uses electricity, as do the engines for your vacuum cleaner, your weed whacker, and your car’s starter. Electricity flows whenever you turn on a light, a TV, a stereo, pick up the phone, cook on an electric range, or play electric guitar. Light is an electromagnetic effect, whether it comes from a light bulb or from the Sun. Your nerves send electric signals, so by the act of reading this sentence, you are causing a multitude of electrical events in your brain and your body. What’s more, all chemical reactions may be traced to the electric and magnetic interactions of the atoms and molecules involved. Your body operates by way of chemical reactions, so electric forces are ultimately responsible for your movement, digestion, breathing, and thinking. It is electric forces that hold matter together, so the chair you are sitting in would not exist without electric forces. Far from being irrelevant for everyday life, electric and magnetic forces, together with gravity, are everyday life, or at least they are the substrate that makes life possible.
The Standard Model contains a complete theory of electric and magnetic forces, together with a description of the particles on which the forces act: protons, electrons, neutrons, and many more that are not as well known. So, in a sense, the Standard Model “explains” all those everyday phenomena, from the structure of the chair you sit on, to your very thoughts. It is not possible, though, to write an equation that describes your chair using the equations of the Standard Model (much less an equation for your thoughts!). The Standard Model equations can only be solved in very simple cases, say one electron interacting with one proton. In those simple cases, however, the Standard Model gives us such incredibly accurate predictions that we have a great deal of confidence that that is really how electrons and protons behave. (Other parts of the Standard Model, for instance the internal structure of the proton, are still not solved, and so our confidence is somewhat less for those areas.) Even though we cannot in practice use the Standard Model to describe a chair, we can say that a chair consists of protons, neutrons, and electrons in various configurations, and so, in principle, the Standard Model “explains” the chair at its most fundamental level.
Consider a computer as an analogy. The computer is made of wires, integrated circuits, a power supply, and so forth. Fundamentally, all that is “really” happening in a computer is that little bunches of electrons are being shuffled around through these circuits. However, when your computer tells you “ERROR 1175: ILLEGAL OPERATION, APPLICATION WILL BE SHUT DOWN,” it is not very useful to pull out the circuit diagram for your CPU. Although it is possible in principle to describe what happened in terms of the circuits (“When memory locations A, B, and C have such-and-such a number of electrons, and some other number of electrons come down wire Q, then...”), this description would be useless for avoiding the problem. Instead, you need to be told something like, “Your operating system will only let you open four programs at a time. Shut down the excess programs before starting this one, and you won’t get that error message.” We can’t locate “the operating system” or “program” on the circuit diagram—it is a higher level of description. Can we understand the error message by looking at the circuit diagram? No. Can we really understand the operation of the computer without understanding the circuits? No again. (Try building your own computer using only the Windows 2000 reference manual!) Both levels of description are necessary to “understand the computer,” but the higher-level (operating system and program) functions can be explained in terms of the lower-level (circuitry) processes, and not the other way around. This is why we call the lower-level description the more fundamental one.
The Standard Model describes the “circuitry” of the universe. We can’t understand everything in the universe using the Standard Model (even if we omit gravity), but we can’t really understand anything at the most fundamental level without the Standard Model. Suppose you are a biologist who wants to understand the function of blood in the body. You need to investigate the penetration of oxygen across membranes, and its uptake by hemoglobin. Your biological question turns out to depend on chemical questions. To understand how fast oxygen is fixed by hemoglobin, you need to know about the configuration of the electrons in the oxygen and hemoglobin molecules. These configurations are determined by the electric and magnetic forces between the electrons and the nuclei, in other words, by the Standard Model.
To tell the story of the Standard Model and its symmetries, this book will follow a roughly chronological sequence. The reader should not be misled by this into thinking I am writing a history of the Standard Model. My goal is to give the reader an understanding of the theory itself. To give an accurate historical picture of the development of the theory, with all of the vagaries of blind theoretical alleys and inconclusive or incorrect experiments, would take us too far from our main goal. I have included some of the history so that the reader can understand the motivation for each new step taken, and to emphasize that the theory was developed in response to specific new discoveries about the way particles behave. It was not invented out of whole cloth by some theorist isolated in an office, but was painstakingly pieced together from the hints that experimenters managed to tease out of nature. The chronological approach may, at times, give a mistaken impression that the Standard Model developed by an orderly series of experimental and theoretical advances. This is far from the truth: the actual historical development was much more messy and interesting than I can convey here. The interested reader should consult the suggestions for further reading at the end of this book.
The story of the Standard Model must begin with the nineteenth-century worldview. Decades of careful experimentation had convinced physicists that everything that happened in the universe was a result of the interaction of particles and fields. Everything material, be it solid, liquid, or gas, consisted of unimaginably small particles, the atoms. They were pictured as tiny billiard balls moving in straight lines unless a force acted on them. A particle was endowed with the capability to generate a field filling all the space around it and influencing the motion of other particles. All forces arose from these fields. Particle generates field, field influences particle: this was all that ever happened in the universe.
The nineteenth-century worldview, known as classical physics, was stirred but not shaken by the discovery of a new symmetry in 1905. In everyday experience, space and time are completely different. We can move about in space; we can return home as many times as we like. Time, on the other hand, moves inexorably forward; there is no return. Albert Einstein’s theory of special relativity forced physicists to change their perception of space and time. They are intricately intertwined—they are, in fact, two aspects of a single reality, which was termed spacetime.
Classical physics was shaken to its foundations by another set of discoveries around the turn of the century. The odd couple that triggered the earthquake was radioactivity and neon lights. According to quantum physics, which was developed to deal with the new phenomena, particles sometimes behaved like waves, as if they were not small and hard but spread out like a field. At the same time, fields could behave like particles. The two entities, particles and fields, that had seemed so different were starting to show a family resemblance.
By mid-century, physicists had successfully woven together the old, classical field idea and the new theories of special relativity and quantum mechanics. The framework that emerged from this union, known as relativistic quantum field theory, would prove remarkably robust. Indeed, it would be the framework used for fundamental physics for the rest of the century and the language in which the Standard Model would be expressed.
The discovery of quarks, hidden inside protons and neutrons, led to the discovery of a new and unsuspected symmetry, a new kind of “twist” of the quarks that leaves the world unchanged. This symmetry, called color symmetry, is intimately connected with the force that binds quarks into protons and neutrons, the strong force.
The great breakthrough that made a Theory of Almost Everything possible came with the realization that a symmetry (of the color symmetry type) could break spontaneously, just as a tree can spontaneously fall. We will learn how spontaneous symmetry breaking allowed physicists to predict the existence of new, never before observed particles. The discovery of all but one of those particles, with precisely the properties predicted by the theory, was the crowning achievement that confirmed the Standard Model. This downfall of symmetry is responsible for the very existence of matter as we know it.
Particles, fields, and symmetry: These are the great themes of twentieth-century physics. At the same time that it answers many questions, the Standard Model raises many new ones. Why do quarks come in six different “flavors”? Why are electrons so much lighter than the quarks, and neutrinos so much lighter than electrons? What’s the deal with that remaining particle of the Standard Model, the Higgs particle, which hasn’t been detected (yet)? What about dark matter and dark energy—where do they fit in? Perhaps the answer lies with new particles, or with new symmetries. Perhaps a completely new approach is needed. We will learn the current ideas and peek at what lies ahead for physics.
If all that had been accomplished in the past century were that a hundred or so fundamental atoms had been replaced by seventeen fundamental subatomic particles, it would still have been a great simplification in our understanding of matter. However, the Standard Model goes much further. With a handful of additional parameters, it specifies all of the interactions between the particles. Including the parameters needed to specify the properties of the seventeen particles, there are just eighteen numbers needed to specify the Standard Model. Instead of an infinite number of possible groupings of atoms into molecules, and therefore an infinite number of chemical reactions whose rates must be measured, we have a mere eighteen parameters. All but one of the particles have now been produced in accelerator experiments, and the values of most of the parameters have been measured. The Standard Model puts us much closer to a complete understanding of the fundamental processes of the universe.
For this reason, the Standard Model is the greatest accomplishment of twentieth-century science. All you need is to measure the values of the eighteen parameters, and you know everything there is to know about everything in the universe, always excepting gravity. In principle, you could deduce the laws of thermodynamics, of optics, of electricity and magnetism, of nuclear energy, from the Standard Model. You could go on to explain the functioning of a star, a microbe, a galaxy, a human being, on the basis of those eighteen numbers.
If this is true, why haven’t we been deafened with the popping of champagne corks, the cries of triumph, and the collective sighs of physicists retiring with the knowledge of a job well done? Why, instead, do we hear mysterious rumors of supersymmetry, string theory, and ten-dimensional spacetimes? One answer is the obvious omission of gravity from the Standard Model. Clearly, the job isn’t done if such a major piece of the puzzle is missing. One might think that we could just tack a theory of gravity onto the Standard Model, call the result the New Standard Model, and be done. Unfortunately, the longer physicists work to do this, the more impossible the task appears. Our best theory of gravity (Einstein’s theory of general relativity) and our best Theory of Almost Everything (the Standard Model) describe the universe in fundamentally different ways. It is far from clear how, or even if, these different structures can be reconciled. A two-word description of the structure of general relativity is curved spacetime, and that’s about all I’m going to say about it. The structure of the Standard Model is what the rest of this book is about.
There is another reason why physicists aren’t content to rest on their laurels and call it quits with the Standard Model: eighteen parameters are still too many! Why six quarks, rather than three, or two, or one? The top quark only showed up when physicists built a huge particle accelerator designed specifically to look for it. Couldn’t the world have gotten along without it? A famous physicist derided the Standard Model saying, “Give me eighteen parameters and I can design an elephant.” We would like the world to be even simpler, even more symmetrical, at its root. Ideally, physicists would prefer a single entity (maybe a string?) instead of the seventeen particles, and one law with one, or maybe no, parameters to be measured. (The great physicist John Archibald Wheeler has suggested that the ultimate laws of the universe, when we at last discover them, will seem so clear and obvious that everyone will nod their heads and agree that the world couldn’t be any other way.) All of the known particles would arise from this fundamental entity behaving in different ways, like different notes played on a bugle.
Finally, the Standard Model can’t be the end of the story because it fails to account for several important phenomena that have been discovered recently. Neutrinos have mass, according to recent experiments, whereas in the Standard Model they are massless. As we will see, neutrino masses can be accommodated in the Standard Model, but only somewhat awkwardly. Then there is the “dark matter” that astronomers tell us makes up most of the mass of the universe. Any theory that misses the majority of the stuff in the universe can’t be complete!
But I am getting ahead of the story. To understand the greatest scientific accomplishment of the twentieth century, we need to back up and discover what physics was like back in the nineteenth century.