Fundamentals Read online

  Accurate agreement between the predicted behavior of an ideally simple model of electrons and experimental observations is what we mean, operationally, when we say that electrons are elementary particles. If electrons, like atoms, had significant internal structure, then they wouldn’t behave so simply. If, for example, an electron’s electric charge were uniformly distributed in a little ball, rather than concentrated at a point, then the predicted value of the electron’s magnetic field would be different, and it would no longer agree with what people have measured. (Of course, if the ball were small enough, the difference might not be noticeable. What we can say for sure is that Nature hasn’t encouraged us to bring in that complication.)

  The same kind of justification could be offered for each of the elementary particles we’re going to discuss. They’ve earned the title “elementary,” until proven otherwise, because that stringent assumption—that they have a very few properties and no others—has lots of impressively successful consequences.

  In the table of elementary particles and their properties, I’ve used the electron mass to set the scale for all other elementary particles’ masses, so by definition it is 1. I’ve also used, as is conventional, the electron’s electric charge as the standard of electric charge. But here there’s a slight complication, courtesy of a great personal hero of mine, Benjamin Franklin. Before he became known as a statesman and diplomat, Franklin made pioneering contributions to early electrical science. He discovered the conservation of electrical charge, and also proved that it comes in both positive and negative varieties.

  By being first, Franklin got to choose which kind of charge to call positive and which negative. He chose to call the charge that accumulates on glass, after it is rubbed with silk, positive. This was long before people knew about electrons. Unfortunately, it turns out that according to Franklin’s choice the electron’s charge is negative. It’s much too late to undo that choice, since it has seeped into thousands of books, papers, and circuit diagrams. Therefore, we list the electron’s electric charge as −1.

  Photons were the next elementary particles to be discovered. The existence of light was a “discovery” known throughout the animal world, and arguably to plants, long before human history began. The discovery that light comes in discrete units, on the other hand, started as a theoretical proposal. Photons are the elementary units of light.

  Einstein first made this suggestion during his “miracle year” of 1905—the same year that contained special relativity, the existence of atoms (Brownian motion), and E = mc2. He called it the hypothesis of light quanta. (The word “photon” was introduced later, in 1925, by the prominent chemist Gilbert Lewis.) It was a revolutionary proposal, which opened to bad reviews. Eight years later, in 1913, toward the end of his glowing recommendation of Einstein for membership in the Prussian Academy of Sciences, Max Planck apologized for Einstein’s embarrassing absurdity by writing, “That sometimes, as for instance in his hypothesis on light quanta, he may have gone overboard in his speculations should not be held against him.”

  Ironically, Einstein’s proposal was based on Planck’s work. Planck had argued that light was emitted and absorbed in lumps based on experiments measuring the glow from heated bodes (so-called blackbody radiation). Einstein interpreted this as evidence that light was made of lumps, period. He used his more specific interpretation to make predictions about several other kinds of possible experiments. The proposed new experiments were very challenging for 1905 technology. It was only in 1914—one year after Planck’s letter—that Robert Millikan carried out truly decisive tests of Einstein’s proposal.

  Though he surely deserved several others, Einstein received his only Nobel Prize in 1921, for his work on light quanta. Einstein himself regarded this as his most revolutionary work.

  When you study the behavior of matter at higher energies than was possible in the early twentieth century, you come upon individual photons that carry significant energy and momentum. This makes them much easier to identify as particles. High-energy photons are known as gamma rays. You can use a Geiger counter to hear gamma rays announcing their arrival, click by click.

  We should consider photons, together with electrons and atomic nuclei, as components of atoms. Indeed, photons are the original “gluons.” It is photons, in their collective incarnation as electric fields, that glue atoms together, binding electrons to their nuclei.

  Protons and neutrons are not elementary particles. Their behavior proves to be too complicated for that description to be viable. The model of protons and neutrons we use today is easy to describe, though it was not easy to discover or to prove. It runs broadly parallel to the theory of atoms. Two kinds of electron-like particles—called u quarks and d quarks—get bound together by photon-like particles called gluons.

  Though the basic idea is similar, there are some notable differences between how atoms are assembled (from electrons, photons, and a nucleus) and how protons are assembled (from quarks and gluons):

  Strong forces, which are controlled by color charge, are much stronger than electromagnetic forces, which are controlled by electric charge. This is why atomic nuclei, which are bound together tightly by the strong force, are much smaller than atoms.

  While electrons always repel one another, quarks, because their color charges come in three varieties, feel more complex forces, which can be attractive. This possibility allows quarks, in contrast to electrons, to bind together without requiring a “nucleus” made of something else.

  While photons are electrically neutral—that is, they have zero electric charge—their strong force analogues, the color gluons, are not color charge neutral. Gluons feel the strong force, just as much as (in fact, more than) quarks do. This is another reason why protons and neutrons are more homogeneous than atoms: The carriers of the force are also under its influence.

  To complete our account of quarks and gluons, we need to discuss their masses.* For gluons this is simple: Like photons, gluons have zero mass. For quarks, the most important thing to note is that while their mass is large relative to electrons, it is very small relative to protons or neutrons.

  It might seem paradoxical that the mass of protons is much larger than the total mass of the things they’re made of. In truth it points to a crowning achievement in the human understanding of Nature: understanding the origin of our mass, in energy. We’ll discuss it further in the next chapter.

  It is difficult to measure the masses of u quarks and d quarks accurately, because it is difficult to discern the influence of those masses amid other, larger effects. That is why I’ve put asterisks in the table next to the best estimates of their values.

  We should add the graviton to our list of particles of construction. The graviton is the particle from which gravitational fields are made. Photons bind together atoms and molecules; gluons bind together quarks, protons, and atomic nuclei; gravitons bind planets, stars, galaxies, and big things in general.

  mass

  electric charge

  color charge

  spin

  graviton

  0

  0

  no

  2

  Gravitons have never been observed as individual particles, because their interactions with ordinary matter are far too feeble for that to be practical. What has been observed are gravitational forces—and, recently, gravitational waves. Theoretically, those observable effects arise from the cumulative action of many individual gravitons.

  Each of the properties of gravitons I’ve listed has a clear connection to observed features of the force which gravitons generate—that is, gravity. Since gravitons have zero electric charge and no color charge, individually they interac
t only feebly with ordinary matter. Yet because they have zero mass, gravitons can be made cheaply in great numbers, to generate gravitational fields and gravitational waves.

  Their relatively large spin implies that gravitons’ interactions are more intricate than those of other elementary particles. Indeed, one can show that the main features of Einstein’s theory of gravity, general relativity, follow directly from those spin-derived properties of gravitons. The fact that you can do so is an impressive demonstration of the power of our three primary properties of matter—mass, charge, and spin—to account for matter’s behavior fully. Einstein himself originally arrived at general relativity by an incredibly brilliant but much less straightforward path.

  This concludes our tour of the particles of construction. If this is your first encounter with these ideas, the unfamiliarity of the concepts and their embodiments might be a little dizzying. The fundamental message, though, should shine through: The physical world is constructed using very few kinds of ingredients. Moreover, those ingredients are ideally simple, in the sense that they have only a handful of properties.

  THE FUTURE OF INGREDIENTS

  The list of elementary particles is significantly shorter than the English alphabet, and much shorter than Mendeleev’s periodic table of chemical elements. Taken together with the laws describing forces—four, to be exact—this list of ingredients gives us a powerful, successful description of matter. We’ll be exploring all that in the next chapter. There we’ll also discuss tantalizing hints and ideas about how we might get an even more compact description.

  But before we get to that, I want to consider the future of world-building ingredients from a different, more practical angle. I’ll describe two promising strategies for making useful new “elementary particles.” Both strategies are inspired by Nature. One strategy, inspired by physics, works from the outside in. The other, inspired by biology, works from the inside out.

  Designer Particles, Take 1: Brave New Worlds

  We can think about materials using the same ideas we use to analyze the world as a whole. When you inject a bit of energy into a material, or a bit of electric charge or spin, the resulting disturbance will generally cohere into a few lumps, or quanta. These “otherworldly” lumps, called quasiparticles, can have quite different properties from the elementary particles we encounter in empty space.

  Holes are a simple but extremely important class of quasiparticles. Inside a typical solid there are many electrons. When the solid is undisturbed, in equilibrium, the electrons arrange themselves in a definite pattern. Now imagine plucking one out. The resulting state will have an empty spot where an electron “ought to be.” After things settle down, which can happen quite quickly, what’s usually left behind is a quasiparticle, which, since it arose from the absence of an electron, carries electric charge +1 (here we recall that the electron’s charge is −1). We call it a hole.

  Holes give us positively charged (quasi)particles that are much lighter and easier to manipulate than their closest empty-space analogues, protons. Holes are star players in transistors, and in modern electronics more generally. Understanding how to make and use holes changed the world.

  In other cases, quasiparticles descend directly from the elementary particles of empty space, but when they are inside the material they acquire distinctly different properties than they had in empty space. An elegant example of this occurs in superconductivity. When photons enter a superconductor, their mass changes from zero to a tiny, but nonzero, value. (The value varies depending on the superconductor in question; a millionth of the electron’s mass is typical.) Indeed, to sophisticated physicists the fact that photons acquire mass is the essence of superconductivity.

  My earliest research in physics focused on elementary particles in the traditional sense. But long before that, during a school trip to Bell Labs, I had an experience that stuck in my mind, and eventually changed my life. During our visit, we listened to a talk in which one of the scientists, trying to explain his work to us, mentioned that phonons are the quanta of vibration. I didn’t understand what he was talking about, but I thought it was the coolest thing I’d ever heard—three weird concepts, each with a resonant name, somehow wrapped into one. On the way home, puzzling it out, I managed to convince myself that his message was that materials are like worlds in themselves, different from ours, which are homes to their own kinds of particles. I loved that idea.

  It’s slow work to invent new kinds of elementary particles. All of the elementary particles that I discussed above, and also those in the appendix, were either known or confidently anticipated already in the 1970s. On the other hand, there’s enormous scope for imagination and creativity in the worlds of quasiparticles. That school expedition, in retrospect, was a glimpse of new horizons.

  Fifteen years later, I finally reached those horizons. Here I’ll just mention one highlight. Anyons are quasiparticles that have a simple kind of memory. I introduced them, and gave them their name, in 1982. At first, it was purely an intellectual exercise. I wanted to demonstrate that quasiparticles could support a tiny memory, as an additional property. (Later I found out that two Norwegian physicists, Jon Magne Leinaas and Jan Myrheim, had discussed related ideas earlier.) At that point, I didn’t have any particular material in mind.

  A few months later, though, I learned about a discovery called the fractional quantum Hall effect (FQHE).* Within FQHE materials, an injected electron divides into several quasiparticles, each of which carries a fraction of its electric charge. I realized that those quasiparticles must exert very peculiar forces on one another, which made me suspect they might be anyons. In 1984, working with Dan Arovas and J. Robert Schrieffer, I managed to prove it.

  Since then I’ve had a lot of fun with anyons, and hundreds of other physicists have joined the party. People hope to use anyons as building blocks for quantum computers, because you can use their memory to store and manipulate information. Microsoft has made a big investment in research toward that goal.

  Physicists and creative engineers have proposed many other interesting and potentially useful new kinds of quasiparticles. They have endearing names like spinon, plasmon, polariton, fluxon, and my favorite: exciton. Some are good at capturing radiant energy, while others are good at transporting energy from one place to another. Those two talents can be combined to design efficient solar energy systems.

  Brave new material worlds with wondrous quasiparticles will be an important part of the future of matter. The burgeoning field of metamaterials designs them systematically.

  Once you get to thinking about materials as homes to quasiparticles, a profound question is not far off: Can we consider “empty space” itself to be a material, whose quasiparticles are our “elementary particles”? We can, and we should. It is a very fruitful line of thought, as you’ll see in later chapters.

  Designer Particles, Take 2: Smart Materials

  Biology suggests another direction for the future of matter. Cells are the “elementary particles” of advanced life forms. They come in many shapes and sizes, but they share a large bag of tricks that enable them to function as repositories of information and as chemical factories. They also have sophisticated interfaces with the external world, which enable them to gather resources and exchange information.

  Biological cells are far from being simple physical objects. It is a daunting challenge to construct from scratch artificial units that have those core functionalities of cells. If one could, then the door would be open to making new cell-like units that could fill in for diseased or senescent cells, or to bring in new capabilities like digesting toxic waste into harmless or useful materials. A more practical short-term strategy, used now with increasing success by many molecular biologists, is to tweak existing cell types.

  On the other hand, it is possible to be inspired by biology without being literal about it. Cars aren’t souped-up horses, nor are airplanes souped-up birds, nor do usef
ul robots have to resemble humans. The most unique feature of biological cells, to which present-day human engineering has no close analogue, is the power of modulated self-reproduction. In appropriate, reasonably forgiving environments, cells will gather ingredients to make new cells that are close, but not necessarily exact, copies of themselves. The differences are not random, but follow programs contained in the cell itself.

  Self-reproduction unleashes the power of exponential growth. Starting with one cell, after ten generations of doubling one has more than a thousand cells, and after forty or so generations one has trillions of cells, which are enough to make a human body. Programmed differences—that is, modulations—can (and do) generate specialized cells appropriate to different functions, as is the case with muscle cells, blood cells, and neurons.

  It should be possible to realize the powerful strategy of modulated self-reproduction in artificial units that are considerably simpler than biological cells, especially if their intended use is less complex and delicate than producing a viable biological organism. Some grand projects, such as terraforming planets or constructing mountain-sized computers, whose realization is both highly repetitive in structure and forgiving in detail, are plausibly of this kind. Modulated self-reproduction is such a powerful concept that I am confident it will feature prominently in the engineering of the future.