Fundamentals Read online

  It is philosophically important to notice that it is unnecessary to take into account what people, or hypothetical superhuman beings, are thinking. Our experience with delicate, ultra-precise experiments puts severe pressure on the idea that minds can act directly on matter, through will. There’s an excellent opportunity here for magicians to cast spells, or for someone with extrasensory powers to show their stuff, or for an ambitious experimenter to earn everlasting glory by demonstrating the power of prayer or wishful thinking. Even very small effects could be detected. But nobody has ever done this successfully.

  WHAT MIGHT HAVE GONE WRONG, BUT HASN’T

  Before concluding our discussion of world-building principles, I will show, using a simple thought experiment, how our principles could have been wrong. In fact, I’ll describe plausible universes of the future in which our principles won’t hold.

  One of my favorite thought experiments, famously embodied in many science-fiction stories and in the Matrix movies, is to consider intelligent, self-aware beings who are oblivious to the physical world that contains them. For purposes of argument, let’s assume that the proponents of strong artificial intelligence have it right, so that such beings could exist. (Given the rapid progress of AI and virtual reality, it’s not implausible.)

  The “sense organs” of these hypothetical beings would not be portals to the physical world. Their input, instead, would be electrical signals, generated by computers. Thus, the “external world” experienced by these beings—that is, the data flow they interpret as perception—is, in our thought experiment, actually a long series of signals generated by a computer program. Since that “external world” follows instructions crafted by a programmer, it can obey whatever rules the programmer cares to impose.

  In this kind of world, each and every one of our principles can be trashed.

  We can, for example, imagine an intelligent, self-aware version of Super Mario, whose sensory universe lies inside that game world. Our self-aware Super Mario lives in a universe governed by laws that depend on where he is—specifically, on which level he’s achieved. It is a universe, more generally, whose rules can be upended by unpredictable, hidden surprises that the programmers built in—not only quirky rules, but also so-called Easter eggs, which purposely break the rules.

  We could construct a world in which astrology is true—where a character’s personality and fate really are determined by the position of the stars and planets when they are born. We could program that in. We could program in different kinds of monsters to spring up suddenly when there’s an eclipse of the Sun or the Moon. We could allow the characters to cast magic spells that strike down distant enemies at once, locality be damned. Using random numbers, we could also introduce noise, to make the rules unpredictable and imprecise. Computer game designers revel in such possibilities.

  We can envision worlds wherein miracles can and do happen. We can envision worlds whose history reaches a preordained climax, according to a planned script. Those thought worlds embody the central ideas of intelligent design theory.

  In this way, we’ve envisioned thought worlds wherein our first principle is misleading and the other principles are flat wrong. These thought experiments demonstrate that those principles are not necessarily true, let alone obvious. The fact that the physical world we presently inhabit appears to obey them is an astonishing discovery. It was not an easy discovery to make—and it is not an easy one to accept.

  Anytime I decide to raise my hand, something that contradicts the principles seems to be happening. Indeed, the grammar of the sentence “I decide to raise my hand” says it all: There is something called “I”—a spirit, or a will—that dictates how a piece of the physical world behaves. It’s an illusion, or at least a take on things, that’s hard to abandon. But our principles ask us to think differently.

  PROPERTIES: WHAT IS MATTER?

  By convention sweet is sweet, bitter is bitter, hot is hot, cold is cold, color is color; but in truth there are only atoms and the void.

  —Democritus, fragment (c. 400 BC)

  That fragment from Democritus can be taken as the founding document of atomism. The second part of the fragment, following the semicolon—“in truth there are only atoms and the void”—is essentially Feynman’s “everything is made of atoms.”

  Democritus’s declaration is deeply challenging. It denies the objective reality of the experiences—taste, warmth, color— through which we access the physical world most directly. No doubt what he intended is that we can understand physical reality in terms of basic units—atoms for him, elementary particles for us—that are not themselves sweet, bitter, hot, cold, or colorful. Those perceptions, he suggests, are a highly processed packaging and summary of what’s happening under the hood, which is just elementary particles going about their business. But in telling us what properties elementary particles don’t have, or at least might not have, Democritus sets up a big, beautiful question: What properties do they have?

  Democritus’s own answer to that question, it appears, was this: Elementary particles have shape and motion, but no other properties. His elementary particles were rigid bodies, with hooks. The hooks explained how they could stick together to make solids, or different sorts of materials in general. He postulated that his elementary particles have spontaneous motion, or “swerve,” as well as preferred positions. The resulting tension between restlessness and desire, according to Democritus, keeps the world a lively place. (Since we have only a few fragments and early commentaries to go on, it’s impossible to know exactly what he had in mind. But I think that gets the gist.)

  Modern science gives an answer that, while completely different in its details, is no less bold. It is even more radical in its simplicity. Most important, it is backed up by mountains of experimental evidence. According to our present best understanding, the primary properties of matter, from which all its other properties can be derived, are these three:

  Mass

  Charge

  Spin

  That’s it.

  From a philosophical perspective, the key takeaways are that there are very few primary properties, and that they are things you can define and measure precisely. And also this: As Democritus anticipated, the connection of the primary properties—the deep structure of reality—to the everyday appearance of things is quite remote. While it seems to me too strong to say that sweet, bitter, hot, cold, and color are “conventions,” it is surely true that it takes quite some doing to trace those things—and the world of everyday experience more generally—to their origins in mass, charge, and spin.

  A detailed discussion of mass and charge, including both electric and color charge, can be found in the appendix. Here I will say a bit about spin, which may be the least familiar property.

  If you’ve ever played with a gyroscope, you’ll have a head start on understanding the spin of elementary particles. The basic idea of spin is that elementary particles are ideal, frictionless gyroscopes, which never run down.

  The fun of a gyroscope, or gyro, is that it moves in ways that are unfamiliar in everyday (nongyro) experience. Specifically, a rapidly spinning gyro resists attempts to alter its axis of rotation. Unless you exert a large force, the orientation of that axis won’t change much. We say that the gyro has orientational inertia. That effect is used to guide aircraft and spacecraft, which carry gyros inside to help keep themselves oriented.

  The faster a gyro rotates, the more effectively it will resist attempts to change its orientation. By comparing the force with the response, you can define a quantity that measures orientational inertia. It is called angular momentum. Big gyros that rotate rapidly have large angular momentum, and show small responses to applied forces.

  Elementary particles, on the other hand, are tiny gyros, indeed. Their angular momentum is very small. When angular momentum gets as small as it does for elementary particles, we enter the domain of qua
ntum physics. Quantum mechanics often reveals that quantities which were once thought to be continuously variable actually come in small discrete units, or quanta. (This is how quantum mechanics got its name.) So it is for angular momentum. According to quantum mechanics, there is a theoretical minimum to the amount of angular momentum any object can carry. All possible angular momenta are whole-number multiples of that minimal unit.

  It turns out that electrons, quarks, and several other kinds of elementary particles carry exactly the theoretical minimum unit of angular momentum. Physicists express that fact by saying that electrons, and the other examples, are particles with spin ½. (There’s an interesting mathematical reason why physicists call the basic unit of angular momentum spin ½, rather than spin 1, but it is beyond the scope of this book.)

  Before concluding this little introduction to spin, I’d like to add a personal note. Spin changed my life. I always liked math and puzzles, and as a child I loved to play with tops. I majored in mathematics as an undergraduate. During my last semester at the University of Chicago, life on campus got disrupted by student protests. Classes became improvised and semi-voluntary. Peter Freund, a famous physics professor, offered an advanced course on the application of mathematical symmetry to physics. I took the opportunity to sit in on it, even though I wasn’t properly prepared.

  Professor Freund showed us how some extremely beautiful mathematics, building on the idea of symmetry, leads directly to concrete predictions about observable physical behavior. His enthusiasm, bordering on rapture, shone through his widened eyes as he spoke. To me, the most impressive example of this connection was—and still is—the quantum theory of angular momentum, which he showed us. When a spinning particle decays into several other spinning particles (which is a very common situation in the quantum world), the quantum theory of angular momentum makes predictions about relationships among the directions in which decay products emerge and the orientations of their rotation axes. Working out those predictions requires substantial calculations, and the behaviors they predict are anything but obvious. Amazingly, though, they work.

  To experience the deep harmony between two different universes—the universe of beautiful ideas and the universe of physical behavior—was for me a kind of spiritual awakening. It became my vocation. I haven’t been disappointed.

  Philosophy of Properties

  Let me emphasize, again, that the most important and remarkable point about our trinity of properties—mass, charge, and spin—is simply that there are so few of them. For any elementary particle, once you’ve specified the magnitude of those three things, together with its position and velocity, you’ve described it completely.

  How different it is for the objects of everyday life! Objects we commonly encounter have all kinds of properties: sizes, shapes, colors, smells, tastes, and many others. And when we describe a person, it is useful to specify their gender, age, personality, state of mind, and a host of other variables. All those properties of objects or people supply more or less independent pieces of information about them. No subset determines the rest. Evidently, there is a startling contrast between the stark simplicity of the basic ingredients and the complexity of the products they produce, just as Democritus suspected.

  Contrary to Democritus, though, our modern basic ingredients don’t have hooks. They aren’t even solid bodies. Indeed, though it’s convenient to call them “elementary particles,” they aren’t really particles. (That is, they have little in common with what the word “particle” suggests.) Our modern fundamental ingredients have no intrinsic size or shape. If we insist on visualizing them, we should think of structureless points where concentrations of mass, charge, and spin reside. We have, in place of “atoms and the void,” space-time and properties.

  THE PARTICULARS

  Not all elementary particles are created equal. They play different roles in our understanding of the world. A few dominate everyday life. A few more come into their own in astronomy and astrophysics. And then there are others whose role in the big scheme of things is not entirely clear.

  In other words, we have particles of construction, particles of change, and bonus particles. They are all fascinating to professional physicists and astronomers, but the particles of construction are by far the most important for understanding the world we experience, and I’ll focus on them here. Some further discussion of the others appears in the appendix.

  Particles of Construction

  Roughly defined, “ordinary matter” is the sort of matter we’re made of and that we commonly encounter in biology, chemistry, geology, and engineering. It is a major achievement of modern science that we can also define ordinary matter in a quite different way, and more precisely: It is the matter we can build up from electrons; photons; two kinds of quarks, commonly called “up” and “down” quarks; and gluons.

  Thus, we can construct the matter that we encounter in ordinary life, and that our bodies are built from, using exactly five kinds of elementary particles as ingredients, each precisely defined by a few limpid properties.

  Here is a table that lists those particles and their properties:

  mass

  electric charge

  color charge

  spin

  electron

  1

  −1

  no

  ½

  photon

  0

  0

  no

  1

  u quark

  10*

  ⅔

  yes

  ½

  d quark

  20*

  −⅓

  yes

  ½

  gluon

  0

  0

  yes

  1

  (The asterisks will be explained in due course.)

  To kick-start this census, let me quickly recall the “classic” description of atoms, coming out of the early twentieth century, which we’ll be refining. In that description, an atom consists of a small central nucleus surrounded by a cloud of electrons. Electrical attraction binds the electrons to the nucleus. The nucleus contains almost all the mass of the atom, and all of its positive electric charge.

  The nucleus in turn is formed out of protons and neutrons. Both protons and neutrons weigh about two thousand times the mass of electrons. Protons carry positive electric charge, such that the positive electric charge of one proton exactly balances one electron’s negative charge. Neutrons carry zero electric charge. Thus, when the number of electrons surrounding a nucleus is equal to the number of protons within it, the atom as a whole carries zero electric charge, and is electrically neutral.

  Electrons were the first elementary particles to be discovered, and in many ways they are the most important. Electrons were first clearly identified by J. J. Thomson in 1897. He studied electrical discharges—essentially, artificial lightning—in highly evacuated “vacuum” tubes. The tubes weren’t quite empty inside—otherwise there would be no electrons to study— but they were empty enough to allow the particles within them some running room. (Today, we understand that when you apply very strong electric fields—in other words, high voltages—across highly evacuated tubes, you “ionize” the atoms, stripping off electrons. The charged particles move in response to the applied fields, and set off some sparks as they do.) By applying electric and magnet
ic fields and looking at how much different parts of the discharges bent, Thomson identified an especially meaningful component of the discharges. This special component appears in all discharges—that is, no matter what gas you fill the tube with—and the way it bends in response to magnetic fields is especially simple. In fact, the shape of this responsive “lightning bolt” matches the path you calculate, using the laws of electricity and magnetism, for the motion of charged, massive points, with specific values of the charge and mass. Naturally, Thomson proposed that his special discharges were made up of particles which have that much mass and carry that much charge. This was the birth of electrons. The observation that electron streams appeared in all discharges, whatever the starting gas, suggested that they were a basic, universal building block of matter.

  Thomson’s pioneering work inspired many follow-up investigations. Before long, those deep dives into the nature of matter gave birth to a technology that is now both familiar and ubiquitous—electronics. Its importance would be hard to overstate.

  The behavior of electrons has been studied from many angles, in many different kinds of experiments. For example, as I mentioned earlier, people have measured the tiny magnetic fields that spinning electrons—that is, all electrons—generate. The magnitude of those fields can be predicted, by calculation, based on the hypothesis that electrons have mass, electric charge, spin, and no other properties. The predictions can be calculated to very high accuracy, and the magnetic fields can be measured to very high accuracy—each at the level of parts per billion. Happily, they agree.