Fundamentals

  For dark energy, we adopt Einstein’s idea that it represents a universal density of space itself, and that it is associated with a universal negative pressure.

  Given those assumptions, we can run the density contrasts we observe in the cosmic microwave background radiation, which date from 380,000 years after the big bang, forward to the present. The addition of dark matter makes the instability work faster than it otherwise would. With dark matter, the model universe evolves to look like ours. Without dark matter, it doesn’t. In this way, the dark side allows us to fulfill the promise of big bang cosmology to produce the structure we observe in the universe today, starting from tiny seed density contrasts, through gravitational instability.

  AXIONS: QUANTA THAT CLEANSE

  When I was a teenager, I sometimes accompanied my mother to the supermarket. On one of those trips, I noticed a laundry detergent called Axion. It occurred to me that “axion” would be a good name for an elementary particle. It was short, catchy, and would fit in nicely alongside proton, neutron, electron, and pion. I had the passing thought that if I ever got a chance to name a particle I’d call it the axion.

  In 1978, I got my chance. I realized that the Peccei-Quinn idea, to introduce a new quantum field, had an important consequence that they hadn’t noticed.* Quantum fields produce particles—their quanta—as we discussed earlier. And this particular field produced an extraordinarily interesting particle. The new particle had the intriguing technical feature that it cleaned up a problem with an axial current. The stars were aligned, and axions entered the world—or at least the world of physics literature.

  (By the way, the naming would never have got past the editors of Physical Review Letters, or possibly the makers of Axion detergent, if I’d broadcast my true motivation prior to publication. Instead, I mentioned the axial current.)

  Looking for Their Lingering Glow

  Axions have the right properties to provide the cosmological dark matter. They interact very feebly with normal matter and with each other. They get produced at a high temperature and then later break free from the cosmic fireball. Their lingering afterglow, the axion background, fills the universe. The calculated density of the axion background is consistent with the observed density of dark matter, and axions are produced almost at rest. Thus, the axion background fulfills the assumptions of “cold dark matter” cosmology.

  It’s a beautiful story, but is it true? Axions, as we’ve said, interact only feebly with matter—but the theory tells us that they do interact, and how. In order to detect the axion background, we’ll need to design sensitive new kinds of detectors, tailored to their properties. Hundreds of physicists, both theoreticians and experimentalists, are taking up this challenge today. If there’s justice in the world, and luck, we may soon witness a success story worthy of a place beside the discoveries of Neptune, the cosmic microwave background, the Higgs particle, gravitational waves, and exoplanets. Scientific mystery stories often have worthy solutions.

  THE FUTURE OF MYSTERY

  How Mysteries End

  Val Fitch, the hero of T violation who appeared earlier, was a wise man with a subtle sense of humor. He was chairman of the Princeton University physics department when I was a professor there, early in my career. In telling him about my emerging ideas on axions and dark matter,* I spoke about T violation as if it were an established fact from ancient history. After all, I’d never known anything else. At some point, he smiled gently and said, “Yesterday’s sensation is today’s calibration.”

  That is the fate of successful scientific mystery stories. I lived through a similar process, on the receiving end, with asymptotic freedom and QCD (quantum chromodynamics). For several years after our breakthrough, there was a lot of excitement and doubt around the question of whether it really did solve the mystery of the strong force. Big international conferences featured talks on “Tests of QCD,” which reported progress in using the theory to make predictions and in testing it experimentally. Gradually, though, excitement dwindled, as the doubts faded. Today, the same sort of work, now vastly more sophisticated, goes on behind the scenes. It is called “calculating background.” Yesterday’s sensation is today’s calibration, and tomorrow’s background.

  Knowing and Wondering

  Besides the future of particular mysteries, there are interesting questions around the future of mystery itself.

  The Clay Foundation has offered a prize of one million dollars for a proof that QCD predicts that quarks are confined. Physicists have lower—or I’d rather say different—standards. As far as I’m concerned, we’ve moved way beyond proving that quarks are confined. With the help of our silicon friends, we can calculate what kinds of particles QCD produces, with no serious room for error. Isolated quarks are not among them. Indeed, the calculations give us the particles with the masses and properties of the particles we observe in Nature—no more, and no less.

  Should a supercomputer get the prize? Or should its programmers?

  In 2017, AlphaZero, a highly innovative computer program using artificial neural nets, after being given the rules of chess, played games against itself for a few hours, learned from the experience, and achieved superhuman performance. Does AlphaZero understand chess? If you’re tempted to answer “No,” I refer you to Emanuel Lasker, the world chess champion for many years, from 1894 through 1921.*

  On the chessboard lies and hypocrisy do not survive long. The creative combination lays bare the presumption of lies; the merciless fact, culminating in checkmate, contradicts the hypocrites.

  Examples like these show that there are ways of knowing that are not available to human consciousness. But really, this should not come as fresh news. Humans themselves know many things that are not available to human consciousness, such as how to process visual information at incredible speeds, or how to make their bodies stay upright, walk, and run.

  The genomes of humans and of Earth’s other creatures are another great repository of unconscious knowledge. They have solved many complex problems that arise in building up organisms that flourish, accomplishing feats far beyond the capabilities of human engineering. They “learned” how to do this through a long, inefficient process of biological evolution, rather than through any process of logical reasoning, and they certainly don’t know what they know, consciously.

  The abilities of our machines to carry lengthy yet accurate calculations, to store massive amounts of information, and to learn by doing at an extremely fast pace are already opening up qualitatively new paths toward understanding. They will move the frontier of knowledge in directions, and arrive at places, that unaided human brains can’t go. Aided brains, of course, can help in the exploration.

  A special quality of humans, not shared by evolution or, as yet, by machines, is our ability to recognize gaps in our understanding and to take joy in the process of filling them in. It is a beautiful thing to experience the mysterious, and powerful, too.

  10

  COMPLEMENTARITY IS MIND-EXPANDING

  The test of a first-rate intelligence is the ability to hold two opposed ideas in the mind at the same time, and still retain the ability to function.

  —F. Scott Fitzgerald

  It is clear that this complementarity overthrows the scholastic ontology. What is truth? We pose Pilate’s question not in a skeptical, anti-scientific sense, but rather in the confidence that further work on this new situation will lead to a deeper understanding of the physical and mental world.

  —Arnold Sommerfeld

  Complementarity, in its most basic form, is the concept that one single thing, when considered from different perspectives, can seem to have very different or even contradictory properties. Complementarity is an attitude toward experiences and problems that I’ve found eye-opening and extremely helpful. It has literally changed my mind. Through it, I’ve become larger: more open to imagination, and more tolerant. Now I’d like to explore with y
ou the mind-expanding insights of complementarity, as I understand them.

  The world is simple and complex, logical and weird, lawful and chaotic. Fundamental understanding does not resolve those dualities. Indeed, as we have seen, it highlights and deepens them. You can’t do justice to physical reality without taking complementarity to heart.

  Humans, too, are wrapped in dualities. We are tiny and enormous, ephemeral and long-lasting, knowledgeable and ignorant. You can’t do justice to the human condition without taking complementarity to heart.

  COMPLEMENTARITY IN SCIENCE

  Niels Bohr, the great Danish quantum physicist, first articulated the unifying power of complementarity. Straightforward history would say that Bohr learned complementarity from his experience with quantum physics. A different perspective would say that this way of thinking came to Bohr naturally, predating and even enabling his unique contributions to quantum physics. Some of Bohr’s biographers have seen here the influence of Søren Kierkegaard, a Danish mystic and philosopher whom Bohr admired.

  Between the first inklings of quantum behavior, around 1900, and the emergence of modern quantum theory in the late 1920s, there was a period of intense struggle when it seemed impossible to reconcile different experimental observations. During this period, Bohr was a master at building models that made sense of some observations, while strategically ignoring others. Albert Einstein wrote of his work:

  That this insecure and contradictory foundation was sufficient to enable a man of Bohr’s unique instinct and tact to discover the major laws . . . of the atom together with their significance for chemistry appeared to me like a miracle—and appears to me as a miracle even today. This is the highest form of musicality in the sphere of thought.

  Coming out of this experience, Bohr developed complementarity into a strong insight that flows from science into philosophy, and becomes wisdom.

  COMPLEMENTARITY IN QUANTUM MECHANICS

  In quantum mechanics, the most basic description of an object—whether the object is an electron or an elephant—is its wave function. An object’s wave function is a kind of raw material, which we can process into predictions about the behavior of the object. We can process the wave function in different ways, in order to address different questions. If we want to predict where the object will be, we must process its wave function in one way. If we want to predict how fast the object is moving, we must do so in a different way.

  These two ways of processing the wave function are broadly similar to two ways of analyzing music, by harmony or by melody. Harmony is a local analysis—here monitoring a moment in time, rather than a point in space—while melody is a more global analysis. Harmony is like position, while melody is like velocity.

  We can’t do those two forms of processing at the same time. They interfere with each other. If you want to get position information, you must process the wave function in a way that destroys velocity information, and vice versa.

  While the precise mathematical details can be complicated, it is vitally important to emphasize that there is a solid mathematical foundation supporting all that talk. In quantum theory, as presently understood, complementarity is a mathematical fact, not just an airy assertion.

  So far, I have discussed quantum complementarity using mathematical concepts—that is, wave functions and processing. We can get a different perspective by considering the same situation more directly, in terms of experiments. In that spirit, instead of asking how we can process a particle’s wave function to make predictions, we ask how we can interact with the particle to measure its properties.

  Given the mathematical framework of quantum theory, the complementarity of position and velocity is a theorem. But the mathematics of quantum theory, with its many weird aspects, is an attempt to describe Nature, not revealed truth. Indeed, many of the pioneers of quantum theory, including Einstein, became skeptics of its mature mathematical form.

  The counterpart of quantum theory’s inability to predict position and velocity simultaneously must be our inability to measure those properties simultaneously in experiments. If it were possible to measure both position and velocity simultaneously, then we would need a new mathematical theory, different from quantum mechanics and its processed wave functions, to let us describe such measurements.

  Soon after he laid the foundations of modern quantum theory, young Werner Heisenberg realized its startling mathematical consequence, that position and velocity could not be measured simultaneously. He formalized that realization as his “uncertainty principle.” One of the key questions that arises from his uncertainty principle is whether or not it correctly describes concrete facts—that is, things we can observe—about the physical world. Heisenberg and then Einstein and Bohr all wrestled with this.

  At the level of physical behavior, this conflict—this complementarity—reflects two key points. The first key point is that to measure something’s properties, you must interact with it. In other words, our measurements do not capture “reality,” but only sample it.

  As Bohr put it:

  In quantum theory . . . the logical comprehension of hitherto unsuspected fundamental regularities . . . has demanded the recognition that no sharp separation can be made between an independent behavior of the objects and their interaction with the measuring instruments.

  The second key point, heightening the first, is that precise measurements require strong interactions.

  With those points in mind, Heisenberg considered many different ways that one might try to measure the position and velocity of elementary particles. He found, in every case, that they conformed to his uncertainty principle. That analysis built up confidence that the strange mathematics of quantum theory reflected strange facts about the physical world.

  The two principles we mentioned above—that observation is an active process and that observation is invasive—were bedrock foundations of Heisenberg’s analysis. Without them, we cannot use the mathematics of quantum theory to describe physical reality. They undermine, however, the world-model we build up as children, according to which there’s a strict separation between an external world, which is “out there” and has properties that our observations reveal, and ourselves. Accepting the lessons of Heisenberg and Bohr, we come to realize that there is no such strict separation. By observing the world, we participate in making it.

  Heisenberg did his work on uncertainty at Bohr’s institute in Copenhagen. Those two pioneers had intense discussions, and developed a kind of scientific father-son relationship. Bohr’s early ideas on complementarity emerged as an interpretation of Heisenberg’s work.

  Einstein disagreed with Bohr and Heisenberg’s findings and was uncomfortable with complementarity. He was uncomfortable with the idea that there could be valid yet incompatible viewpoints. He hoped for a more complete understanding, which could encompass all possible viewpoints at once. In particular—as a test case—he hoped that both the position and the velocity of a particle could be measured simultaneously. He thought hard about that issue, and he tried to design experiments that could reveal both the position and the velocity (or momentum*) of a particle at the same time. Einstein’s ingenious thought experiments were more intricate than those Heisenberg had considered.

  In the famous Bohr-Einstein debates, as described by Bohr in “Discussions with Einstein on Epistemological Problems in Atomic Physics,” Einstein challenged Bohr with a series of thought experiments. These challenged aspects of quantum-mechanical complementarity, notably including the complementarity of energy and time. In responding to every one of those challenges, Bohr was able to identify subtle flaws in Einstein’s analysis, and to uphold the physical consistency of quantum theory.

  Those debates, and others that followed them, have clarified the nature of quantum theory, but so far they have never successfully challenged its correctness. Meanwhile, people have used quantum theory to design many wonders, from lasers to iPhones to GPS. Th
ose quantum theory–based designs might not have worked—but they do. If “what doesn’t kill you makes you stronger,” then quantum theory, and the complementarity it implies, are now strong, indeed.

  (In case you’ve been wondering what this means for the aforementioned elephant: Quantum uncertainty, although present in principle, can be safely ignored. We have no trouble measuring both the position and the momentum of an elephant well enough to serve all practical purposes. The uncertainty in those things, compared with their actual value, is a negligible fraction. For electrons in atoms, it’s a different story.)

  LEVELS OF DESCRIPTION

  Another source of complementarity is the use of different levels of description. When the description of a system using one kind of model gets too complicated to work with, we sometimes can find a complementary model, based on different concepts, to answer important questions.

  A humble, concrete example will bring out the basic idea, which has profound implications and many applications. The gas that fills a hot-air balloon is composed of a vast number of atoms. If we wanted to predict the behavior of the gas by applying the laws of mechanics to its atoms, we’d face two big problems:

  Even if we were content to start with classical mechanics (as an approximation), we’d need to know the position and velocity of each atom at some initial time, to give the equations the data they need to work with. Gathering and storing that much data is totally impractical. Quantum mechanics only makes this problem worse.