Fundamentals

  A promising idea has emerged that may help to solve these mysteries. The time-reversal problem has led many physicists to suspect the existence of a new kind of particle, the axion. The lingering afterglow of axions, left over from the big bang, has the right properties to be dark matter. A flurry of developments surrounding this idea have led to a spirited race for discovery, involving hundreds of scientists around the world.

  TIME REVERSAL (T)

  Time’s Mirror Image

  Few aspects of experienced reality are as obvious as the asymmetry between past and future. We remember the past, but can only guess about the future. If you run a movie—say, Charlie Chaplin’s City Lights—backward, it doesn’t look remotely like a sequence of events that could unfold in reality. You would never confuse it with a legitimate movie.

  Yet beginning with the birth of modern science, in Newton’s classical mechanics, and until quite recently, the fundamental laws had the character that you could run them backward in time. That is, the laws you need to predict past states, given present states, are the same laws that you use to predict future states. For example, if you imagine filming a movie of planets orbiting the Sun, according to Newton’s laws, and run it backward, the movie will still obey Newton’s laws. This feature of the laws is called time-reversal symmetry, or T for short.

  Time-reversal symmetry continued to hold up as the scope of the laws expanded. Maxwell’s equations of electromagnetism and Einstein’s revised equations of gravity both have it, for example, as do the quantum versions of those equations. And observations of fundamental interactions seemed to bear T out.

  This contrast between everyday experience and the fundamental laws poses two problems. One is how the actual universe finds a preferred direction for the flow of time. We got an answer to that in chapters 6 and (especially) 7, where we saw that gravity started way out of equilibrium.* The other is, simply, Why? Why in the world should our fundamental description of Nature have this feature, T, that the world we experience so blatantly lacks?

  Why? First Pass: Rock Bottom

  Parents of young children sometimes have the exasperating experience of never-ending “Why”s. (Why do I have to go to bed? Because people need to rest. Why? Because their bodies get tired. Why? Because after we use our muscles for a while they don’t work as well. Why? Because they use up the food we ate, and some junk gets left behind, which has to get cleaned up. Why? Because everything runs down, according to the second law of thermodynamics. Why? Because during the big bang, gravity was out of equilibrium . . .) Eventually you will run out of answers.* At some point you hit rock bottom, with some answer so basic that it can’t be further explained: That’s just the way it is.

  It was unclear, while T appeared to be an exact feature of fundamental laws, that asking “Why?” would be fruitful. It appeared to be an elegant, if slightly peculiar, property of the laws. T might be rock bottom. Most physicists thought that it was.

  Why? Second Pass: Sacred Principles

  The situation changed in 1964, when James Cronin, Val Fitch, and their collaborators discovered a tiny, obscure effect in the decays of K mesons* that violates T. Since T is not quite right, it can’t be rock bottom. At that point there clearly was a question to pursue further: Why does Nature obey T very nearly, but not exactly? That question proves to be wonderfully fruitful.

  In 1973, Makoto Kobayashi and Toshihide Maskawa made a theoretical breakthrough on this problem. They built upon the imposing framework of quantum field theory and our Core theories of the forces (which at the time were not yet firmly in place). That framework is very rigid, as I mentioned earlier—you can’t easily change it without ruining its consistency. No one knows how to change its structure without violating the sacred principles* of relativity, quantum mechanics, and locality. But you can add to it. What Kobayashi and Maskawa discovered is that by adding a third family of quarks and leptons* to the two that were then known, you have the possibility of introducing an interaction that violates T and generates the effect that Cronin and Fitch observed. With only the two known families, there was no such possibility.

  Soon after Kobayashi and Maskawa’s work, the particles from the third family they predicted began to show up at particle accelerators, as they operated at higher energies. Since then, many experiments have vindicated the interaction they proposed as well.

  That isn’t the end of the story, though. Besides the interaction that Kobayashi and Maskawa made use of, there is exactly one other possible interaction that violates T but is completely consistent with the rigid framework of our Core theories and quantum field theory. This interaction isn’t necessary to explain what Cronin and Fitch saw, or any other observation. Nature doesn’t seem to use it. Why?

  Why? Third Pass: Evolution

  In 1977, Roberto Peccei and Helen Quinn proposed an answer to that third and potentially final “Why?” about T. It is a theory of evolution, opened up by expanding the Core. What they proposed is that the strength of the unwanted additional interaction is not simply a number, but a quantum field, which can vary in space and time. They showed that if the new field has some appropriate, reasonably simple properties, then the forces acting upon it will tend to drive it toward zero. Peccei and Quinn implicitly assumed that the field takes on its favored value, zero. Big bang cosmology suggests that the field evolves toward that value.*

  That would leave us, at last, with a satisfying answer to our questions: T is very nearly, but not exactly, a feature of fundamental laws, as an indirect consequence of how deeper principles—relativity, quantum mechanics, and locality—act upon the fundamental ingredients of the world.

  These theoretical ideas have a dramatic consequence. We’ll take it up shortly. First, let’s visit the dark side.

  THE DARK SIDE

  Dark matter and dark energy have a similar character, so it makes sense to introduce them together. They both refer to observed motions that have no apparent cause. It would be more accurate, if less evocative, to say we have “unexplained accelerations,” rather than “dark matter” and “dark energy.” But the extra motions are all of a pattern, which suggests that they are caused by gravity from sources that are otherwise invisible. In order to account for all the observations, we need two distinct new sources. These, by definition, are dark matter and dark energy. Let me emphasize that neither dark matter nor dark energy is “dark” in the usual sense of English. Both have proved to be invisible, so far. Neither emission nor absorption of light has been detected from where the “dark” stuff is supposed to be.

  Dark matter could be composed of a new kind of particle, produced during the big bang, that interacts only very feebly with ordinary matter. Dark energy could be a universal density of space itself. Those are the most popular ideas about what they are among researchers on the subject, and they do account for a wide range of observations fairly convincingly. Other ideas have advocates, too, but they’re (even more) speculative.

  Problems similar to this—missing acceleration problems— have happened before in astronomy. A little history will set the stage for us.

  For many decades following their introduction in 1687, Newtonian mechanics and his law of gravitation—what he called his “System of the World”—went from triumph to triumph. Many people made much more accurate observations of astronomical motions, and others made much more accurate and extensive calculations of the theory’s predictions. Almost without exception, the observations were consistent with the predictions.

  There were, however, two nagging problems. They concerned the motions of the planets Uranus and Mercury. Clear discrepancies emerged between the predictions of Newton’s theory and the observed positions of those planets. The discrepancies were quite small—they amount to far less than the size of the Moon in the sky, for example—but they were well outside what the accuracy of the observations could permit. Something had to give. Either the calculations were missing something, or the th
eory was wrong.

  When an otherwise extremely successful theory hits a snag, the conservative hypothesis is that something is missing. And so both John Couch Adams and Urbain Le Verrier considered the possibility that there might be another planet, not yet recognized, whose gravity was throwing Uranus off course. In other words, they proposed that a very specific kind of “dark matter” was involved.

  Adams and Le Verrier calculated where the new planet would have to be, and where it would appear in the night sky. Le Verrier communicated his prediction to the Berlin Observatory. The observers looked, and they saw it. The new planet, discovered in 1846, is what we now call Neptune.

  Le Verrier tried a similar approach for the problem with Mercury. He postulated the existence of another new planet, which he called Vulcan. Vulcan had to be very close to the Sun, so that its gravity would influence Mercury but not make a noticeable impression on the other planets. That would also explain why Vulcan had not been observed, since the Sun presents a formidable background.

  Astronomers set out to find Vulcan, especially during solar eclipses. Quite a few even reported success. But none of those sightings convinced the community, and the problem festered. Ultimately the solution came from quite a different direction. In 1915, Albert Einstein proposed a profoundly new theory of gravity, his general relativity theory. Although Newton’s theory and general relativity are based on radically different ideas, in many situations they give similar predictions. Within the solar system, by far the biggest difference (still a small one) concerns the motion of Mercury. One of the first major triumphs of Einstein’s theory, already in his original paper, was its ability to reproduce the observed motion of Mercury, without requiring an additional planet. After that, Vulcan was never seen again.

  “Dark energy” is another theoretically motivated modification to the law of gravity, also considered by Einstein. He called it by a different name: the cosmological constant. It builds on general relativity. If you stay within the conceptual framework of general relativity, there is basically just one way to change the law of gravity—one “free parameter,” we say— and that’s to add a cosmological constant. At the time when he considered it, there were no observations that required a nonzero cosmological constant, and in the spirit of Occam’s razor, Einstein set it to zero. But it was ready for use, if observations required it.

  As a little joke, to summarize their historical parallels, we could say that dark matter is from Neptune, while dark energy is from Mercury. The encouraging message from history is that good scientific mysteries often find worthy solutions.

  Dark Matter

  The modern dark matter problem plays out over the whole universe. On several scales, in many different circumstances, astronomers observe “excess” acceleration. Here I’ll mention two classes of observations, which encompass dozens if not hundreds of well-documented examples.

  The first concerns the speed at which stars and gas clouds in the outer fringes of galaxies rotate around those galaxies. One of Kepler’s laws, which today follows both from Newton’s and Einstein’s theories of gravity, connects the speed of rotation around an orbit to the amount of mass inside. Thus, from the observed rotation speeds, you can infer how mass is distributed within a galaxy of interest. What people find is that to explain the observed speeds, you need lots of mass in places where there isn’t much light being emitted. It seems, in essentially all cases that have been studied, that the galaxy is surrounded by an extended halo of dark (invisible) matter. Indeed, it would be more appropriate to say that the lit-up part of the galaxy is an impurity within a cloud of dark matter. The dark matter halo, when you add it all up, weighs about six times more than the visible impurity.

  The second concerns the bending of light, or what is called gravitational lensing. Astronomers have observed in many cases that the image of very distant galaxies is grossly distorted, as if you were looking at it through a glass of water or a Coke bottle. This occurs in particular when the light of the galaxy you’re looking at passes through a region of space containing a cluster of other galaxies. General relativity predicts that gravity should bend light, so the existence of this gravitational lensing is not surprising. What is surprising is the size of the effect. Here again, astronomers find that they need the galaxies in the cluster to weigh about six times what the visible stars and gas clouds supply.

  These and other observations suggest that dark matter provides about 25 percent of the mass in the universe. “Normal” matter—the kind that we understand and are made of—provides about 4 percent. Most of the rest is dark energy.

  Dark Energy

  A different class of observations leads us to dark energy. Here there is an important backstory. Albert Einstein formulated his theory of gravitation, general relativity, in 1915. Not long afterward, in 1917, he considered a modification of the equations, to allow for what he called a “cosmological constant.” Physically, introducing the cosmological constant corresponds to assigning a nonzero density to space itself. Thus, a nonzero value of the cosmological constant means that every unit of volume in space contributes an equal, nonzero amount to the total mass of the universe, even when there’s (apparently) nothing there.

  A nonzero cosmological constant fits easily into the framework of general relativity. It does not require a significant change to the theory’s basic principles. Matter still bends space-time in the same way as before, and matter responds to space-time curvature in the same way as before. The cosmological constant merely recognizes the possibility that space-time itself, a material that general relativity allows to bend, push, and shake, might also have inertia. Other possible modifications of general relativity are, by contrast, either highly contrived or tiny in their physical effects.

  The cosmological constant’s universal density comes paired with a peculiar partner property. Together with space’s positive density of mass, one must include a negative pressure, whose magnitude is equal to the density times the square of the speed of light. That relation between density and pressure is the analogue, for mass tied up in space, of the more famous relation E = mc2, which connects energy to mass for particles.

  During the 1990s, the cosmological constant got rebranded as dark energy. The new name reflects a new attitude. Modern physicists, internalizing the lessons they learned in understanding the other forces, recognize that the density of space is not merely a parameter that appears in general relativity, whose value has no other meaning. It is tied up with the rest of physics, and it can receive contributions from many different sources. In a universe filled with restless quantum fields, it would be surprising if space didn’t have inertia.

  In 1998, astronomers discovered dark energy. What they observed, to be specific, is that the rate of expansion of the universe has been increasing, consistent with a universal negative pressure. This was inferred from measurements of redshifts, in the spirit of Hubble, but using supernovas in place of Cepheid variables. Supernovas, being much brighter, allow access to larger distances.

  The density of space they measured is, by most standards, exceedingly small. A volume of space equal to the Earth’s volume weighs about 7 milligrams. Within the solar system, or even the galaxy, the mass contributed by space is utterly negligible compared with the mass contributed by ordinary matter (or dark matter). But such is the vast emptiness of intergalactic space that this small density, present everywhere, comes to dominate the total mass of the universe.

  Dark energy presently accounts for about 70 percent of the universe’s mass. Nobody knows why several different, much larger contributions from various sources—some positive, some negative—conspire to give that particular final result. It’s a big cosmic mystery.

  A Cosmological “Standard Model”

  Understanding that together dark matter and dark energy (hypothetically) presently constitute most of the mass in the universe, we might anticipate that they played a significant role in the history of the un
iverse, too. To “run the movie backward” and check that intuition, we need to be more specific about what the properties of dark matter and dark energy are. Revisiting the big bang gives us a chance to learn about dark side properties. If we guess wrong about them, then our model of the big bang won’t produce the universe we observe.

  Given how little we know about the dark side, the task of guessing how dark matter and dark energy might have behaved during the early moments of the big bang might seem hopeless. Fortunately, it turns out that we don’t need to know much, and some simple guesses have worked out remarkably well.

  For dark matter, we assume that it is made from some kind of particle that interacts feebly both with normal matter and with itself. We also assume that it was in equilibrium with the rest of the cosmic fireball early on, but that it cut away relatively shortly thereafter, becoming a lingering afterglow of the kind we discussed in chapter 6. One subtle point, on which some early proposals for dark matter foundered, is that when they cut away, the particles must have been moving much slower than the speed of light.* Because (by assumption) gravity is the only relevant force, and gravity doesn’t distinguish among different forms of matter, that’s all we need to know. We can calculate how dark matter moves, and how it affects the rest of the universe, once it has cut away. This defines the so-called cold dark matter model.