The naive answer is simple. Since half the integers are even, the probability must be one-half—50 percent. But we can’t really do this experiment because no one can make an infinite bag of integers. So to test the theory, we can cheat a little and use a finite bag, containing, let’s say, the first thousand integers. Sure enough if we do the experiment over and over we will, indeed, find the probability to pull an even integer is one-half. Next we can do the same experiment with a bag filled with the first ten thousand integers. Again, since half the scraps are even and half are odd, we will find the probability for an even integer is one-half. Do it again with the first one hundred thousand integers, the first million integers, the first billion, and so on. Each time the probability is one-half. It is reasonable to extrapolate from this that if the bag had an infinite number of scraps, the probability would remain one-half.
But wait. We could modify the contents of the bag in the following way. Start with the first one thousand even integers and the first two thousand odd integers. Now there are twice as many odds as evens, and the probability to draw an even number is only one-third. Next repeat the experiment with the first ten thousand even integers and the first twenty thousand odd integers. Again the probability is one-third. As before, we can extrapolate to the limit of an infinite bag, but each time the result will be one-third. In fact we can make the answer come out any way we want by varying how we define the limit of an infinite experiment.
The eternally inflating universe is an infinite bag, not of paper scraps with numbers but of pocket universes. In fact it is a bag in which each possible type of universe—each valley of the Landscape—is represented a countably infinite number of times. There is no obvious mathematical way to compare one kind of pocket universe with another and to declare that one is more probable than the other. The implication is very disquieting: there seems no way to define the relative likelihood of different anthropically acceptable vacuums.
The measure problem (the term measure referring to the relative probabilities of different vacuums) has vexed some of the greatest minds in cosmology, Vilenkin and Linde especially. It could prove to be the Achilles heel of Eternal Inflation. On the one hand, it is hard to see how Eternal Inflation can be avoided in a theory with any kind of interesting Landscape. But it is equally hard to see how it can be used to make scientific predictions of the kind that would establish it as science in the traditional sense.
In the past physics has faced many other problems involving infinite numbers: the ultraviolet catastrophe confronting Planck or the strange infinities that were the bane of quantum field theory in the early days. Even the problems of black holes that Hawking, ’t Hooft, and I debated are problems of the infinite. According to Hawking’s calculations, a black hole horizon is able to store an infinite amount of information without giving it back to the environment. These all were deep problems of transfinite, or infinite, numbers. In each case new physical principles had to be discovered before progress could be made. In Planck’s case it was quantum mechanics itself—Einstein’s recognition that light was made of quanta. The infinite numbers that plagued quantum field theory were purged only when the new principles of renormalization theory were uncovered and eventually understood by Kenneth Wilson. The black hole story is still being understood, but the outlines of a solution in terms of the Holographic Principle are in place. In each case it was found that the classical rules of physics overestimated the number of degrees of freedom that describe the world.
I believe the measure problem will also require a major new idea before we can understand how to make predictions about the Landscape. If I had to make a guess, I would say that it has something to do with the Holographic Principle and the way that information beyond our horizon is contained in the cosmic radiation in our own pocket. But if I were an opponent of the populated Landscape, I would aim my attack at these conceptual problems of Eternal Inflation.
The measure problem aside, the practical difficulty of making testable predictions that can be compared with experiments or observations is a serious problem. But I think the situation is far from hopeless. There are a few types of evidence that could be obtained in the near future.
The Beginning of Inflation
In chapter 4 I explained how the tiny density contrasts in the early universe (observed in the cosmic microwave background) were created during the final Inflation that took place on a ledge overlooking our valley. These were the seeds that evolved into galaxies. There was lumpiness on many different scales, some occupying tiny portions of the sky and some much bigger structures, occupying almost the entire sky. The cosmic lumps and bumps we can observe now are fossil remnants dating to different eras. The important correlation to remember is that the biggest lumps were frozen in at the earliest times.
If we are very, very lucky, the largest lumps in the CMB might date to a time just before the usual Inflation got started—in other words, just as the universe was settling onto the inflationary ledge. If that were the case, the largest lumps would be a bit less lumpy than the slightly smaller lumps, which were produced after the Inflation was going on for a while. Indeed, there is some evidence that the very largest lumps are weaker than the others. It is a long shot, but those large-scale density contrasts could have information about the formation of our bubble from a previous epoch with a larger cosmological constant.
If we are that lucky, then the Inflation did not go on long enough to wipe out evidence for the curvature of space. Here again bubble nucleation has a distinct signature. If our pocket universe was born in a bubble-nucleation event, the universe must be negatively curved. The interior angles of cosmic triangles will add up to less than 180 degrees.
At the level of accuracy that the curvature of space has been measured, there is no indication of such curvature. This idea may fail because standard Inflation probably had been going on for a long time when the largest visible lumps were formed. But if we do detect negative curvature, that will be a smoking gun telling us that our universe was born as a tiny bubble in a vacuum with a larger cosmological constant.
Superstrings in the Sky
We have not exhausted all our options for observing the universe yet. Is it possible that we can actually see superstrings? The obvious answer is that they are much too small to be seen. But the same thing could have been said about the tiny quantum fluctuations that occurred during Inflation. In chapter 5 we saw that the expansion of the universe, and the effects of gravity, somehow inflated these fluctuations until they became first the density contrasts in the cosmic microwave background and eventually the eminently visible galaxies in today’s sky. That we can see the effects of microscopic quantum phenomena frozen onto the sky like an expanding pointillist abstract painting is an incredible fact. It came as a complete surprise to most physicists, who were used to thinking of the quantum world as strictly microscopic. So perhaps we shouldn’t be too quick to assume that small-scale objects like strings can’t do something similar: perhaps turn the sky into a giant Jackson Pollock canvas.
Building on the work of their colleagues, Thibault Damour, Alex Vilenkin, Joe Polchinski, and others have begun to explore an enormously exciting new opportunity, once again originating from phenomena connected with Inflation. Inflation is caused by vacuum energy that was present long ago. That vacuum energy disappeared as the universe slid down the Landscape to its present very low altitude, but the vacuum energy didn’t depart without leaving something behind. It was converted into more ordinary forms of energy, namely, heat and particles, the stuff of the current universe.
But there is also another form the energy can take. Some of it can get converted into a tangled collection of string resembling an incredibly snarled fishing line or a ball of wool after the cat got a hold of it. The tangle could include not just the ordinary strings of String Theory but also the string-like D1-branes devised by Polchinski.
If such a tangle were created in the early universe, the subsequent expansion would stretch the tangle to
enormous proportions: tiny microscopic loops and swirls, growing to hundreds of millions of light-years in size. But some portion of the strings would remain till today, flapping around on a vast scale of space and time. The strings would not be visible by means of light or any other electromagnetic radiation, but luckily there is another way to detect them. Damour and Vilenkin have demonstrated that such cosmic strings would emit gravity waves (wavelike disturbances of the gravitational field) that may very well be detectable in the next decade. Observing such strings in the sky would be an extraordinary triumph for String Theory.
Studying these cosmic superstrings, if indeed they exist, can tell us a great deal—not about the entire Landscape but at least about our immediate neighborhood. Polchinski and collaborators have studied the detailed conditions under which string tangles occur and the nature of the networks they form. The details are very sensitive to things like the dimensionality of the Landscape, the presence of branes and fluxes in the compact dimensions, and more. The sky, rather than particle accelerators, may well be the place to look for the smoking gun of String Theory.
High-Energy Physics
Astronomical and cosmological observations are probably the wave of the future, but we have not yet reached the limits of laboratory science. Our greatest short-term hope for gaining new groundbreaking information about the Laws of Physics is what it always was—experimental high-energy (elementary-particle) physics done at accelerator laboratories. It may be true that we are reaching the limits of this kind of science, but no doubt we are going to push the frontiers to at least one more level. The largest accelerator in the world and probably the only one big enough to tell us a great deal of new information is presently nearing completion and should be operating by 2007. Geneva, Switzerland, the location of CERN, is the site of the Large Hadron Collider, or LHC, as it is called. Originally conceived for the purpose of studying the Higgs boson, it is also the ideal machine for discovering the supersymmetric twins of the elementary particles.
In chapter 7 I explained why many physicists think that supersymmetry “is just around the corner.” The argument, first made twenty-five years ago, is that supersymmetry would ensure that the violent quantum fluctuations of the vacuum do not create an enormous mass for the Higgs boson and, thereby, ruin the Standard Model. Supersymmetry may well be around the next corner. The majority of theoretical physicists expect it to be so, at least if you go by the number of papers published on the subject.
But there is another possibility. Like the vacuum energy (or cosmological constant), too large a Higgs mass would ruin the possibility of life evolving in our pocket universe. So perhaps the answer is not supersymmetry but a more anthropic consideration. If the world is big enough and the Landscape diverse enough, then some tiny fraction of the megaverse will have a small enough Higgs mass for life to flourish—end of story. As in the case of the cosmological constant, supersymmetry would be irrelevant and unnecessary.
The two explanations do not necessarily exclude each other. The most likely possibility for finding a valley with sufficiently small Higgs mass may be to find one with supersymmetry just around the corner. It is even possible that all of the valleys with small Higgs mass are of this type.
Or the opposite may be true: the vast majority of vacuums with small Higgs mass may completely lack any kind of supersymmetry. The exploration of the Landscape is still in its early infancy, and we don’t know the answer to this question. My original guess was that supersymmetry was not favored, and I said so in print. But I have since changed my mind—twice—and probably not for the last time.
In trying to predict the relative probability of supersymmetry versus no supersymmetry, we run head on into the measure problem. Perhaps we should stop right there. But there is a strong temptation to dismiss the subtleties and push on. Theoretical physicists such as Michael Douglas, Shamit Kachru, and many others are developing methods to count the number of sites on the Landscape with different properties. Here I mean the number of possibilities, not the number of actual pocket universes. Then, having no other information, we might guess that if there are vastly more anthropic vacuums with approximate supersymmetry than without, approximate supersymmetry is overwhelmingly likely. But the measure problem is another huge elephant in the room that may be quietly laughing at us.
In any case the difficulties in testing the Landscape, Eternal Inflation, and the Anthropic Principle are real, but there are many ways to test a theory. Mathematical consistency may not impress the most hard-nosed experimental physicist, but it should not be underestimated. Consistent theories that combine quantum mechanics and general relativity are far from common. Indeed, this is the reason that String Theory has so little competition. If no alternatives show up and if String Theory proves to have as varied a Landscape as it seems, then the populated Landscape will be the default position—the theory to beat, so to speak.
But giving up on the possibility of more direct tests is certainly premature. It is true that theory and experiment usually proceed “hand in hand,” but it’s not always the case. It took more than two decades for Alan Guth’s inflationary universe to be tested by observation. In the early days almost everyone thought the idea was interesting but could never be tested. I think even Alan himself was skeptical of ever confirming its truth.
Even more extreme was Darwin’s theory. It was based on general observations about the world and a very clever hunch. But a direct, controlled, experimental test must have seemed completely impossible—you would need a time machine to take you back millions, if not billions, of years. In fact it took about one hundred years for ingenious biologists and chemists to figure out how to subject the theory to rigorous laboratory tests. Sometimes theory has to forge ahead to light the way.
Epilogue
Just before boarding the giant Hercules aircraft that was to take us to Punta Arenas from the Chilean Antarctic station, I hugged my friend Victor farewell. An emotional and sentimental Russian, Victor was saddened by our leaving. The last thing I said to him before trekking out into the blizzard was, “Victor, don’t you think Antarctica is beautiful?” He was lost in melancholy thought for a brief moment and then quietly smiled and said, “Yes, like some women: beautiful—but cruel.” Had Victor asked me whether I thought our universe and its Laws of Physics are beautiful, I might have answered, “No, not beautiful. But rather friendly.”
Throughout this book I have dismissed beauty, uniqueness, and elegance as false mirages. The Laws of Physics (in the sense that I defined them in chapter 1) are neither unique nor elegant. It seems that the world, or our part of it, is a Rube Goldberg machine. But I confess: I am as vulnerable to the seductive charms of Uniqueness and Elegance as any one of my colleagues. I, too, want to believe that the grand overarching principles that transcend the rules governing any particular pocket of the universe are unique, elegant, and wonderfully simple. But the results of those rules need not be elegant in the least. Quantum mechanics, which rules the microscopic world of atoms, is very elegant—but not everything made of atoms is. The simple laws that give rise to tremendously complicated molecules, liquids, solids, and gases yield stinkweeds as well as roses. I think I might find the universal principles of String Theory most elegant—if I only knew what they were.
I often joke that if the best theories are the ones with the minimum number of defining equations and principles, String Theory is by far the best—no one has ever found even a single defining equation or principle! String Theory gives every indication of being a very elegant mathematical structure with a degree of consistency far beyond any other physical theory. But nobody knows what its defining rules are, nor does anyone know what the basic “building blocks” are.
Remember, building blocks are the simple objects that everything else is made of. For a housing contractor, building blocks may be exactly that—the blocks or bricks that compose the walls and foundation. The relation between building blocks and the composite objects that they compose is very asymmet
rical: houses are made of bricks. Only someone with a severe perceptual disorder—perhaps an Oliver Sacks patient, “The Man Who Mistook His House for a Brick”—would get this relationship backward.
The basic building blocks of science depend on context and the state of knowledge at the time. In the nineteenth century the building blocks of matter were the atoms of the periodic table. The same ninety-two elements can be combined into an endless variety of composites called molecules. Later, atoms were discovered to be composite, and they gave way to electrons, protons, and neutrons. The pattern that we have learned to expect is that big things are made up of littler things. For a physicist probing deeper into the laws of nature, this has usually meant uncovering a substructure of smaller building blocks. At the present stage of physics, ordinary matter is believed to be composed of electrons and quarks. The questions that people, both laymen and scientists, often ask is, “Do you think this will go on forever, or do you think there is a smallest building block?” These days the question often takes the form, “Is there anything smaller than the Planck length?” or “Are strings the most fundamental objects or are they made of smaller things?”
These may be the wrong questions. The way String Theory seems to work is subtler than this. What we find is that if we focus attention on some particular region of the Landscape, everything is built out of one specific set of building blocks. It may be closed or open strings of some specific type in certain regions. In other regions all matter is composed of D-branes. In yet other parts of the Landscape, objects similar to ordinary field quanta can be assembled into strings, branes, black holes, and more. Whatever is singled out as “most fundamental,” the other objects of the theory behave like composites—composites in the same sense that atoms and molecules are composites of electrons, protons, and neutrons.
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