The Statistical Universe

Incubator / by Raphael Bousso /

We look up to an expanse of sky that is billions of light-years in size, but the universe may be far larger than what we are able to see.

Illustration by Erik Natzke

We cannot see farther into the universe because the big bang happened only 14 billion years ago and light from distant regions has not had enough time to reach Earth. Yet subtle clues are beginning to reveal some of the properties of the regions of space hidden beyond our cosmic horizon. Our world appears to be only a small part of a “multiverse,” an expanse vastly larger than the visible universe, and for the most part completely different from it.

To account for what we do see, cosmologists invented a theory many years ago called “inflation,” in which a brief, ultra-accelerated expansion of the early universe stretched space to a size far greater than what we observe. Inflation explains why, despite the violence of the big bang, the universe appears to us uniform and smooth, and the theory has made predictions confirmed by measurements of subtle variations in the radiation left over from the big bang. But inflation does not really make the universe more uniform — just huge. If inflation is correct, then the billions of light-years that our telescopes probe are a mere dot on a far vaster canvas.

The multiverse comprises a large number of distinct patches, each far bigger than our night sky. What observers see, therefore, also depends on where they find themselves. Most of the regions in the multiverse are inhospitable to life, and their properties will not be observed. But what exactly is life? In order to extract predictions from the multiverse, my colleagues and I have developed a statistical tool to find regions with observers: We look not for life itself but for the disorder left behind by the complex processes that its formation depends on. To understand the physical signatures of life in this way may help us finally to comprehend our own little corner of the multiverse.

String theory is the leading candidate for reconciling two very fundamental laws — gravity and quantum mechanics. But to accomplish this feat requires at least nine dimensions of space, when we see only three. In order for six dimensions to have remained undetected, they must be tied up into loops too small to see under our best microscopes. In physics there are fundamental laws and local laws, which depend on the environment. Iron and carbon are made from the same elementary particles but assembled differently. As a result local properties like density and conductivity differ widely. The fundamental laws of string theory also appear as different local laws, depending on how the extra dimensions are tied up. If we could open the knots and tie them differently, then supposedly “fundamental” phenomena, like neutrons or the electric force, would disappear and be replaced by an utterly different set of particles and forces.

Because extra dimensions need not be tied up the same way everywhere, physical laws may vary from place to place. Inflation makes each “legal district” much larger than the visible universe, giving us the illusion that particles and forces are the same everywhere. But beyond our cosmic horizon, inflation allows the universe to grow so enormous that it contains every set of possible laws that can be constructed from string theory. Eight years ago, Joe Polchinski and I estimated that the number of possibilities is truly enormous: a one with roughly 500 zeros behind it (10500).

It is hard to imagine how one might test all of these different laws of physics and discover ours among them. A straightforward idea would be to work out the 10500 possibilities individually and verify that at least one of them agrees with our universe. But this would be as difficult, and as pointless as it would be to track the motion of every gas molecule to know how air is distributed in a room. When dealing with large numbers, probabilities are your friend. Air molecules distribute evenly and do not collect in one corner — the event is just too improbable to ever happen. In this spirit, we can study which local physical laws are most probable in the multiverse and compare these laws to those we see. But there is a subtlety in this approach.

In the visible universe, we occupy a very special place. Most regions are empty, yet we find ourselves on a planet near a powerful star. This should not surprise us. Intergalactic space lacks both the particles to form us, and the energy to sustain us. It is self-evident that we live in one of the regions that are life friendly. In the multiverse, too, many regions have properties that are incompatible with the existence of observers: They might be entirely empty, or their physical laws preclude any complex structures. The difference is that observers are prevented by their cosmic horizon from looking at those regions. Their own life-friendly physical laws are all they ever get to see. Unlike the lifeless voids in the visible universe, distant multiverse regions without observers will not be observed by anyone, no matter how abundant they may be.

To make predictions in the multiverse we must compute not just what is likely, but what is likely to be observed. We need to understand both the statistical properties of the multiverse, and those of observers. How abundant are different sets of physical laws? Which of these sets allow observers to form?

By giving observers a role in our equations, aren’t we confusing cause and effect: humans first, the laws of nature second? Scientists rightfully frown upon this sort of “anthropic” reasoning. But we started with fundamental laws: string theory. String theory as we currently understand it may turn out to be wrong, but this is a scientific question. To decide it, we must learn what the theory predicts. If its fundamental laws lead to a multiverse, as they appear to, then it would be irrational to deny that observations will be colored by the location of the observers.

How can we hope to divine the life forms that might inhabit regions with totally different laws of physics? Do they live on planets orbiting stars? With different laws of physics, there may be no analogue of “planet” or “star.” Are observers made of organic molecules? The elementary particles we know do not exist in most other regions — forget about combining them into carbon. To say that life requires galaxies, stars, or certain molecules is to make some rather self-centered assumptions about what an intelligent observer should look like. The very vocabulary — “galaxies,” “molecules” — makes no sense in most of the multiverse.

Fortunately, there are ways to sidestep this problem. Let us be a little self-centered and ask what observers living near stars in galaxies are likely to see. This means ignoring all regions in which words like “star” and “galaxy” make no sense. The resulting “trimmed down” multiverse looks less exotic, but still contains an enormous multiplicity of regions, whose physical laws can differ from our own in important respects. Suppose that after a careful survey of the trimmed-down multiverse, we found that our local laws are highly improbable among those observed. This would be enough to falsify the multiverse idea. If our observations were not typical among observers that live near stars, then they certainly would not be typical among all observers.

So far, the multiverse has passed such tests. But most important, it succeeds where no other theory has before: It explains why empty space weighs so little. This may seem laughable, but without the multiverse our finest theories predict that empty space should contain about 10123 times more energy than it actually does. This is known as the “cosmological constant” or “dark energy” problem. It has been called the “worst prediction in the history of science” and the “mother of all physics problems.” And it was the main reason why Polchinski and I, building on work of Steven Weinberg and others, began studying the multiverse of string theory.

To probe the multiverse more deeply, we must learn how to characterize observers in entirely different regions. Despite the great variability of local physical laws, there are a few laws that operate everywhere. Gravity is a universal force. All other forces and particles, provincial details aside, fit into the general framework of quantum mechanics. The laws of thermodynamics rule the whole multiverse. The challenge is to phrase the conditions for life in this universal language.

A central tenet of thermodynamics is the “second law,” which states that a quantity called entropy cannot decrease. Entropy reflects the number of different microscopic configurations that are available to a system. For example, there are only a few ways to stack up a brick wall. But there are many ways to arrange the same bricks into a messy pile, so the pile has more entropy. In other words, entropy measures disorder. All the second law says, then, is that things don’t tend to order themselves when left alone: Walls collapse into piles, but piles don’t assemble themselves into walls.

Some structures actually do assemble themselves, though the second law still holds. A bucket of water left outside on a cold night will contain a crystal the next morning. Diffuse particles condense into spiral galaxies. Hydrogen clouds collapse to form stars. Dust coalesces into planets. On a few planets, self-replicating organisms arise from organic molecules. But in every one of these processes, the overall entropy grows. As a system becomes ordered, radiation escapes into its surroundings where it vastly increases the overall disorder.

The second law in no way forbids orderly structures from forming so long as enough disorder is created elsewhere. But conversely, if no disorder is produced, then no order can form. Taking this one step further, I recently proposed that the production of disorder could be used as a kind of cosmic life-detector. The more entropy is created in a given region, the more likely it is that complex structures such as life are forming in it. To a physicist this idea is attractive: Unlike life, entropy is a number, and one that can be defined in every region, whatever its local laws of physics.

Sometimes, of course, a mess is just a mess. Not every entropy increase is accompanied by the formation of an ordered structure. Our life-detector, in other words, is susceptible to false alarms. To check that this does not spoil its usefulness, Roni Harnik, Graham Kribs, Gilad Perez, and I decided to identify the chief sources of entropy production in the visible universe. Amazingly, almost every one of the biggest entropy-producing processes turned out to be essential to the development of life: the formation of galaxies and the burning of stars; supernova explosions, which forged the elements we are made from; large molecules that scatter starlight. Most remarkably, the last process produced more entropy than all the others put together. This was good news. The digestion of solar power into messy thermal radiation is precisely what allowed planet Earth to play host to increasingly sophisticated life forms. Without complex molecules, entropy production would drop sharply — and human life would be impossible.

Just because our local test run went well does not mean that entropy production alone can reliably determine whether observers are present in a given region of the multiverse. But remember that a one-by-one approach would be futile; the multiverse is so large that statistical methods are more powerful. What we needed was a criterion that told us which physical laws, on average, tend to be associated with the presence of complex structures like observers. Estimating entropy production may prove to be a first, crude technique that will help us step back and study the vast canvas of the multiverse — and, ultimately, to learn whether we can discern in its intricate patterns the tiny, billion-light-year brushstroke that fills our night sky. —Raphael Bousso is a theoretical physicist at The University of California, Berkeley.

Originally published October 17, 2008

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