The Cosmic Landscape (46 page)

What is the alternative? The answer is that nature somehow makes use of all the possibilities. Is there a natural mechanism that would have populated a megaverse with all possible environments, turning them from mathematical possibilities to physical realities? This is what an increasing number of theoretical physicists believe—myself included. I call this view the
populated Landscape
.
¹

In this chapter I will explain the main idea of the populated Landscape viewpoint: that mechanisms that rely on well-tested physical principles gave rise to a huge, or even an infinite, number of pocket universes, with each and every valley in the Landscape being represented.

The mechanisms that underlie the populated Landscape rely only on the principles of general relativity and very conventional applications of quantum mechanics. To understand how the Landscape becomes populated, we will need to examine two very basic physics concepts. The first is
metastability of the vacuum.
It refers to the fact that the properties of the vacuum can suddenly change with little or no warning. The second concept is that
space clones itself.

In Kurt Vonnegut’s darkly hilarious science-fiction satire
Cat’s Cradle,
physicist Felix Hoenikker discovers a new form of solid water called ice-nine. The crystalline structure of ice-nine is somewhat different from usual ice—a new way of stacking up the cannon balls, so to speak—and as a result the new crystal lattice is so stable that it doesn’t melt until the temperature reaches 114 degrees Fahrenheit. In Vonnegut’s fantasy the reason that the waters of the earth previously remained liquid is that a tiny seed of the new crystal would be needed to “teach” the water molecules how to reassemble themselves into the more stable ice-nine lattice. Once such a tiny “teacher crystal” was introduced, the surrounding water would coagulate around it, forming a rapidly expanding bubble of ice-nine. Until Hoenikker’s playful little experiment, no one had ever made a crystal of ice-nine, so the earth’s H
₂
O was uncorrupted by the more deadly cousin of ordinary ice.

Uncorrupted, that is, until a chip of Hoenikker’s new stuff gets into the hands of “Papa” Monzano, president and dictator of San Lorenzo. Papa ends his own life by swallowing a bit of it, thereby destabilizing his own fluids. They turn into the lethal ice-nine, and his whole body freezes in a fraction of a second. When Papa’s fortress collapses and falls into the sea, his ice-nine-laden corpse follows and starts a chain reaction. A crystal expands at breakneck speed and immediately freezes every bit of water on earth, thus ending all life.

Ice-nine is of course a fiction. There is no form of water that is solid above 32 degrees Fahrenheit.
Cat’s Cradle
is really a cautionary tale about the madness and instability of a world full of nuclear weapons. But, although fictional, the ice-nine story is based on serious principles of physics and chemistry: in particular, the concept of metastability.

Stability implies a degree of resistance to sudden, unpredictable change. A pendulum hanging in the vertical position is very stable. Instability is the opposite: a pencil standing on its tip will fall in an unpredictable direction. Metastability is something in between. Some systems have the remarkable property that they appear stable for long periods of time but eventually undergo very sudden and unforeseen catastrophic changes. These systems are called metastable.

In the real world a closed tank of liquid water at room temperature is stable. But in the fictitious world of Felix Hoenikker and Papa Monzano, it is only metastable. Real water can also be metastable, but not at room temperature. Surprisingly, if it is carefully cooled below freezing or heated above boiling, water can remain liquid for a long time until it suddenly changes to ice or steam. Even odder, the vacuums of String Theory are often metastable. But before plunging into meta-stable water or even empty space, I want to explain a simpler example of metastability.

Some things are flat out impossible. No matter how long you wait, they will never happen. Others are just very unlikely, but if you wait long enough, they will eventually occur. Here is something that according to
classical
physics is impossible. Once again let’s imagine a small ball rolling on a simple, one-dimensional landscape. In fact it’s not rolling; it is trapped at the bottom of a valley between two high mountains. There’s another lower valley on the other side of one of the mountains, but the ball is stuck where it is. In order to roll over the mountain and get to the lower valley, it would have to have enough kinetic energy to compensate for the extra potential energy at the summit. Standing still, it lacks the energy to climb even a short way up the hill. Getting to the other side without a push is not only unlikely, it’s just plain impossible. This is an example of perfect stability.

But now let’s add a bit of heat. The ball might be exposed to some random collisions with the molecules of a warm gas. It has the thermal jitters. If we wait long enough, at some point an unusually energetic molecule, or random succession of collisions, will give it enough of a kick to go over to the other side and down to the lower valley. The probability that such a random accident will occur in the next hour may be exceedingly small. But no matter how small, as long as the probability is not zero, given enough time the ball will eventually go over the barrier and land in the lower valley.

But wait! We’ve neglected the quantum jitters. Even without any heat—even at a temperature of absolute zero—the ball fluctuates because of the quantum jitters. You may suspect that even in the absence of thermal energy, quantum fluctuations would eventually kick the ball over the hill. If so, you’re right. A quantum-mechanical ball trapped in an energy valley is not completely stable; it has a small probability of appearing on the other side of the mountain. Physicists call this weird, unpredictable quantum jump
quantum tunneling.
Typically, quantum tunneling is a very unlikely event that can take as long as the proverbial room full of monkeys who are randomly banging away at typewriters would take to write a Shakespeare play.

Systems of this type, which are not truly stable but can last for an extremely long time, are metastable. There are many examples of metastability in physics and chemistry: systems that seem stable but eventually tunnel to new configurations without warning. In Vonnegut’s satire ordinary water at room temperature is metastable. Sooner or later a tiny crystal of ice-nine will form, even if only by the random motion of molecules, and then a chain reaction will rearrange the metastable liquid water into the more stable ice-nine. As we will soon see, real examples involving nothing more than ordinary ice and water also exist. But most important for this book, vacuums can be metastable. Bubbles of space with strangely different properties can spontaneously appear and grow, much like ice-nine did in
Cat’s Cradle.
This is how the Landscape becomes populated and the universe becomes diverse.

Water freezes solid at a temperature of 32 degrees Fahrenheit or, what is the same thing, zero degrees on the centigrade scale. However, you can cool very pure water to a lower temperature without its becoming solid if you do it slowly and very carefully. Liquid water below freezing temperature is called
supercooled.

Supercooled water, just below the usual freezing temperature, can last for a very long time. But introducing a small bit of ordinary ice will cause the water suddenly to crystallize around it and form a rapidly growing chunk of ice. Just as ice-nine destroyed the world, the real ice chunk will quickly take over the entire body of water.

Putting the ice crystal into the supercooled water is very similar to giving the rolling ball a shove over the nearby hill. It’s the event that pushes the system “over the edge.” In the case of the rolling ball, the shove has to be strong enough to push it over the barrier. A tiny push won’t do it. The ball will just roll back to the starting position. The same is true for the supercooled water. If the ice crystal is smaller than a certain critical size, it will just melt back into the surrounding liquid. For example, an ice crystal just a few molecules in diameter will not grow and take over.

But even without someone adding a chip of ice, the supercooled water will not last forever. The reason is that the molecules in the liquid are constantly fluctuating, bouncing off one another and rearranging themselves. This motion is due to both the thermal jitters and the quantum jitters. Every once in a while, by accident, a group of molecules will arrange themselves into a small crystal. Most of the time the crystal will be so small that it will quickly melt into its surroundings.

Very rarely, however, a larger crystal will spontaneously form by random accident. Then the crystal will explosively grow, and everything will freeze. The phenomenon is called bubble nucleation, the growing ice crystal being thought of as an expanding bubble. A very similar thing will happen to water that is superheated above the boiling point. The only difference is that a bubble of steam will spontaneously nucleate and grow.

The boundary between the solid ice and the liquid water (or the steam and water) is called a
domain wall.
It is like a membrane between the two different phases.
²
In fact the domain wall has properties of its own, for example, surface tension that tries to shrink the bubble. Another example of a domain wall is the boundary between ordinary water and air. As a child I was fascinated by the trick of floating a steel sewing needle on the surface of a cup of water. The domain boundary separating air and water is like a skin stretched over the liquid. It has surface tension, which actually has to be pierced in order for an object to penetrate it.

A vacuum with a positive cosmological constant is a lot like a supercooled or superheated liquid. It is metastable and can decay by nucleating bubbles. Every vacuum corresponds to a valley in the Landscape with a particular altitude or energy density. However, although the vacuum may seem quiet and featureless to our coarse senses, quantum fluctuations continually create tiny bubbles of space whose properties correspond to neighboring valleys. Usually the bubbles quickly shrink and disappear. But if the neighboring valley has lower altitude, then every so often a bubble will appear that is large enough to start growing. Will it take over everything? We will see shortly.

The domain walls that separate a bubble from its environment are two-dimensional surfaces that resemble membranes. These are not the first membranes we have encountered. In chapter 10 we learned about Polchinski’s D-branes. In many cases the domain walls are nothing but the membranelike D2-branes.

One thing is missing in the analogy between the cosmic bubbling of pocket universes and the bubbling of ice crystals in supercooled fluids: namely, the tendency for space to expand. Each point on the Landscape has a cosmological constant. Recall that a positive cosmological constant means a universal repulsion, which causes matter to separate. A modern general relativist would say that space itself is expanding, or inflating, and that matter is simply being carried along for the ride.

Long ago, when Einstein was still experimenting with the cosmological constant, the Dutch astronomer Willem de Sitter began the study of inflating space. The space or, more accurately, space-time that de Sitter discovered, and which carries his name, is the solution to Einstein’s equations when there is no energy or gravitating matter other than the ubiquitous vacuum energy of empty space, i.e., a cosmological constant. Like Einstein, de Sitter assumed the cosmological constant was positive. What he found was an inflating space that grows exponentially with time. Exponential expansion means that in a certain time interval space doubles; then, in the next time interval, it doubles again; and then again. It grows to two times—four times—eight times—sixteen times its original size, in the same way that compound interest expands money. At a rate of 5 percent interest, your capital would double in fourteen years. The cosmological constant is like the interest rate: the bigger the cosmological constant, the faster the space inflates. Like any expanding space, de Sitter space satisfies Hubble’s Law—velocity proportional to distance.

We have used the analogy of an expanding rubber balloon to visualize a growing universe. But de Sitter space is different from the rubber of an exponentially expanding balloon in an important way. In the case of a balloon, the rubber—the fabric of the balloon—becomes increasingly stretched, stressed, and thinned out by the expansion. Eventually it reaches its limits, and the balloon pops. But the fabric of de Sitter space never changes. It is as though the rubber molecules were continually giving birth to new rubber molecules in order to fill the spaces created by the expansion. Think of the rubber molecules as cloning themselves to fill in the gaps.

Of course no real rubber molecules are being continuously created. Space itself is reproducing to fill the gaps. One might say that space is cloning itself—each small volume giving birth to offspring, thereby growing exponentially.

Suppose an observer in de Sitter space, moving with the general expansion, looked around at her surroundings: what would she see? You might expect that she would see the universe changing with time, getting bigger and bigger. Surprisingly, that’s not the case. All around her she would see space flowing away according to Hubble’s Law: the close things moving slowly, the distant things moving faster. At some distance the fluid of space would be rushing away so rapidly that the recessional velocity would become equal to the speed of light. At even farther distances the outgoing points would recede with an even greater velocity! Space in those regions would be flowing away so fast that even light signals, emitted straight toward the observer, would be swept away. Because no signal can travel faster than light, contact with these distant regions is completely cut off. The farthest points that can be observed, i.e., the point where the recessional velocity is the speed of light, is called the
horizon,
or more properly, the
event horizon.