From Eternity to Here (66 page)

Even if we do allow ourselves to contemplate the possibility of the extraordinary amount of fine-tuning necessary to let entropy increase consistently for all time, we are left with absolutely no good reason why our universe should actually be that way. We have so far provided no justification for why our universe should be finely tuned at all, and now we are suggesting an infinite amount of fine-tuning. This doesn’t really sound like progress.

A MIDDLE HYPOTHESIS

So we are led to consider the alternative, portrayed at bottom right in Figure 84: a bouncing universe where entropy
decreases
during the contracting phase, reaches a minimum value at the bounce, and begins to increase thereafter. Now, perhaps, we are getting somewhere. An explicit model of such a bouncing cosmology was proposed by Anthony Aguirre and Steven Gratton in 2003. They based their construction on inflation and showed that by clever cutting and pasting we could take an inflationary universe that was expanding forward in time and glue it at the beginning to an inflationary universe expanding backward in time, to obtain a smooth bounce.
²⁹⁰

This alternative comes with a dramatic advantage: The behavior of the universe is symmetric in time. Both the size of the universe, and its entropy, would have a minimum value at the bounce, and increase in either direction. Conceptually, that’s a big improvement over any of the other models we’ve contemplated; the underlying time-reversal symmetry of the laws of physics is reflected in the large-scale behavior of the universe. In particular, we avoid the pitfall of temporal chauvinism—the temptation to treat the “initial” state of the universe differently from the “final” state. It was our wish to sidestep that fallacy that led us to contemplate the Gold universe, which was also symmetric about one moment in time. But now that we allow ourselves to think about a possible universe before the Big Bang, the solution seems more acceptable: The universe is symmetric, not because entropy is low at either end of time, but because it’s
high
at either end.

Nevertheless, this is a funny universe. The evolution of entropy is responsible for all the various manifestations of the arrow of time, including our ability to remember the past and our feeling that we move through time. In the bouncing-entropy scenario, the arrow of time
reverses direction
at the bounce. From the perspective of our observable universe, portrayed on the right-hand side of the plots in Figure 84, the past is the low-entropy direction of time, toward the bounce. But observers on the other side of the bounce, which we have (given our own perspective) labeled “contraction” in the plots, would also define the “past” as the direction of time in which entropy was lower—that is, the direction of the bounce. The arrow of time always points in the direction in which entropy is increasing, from the point of view of a local observer. On either side of the bounce, the arrow points toward a “future” in which the universe is expanding and emptying out. To observers on either side, observers on the other side experience time “running backward.” But this mismatch of arrows is completely unobservable—people on one side of the bounce can’t communicate with people on the other, any more than we can communicate with anyone else in our past. Everyone sees the Second Law of Thermodynamics operating normally in his or her observable part of the universe.

Unfortunately, a bouncing-entropy cosmos is not quite enough to allow us to declare in good conscience that we have solved the problem we set out at the beginning of this chapter. Sure, allowing for a cosmological bounce that is also a minimum point for the entropy of the universe avoids the philosophical pitfall of placing initial conditions and final conditions on a different footing. But it does so at the cost of a new puzzle: Why is the entropy so low in the
middle
of the history of the universe?

In other words, the bouncing-entropy model doesn’t, by itself, actually
explain
anything at all about the arrow of time. Rather, it takes the need for a Past Hypothesis and replaces it with the need for a “Middle Hypothesis.” There is just as much fine-tuning as ever; we are still stuck trying to explain why the configuration of our comoving patch of space found itself in such a low-entropy state near the cosmological bounce. So it would appear that we still have some work to do.

BABY UNIVERSES

To make an honest attempt at providing a robust dynamical explanation of the low entropy of our early universe, let’s take it backward. Put aside for a moment what we know about our actual universe, and return to the question we asked in Chapter Thirteen: What
should
the universe look like? In that discussion, I argued that a natural universe—one that didn’t rely on finely tuned low-entropy boundary conditions at any point, past, present, or future—would basically look like empty space. When we have a small positive vacuum energy, empty space takes the form of de Sitter space.

The question that any modern theory of cosmology must therefore answer is: Why don’t we live in de Sitter space? It has a high entropy, it lasts forever, and the curvature of spacetime induces a small but nonzero temperature. De Sitter space is empty apart from the thin background of thermal radiation, so for the most part it is completely inhospitable to life; there is no arrow of time, since it’s in thermal equilibrium. There will be thermal fluctuations, just as we would expect in a sealed box of gas in a Newtonian spacetime. Such fluctuations can give rise to Boltzmann brains, or entire galaxies, or whatever other macrostate you have in mind, if you wait long enough. But we do not appear to be such a fluctuation—if we were, the world around us would be as high entropy as it could possibly get, which it clearly is not.

There is a way out: De Sitter space might not simply stretch on for all eternity, uninterrupted. Something might happen to it. If that were the case, everything we have said about Boltzmann brains would be out the window. That argument made sense only because we knew exactly what kind of system we were dealing with—a gas at a fixed temperature—and we knew that it would last forever, so that even very improbable events would eventually occur, and we could reliable calculate the relative frequencies of different unreliable events. If we introduce complications into that picture, all bets are off. (Most bets, anyway.)

It’s not hard to imagine ways that de Sitter space could fail to last forever. Remember that the “old inflation” model was basically a period of de Sitter space in the early universe, with a very high energy density provided by an inflaton field stuck in a false vacuum state. As long as there is another vacuum state of lower energy, that de Sitter space will eventually decay via the appearance of bubbles of true vacuum. If bubbles appear rapidly, the false vacuum will completely disappear; if they appear slowly, we’ll end up with a fractal mixture of true-vacuum bubbles in a persistent false-vacuum background.

In the case of inflation, a crucial point was that the energy density during the de Sitter phase was very high. Here we are interested in the opposite end of the spectrum—where the vacuum energy is extremely low, as it is in our current universe.

That makes a huge difference. High-energy states naturally like to decay into states of lower energy, but not vice versa. The reason is not because of energy conservation, but because of entropy.
²⁹¹
The entropy associated with de Sitter space is low when the energy density is high, and high when the energy density is low. The decay of high-energy de Sitter space into a state with lower vacuum energy is just the natural evolution of a low-entropy state into a high-entropy one. But we want to know how we might escape from a situation like the one into which our current universe is evolving: empty de Sitter space with a very small vacuum energy, and a very high entropy. Where do we go from there?

If the correct theory of everything were quantum field theory in a classical de Sitter space background, we’d be pretty much stuck. Space would keep expanding, quantum fields would keep fluctuating, and we’d be more or less in the situation described by Boltzmann and Lucretius. But there is (at least) one possible escape route, courtesy of quantum gravity: the creation of
baby universes
. If de Sitter space gives birth to a continuous stream of baby universes, each of which starts with a low entropy and expands into a high-entropy de Sitter phase of its own, we could have a natural mechanism for creating more and more entropy in the universe.

As we’ve reiterated at multiple points, there’s a lot we don’t understand about quantum gravity. But there’s a lot that we do understand about classical gravity, and about quantum mechanics; so we have certain reasonable expectations for what should happen in quantum gravity, even if the details remain to be ironed out. In particular, we expect that spacetime itself should be susceptible to quantum fluctuations. Not only should quantum fields in the de Sitter background be fluctuating, but the de Sitter space itself should be fluctuating.

One way in which spacetime might fluctuate was studied in the 1990s by Edward Farhi, Alan Guth, and Jemal Guven.
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They suggested that spacetime could not only bend and stretch, as in ordinary classical general relativity, but also split into multiple pieces. In particular, a tiny bit of space could branch off from a larger universe and go its own way. The separate bit of space is, naturally, known as a baby universe. (In contrast to the “pocket universes” mentioned in the last chapter, which remained connected to the background spacetime.)

We can be more specific than that. The thermal fluctuations in de Sitter space are really fluctuations of the underlying quantum fields; the particles are just what we see when we observe the fields. Let’s imagine that one of those fields has the right properties to be an inflaton—there are places in the potential where the field could sit relatively motionless in a false vacuum valley or a new-inflation plateau. But instead of starting it there, we consider what happens when the field starts at the bottom, where the vacuum energy is very small. Quantum fluctuations will occasionally push the field
up
the potential, from the true vacuum to the false vacuum—not everywhere at once, but in some small region of space.

What happens when a bubble of false vacuum fluctuates into existence in de Sitter space? To be honest once again, we’re not sure.
²⁹³
One thing seems likely: Most of the time, the field will simply dissipate away back into its thermal surroundings. Inside, where we’ve fluctuated into the false vacuum, space wants to expand; but the wall separating the inside from the outside of the bubble wants to shrink, and usually it shrinks away quickly before anything dramatic happens.

Figure 85:
Creation of a baby universe via quantum fluctuation of a false-vacuum bubble.

Every once in a while, however, we could get lucky. The process of getting lucky is portrayed in Figure 85. What we see is a simultaneous fluctuation of the inflaton field, creating a bubble of false vacuum, and of space itself, creating a region that pinches off from the rest of the universe. The tiny throat that connects the two is a wormhole, as we discussed way back in Chapter Six. But this wormhole is unstable and will quickly collapse to nothing, leaving us with two disconnected spacetimes: the original parent universe and the tiny baby.

Now we have a baby universe, dominated by false vacuum energy, all set up to undergo inflation and expand to a huge size. If the properties of the false vacuum are just right, the energy will eventually be converted into ordinary matter and radiation, and we’ll have a universe that evolves according to the standard i nflation-plus-Big-Bang story. The baby universe can grow to an arbitrarily large size; there is no limitation imposed, for example, by energy conservation. It is a curious feature of general relativity that the total energy of a closed, compact universe is exactly zero, once we account for the energy of the gravitational field as well as everything else. So inflation can take a microscopically tiny ball of space and blow it up to the size of our observable universe, or much larger. As Guth puts it: “Inflation is the ultimate free lunch.”

Of course the entropy of the baby universe starts out very small. That might seem like cheating—didn’t we go to great lengths to argue that there are many degrees of freedom in our observable universe, and all of them still existed when the universe was young, and if we picked a configuration of them randomly it would be preposterously unlikely to obtain a low-entropy state? All that is true, but the process of making a baby universe is not one where we choose the configuration of our universe randomly. It’s chosen in a very specific way: the configuration that is most likely to emerge as a quantum fluctuation in an empty background spacetime that is able to pinch off and become a disconnected universe. Considered as a whole, the entropy of the multiverse doesn’t go down during this process; the initial state is high-entropy de Sitter space, which evolves into high-entropy de Sitter space plus a little extra universe. It’s not a fluctuation of an equilibrium configuration into a lower-entropy state, but a leakage of a high-entropy state into one with an even higher entropy overall.