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.
You might think that the birth of a new universe is a dramatic and painful event, just like the birth of a new person. But it’s actually not so. Inside the bubble, of course, things are pretty dramatic—there’s a new universe where there was none before. But from the point of view of an outside observer in the parent universe, the entire process is almost unnoticeable. What it looks like is a fluctuation of thermal particles that come together to form a tiny region of very high density—in fact, a black hole. But it’s a microscopic black hole, with a tiny entropy, which then evaporates via Hawking radiation as quickly as it formed. The birth of a baby universe is much less traumatic than the birth of a baby human.
Indeed, if this story is true, a baby universe could be born right in the room where you’re reading this book, and you would never notice. It’s not very likely; in all the spacetime of the universe we can currently observe, chances are it never happened. If it did, the action would all be on a microscopic scale. The new universe could grow to a tremendous size, but it would be completely disconnected from the original spacetime. Like some other children, there is absolutely no communication between the baby universe and its parent—once they split, they remain separate forever.
A RESTLESS MULTIVERSE
So it’s possible that, even when de Sitter space is in a high-entropy true-vacuum state, it’s not completely stable. Rather, it can give birth to new baby universes, which grow up into large universes in their own right (and could very well give rise to new babies themselves). The original de Sitter space continues on its way, essentially unperturbed.
The prospect of baby universes makes all the difference in the world to the question of the arrow of time. Remember the basic dilemma: The most natural universe to live in is de Sitter space, empty space with a positive vacuum energy, which acts like an eternal box of gas at a fixed temperature. The gas spends most of its time in thermal equilibrium, with rare fluctuations into states of lower entropy. With that kind of setup, we could fairly reliably quantify what kinds of fluctuations there will be, and how often they will happen. Given any particular thing you would want the fluctuation to contain—a person, or a galaxy, or even a hundred billion galaxies—this scenario strongly predicts that most such fluctuations will look like they are in equilibrium, apart from the presence of the fluctuation itself. Furthermore, most such fluctuations will arise from higher-entropy states, and evolve back into higher-entropy states. So most observers will find themselves alone in the universe, having arisen as random arrangements of molecules out of the surrounding high-entropy gas of particles; likewise most galaxies, and so on. You could potentially fluctuate into something that looks just like the history of our Big Bang cosmology; but the number of observers within such a fluctuation is much smaller than the number of observers who are otherwise alone.
Baby universes change this picture in a crucial way. Now it’s no longer true that the only thing that can happen is a thermal fluctuation away from equilibrium and then back again. A baby universe is a kind of fluctuation, but it’s one that never comes back—it grows and cools off, but it doesn’t rejoin the original spacetime.
What we’ve done is given the universe a way that it can increase its entropy without limit. In a de Sitter universe, space grows without bound, but the part of space that is visible to any one observer remains finite, and has a finite entropy—the area of the cosmological horizon. Within that space, the fields fluctuate at a fixed temperature that never changes. It’s an equilibrium configuration, with every process occurring equally as often as its time-reverse. Once baby universes are added to the game, the system is no longer in equilibrium, for the simple reason that there is no such thing as equilibrium. In the presence of a positive vacuum energy (according to this story), the entropy of the universe never reaches a maximum value and stays there, because there is no maximum value for the entropy of the universe—it can always increase, by creating new universes. That’s how the paradox of the Boltzmann-Lucretius scenario can be avoided.
Consider a simple analogy: a ball rolling on a hill. Not a quantum field moving in a potential, an actual down-to-Earth ball. But a very special hill: one that doesn’t ever reach a particular bottom, but rolls smoothly away to infinity. And one on which there is absolutely no friction, so the ball can roll forever with the same amount of total energy.
Now let’s ask ourselves: What should the ball be doing? That is, if we imagine finding such a ball, which has miraculously been operating as an isolated system for all of eternity, undisturbed by the rest of the universe, what kind of state would we expect the ball to be in?
Figure 86: A ball rolling on a hill that doesn’t have a bottom. There is only one kind of trajectory such a ball could have: coming in from infinitely far away in the infinite past, rolling up to a turning point, reversing direction, and rolling back out to infinity in the infinite future.
That may or may not be a sensible question, but it’s not that hard to answer, because there aren’t that many things the ball possibly could be doing. Every allowed trajectory for the ball looks basically the same: It rolls in from infinity, turns around, and rolls back out again. Depending on the total energy that the ball has, the turning point will reach different possible heights up the hill, but the qualitative behavior will be the same. So there will be precisely one moment in the lifetime of the ball when it isn’t moving: the point where it turns around. At every other moment, it’s either moving to the left, or moving to the right. Therefore, when we observe the ball at some random time, it seems very likely that it will be moving in one direction or the other.
Now imagine further that there is an entire tiny civilization living inside the ball, complete with
tiny scientists and philosophers. One of their favorite topics of discussion is what they call the “arrow of motion.” These thinkers have noticed that their ball evolves in perfect accord with Newton’s laws of motion. Those laws don’t distinguish between left and right: They are completely reversible. If a ball were to be placed at the bottom of a valley, it would simply sit there forever, motionless. If it were not quite at the bottom, it would start rolling toward the bottom, and then oscillate back and forth in that vicinity. Yet, their ball seems to be rolling consistently in the same direction for very long periods of time! What can be going on?
In case the terms of this somewhat-off-kilter analogy are not immediately clear, the ball represents our universe, and the position from left to right represents entropy. The reason why it’s not surprising to find the ball moving in a consistent direction is that it tends to always be moving in the same direction, with the exception of the one special turnaround point. Despite appearances, the portion of the trajectory where the ball is coming in from right to left is not any different from the portion where it is moving away from left to right; the motion of the ball is time-reversal symmetric around that turning point.
Perhaps the entropy of our universe is like that. The real problem with de Sitter space (without baby universes) is that it’s almost always in equilibrium—any particular observer sees a thermal bath that lasts forever, with predictable fluctuations. More generally, if there exists any such thing as “equilibrium” in the context of cosmology, it’s hard to understand why we don’t find the universe in that state. By suggesting that there is no such thing as equilibrium, we can avoid this dilemma. It becomes natural to observe entropy increasing, simply because entropy can always increase.
This is the scenario suggested by Jennifer Chen and me in 2004.294 We started by assuming that the universe is eternal—the Big Bang is not the beginning of time—and that de Sitter space was a natural high-entropy state for the universe to be in. That means we can “start” with almost any state you like—pick some favorite distribution of matter and energy throughout space, and let it evolve. We put start in quotation marks because we don’t want to prejudice initial conditions over conditions at any other time; respecting the reversibility of the laws of physics, we evolve the state both forward and backward in time. As I’ve argued here, the natural evolution forward in time is for space to expand and empty out, eventually approaching a de Sitter state. But from there, if we wait long enough, we will see the occasional production of baby universes via quantum fluctuations. These baby universes will expand and inflate, and their false vacuum energy will eventually convert into ordinary matter and radiation, which eventually dilutes away until we achieve de Sitter space once again. From there, both the original universe and the new universe can give birth to new babies. This process continues forever. In the parts of spacetime that look like de Sitter, the universe is in equilibrium, and there is no arrow of time. But in baby universes, for the time in between the initial birth and the final cooling off, there is a pronounced arrow of time, as the entropy starts near zero and expands to its equilibrium value.
Most interestingly, the same story can be told backward in time, starting from the initial state, as depicted in Figure 87. If it is not de Sitter already, the universe will empty out backward in time as well as forward. From there it will give birth to baby universes, which expand and cool off. In these baby universes, the arrow of time is oriented in the opposite direction to those in the universes we have put in “the future.” The overall direction of the time coordinate is utterly arbitrary, of course. Observers in the universes at the top of the diagram will think of the bottom of the diagram as “the past,” while observers in the universes at the bottom of the diagram will think of the top as “the past.” Their arrows of time are incompatible, but that doesn’t lead to any Benjamin Button unpleasantness; these baby universes are completely separate from one another in time, and their arrows point away from each other, so no communication between them is possible.
In this scenario, the multiverse on ultra-large scales is symmetric about the middle moment; statistically, at least, the far future and the far past are indistinguishable. In that sense this picture resembles the bouncing cosmologies we discussed earlier; entropy increases forever in both directions of time, around a middle point of lowest entropy. There is a crucial difference, however: The moment of “lowest” entropy is not actually a moment of “low” entropy. That middle moment was not finely tuned to some special very-low-entropy initial condition, as in typical bouncing models. It was as high as we could get, for a single connected universe in the presence of a positive vacuum energy. That’s the trick: allowing entropy to continue to rise in both directions of time, even though it started out large to begin with. There isn’t any state we could possibly have chosen that would have prevented this kind of evolution from happening. An arrow of time is inevitable.295
Figure 87: Baby universes created in a background de Sitter space, both to the past and to the future. Each baby universe starts in a dense, low-entropy state, and exhibits a local arrow of time as it expands and cools. The multiverse manifests overall time-reversal symmetry, as baby universes born in the past have an arrow of time pointing in the opposite direction to those in the future.
Having said all that, we may still want to ask why our patch of observable universe has such a low-entropy boundary condition at one end of time—why were our particular degrees of freedom ever found in such an unnatural state? But in this picture, that’s not quite the right question to ask. We don’t start by knowing which degrees of freedom we are, and then asking why they are (or were) in a certain configuration. Rather, we need to look at the multiverse as a whole, and ask what is most often experienced by observers like us. (If our scenario is going to be useful, the specific definition of “like us” shouldn’t matter.)
This version of the multiverse will feature both isolated Boltzmann brains lurking in the empty de Sitter regions, and ordinary observers found in the aftermath of the low-entropy beginnings of the baby universes. Indeed, there should be an infinite number of both types. So which infinity wins? The kinds of fluctuations that create freak observers in an equilibrium background are certainly rare, but the kinds of fluctuations that create baby universes are also very rare. Ultimately, it’s not enough to draw fun pictures of universes branching off in both directions of time; we need to understand things at a quantitative level well enough to make reliable predictions. The state of the art, I have to admit, isn’t up to that task just yet. But it’s certainly plausible that a lot more observers arise as the baby universes grow and cool toward equilibrium than come about through random fluctuations in empty space.
BRINGING IT HOME
Does it work? Does a multiverse scenario with baby universes offer a satisfactory explanation for the arrow of time?
We’ve covered a lot of possible approaches to the problem of the arrow of time: a space of states that changes with time, intrinsically irreversible dynamical laws, a special boundary condition, a symmetric re-collapsing universe, a bouncing universe with and without overall time-symmetry, an unbounded multiverse, and of course the Boltzmann-Lucretius scenario of fluctuations around an eternal equilibrium state. The re-collapsing Gold universe seems pretty unlikely on empirical grounds, since the expansion of the universe is accelerating; and the Boltzmann-Lucretius universe also seems ruled out by observation, since the Big Bang had a much lower entropy than it had any right to in that picture. But the other possibilities are still basically on the table; we may find them more or less satisfying, but we can’t be confident enough to dismiss them out of hand. Not to mention the very real possibility that the right answer is something we simply haven’t thought of yet.
It’s hard to tell whether baby universes and the multiverse will ultimately play a role in understanding the arrow of time. For one thing, as I’ve taken pains (perhaps too many) to emphasize, there were many steps along the way where we were fearlessly
speculative, to say the least. Our understanding of quantum gravity is not good enough to say for sure whether baby universes really do fluctuate into existence from de Sitter space; there seem to be arguments both for and against. We also don’t completely understand the role of the vacuum energy. We’ve been speaking as if the cosmological constant we observe in our universe today is really the minimum possible vacuum energy, but there is little hard evidence for that assumption. In the context of the string theory landscape, for example, it’s easy enough to get states with the right value of the vacuum energy, but it’s also easy to get all kinds of states, including ones with negative vacuum energy or precisely zero vacuum energy. A more comprehensive theory of quantum gravity and the multiverse would predict how all of these possible states fit together, including transitions between different numbers of macroscopic dimensions as well as different values of the vacuum energy. Not to mention that we haven’t really taken quantum mechanics completely seriously—we’ve nodded in the direction of quantum fluctuations but have drawn pictures of what are essentially classical space times. The right answer, whatever it may turn out to be, will more likely be phrased in terms of wave functions, Schrödinger’s equation, and Hilbert spaces.
The important point is not the prospects of any particular model, but the crucial clue that the arrow of time provides us as we try to understand the universe on the largest possible scales. If the universe we see is really all there is, with the Big Bang as a low-entropy beginning, we seem to be stuck with an uncomfortable fine-tuning problem. Embedding our observable patch in a wider multiverse alleviates this problem by changing the context: The goal is not to explain why the whole universe has a low-entropy boundary condition at the beginning of time, but why there exist relatively small regions of spacetime, arising within a much larger ensemble, where the entropy dramatically increases. That question, in turn, can be answered if the multiverse doesn’t have any state of maximum entropy: The entropy increases because it can always increase, no matter what state we are in. The trick is to set things up so that the mechanism by which entropy increases overall is the production of universes that resemble our own.
From Eternity to Here: The Quest for the Ultimate Theory of Time Page 46
