From Eternity to Here (68 page)

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.

The nice thing about a multiverse based on de Sitter space and baby universes is that it avoids all of the standard pitfalls that beset many approaches to the arrow of time: It treats the past and future on an equal footing, doesn’t invoke irreversibility at the level of fundamental dynamics, and never assumes an ad hoc low-entropy state for the universe at any moment in time. It serves as a demonstration that such an explanation is at least conceivable, even if we aren’t yet able to judge whether this particular one is sensible, much less part of the ultimately correct answer. There’s every reason to be optimistic that we will eventually settle on an understanding of how the arrow of time arises naturally and dynamically from the laws of physics themselves.

16

EPILOGUE

Glance into the world just as though time were gone: and everything crooked will become straight to you.

—Friedrich Nietzsche

Unlike many authors, I had no struggle settling on the title for this book.
²⁹⁶
Once I had come up with
From Eternity to Here
, it seemed irresistible. The connotations were perfect: On the one hand, a classic movie (based on a classic novel), with that iconic scene of untamed waves from the Pacific crashing around lovers Deborah Kerr and Burt Lancaster caught in a passionate embrace. On the other hand, the cosmological grandeur implicit in the word
eternity
.

But the title is even more appropriate than those superficial considerations might suggest. This book has not only been about “eternity”; it’s also been about “here.” The puzzle of the arrow of time doesn’t begin with giant telescopes or powerful particle accelerators; it’s in our kitchens, every time we break an egg. Or stir milk into coffee, or put an ice cube into warm water, or spill wine onto the carpet, or let aromas drift through a room, or shuffle a new deck of cards, or turn a delicious meal into biological energy, or experience an event that leaves a lasting memory, or give birth to a new generation. All of these commonplace occurrences exhibit the fundamental irreversibility that is the hallmark of the arrow of time.

The chain of reasoning that started with an attempt to understand that arrow led us inexorably to cosmology—to eternity. Boltzmann provided us with an elegant and compelling microscopic understanding of entropy in terms of statistical mechanics. But that understanding does not explain the Second Law of Thermodynamics unless we also invoke a boundary condition—why was the entropy ever low to start with? The entropy of an unbroken egg is much lower than it could be, but such eggs are nevertheless common, because the overall entropy of the universe is much lower than it could be. And that’s because it used to be even lower, all the way back to the beginning of what we can observe. What happens here, in our kitchen, is intimately connected with what happens in eternity, at the beginning of the universe.

Figures such as Galileo, Newton, and Einstein are celebrated for proposing laws of physics that hadn’t previously been appreciated. But their accomplishments also share a common theme: They illuminate the
universality
of Nature. What happens here happens everywhere—as Richard Feynman put it, “The entire universe is in a glass of wine, if we look at it closely enough.”
²⁹⁷
Galileo showed that the heavens were messy and ever changing, just like conditions here on Earth; Newton understood that the same laws of gravity that accounted for falling apples could explain the motions of the planets; and Einstein realized that space and time were different aspects of a single unified spacetime, and that the curvature of spacetime underlies the dynamics of the Solar System and the birth of the universe.

Likewise, the rules governing entropy and time are common to our everyday lives and to the farthest stretches of the multiverse. We don’t yet know all the answers, but we’re on the threshold of making progress on some big questions.

WHAT’S THE ANSWER?

Over the course of this book, we’ve lovingly investigated what we know about how time works, both in the smooth deterministic context of relativity and spacetime, and in the messy probabilistic world of statistical mechanics. We finally arrived at cosmology, and explored how our best theories of the universe fall embarrassingly short when confronted with the universe’s most obvious feature: the difference in entropy between early times and late times. Then, after fourteen chapters of building up the problems, we devoted a scant single chapter to the possible solutions, and fell short of a full-throated endorsement of any of them.

That may seem frustrating, but the balance was entirely intentional. Understanding a deeply puzzling feature of the natural world is a process that can go through many stages—we may be utterly clueless, we may understand how to state the problem but not have any good ideas about the answer, we may have several reasonable answers at our disposal but not know which (if any) are right, or we may have it all figured out. The arrow of time falls in between the second and third of these options—we can state the problem very clearly but have only a few vague ideas of what the answer might be.

In such a situation, it’s appropriate to dwell on understanding the problem, and not become too wedded to any of the prospective solutions. A century from now, most everything we covered in the first three parts of this book should remain standing. Relativity is on firm ground, as is quantum mechanics, and the framework of statistical mechanics. We are even confident in our understanding of the basic evolution of the universe, at least from a minute or so after the Big Bang up to today. But our current ideas about quantum gravity, the multiverse, and what happened at the Big Bang are still very speculative. They may grow into a robust understanding, but many of them may be completely abandoned. At this point it’s more important to understand the map of the territory than to squabble over what is the best route to take through it.

Our universe isn’t a fluctuation around an equilibrium background, or it would look very different. And it doesn’t seem likely that the fundamental laws of physics are irreversible at a microscopic level—or, if they are, it’s very hard to see how that could actually account for the evolution of entropy and complexity we observe in our universe. A boundary condition stuck at the beginning of time is impossible to rule out, but also seems to be avoiding the question more than answering it. It may ultimately be the best we can do, but I strongly suspect that the low entropy of our early universe is a clue to something deeper, not just a brute fact we can do no more than accept.

We’re left with the possibility that our observable universe is part of a much larger structure, the multiverse. By situating what we see inside a larger ensemble, we open the possibility of explaining our apparently finely tuned beginning without imposing any fine-tuning on the multiverse as a whole. That move isn’t sufficient, of course; we need to show why there should be a consistent entropy gradient, and why that gradient should be manifested in a universe that looks like our own, rather than in some other way.

We discussed a specific model of which I am personally fond: a universe that is mostly high-entropy de Sitter space, but which gives birth to disconnected baby universes, allowing the entropy to increase without bound and creating patches of spacetime like the one around us along the way. The details of this model are highly speculative, and rely on assumptions that stretch beyond what the state of the art allows us to reliably compute, to put it mildly. More important, I think, is the general paradigm, according to which entropy is seen to be increasing because entropy can always increase; there is no equilibrium state for the universe. That setup naturally leads to an entropy gradient, and is naturally time-symmetric about some moment of minimal (although not necessarily “small”) entropy. It would be interesting to see if there are other ways of possibly carrying out this general program.

There is one other approach lurking in the background, which we occasionally acknowledged but never granted our undivided attention: the idea that “time” itself is simply an approximation that is occasionally useful, including in our local universe, but doesn’t have any fundamental meaning. This is a perfectly legitimate possibility. Lessons from the holographic principle, as well as a general feeling that the underlying ingredients of a quantum mechanical theory may appear very different from what shows up in the classical regime, make it quite reasonable to imagine that time might be an emergent phenomenon rather than a necessary part of our ultimate description of the world.

One reason why the time-is-just-an-approximation alternative wasn’t emphasized in this book is that there doesn’t seem to be too much to say about it, at least within our present state of knowledge. Even by our somewhat forgiving standards, the way in which time might emerge from a more fundamental description is not well understood. But there is a more compelling reason, as well: Even if time is only an approximation, it’s an approximation that seems extremely good in the part of the universe we can observe, and that’s where the arrow-of-time problem is to be found. Sure, we can imagine that the viability of classical spacetime as a useful concept breaks down completely near the Big Bang. But, all by itself, that doesn’t tell us anything at all about why conditions at that end of time (what we call “the past”) should be so different from conditions at the other end of time (“the future”) within our observable patch. Unless you can say, “Time is only an approximate concept, and therefore entropy should behave as follows in the regime where it’s valid to speak about time,” this alternative seems more like an evasive maneuver than a viable strategy. But that is largely a statement about our ignorance; it is certainly possible that the ultimate answer might lie in this direction.