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.
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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 i
ngredients 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.
THE EMPIRICAL CIRCLE
The pioneers of thermodynamics—Carnot, Clausius, and others—were motivated by practical desires; among other things, they wanted to build better steam engines. We’ve traveled directly from their insights to grand speculations about universes beyond our own. The crucial question is: How do we get back? Even if our universe does have an arrow of time because it belongs to a multiverse with an unbounded entropy, how would we ever know?
Scientists are fiercely proud of the empirical nature of what they do. Scientific theories do not become accepted because they are logical or beautiful, or fulfill some philosophical goal cherished by the scientist. Those might be good reasons why a theory is proposed—but being accepted is a much higher standard. Scientific theories must, at the end of the day, fit the data. No matter how intrinsically compelling a theory might be, if it fails to fit the data, it’s a curiosity, not an achievement.
But this criterion of “fitting the data” is more slippery than it first appears. For one thing, lots of very different theories might fit the data; for another, a very promising theory might not completely fit the data as it currently stands, even though there is a kernel of truth to it. At a more subtle level, one theory might seem to fit the data perfectly well, but lead to a conceptual dead end, or to an intrinsic inconsistency, while another theory doesn’t fit the data well at all, but holds promise for developing into something more acceptable. After all, no matter how much data we collect, we have only ever performed a tiny fraction of all possible experiments. How are we to choose?
The reality of how science is done can’t be whittled down to a few simple mottos. The issue of distinguishing “science” from “not science” is sufficiently tricky that it goes by its own name: the demarcation problem. Philosophers of science have great fun arguing into the night about the proper way to resolve the demarcation problem.
Despite the fact that the goal of a scientific theory is to fit the data, the worst possible scientific theory would be one that fit all possible data. That’s because the real goal isn’t just to “fit” what we see in the universe; it’s to explain what we see. And you can explain what we see only if you understand why things are the particular way they are, rather than some other way. In other words, your theory has to say that some things do not ever happen—otherwise you haven’t said very much at all.
This idea was put forth most forcefully by Sir Karl Popper, who claimed that the important feature of a scientific theory wasn’t whether it was “verifiable,” but whether it was “falsifiable.”298 That’s not to say that there are data that contradict the theory—only that the theory clearly makes predictions that could, in principle, be contradicted by some experiment we could imagine doing. The theory has to stick its neck out; otherwise, it’s not scientific. Popper had in mind Karl Marx’s theory of history, and Sigmund Freud’s theory of psychoanalysis. These influential intellectual constructs, in his mind, fell far short of the scientific status their proponents liked to claim. Popper felt that you could take anything that happened in the world, or any behavior shown by a human being, and come up with an “explanation” of those data on the basis of Marx or Freud—but you wouldn’t ever be able to point to any observed event and say, “Aha, there’s no way to make that consistent with these theories.” He contrasted these with Einstein’s theory of relativity, which sounded equally esoteric and inscrutable to the person on the street, but made very definite predictions that (had the experiments turned out differently) could have falsified the theory.
THE MULTIVERSE IS NOT A THEORY
Where does that leave the multiverse? Here we are, claiming to be engaged in the practice of science, attempting to “explain” the observed arrow of time in our universe by invoking an infinite plethora of unobservable other universes. How is the claim that other universes exist falsifiable? It should come as no surprise that this kind of speculative theorizing about unobservable things leaves a bad taste in the mouths of many scientists. If you can’t make a specific prediction that I could imagine doing an experiment to falsify, they say, what you’re doing isn’t science. It’s philosophy at best, and not very good philosophy at that.
But the truth, as is often the case, is a bit more complicated. All this talk of mul tiverses might very well end up being a dead end. A century from now, our successors might be shaking their heads at all the intellectual effort that was wasted on trying to figure out what came before the Big Bang, as much as we wonder at all that work put into alchemy or the caloric theory of heat. But it won’t be because modern cosmologists had abandoned the true path of science; it will (if that’s how things turn out) simply be because the theory wasn’t correct.
Two points deserve to be emphasized concerning the role of unobservable things in science. First, it’s wrong to think of the goal of science as simply to fit the data. The goal of science goes much deeper than that: It’s to understand the behavior of the natural world.299 In the early seventeenth century, Johannes Kepler proposed his three laws of planetary motion, which correctly accounted for the voluminous astronomical data that had been collected by his mentor, Tycho Brahe. But we didn’t really understand the dynamics of planets within the Solar System until Isaac Newton showed that they could all be explained in terms of a simple i nverse-square law for gravity. Similarly, we don’t need to look beyond the Big Bang to understand the evolution of our observable universe; all we have to do is specify what conditions were like at early times, and leave it at that. But that’s a strategy that denies us any understanding of why things were the way they were.
Similar logic would have argued against the need for the theory of inflation; all inflation did was take things that we already knew were true about the universe (flatness, uniformity, absence of monopoles) and attempt to explain them in terms of simple underlying rules. We didn’t need to do that; we could have accepted things as they are. But as a result of our desire to do better, to actually understand the early universe rather than simply accept it, we discovered that inflation provides more than we had even asked for: a theory of the origin and nature of the primordial perturbations that grow into galaxies and large-scale structure. That’s the benefit to searching for understanding, rather than being content with fitting the data: True understanding leads you places you didn’t know you wanted to go. If we someday understand why the early universe had a low entropy, it is a good bet that the underlying mechanism will teach us more than that single fact.
The second point is even more important, although it sounds somewhat trivial: science is a messy, complica
ted business. It will never stop being true that the basis of science is empirical knowledge; we are guided by data, not by pure reason. But along the way to being guided by data, we use all sorts of nonempirical clues and preferences in constructing models and comparing them to one another. There’s nothing wrong with that. Just because the end product must be judged on the basis of how well it explains the data, doesn’t mean that every step along the way must have the benefit of an intimate and detailed contact with experiment.
More specifically: The multiverse is not a “theory.” If it were, it would be perfectly fair to criticize it on the basis of our difficulty in coming up with possible experimental tests. The correct way to think about the multiverse is as a prediction . The theory—such as it is, in its current underdeveloped state—is the marriage of the principles behind quantum field theory to our basic understanding of how curved spacetime works. Starting from those inputs, we don’t simply theorize that the universe could have undergone an early period of superfast acceleration; we predict that inflation should occur, if a quantum inflaton field with the right properties finds itself in the right state. Likewise, we don’t simply say, “Wouldn’t it be cool if there were an infinite number of different universes?” Rather, we predict on the basis of reasonable extrapolations of gravity and quantum field theory that a multiverse really should exist.
From Eternity to Here: The Quest for the Ultimate Theory of Time Page 47
