Previously I did one on dark energy. It came out right after the Nobel Prize announcement, but don’t let that trick you into thinking I won the Prize myself. (Some people were tricked.)

Meanwhile, in a parallel universe, instead of writing Spacetime and Geometry, I wrote a massive tome on Cosmology. This parallel universe was featured on this week’s episode of Fringe. Here’s Walter Bishop retrieving his copy from Peter.

I helped with some of the equations on the episode. Thanks to Glen Whitman and Rob Chiappetta for the shout-out.

Here’s neuroscientist David Eagleman, talking about how we perceive time.

Here’s physicist-turned-complexity-theorist Raissa D’Souza, talking about complexity.

Here’s another physicist-turned-complexity-theorist, Geoffrey West, taking the complexity story even further.

Here’s former guest-blogger, now Discover blogger, and engineer/roboticist/neuroscientist/philosopher Malcolm Maciver, talking about making choices and the evolution of consciousness.

And to top things off, here’s one of those mock debates (where participants attempt to defend the side they don’t believe in). This time it’s David Albert vs. David Wallace, on the many-worlds interpretation of quantum mechanics.

Seriously good stuff. There are still more talks not yet up, I’ll let you know.

Update: I didn’t realize my own talk was up. Here it is.

So we asked them to go at it, with a twist: here Tim defends the proposition that time doesn’t exist, while Julian argues that it is real. I was not the only one to conclude that these guys were just as good at arguing this side as the one they actually believed.

Well worth watching — both talks are quite brilliant, in very different ways.

1. Time exists. Might as well get this common question out of the way. Of course time exists — otherwise how would we set our alarm clocks? Time organizes the universe into an ordered series of moments, and thank goodness; what a mess it would be if reality were complete different from moment to moment. The real question is whether or not time is fundamental, or perhaps emergent. We used to think that “temperature” was a basic category of nature, but now we know it emerges from the motion of atoms. When it comes to whether time is fundamental, the answer is: nobody knows. My bet is “yes,” but we’ll need to understand quantum gravity much better before we can say for sure.

2. The past and future are equally real. This isn’t completely accepted, but it should be. Intuitively we think that the “now” is real, while the past is fixed and in the books, and the future hasn’t yet occurred. But physics teaches us something remarkable: every event in the past and future is implicit in the current moment. This is hard to see in our everyday lives, since we’re nowhere close to knowing everything about the universe at any moment, nor will we ever be — but the equations don’t lie. As Einstein put it, “It appears therefore more natural to think of physical reality as a four dimensional existence, instead of, as hitherto, the evolution of a three dimensional existence.”

3. Everyone experiences time differently. This is true at the level of both physics and biology. Within physics, we used to have Sir Isaac Newton’s view of time, which was universal and shared by everyone. But then Einstein came along and explained that how much time elapses for a person depends on how they travel through space (especially near the speed of light) as well as the gravitational field (especially if its near a black hole). From a biological or psychological perspective, the time measured by atomic clocks isn’t as important as the time measured by our internal rhythms and the accumulation of memories. That happens differently depending on who we are and what we are experiencing; there’s a real sense in which time moves more quickly when we’re older.

4. You live in the past. About 80 milliseconds in the past, to be precise. Use one hand to touch your nose, and the other to touch one of your feet, at exactly the same time. You will experience them as simultaneous acts. But that’s mysterious — clearly it takes more time for the signal to travel up your nerves from your feet to your brain than from your nose. The reconciliation is simple: our conscious experience takes time to assemble, and your brain waits for all the relevant input before it experiences the “now.” Experiments have shown that the lag between things happening and us experiencing them is about 80 milliseconds. (Via conference participant David Eagleman.)

5. Your memory isn’t as good as you think. When you remember an event in the past, your brain uses a very similar technique to imagining the future. The process is less like “replaying a video” than “putting on a play from a script.” If the script is wrong for whatever reason, you can have a false memory that is just as vivid as a true one. Eyewitness testimony, it turns out, is one of the least reliable forms of evidence allowed into courtrooms. (Via conference participants Kathleen McDermott and Henry Roediger.)

6. Consciousness depends on manipulating time. Many cognitive abilities are important for consciousness, and we don’t yet have a complete picture. But it’s clear that the ability to manipulate time and possibility is a crucial feature. In contrast to aquatic life, land-based animals, whose vision-based sensory field extends for hundreds of meters, have time to contemplate a variety of actions and pick the best one. The origin of grammar allowed us to talk about such hypothetical futures with each other. Consciousness wouldn’t be possible without the ability to imagine other times. (Via conference participant Malcolm MacIver.)

7. Disorder increases as time passes. At the heart of every difference between the past and future — memory, aging, causality, free will — is the fact that the universe is evolving from order to disorder. Entropy is increasing, as we physicists say. There are more ways to be disorderly (high entropy) than orderly (low entropy), so the increase of entropy seems natural. But to explain the lower entropy of past times we need to go all the way back to the Big Bang. We still haven’t answered the hard questions: why was entropy low near the Big Bang, and how does increasing entropy account for memory and causality and all the rest? (We heard great talks by David Albert and David Wallace, among others.)

8. Complexity comes and goes. Other than creationists, most people have no trouble appreciating the difference between “orderly” (low entropy) and “complex.” Entropy increases, but complexity is ephemeral; it increases and decreases in complex ways, unsurprisingly enough. Part of the “job” of complex structures is to increase entropy, e.g. in the origin of life. But we’re far from having a complete understanding of this crucial phenomenon. (Talks by Mike Russell, Richard Lenski, Raissa D’Souza.)

9. Aging can be reversed. We all grow old, part of the general trend toward growing disorder. But it’s only the universe as a whole that must increase in entropy, not every individual piece of it. (Otherwise it would be impossible to build a refrigerator.) Reversing the arrow of time for living organisms is a technological challenge, not a physical impossibility. And we’re making progress on a few fronts: stem cells, yeast, and even (with caveats) mice and human muscle tissue. As one biologist told me: “You and I won’t live forever. But as for our grandkids, I’m not placing any bets.”

10. A lifespan is a billion heartbeats. Complex organisms die. Sad though it is in individual cases, it’s a necessary part of the bigger picture; life pushes out the old to make way for the new. Remarkably, there exist simple scaling laws relating animal metabolism to body mass. Larger animals live longer; but they also metabolize slower, as manifested in slower heart rates. These effects cancel out, so that animals from shrews to blue whales have lifespans with just about equal number of heartbeats — about one and a half billion, if you simply must be precise. In that very real sense, all animal species experience “the same amount of time.” At least, until we master #9 and become immortal. (Amazing talk by Geoffrey West.)

The topic, if you haven’t guessed, is time. That’s a big subject, one that can hardly be done justice by sprawling books with hundreds of (admittedly quite charming) footnotes. You can see why the conference has to spread over two countries. We’re trying an experiment in interdisciplinarity: while the conference is a serious event meant for researchers, we have a wide variety of specialties represented, including biologists, computer scientists, philosophers, and neuroscientists, as well as the inevitable physicists and cosmologists. (There is also a public event, for those of you who find yourselves in Copenhagen next week.) I can’t wait to hear some of these talks, it should be a blast.

My job is to open the conference with an introductory talk that hits on some of the big questions. Here are the slides, at least as they are right now; last-minute editing is always a possibility. I think I put enough in there to provoke almost everyone at the conference one way or another.

Oedipus and the Riddle

Quadruped in the dawn, erect at noon,
and wandering on three legs across the blind
spaces of afternoon; so the eternal
Sphinx saw her inconstant brother, Man.
And to her rocky silence came a man
who unlocked the riddle in the mirror;
terrified, he saw the shattering image
of his destruction and his error.
We are Oedipus, doomed as he, to be
the triple beast: child, saviour, suppliant-
all that we will be, all that we have been.
It would annihilate us in an instant
to glimpse our monstrous being; mercifully
God grants us issue and oblivion.

Sadly, God grants us nothing of the sort. But happily, we are not annihilated by glimpsing our monstrous being. We may be disappointed, disillusioned, or discombobulated; but those are temporary conditions that we can strive to overcome. Embrace your monstrous being! It’s the only true strategy in the face of Time’s relentless march.

My consciousness freely travels up and down my world line, but sadly it only carries the memories appropriate to the moment it inhabits.

The point is that (some) people don’t think about the flow of time in the right way, and this leads to a couple of unfortunate consequences: a difficulty in understanding the psychology of time, and a scattering of entertaining but illogical science-fiction scenarios.

Modern physics suggests that we can look at the entire history of the universe as a single four-dimensional thing. That includes our own personal path through it, which defines our world line. This seemingly conflicts with our intuitive idea that we exist at a moment, and move through time. Of course there is no real conflict — just two different ways of looking at the same thing. There is a four-dimensional universe that includes all of our world line, from birth to death, once and for all; and each moment along that world line defines an instantaneous person with the perception that they are growing older, advancing through time.

But if you don’t play too much attention to the way these two views fit together, you are tempted to imagine that “you” might actually, in some set of laws of physics if not actually in our own, go visit different moments in your own life, carrying along the consciousness of your “present” self. Something like that happens in SF stories from Slaughterhouse-Five to Back to the Future. But it’s not consistent — it requires the implicit introduction of a kind of “meta-time” that keeps track of when we visit the ordinary time with which we are familiar. That’s not how nature works; my tweet was trying to point out the inconsistency of taking this idea seriously, subject to the strictures of 140 characters or less. (To be earnestly explicit: if you did manage to travel up and down your world line at will, you would indeed have whatever memories were appropriate to the moment you were inhabiting — which means it would be exactly like not traveling at all.)

Sometimes, unfortunately, people go further than science fiction. I’ve run into folks who believe that our conscious perception of time passing is actually evidence against modern physics — arguing that we need to change the known laws of physics to account for the flow of time. It’s always conceivable, in principle, that what we think we understand at a basic level is completely wrong. But the evidence had better be pretty overwhelming. The brain is a complicated thing, and I don’t think that our present inability to provide a complete and comprehensive theory of conscious perceptions should be held as compelling evidence that the laws of physics are in need of overthrowing.

Stephen Hawking‘s favorite idea is that the universe came out of “nothing” — it arose (although that’s not really the right word) as a quantum fluctuation with literally no pre-existing state. No space, no time, no anything. But there’s another idea that’s at least as plausible: that the universe arose out of something, but that “something” was simply “chaos,” whatever that means in the context of quantum gravity. Space, time, and energy, yes; but no order, no particular arrangement.

It’s an old idea, going back at least to Lucretius, and contemplated by David Hume as well as by Ludwig Boltzmann. None of those guys, of course, knew very much of our modern understanding of cosmology, gravitation, and quantum mechanics. So what would the modern version look like?

That’s the question that Anthony Aguirre, Matt Johnson and I tackled in a paper that just appeared on arxiv. (Both of my collaborators have also been guest-bloggers here at CV.)

Out of equilibrium: understanding cosmological evolution to lower-entropy states
Anthony Aguirre, Sean M. Carroll, Matthew C. Johnson

Despite the importance of the Second Law of Thermodynamics, it is not absolute. Statistical mechanics implies that, given sufficient time, systems near equilibrium will spontaneously fluctuate into lower-entropy states, locally reversing the thermodynamic arrow of time. We study the time development of such fluctuations, especially the very large fluctuations relevant to cosmology. Under fairly general assumptions, the most likely history of a fluctuation out of equilibrium is simply the CPT conjugate of the most likely way a system relaxes back to equilibrium. We use this idea to elucidate the spacetime structure of various fluctuations in (stable and metastable) de Sitter space and thermal anti-de Sitter space.

It was Boltzmann who long ago realized that the Second Law, which says that the entropy of a closed system never decreases, isn’t quite an absolute “law.” It’s just a statement of overwhelming probability: there are so many more ways to be high-entropy (chaotic, disorderly) than to be low-entropy (arranged, orderly) that almost anything a system might do will move it toward higher entropy. But not absolutely anything; we can imagine very, very unlikely events in which entropy actually goes down.

In fact we can do better than just imagine: this has been observed in the lab. The likelihood that entropy will increase rather than decrease goes up as you consider larger and larger systems. So if you want to do an experiment that is likely to observe such a thing, you want to work with just a handful of particles, which is what experimenters succeeded in doing in 2002. But Boltzmann teaches us than any system, no matter how large, will eventually fluctuate into a lower-entropy state if we wait long enough. So what if we wait forever?

It’s possible that we can’t wait forever, of course; maybe the universe spends only a finite time in a lively condition like we see around us, before settling down to a truly stable equilibrium that never fluctuates. But as far as we currently know, it’s equally reasonable to imagine that it does last forever, and that it is always fluctuating. This is a long story, but a universe dominated by a positive cosmological constant (dark energy that never fades away) behaves a lot like a box of gas at a fixed temperature. Our universe seems to be headed in that direction; if it stays there, we will have fluctuations for all eternity.

Which means that empty space will eventually fluctuate into — well, anything at all, really. Including an entire universe.

This basic story has been known for some time. What Anthony and Matt and I have tried to add is a relatively detailed story of how such a fluctuation actually proceeds — what happens along the way from complete chaos (empty space with vacuum energy) to something organized like a universe. Our answer is simple: the most likely way to go from high-entropy chaos to low-entropy order is exactly like the usual way that systems evolve from low entropy to high-, just played backward in time.

Here is an excerpt from the paper:

The key argument we wish to explore in this paper can be illustrated by a simple example. Consider an ice cube in a glass of water. For thought-experiment purposes, imagine that the glass of water is absolutely isolated from the rest of the universe, lasts for an infinitely long time, and we ignore gravity. Conventional thermodynamics predicts that the ice cube will melt, and in a matter of several minutes we will have a somewhat colder glass of water. But if we wait long enough … statistical mechanics predicts that the ice cube will eventually re-form. If we were to see such a miraculous occurrence, the central claim of this paper is that the time evolution of the process of re-formation of the ice cube will, with high probability, be roughly equivalent to the time-reversal of the process by which it originally melted. (For a related popular-level discussion see From Eternity to Here, ch. 10.) The ice cube will not suddenly reappear, but will gradually emerge over a matter of minutes via unmelting. We would observe, therefore, a series of consecutive statistically unlikely events, rather than one instantaneous very unlikely event. The argument for this conclusion is based on conventional statistical mechanics, with the novel ingredient that we impose a future boundary condition — an unmelted ice cube — instead of a more conventional past boundary condition.

Let’s imagine that you want to wait long enough to see something like the Big Bang fluctuate randomly out of empty space. How will it actually transpire? It will not be a sudden WHAM! in which nothingness turns into the Big Bang. Rather, it will be just like the observed history of our universe — just played backward. A collection of long-wavelength photons will gradually come together; radiation will focus on certain locations in space to create white holes; those white holes will spit out gas and dust that will form into stars and planets; radiation will focus on the stars, which will break down heavy elements into lighter ones; eventually all the matter will disperse as it contracts and smooths out to create a giant Big Crunch. Along the way people will un-die, grow younger, and be un-born; omelets will convert into eggs; artists will painstakingly remove paint from their canvases onto brushes.

Now you might think: that’s really unlikely. And so it is! But that’s because fluctuating into the Big Bang is tremendously unlikely. What we argue in the paper is simply that, once you insist that you are going to examine histories of the universe that start with high-entropy empty space and end with a low-entropy Bang, the most likely way to get there is via an incredible sequence of individually unlikely events. Of course, for every one time this actually happens, there will be countless times that it almost happens, but not quite. The point is that we have infinitely long to wait — eventually the thing we’re waiting for will come to pass.

And so what?, you may very rightly ask. Well for one thing, modern cosmologists often imagine enormously long-lived universes, and events like this will be part of them, so they should be understood. More concretely, we are of course all interested in understanding why our actual universe really does have a low-entropy boundary condition at one end of time (the end we conventionally refer to as “the beginning”). There’s nothing in the laws of physics that distinguishes between the crazy story of the fluctuation into the Big Crunch and the perfectly ordinary story of evolving away from the Big Bang; one is the time-reverse of the other, and the fundamental laws of physics don’t pick out a direction of time. So we might wonder whether processes like these help explain the universe in which we actually live.

So far — not really. If anything, our work drives home (yet again!) how really unusual it is to get a universe that passes through such a low-entropy state. So that puzzle is still there. But if we’re ever going to solve it, it will behoove us to understand how entropy works as well as we can. Hopefully this paper is a step in that direction.

The talk is a punchy, 15-minute version of my usual cosmology-and-the-arrow-of-time schtick. Glad to see the arrow of time get some more publicity; sophisticated Cosmic Variance readers know all about it, but not everyone is so lucky. When Brian Cox did an episode of Wonders of the Universe that discussed the arrow of time, the comments were all “Wow, what an amazing concept, never heard of that!” Obviously reading the wrong blogs.

But I can’t help but notice something about the presentation on the TED home page…

Each talk is advertised by an image from the video; in most cases it’s a picture of the speaker actually giving the talk. But for mine, they (wisely) went with the Hubble Deep Field.

Lesson: you can’t compete with the universe! It’s bigger, smarter, and prettier, too.

David Eagleman is an interesting guy, as a recent New Yorker profile reveals. Mild-mannered neuroscientist by day, in his spare time he manages to write fiction as well as iPad-based superbooks. But his research focuses on how the mind works, in particular how we perceive time.

I’ve written previously about how, as far as the brain is concerned, remembering the past is like imagining the future. Eagleman studies a different neurological feature of time: how we perceive it passing under a variety of different conditions. You might be familiar with the feeling that “time slows down” when you are frightened or in some extreme environment. The problem is, how to test this hypothesis? It’s hard to come up with experimental protocols that frighten the crap out of human subjects while remaining consistent with all sorts of bothersome regulations.

So Eagleman and collaborators did the obvious thing: they tied subjects very carefully into harnesses, and threw them from a very tall platform. The non-obvious thing is that they invented a gizmo that flashed numbers as they fell, so that they could determine whether the brain really did speed up (perceiving a larger number of subjective moments per objective second) during this period of fear.

Answer: no, not really. There is a perceptual effect that kicks in after the event, giving the subject the impression that time moved more slowly; but in fact they didn’t perceive any more moments than a non-terrified person would have. Still, incredibly interesting results; for example, when you’re afraid, the brain lays down memories differently than when you’re in a normal state.

Obviously, of course, these findings need to be replicated. If you’ll excuse me, I’m off to find some grad students and a tall building.

(Those viewing in an RSS reader, you have to visit the page to click the audio link.)

David assumes the listeners have been following along previous shows, so we don’t spend too much time defining general relativity and the Big Bang; we go right for the cutting edge. But we also covered a lot of meta ground, about the process of doing physics. He also gave me the most comprehensive list of errata (mostly minor typos) for my book, so I know he read the whole thing!

Here are the slides from my own talk, which was supposed to be about time but ended up being more about space. Not much in the way of original research, just some ruminations on what is and is not “fundamental” about spacetime (with the caveat that this might not be a sensible question to ask). I made two basic points, which happily blended into each other: first, that the distinction between “position” (space) and “momentum” is not a fundamental aspect of classical mechanics or quantum mechanics, but instead reflects the particular Hamiltonian of our world; and second that holography implies that space is emergent, but in a very subtle and non-local way. This latter point is one reason why many of us are skeptical of approaches like loop quantum gravity, causal set theory, or dynamical triangulations; these all start by assuming that there are independent degrees of freedom at each spacetime point, and quantum gravity doesn’t seem to work that way.

Sadly the slides aren’t likely to be very comprehensible. There’s a lot of math, and the equations don’t come out completely clearly — my first time using Slideshare, so perhaps they would look better if I uploaded a pdf file rather than PowerPoint. (Hint: the slides are much more clear if you click “Menu” at the bottom left, and switch to full-screen mode.) Also I didn’t make any attempt to have the slides stand by themselves without the accompanying words. But at least this will serve as documentation that I really did give a talk at the conference, no just hang out in restaurants in Montreal.

We should celebrate with a contest or something — I have a few copies of the paperback that could be given away, but no clever ideas to spark a competition. Best short story about the arrow of time? Limericks are out, but perhaps sonnets? Or just for the biggest contributors to our Donors Choose campaign? Suggestions welcome. (Best suggestion for a contest? How deliciously meta.)

At the moment Amazon is offering a bargain price on the hardcover, even cheaper than the paperback (presumably to clear out inventory). They are also pushing their Kindle editions, presumably to help stave off the iPad onslaught. Truth is, there are a lot more books available for Kindle than in the iBooks store, so like many people I read books on my iPad using the Kindle app.

Anyway, Amazon is allowing readers to peruse the first chapters of some of their Kindle books — so here you go! I wish it had been the second chapter, to be honest; that is where we get into some of the mysteries of entropy and the arrow of time. Chapter One is a bit more scene-setting (but it’s a pretty awesome scene).

Actually, looking at the sample more closely, they seem to have included the Prologue and some of Chapter Two. Even better! Note you can click the “Aa” icon near the top of the viewer to change the font size and line spacing, if you like to read more than twenty words of text at a time.

Here is the talk, which is basically at a popular level, although I felt empowered to use the word “logarithm” without explanation. I’ve also tried to collect other talks by me onto one page, for those who just can’t get enough. (Hi, Mom!)

Unitary Evolution and Cosmological Fine-Tuning
Authors: Sean M. Carroll, Heywood Tam
(Submitted on 8 Jul 2010)

Abstract: Inflationary cosmology attempts to provide a natural explanation for the flatness and homogeneity of the observable universe. In the context of reversible (unitary) evolution, this goal is difficult to satisfy, as Liouville’s theorem implies that no dynamical process can evolve a large number of initial states into a small number of final states. We use the invariant measure on solutions to Einstein’s equation to quantify the problems of cosmological fine-tuning. The most natural interpretation of the measure is the flatness problem does not exist; almost all Robertson-Walker cosmologies are spatially flat. The homogeneity of the early universe, however, does represent a substantial fine-tuning; the horizon problem is real. When perturbations are taken into account, inflation only occurs in a negligibly small fraction of cosmological histories, less than 10^{-6.6×10^7}. We argue that while inflation does not affect the number of initial conditions that evolve into a late universe like our own, it nevertheless provides an appealing target for true theories of initial conditions, by allowing for small patches of space with sub-Planckian curvature to grow into reasonable universes.

In English: our universe looks very unusual. You might think we have nothing to compare it to, but that’s not quite right; given the particles that make up the universe (or the quantum degrees of freedom, to be technical about it), we can compare their actual configuration to all the possible configurations they could have been in. The answer is, our observed universe is highly non-generic, and in the past it was even more non-generic, or “finely tuned.” One way of describing this state of affairs is to say that the early universe had a very low entropy. We don’t know why; that’s an important puzzle, worth writing books about.

Part of the motivation of this paper was to put some quantitative meat on some ideas I discussed in my book. The basic argument is an old one, going back to Roger Penrose in the late 1970′s. The advent of inflation in the early 1980′s seemed to change things — it showed how to get a universe just like ours starting from a tiny region of space dominated by “false vacuum energy.” But a more careful analysis shows that inflation doesn’t really change the underlying problem — sure, you can get our universe if you start in the right state, but that state is even more finely-tuned than the conventional Big Bang beginning.

We revisit this question, bringing to bear some mathematical heavy machinery developed in the 1980′s by Gary Gibbons, Stephen Hawking, and John Stewart. Previous discussions have invoked general ideas of entropy or reversibility, but we were able to do a relatively down-to-earth calculation using conventional cosmological models. And we tried our best to explicitly list all of the caveats of the argument, which is important in a context like this where we don’t know all the rules.

We find that inflation is very unlikely, in the sense that a negligibly small fraction of possible universes experience a period of inflation. On the other hand, our universe is unlikely, by exactly the same criterion. So the observable universe didn’t “just happen”; it is either picked out by some general principle, perhaps something to do with the wave function of the universe, or it’s generated dynamically by some process within a larger multiverse. And inflation might end up playing a crucial role in the story. We don’t know yet, but it’s important to lay out the options to help us find our way.

Excerpt:

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.

This is the chapter where we attempt to put it all together. The idea was that we had been so careful and thorough in the previous chapters that in this one we could be fairly terse, setting up ideas and knocking them down with our meticulously-prepared bludgeon of Science. I’m not sure if it actually worked that way; one could argue that it would have been more effective to linger lovingly over the implications of some of these scenarios. But there was already a lot of repetition throughout the book (intentionally, so that ideas remained clear), and I didn’t want to add to it.

Of course my own current favorite idea involves baby universes pinching off from a multiverse, and I’m certainly happy to explain my reasons in favor of it. But there are also good reasons to be skeptical, especially when it comes to our lack of knowledge concerning whether baby universes actually are formed in de Sitter space. What I hope comes across is the more generic scenario: a multiverse where entropy is increasing locally because it can always increase, and does so both toward the far past and the far future. While there’s obviously a lot of work to be done in filling in the details, I haven’t heard any other broad-stroke idea that sounds like a sensible dynamical origin for the arrow of time. (Which isn’t to say that one won’t come along tomorrow.)

Chapter 16 is the Epilogue, where I reflect on where we’ve been and what it all means. I talk a little about why thinking about the multiverse is a very respectable part of the scientific endeavor, and how we should think about the fact that we are a very tiny part of a very big cosmos. Finally, I wanted to quote the very last paragraph of text in the book, at the end of the Acknowledgments:

I’m the kind of person who grows restless working at home or in the office for too long, so I frequently gather up my physics books and papers and bring them to a restaurant or coffee shop for a change of venue. Almost inevitably, a stranger will ask me what it is I’m reading, and—rather than being repulsed by all the forbidding math and science—follow up with more questions about cosmology, quantum mechanics, the universe. At a pub in London, a bartender scribbled down the ISBN number of Scott Dodelson’s Modern Cosmology; at the Green Mill jazz club in Chicago, I got a free drink for explaining dark energy. I would like to thank every person who is not a scientist but maintains a sincere fascination with the inner workings of nature, and is willing to ask questions and mull over the answers. Thinking about the nature of time might not help us build better TV sets or lose weight without exercising, but we all share the same universe, and the urge to understand it is part of what makes us human.

Among those people who share a fascination with the inner workings of nature, I of course include people who regularly read this blog. So — thanks!

Excerpt:

There is a lot to say about eternal inflation, but let’s just focus on one consequence: While the universe we see looks very smooth on large scales, on even larger (unobservable) scales the universe would be very far from smooth. The large-scale uniformity of our observed universe sometimes tempts cosmologists into assuming that it must keep going like that infinitely far in every direction. But that was always an assumption that made our lives easier, not a conclusion from any rigorous chain of reasoning. The scenario of eternal inflation predicts that the universe does not continue on smoothly as far as it goes; far beyond our observable horizon, things eventually begin to look very different. Indeed, somewhere out there, inflation is still going on. This scenario is obviously very speculative at this point, but it’s important to keep in mind that the universe on ultra-large scales is, if anything, likely to be very different than the tiny patch of universe to which we have immediate access.

This is a fairly straightforward chapter, trying to explain how inflation works. Given that by this point the reader already is familiar with dark energy making the universe accelerate, and with the fine-tuning problem represented by the low entropy of the early universe, the basic case isn’t that hard to put together. Of course we have an additional non-traditional goal as well: to illuminate the tension between the usual story we tell about inflation and the “information-conserving evolution of our comoving patch” story we told in the last chapter. Here’s where I argue that inflation is not the panacea it’s sometimes presented as, primarily because it’s not that easy to take all the degrees of freedom within the universe we observe and pack them delicately into a tiny patch dominated by false vacuum energy. Put that way, it doesn’t seem all that surprising, but too many people don’t want to get the message.

This is also the chapter where we first introduce the idea of the multiverse. (The multiverse occupies less than 15 pages or so in the entire book, but to read some reactions you would think it was the dominant theme. The publicists and I must share some of the blame for that perspective, as it is an irresistible thing to mention when talking about the book.) Mostly I wanted to demystify the idea of the multiverse, presenting it as a perfectly natural outgrowth of the idea of inflation. What we’re supposed to make of it is of course a different story.

Looking back, I think the chapter is a mixed success. I like the gripping narrative of the opening pages. But the actual explanation of inflation is kind of workmanlike and uninspiring. I really put a lot of effort into coming up with novel explanations of entropy and quantum mechanics, which didn’t simply rehash the expositions found in other books; but for inflation I didn’t try as hard. Partly simply because of looming deadlines, partly because I was eager to get to the rest of the book. Hopefully the basic points are more or less clear.

Excerpt:

If our comoving patch defines an approximately closed system, the next step is to think about its space of states. General relativity tells us that space itself, the stage on which particles and matter move and interact, evolves over time. Because of this, the definition of the space of states becomes more subtle than it would have been in if spacetime were absolute. Most physicists would agree that information is conserved as the universe evolves, but the way that works is quite unclear in a cosmological context. The essential problem is that more and more things can fit into the universe as it expands, so—naively, anyway—it looks as if the space of states is getting bigger. That would be in flagrant contradiction to the usual rules of reversible, information-conserving physics, where the space of states is fixed once and for all.

Of course we’ve already looked a bit at the life of the universe, way back in Chapter Three. The difference is that we’re now focusing on how entropy evolves, given our hard-acquired understanding of what entropy is and how it works for black holes. This is where we review Roger Penrose’s well-known-yet-still-widely-ignored argument that the low entropy of the early universe is something that needs to be explained.

In a sense, this is pretty straightforward stuff, following directly from what we’ve already done in the book. But it’s also somewhat controversial among professional cosmologists. The reason why can be found in the slightly technical digression that begins on page 292, “Conservation of information in an expanding universe.”

The point is that physicists often think of “the space of states in a region of spacetime” as being equal to “the space of states we can describe by quantum field theory.” They know that’s not right, because gravity doesn’t fit into that description, but these are the states they know how to deal with. This collection of states isn’t fixed; it grows with time as the universe expands. You will therefore sometimes hear cosmologists talk about the high entropy of the early universe, under the misguided assumption that there were fewer states that could “fit” into the universe at that time. (Equivalently, that gravity can be ignored.) This approach has, in my opinion anyway, done great damage to how cosmologists think about fine-tuning problems. One of the major motivations for writing the book was to explain these issues, not only to the general reader but also to my scientist friends.

At the end of the chapter I deviate from Penrose’s argument a bit. He believes that a high-entropy state of the universe would be one that was highly inhomogeneous, full of black holes and white holes and what have you. I think that’s right if you are thinking about a very dense configuration of matter. But matter doesn’t have to be dense — the expansion of the universe can dilute it away. So I argue that the truly highest-entropy configuration is one where space is essentially empty, with nothing but vacuum energy. This is also very far from being widely accepted, and certainly relies on a bit of hand-waving. But again, I think the failure to appreciate this point has distorted how cosmologists think about the problems presented by the early universe. So hopefully they read this far in the book!

Excerpt:

Unlike boxes full of atoms, we can’t make black holes with the same size but different masses. The size of a black hole is characterized by the “Schwarzschild radius,” which is precisely proportional to its mass. If you know the mass, you know the size; contrariwise, if you have a box of fixed size, there is a maximum mass black hole you can possibly fit into it. But if the entropy of the black hole is proportional to the area of its event horizon, that means there is a maximum amount of entropy you can possibly fit into a region of some fixed size, which is achieved by a black hole of that size.

That’s a remarkable fact. It represents a dramatic difference in the behavior of entropy once gravity becomes important. In a hypothetical world in which there was no such thing as gravity, we could squeeze as much entropy as we wanted into any given region; but gravity stops us from doing that.

It’s not surprising to find a chapter about black holes in a book that talks about relativity and cosmology and all that. But the point here is obviously a slightly different one than usual: we care about the entropy of the black hole, not the gruesome story of what happens if you fall into the singularity.

Black holes are important to our story for a couple of reasons. One is that gravity is certainly important to our story, because we care about the entropy of the universe and gravity plays a crucial role in how the universe evolves. But that raises a problem that people love to bring up: because we don’t understand quantum gravity (and in particular we don’t have a complete understanding of the space of microstates), we’re not really able to calculate the entropy of a system when gravity is important. The one shining counterexample to this is when the system is a black hole; Bekenstein and Hawking gave us a formula that allows us to calculate the entropy with confidence. It’s a slightly weird situation — we know how to calculate the entropy of a system when gravity is completely irrelevant, and we also know how to calculate the entropy when gravity is completely dominant and you have a black hole. It’s only the messy in-between situations that give us trouble.

The other reason black holes are important, of course, is that the answer that Bekenstein and Hawking derive is somewhat surprising, and ultimately game-changing. The entropy is not proportional to the volume inside the black hole (whatever that might have meant, anyway) — it’s proportional to the area of the event horizon. That’s the origin of the holographic principle, which is perhaps the most intriguing result yet to come out of the thought-experiment-driven world of quantum gravity.

The holographic principle is undoubtedly going to have important consequences for our ultimate understanding of spacetime and entropy, but how it will all play out is somewhat unclear right now. I felt it was important to cover this stuff in the book, although it doesn’t really lead to any neat resolutions of the problems we are tackling. Still, hopefully it was somewhat comprehensible.

Excerpt:

This distinction between “incomplete knowledge” and “intrinsic quantum indeterminacy” is worth dwelling on. If the wave function tells us there is a 75 percent chance of observing the cat under the table and a 25 percent chance of observing her on the sofa, that does not mean there is a 75 percent chance that the cat is under the table and a 25 percent chance that she is on the sofa. There is no such thing as “where the cat is.” Her quantum state is described by a superposition of the two distinct possibilities we would have in classical mechanics. It’s not even that “they are both true at once”; it’s that there is no “true” place where the cat is. The wave function is the best description we have of the reality of the cat.

It’s clear why this is hard to accept at first blush. To put it bluntly, the world doesn’t look anything like that. We see cats and planets and even electrons in particular positions when we look at them, not in superpositions of different possibilities described by wave functions. But that’s the true magic of quantum mechanics: What we see is not what there is. The wave function really exists, but we don’t see it when we look; we see things as if they were in particular ordinary classical configurations.

Title notwithstanding, the point of the chapter is not that there’s some “quantum” version of time that we have to understand. Some people labor under the impression that the transition from classical mechanics to quantum mechanics ends up “quantizing” everything, and turning continuous parameters into discrete ones, perhaps even including time. It doesn’t work that way; the conventional formalism of quantum mechanics (such as the Schrödinger equation) implies that time should be a continuous parameter. Things could conceivably change when we eventually understand quantum gravity, but they just as conceivably might not. In fact, I’d argue that the smart money is on time remaining continuous once all is said and done. (As a small piece of evidence, the context in which we understand quantum gravity the best is probably the AdS/CFT correspondence, where the Schrödinger equation is completely conventional and time is perfectly continuous.)

However, we still need to talk about quantum mechanics for the purposes of this book, for one very good reason: we’ve been making a big deal about how the fundamental laws of physics are reversible, but wave function collapse (under the textbook Copenhagen interpretation) is an apparent counterexample. Whether it’s a real counterexample, or simply an artifact of an inadequate interpretation of quantum mechanics, is a matter of much debate. I personally come down on the side that believes that there’s no fundamental irreversibility, only apparent irreversibility, in quantum mechanics. That’s basically the many-worlds interpretation, so I felt the book needed a chapter on what that was all about.

Along the way, I get to give my own perspective on what quantum mechanics really means. Unlike certain parts of the book, I’m pretty happy with how this one came out — feel free to correct me if you don’t completely agree. Quantum mechanics can certainly be tricky to understand, for the basic reason that what we see isn’t the same as what there is. I’m firmly convinced that most expositions of the subject make it seem even more difficult than it should be, by speaking as if “what we see” really does reflect “what there is,” even if we should know better.

So I present a number of colorful examples of two-state systems involving cats and dogs. Experts will recognize very standard treatments of the two-slit experiment and the EPR experiment, but in very different words. Things that seem very forbidding when phrased in terms of interference fringes and electron spins hopefully become a bit more accessible when we’re asking whether the cat is on the sofa or under the table. I did have to treat complicated macroscopic objects with many moving parts as if they could be described as very simple systems, but I judged that to be a worthwhile compromise in the interests of pedagogy. And no animals were harmed in the writing of this chapter! Let me know how you think the strategy worked.