Words

And we’ve reached the final installment of the From Eternity to Here book club. Chapter Fifteen is entitled “The Past Through Tomorrow,” in an oblique allusion to Robert Heinlein, my favorite author when I was younger. We’re going to throw in the Epilogue for good measure.

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!

Welcome to this week’s installment of the From Eternity to Here book club. We’re on to Chapter Fourteen, “Inflation and the Multiverse.” Only one more episode to go! It’s like the upcoming finale of Lost, with a slightly lower level of message-board frenzy.

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.

Welcome to this week’s installment of the From Eternity to Here book club. Today we have a look at Chapter Thirteen, “The Life of the Universe.”

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!

Welcome to this week’s installment of the From Eternity to Here book club. Part Four opens with Chapter Twelve, “Black Holes: The Ends of Time.”

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.