Blogs / Cosmic Variance

Welcome to this week’s installment of the From Eternity to Here book club. This week we’re tackling two chapters at once: Chapter Four, “Time is Personal,” and Chapter Five, “Time is Flexible.” That’s just because these chapters are relatively short; next time we’ll return to one chapter per week.

Excerpt:

Starting from a single event in Newtonian spacetime, we were able to define a surface of constant time that spread uniquely throughout the universe, splitting the set of all events into the past and the future (plus “simultaneous” events precisely on the surface). In relativity we can’t do that. Instead, the light cone associated with an event divides spacetime into the past of that event (events inside the past light cone), the future of that event (inside the future light cone), the light cone itself, and a bunch of points outside the light cone that are neither in the past nor the future.

It’s that last bit that really gets people. In our reflexively Newtonian way of thinking about the world, we insist that some far away event either happened in the past, the future, or at the same time as some event on our own world line. In relativity, for spacelike separated events (outside one another’s light cones), the answer is “none of the above.” We could choose to draw some surfaces that sliced through spacetime, and label them “surfaces of constant time,” if we really wanted to. That would be taking advantage of the definition of time as a coordinate on spacetime, as discussed in Chapter One. But the result reflects our personal choice, not a real feature of the universe. In relativity, the concept of “simultaneous faraway events” does not make sense.

These two chapters take on a task that is part of the responsibility of any good book on modern cosmology or gravity: explaining Einstein’s theory of relativity. Both special relativity and general relativity, hence two chapters. In retrospect they are pretty short, so an argument could be made that I should have just combined them into a single chapter.

The special challenge of these chapters is precisely that many readers — but not all — will already have read numerous other popular-level expositions of relativity. But you have to do it. Fortunately, my favorite way of talking about relativity is a little bit different from the standard one, and lines up well with the overarching goal of understanding the meaning of “time.” In particular, I try to make the point that the secret to relativity is to think locally — to compare things happening right next to each other in spacetime, not events that are widely separated. You’re allowed to compare separated events, of course, but the answers are necessarily dependent on arbitrary choices of coordinates, and that leads to endless confusion. So you won’t read a lot about “length contraction” or “time dilation,” but you will read a lot about the actual amount of time measured along a trajectory.

Unfortunately, a search for vivid examples of the maxim “freely-falling paths through spacetime experience the longest amount of proper time” led me directly to the most embarrassing mistake in the book. (At least, “most embarrassing mistake so far uncovered.”) Sordid details below the fold!

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From Eternity to Here addresses the problem of the arrow of time — why is the past different from the future? But Chapter Six is all about time travel, and in particular the interesting version in which you travel backwards in time. Whether it’s possible, what rules it would have to obey, and so on. And now — even though I’m sure there aren’t more than two or three of you out there who haven’t purchased the book already — you can get a sneak peek of part of that chapter. It’s going to be the cover story in the March issue of Discover, and the story is already available online.

And here’s a bit of multimedia bonus: to get the cool exploding-clock image, the intrepid editors worked with Biwa Studios to film high-speed video of exploding clocks, and you can see the whole videos online. They run the events forwards and backwards, just in case your personal arrow of time needs to be calibrated.

One may ask, why is there a chapter about time travel in a book about time’s arrow? Just couldn’t resist the temptation to talk about everything related to “time”? In fact there is a deeper reason. In the real world, the laws of physics may or may not allow for closed timelike curves — physicist-speak for time machines. (Probably not, but we’re not as sure as we could be.) But apart from the difficulty in constructing them, time machines boggle our minds by offering up logical paradoxes — what’s to prevent you from traveling into the past and killing your parents before they met? There is a consistent way to handle these paradoxes, simply by insisting that they never happen. (And we’re still hopeful that the folks at Lost adhere to this principle, regardless of the surface interpretation of last night’s Season Six premiere.)

The reason why that’s hard to swallow is because we can’t imagine anything that stops us from killing our parents, once we grant the existence of time machines. We conceptualize the past and future very differently — the past is settled once and for all, while we can still make choices about what happens in the future. That, of course, is the arrow of time. At the heart of what bothers us about time-travel paradoxes is the difficulty of establishing a uniform arrow of time in a universe where time loops back on itself.

Of course the easy, and probably correct, way out is to simply believe that time machines don’t and can’t exist. But disentangling the demands of logic from the demands of common sense is always a rewarding exercise in its own right.

Welcome to this week’s installment of the From Eternity to Here book club. Next up is Chapter Three: “The Beginning and End of Time.” Remember that next week we’re doing two chapters at once, Four and Five.

For those who missed them, here’s the Science Friday discussion, and here’s the Firedoglake book salon with Chad. I should also point to some substantive review/discussions: Wall Street Journal, New Scientist, USA Today, and Overcoming Bias.

Excerpt:

For the most part, people interested in statistical mechanics care about experimental situations in laboratories or kitchens here on Earth. In an experiment, we can control the conditions before us; in particular, we can arrange systems so that the entropy is much lower than it could be, and watch what happens. You don’t need to know anything about cosmology and the wider universe to understand how that works.

But our aims are more grandiose. The arrow of time is much more than a feature of some particular laboratory experiments; it’s a feature of the entire world around us. Conventional statistical mechanics can account for why it’s easy to turn an egg into an omelet, but hard to turn an omelet into an egg. What it can’t account for is why, when we open our refrigerator, we are able to find an egg in the first place. Why are we surrounded by exquisitely ordered objects such as eggs and pianos and science books, rather than by featureless chaos?

This chapter is a fairly straightforward review of the modern understanding of cosmology, with a particular eye on those issues that will become important later in the book. We zip through the expansion, structure formation, and dark energy. There I got to tell a fun personal story of my wager with Brian Schmidt. At least I think it’s fun — including personal stories is not my natural tendency, but at the right moments it can help to humanize all the forbidding science. Hopefully this was one such moment.

A few topics go beyond the standard cosmology summary. I discussed the Steady State theory a bit, because it’s a relevant historical example when we will much later turn to the question of what the universe should look like. I also dwell a bit on vacuum fluctuations and dark energy, because those will pay a crucial role in my personal favorite explanation for the arrow of time. And we close the chapter with a very brief overview of the evolution of entropy. It has to be brief, because we haven’t laid nearly enough groundwork to do the job right. This is a conscious choice, which may or may not work: rather than simply progressing on an absolutely logical path from foundations to conclusions, I felt free to mention points that would be important later, on the theory that they would come as less of a shock if we had established some familiarity. Again, hope that worked.

Tom Levenson, who is an actual writer, advised me to omit “smoking a pipe” from the caption to Figure 7, on the theory that what is shown should not also be told. I left it in anyway. It’s my book!

Fans of the hit TV series Lost are awaiting the big event next week: the premiere of Season Six on Tuesday night. The show is famous for its mysteries and plot twists, so this year has a special status: it’s the final season, where everything that’s going to be revealed will be revealed. That might not be absolutely everything, but it should be a lot.

Lost has always played with time and narrative — characters’ backstories were told through elaborate flashbacks, lending a richness of nuance to their behavior in the main story. But time travel as a plot device was established as a central theme during Season Five. One happy consequence was the invention of Lost University, through which fans could learn a little about physics and other real-world subjects underlying events in the show.

Naturally, scientifically-minded folks want to know: how respectable is the treatment of time travel, anyway? We are, as always, here to help. My short take: Lost is a TV fantasy, not a documentary, and it doesn’t try all that hard to conform to general relativity or the other known laws of physics. But happily, the most important of the Rules for Time Travelers is very much obeyed: there are no paradoxes. And more interestingly, the spirit of the rules is obeyed, and indeed put to good narrative effect. The potential for time-travel paradoxes helps illuminate issues of free will vs. predestination, a central theme of the show. And what more can you ask for in a time-travel story than that?

Details below the fold, full of spoilers. (Not for the upcoming season, of course.) See also discussions from io9, Popular Mechanics, and Sheril.

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Welcome to this week’s installment of the From Eternity to Here book club. Today we look at Chapter Two, “The Heavy Hand of Entropy.”

[By the way: are we going too slowly? If there is overwhelming sentiment to move to two chapters per week, that would be no problem. But if sentiment is non-overwhelming, we'll stick to the original plan.]

Excerpt:

While it’s true that the presence of the Earth beneath our feet picks out an “arrow of space” by distinguishing up from down, it’s pretty clear that this is a local, parochial phenomenon, rather than a reflection of the underlying laws of nature. We can easily imagine ourselves out in space where there is no preferred direction. But the underlying laws of nature do not pick out a preferred direction of time, any more than they pick out a preferred direction in space. If we confine our attention to very simple systems with just a few moving parts, whose motion reflects the basic laws of physics rather than our messy local conditions, there is no arrow of time—we can’t tell when a movie is being run backward…

The arrow of time, therefore, is not a feature of the underlying laws of physics, at least as far as we know. Rather, like the up/down orientation space picked out by the Earth, the preferred direction of time is also a consequence of features of our environment. In the case of time, it’s not that we live in the spatial vicinity of an influential object, it’s that we live in the temporal vicinity of an influential event: the birth of the universe. The beginning of our observable universe, the hot dense state known as the Big Bang, had a very low entropy. The influence of that event orients us in time, just as the presence of the Earth orients us in space.

This chapter serves an obvious purpose — it explains in basic terms the ideas of irreversibility, entropy, and the arrow of time. It’s a whirlwind overview of concepts that will be developed in greater detail in the rest of the book, especially in Part Three. As a consequence, there are a few statements that may seem like bald assertions that really deserve more careful justification — hopefully that justification will come later.

Here’s where I got to use those “incompatible arrows” stories I blogged about some time back (I, II, III, IV). The fact that the arrow of time is so strongly ingrained in the way we think about the world makes it an interesting target for fiction — what would happen if the arrow of time ran backwards? The straightforward answer, of course, is “absolutely nothing” — there is no prior notion of “backwards” or “forwards.” As long as there is an arrow of time that is consistent for everyone, things would appear normal to us; there is one direction of time we all remember, which we call “the past,” when the entropy was lower. It’s when different interacting subsystems of the universe have different arrows of time that things get interesting. So we look briefly at stories by Lewis Carroll, F. Scott Fitzgerald, and Martin Amis, all of which use that trick. (Does anyone know of a reversed-arrow story that predates Through the Looking Glass?) Of course these are all fantasies, because it can’t happen in the real world, but that’s part of the speculative fun.

Then we go into entropy and the Second Law, from Sadi Carnot and Rudolf Clausius to Ludwig Boltzmann, followed by some discussion of different manifestations of time’s arrow. All at lightning speed, I’m afraid — there’s a tremendous amount of fascinating history here that I don’t cover in anywhere near the detail it deserves. But the real point of the chapter isn’t to tell the historical stories, it’s to emphasize the ubiquity of the arrow of time. It’s not just about stirring eggs to make omelets — it has to do with metabolism and the structure of life, why we remember the past and not the future, and why we think we have free will. Man, someone should write a book about this stuff!

Welcome to the first installment of the From Eternity to Here book club. We’re starting at the beginning, with Chapter One, “The Past is Present Memory.”

Excerpt:

The world does not present us with abstract concepts wrapped up with pretty bows, which we then must work to understand and reconcile with other concepts. Rather, the world presents us with phenomena, things that we observe and make note of, from which we must then work to derive concepts that help us understand how those phenomena relate to the rest of our experience. For subtle concepts such as entropy, this is pretty clear. You don’t walk down the street and bump into some entropy; you have to observe a variety of phenomena in nature and discern a pattern that is best thought of in terms of a new concept you label “entropy.” Armed with this helpful new concept, you observe even more phenomena, and you are inspired to refine and improve upon your original notion of what entropy really is.

For an idea as primitive and indispensable as “time,” the fact that we invent the concept rather than having it handed to us by the universe is less obvious—time is something we literally don’t know how to live without. Nevertheless, part of the task of science (and philosophy) is to take our intuitive notion of a basic concept such as “time” and turn it into something rigorous. What we find along the way is that we haven’t been using this word in a single unambiguous fashion; it has a few different meanings, each of which merits its own careful elucidation.

The book is divided into four major parts — Part One gives an overview of the issues, Part Two discusses relativity and time travel, Part Three (the longest and best part of the book) is about reversibility, entropy, and the arrow of time proper, and Part Four puts it all into a cosmological context. So Part One is somewhat out of logical order — it’s an attempt to survey the terrain and raise some ideas that will come to fruition later in the book.

The basic point of Chapter One is to examine the ways in which we use the concept of “time.” I’ll readily admit that this doesn’t sound like the sexiest idea for an opening chapter. (In my next book, an important character will be murdered within the first few pages, after which his beautiful daughter will be compelled to search for his killer in various exotic locales.) The first chapter has to serve multiple purposes — it obviously needs to provide some background for the rest of the book, but this is not a classroom where you can assume the audience will necessarily follow you to the end. So the first chapter also has to be fun and engaging, hinting at some of the mysteries to come.

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As promised, we’re going to have a book club to talk about From Eternity to Here. Roughly speaking, every Tuesday I’ll post about another chapter, and we’ll talk about it. Easy enough, right? (Chapters 4 and 5, about relativity, are pretty short and will be combined into one week.)

For the most part I won’t be summarizing each chapter — because you’ll all have read the book, so that would be boring. Instead, I want to give some behind-the-scenes insight about what was going through my mind when I put each chapter together — a little exclusive for readers of the blog. Of course, in the comments I hope we can discuss the substance of the chapters in as much detail as we like. I’m going to try to participate actively in all the discussions, so I hope to answer questions when I can — and certainly expect to learn something myself along the way.

The book is divided into four parts: an overview, spacetime and relativity, entropy and the Second Law, and a discussion of how it all fits into cosmology. You can find a more detailed table of contents here, and here is the prologue to get you in the mood. Part Three is definitely the high point of the book, so be sure to stick around for that.

So see you next Tuesday! Get reading!

Part One: Overview

• January 19: Chapter One (What is time?)
• January 26: Chapter Two (Entropy and the Second Law)
• February 2: Chapter Three (The expanding universe)

Part Two: Relativity

• February 9: Chapters Four and Five (Special and general relativity)
• February 16: Chapter Six (Time travel)

Part Three: Entropy and the Arrow of Time

• February 23: Chapter Seven (Determinism and reversibility)
• March 2: Chapter Eight (Entropy according to Boltzmann)
• March 9: Chapter Nine (Information, memory, life…)
• March 16: Chapter Ten (Recurrence and Boltzmann brains)
• March 23: Chapter Eleven (Quantum mechanics)

Part Four: Time and the Universe

• March 30: Chapter Twelve (Black holes)
• April 6: Chapter Thirteen (Evolution of the universe)
• April 13: Chapter Fourteen (Inflation)
• April 20: Chapter Fifteen and Epilogue (Explaining the arrow of time)

And here you thought the holidays were over. Silly you. Today is the greatest holiday of all: Book Release Day!

That’s right — From Eternity to Here: The Quest for the Ultimate Theory of Time is out today. That means you could head over to Amazon.com and buy the book right now:

From Eternity to Here at Amazon

Don’t worry, we’ll wait. Of course you could also buy it later, but there are benefits to having a great first day, and we’re aiming to get as many Amazon purchases as we can. So you might want to take Lee Billings’s advice:

Just drafted a micro-review of @seanmcarroll’s “From Eternity to Here”. It’s really quite good–I suggest you all buy several copies.

I’m excited, anyway. You can find various goodies on the web page, including a reprint of the prologue, an annotated table of contents, a list of upcoming events, links to blurbs and reviews and other commentary, and a collection of related articles. Heck, I even went out and made a video:

I don’t think Spielberg is checking his rear-view mirror, but my budget was a bit lower.

Looking back through my old emails, I was first talking seriously about writing a book on the arrow of time in August, 2006. The contract with Dutton was agreed upon in May, 2007. Worked on it on and off, and finally started working in earnest in mid/late-2008. I emailed the manuscript to the publisher at 2:42 a.m. on Friday, May 8, 2009. And now it’s released to the world.

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I think we can all agree that I’ve been admirably restrained with respect to talking about my upcoming book before it even appears. (Maybe you don’t think so, but believe me — I’ve been restraining myself.) Die-hards have been able to follow the excitement at the Facebook page, where fascinating details about cover blurbs and review copies have been politely sequestered.

All that is about to end soon! Yesterday I received in the mail an actual copy of the hardcover, a tangible artifact testifying to the reality of this long-anticipated event. Here it is, rubbing shoulders with a few other well-known bestsellers.

The official release date is January 7. Yes, there will be a Kindle edition; at some point later in January there will even be an audio book. And I’m certainly not going to stop you from ordering it. But my publisher tells me that what would be really great is if a bunch of people ordered it exactly on January 7. So that’s when I’ll really be encouraging you.

Even after the book is out, I don’t want to turn the blog into all book, all the time. But I do want to try a book club experiment, where we go through individual chapters, one week at a time, with me revealing some of the thought processes that went into each chapter and all of us having a back-and-forth discussion. Should be fun!

No formal book tour, but I’ll be doing a few readings and events. Check the Facebook page or book web page for more.

You know, other people talk a lot about time, too — it’s not just me. Here’s a great video from Nature, featuring a conversation between David Gross and Itzhak Fouxon about the existence of time. (Via Sarah Kavassalis.) Itzhak plays the role of the starry-eyed young researcher — he opens the video by telling us how he originally went into physics to impress girls, although apparently he has stuck with it for other reasons. Gross, of course, shared a Nobel Prize for asymptotic freedom, and has become one of the most influential string theorists around. David plays the role of the avuncular elder statesman (I’ve seen him be somewhat more acerbic in his criticisms) — but he’s one of the smartest people in physics, and his admonitions are well worth listening to. He gives some practical advice, but also advises young people to think big.

Unfortunately the video doesn’t seem to be embeddable, but you can go to the video page and click on the “David Gross” entry. (The others are good, too!)

You all know my perspective here — time probably exists, and we should try to understand it rather than replace it. But I’ll agree with David — let’s not ignore more “practical” problems, but not be afraid to tackle the big ideas!