Blogs / Cosmic Variance

With the new Star Trek out, it’s long past time (as it were) that we laid out the rules for would-be fictional time-travelers. (Spoiler: Spock travels to the past and gets a sex change and becomes Kirk’s grandfather lover.*) Not that we expect these rules to be obeyed; the dramatic demands of a work of fiction will always trump the desire to get things scientifically accurate, and Star Trek all by itself has foisted half a dozen mutually-inconsistent theories of time travel on us. But time travel isn’t magic; it may or may not be allowed by the laws of physics — we don’t know them well enough to be sure — but we do know enough to say that if time travel were possible, certain rules would have to be obeyed. And sometimes it’s more interesting to play by the rules. So if you wanted to create a fictional world involving travel through time, here are 10+1 rules by which you should try to play.

0. There are no paradoxes.

This is the overarching rule, to which all other rules are subservient. It’s not a statement about physics; it’s simply a statement about logic. In the actual world, true paradoxes — events requiring decidable propositions to be simultaneously true and false — do not occur. Anything that looks like it would be a paradox if it happened indicates either that it won’t happen, or our understanding of the laws of nature is incomplete. Whatever laws of nature the builder of fictional worlds decides to abide by, they must not allow for true paradoxes.

1. Traveling into the future is easy.

We travel into the future all the time, at a fixed rate: one second per second. Stick around, you’ll be in the future soon enough. You can even get there faster than usual, by decreasing the amount of time you experience elapsing with respect to the rest of the world — either by low-tech ways like freezing yourself, or by taking advantage of the laws of special relativity and zipping around near the speed of light. (Remember we’re talking about what is possible according to the laws of physics here, not what is plausible or technologically feasible.) It’s coming back that’s hard.

2. Traveling into the past is hard — but maybe not impossible.

If Isaac Newton’s absolute space and time had been the correct picture of nature, we could simply say that traveling backwards in time was impossible, and that would be the end of it. But in Einstein’s curved-spacetime universe, things are more flexible. From your own personal, subjective point of view, you always more forward in time — more technically, you move on a timelike curve through spacetime. But the large-scale curvature of spacetime caused by gravity could, conceivably, cause timelike curves to loop back on themselves — that is to say, become closed timelike curves — such that anyone traveling on such a path would meet themselves in the past. That’s what respectable, Einstein-approved time travel would really be like. Of course, there’s still the little difficulty of warping spacetime so severely that you actually create closed timelike curves; nobody knows a foolproof way of doing that, or even whether it’s possible, although ideas involving wormholes and cosmic strings and spinning universes have been bandied about.

3. Traveling through time is like traveling through space.

I’m only going to say this once: there would be no flashing lights. At least, there would only be flashing lights if you brought along some strobes, and decided to start them flashing as you traveled along your closed timelike curve. Likewise, there is no disappearance in a puff of smoke and re-appearing at some other time. Traveling through time is just like traveling through space: you move along a certain path, which (we are presuming) the universe has helpfully arranged so that your travels bring you to an earlier moment in time. But a time machine wouldn’t look like a booth with spinning wheels that dematerializes now and rematerializes some other time; it would look like a rocket ship. Or possibly a DeLorean, in the unlikely event that your closed timelike curve started right here on Earth and never left the road.

Think of it this way: imagine there were a race of super-intelligent trees, who could communicate with each other using abstract concepts but didn’t have the ability to walk. They might fantasize about moving through space, and in their fantasies “space travel” would resemble teleportation, with the adventurous tree disappearing in a puff of smoke and reappearing across the forest. But we know better; real travel from one point to another through space is a continuous process. Time travel would be like that.

4. Things that travel together, age together.

If you travel through time, and you bring along with you some clocks or other objects, all those things experience time in exactly the same way that you do. In particular, both you and the clocks march resolutely forward in time, from your own perspective. You don’t see clocks spinning wildly backwards, nor do you yourself “age” backwards, and you certainly don’t end up wearing the clothes you favored back in high school. Your personal experience of time is governed by clocks in your brain and body — the predictable beating of rhythmic pulses of chemical and biological processes. Whatever flow of time is being experienced by those processes — and thus by your conscious perception — is also being experienced by whatever accompanies you on your journey.

5. Black holes are not time machines.

Sadly, if you fell into a black hole, it would not spit you out at some other time. It wouldn’t spit you out at all — it would gobble you up and grow slightly more corpulent in the process. If the black hole were big enough, you might not even notice when you crossed the point of no return defined by the event horizon. But once you got close to the center of the hole, tidal forces would tug at you — gently at first, but eventually tearing you apart. The technical term is spaghettification. Not a recommended strategy for would-be time adventurers.

Wormholes — tunnels through spacetime, which in principle can connect widely-separated events — are a more promising alternative. Wormholes are to black holes as elevators are to deep wells filled with snakes and poisoned spikes. The problem is, unlike black holes, we don’t know whether wormholes exist, or even whether they can exist, or how to make them, or how to preserve them once they are made. Wormholes want to collapse and disappear, and keeping them open requires a form of negative energies. Nobody knows how to make negative energies, although they occasionally slap the name “exotic matter” on the concept and pretend it might exist.

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Since no one is blogging around here, and I’m still working on my book, I will cheat and just post an excerpt from the manuscript. Not an especially original one, either; in this section I steal shamelessly from the nice paper that Ted Bunn wrote last year about evolution and entropy (inspired by an previous paper by Daniel Styer).

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Without even addressing the question of how “life” should be defined, we can ask what sounds like a subsequent question: does life make thermodynamic sense? The answer, before you get too excited, is “yes.” But the opposite has been claimed – not by any respectable scientists, but by creationists looking to discredit Darwinian natural selection as the correct explanation for the evolution of life on Earth. One of their arguments relies on a misunderstanding of the Second Law, which they read as “entropy always increases,” and then interpret as a universal tendency toward decay and disorder in all natural processes. Whatever life is, it’s pretty clear that life is complicated and orderly – how, then, can it be reconciled with the natural tendency toward disorder?

There is, of course, no contradiction whatsoever. The creationist argument would equally well imply that refrigerators are impossible, so it’s clearly not correct. The Second Law doesn’t say that entropy always increases. It says that entropy always increases (or stays constant) in a closed system, one that doesn’t interact noticeably with the external world. But it’s pretty obvious that life is not like that; living organisms interact very strongly with the external world. They are the quintessential examples of open systems. And that is pretty much that; we can wash our hands of the issue and get on with our lives.

But there’s a more sophisticated version of the argument, which you could imagine being true – although it still isn’t – and it’s illuminating (and fun) to see exactly how it fails. The more sophisticated argument is quantitative: sure, living beings are open systems, so in principle they can decrease entropy somewhere as long as it increases somewhere else. How do you know that the increase in entropy in the outside world is really enough to account for the low entropy of living beings?

As we mentioned way back in Chapter Two, the Earth and its biosphere are systems that are very far away from thermal equilibrium. In equilibrium, the temperature is the same everywhere, whereas when we look up we see a very hot Sun in an otherwise very cold sky. There is plenty of room for entropy to increase, and that’s exactly what’s happening. But it’s instructive to run the numbers.

The energy budget of the Earth, considered as a single system, is pretty simple. We get energy from the Sun, via radiation; we lose the same amount of energy to empty space, also via radiation. (Not exactly the same; processes such as nuclear decays also heat up the Earth and leak energy into space, and the rate at which energy is radiated is not strictly constant. Still, it’s an excellent approximation.) But while the amount is the same, there is a big difference in the quality of the energy we get and the energy we give back. Remember back in the pre-Boltzmann days, entropy was understood as a measurement of the uselessness of a certain amount of energy; low-entropy forms of energy could be put to useful work, such as powering an engine or grinding flour, while high-entropy forms of energy just sat there.

The energy we get from the Sun is of a low-entropy, useful form, while the energy we radiate back out into space has a much higher entropy. The temperature of the Sun is about twenty times the average temperature of the Earth. The temperature of radiation is just the average energy of the photons of which it is made, so the Earth needs to radiate twenty low-energy (long-wavelength, infrared) photons for every one high-energy (short-wavelength, visible) photon it receives. It turns out, after a bit of math, that twenty times as many photons directly translates into twenty times the entropy. The Earth emits the same amount of energy as it receives, but with twenty times higher entropy.

The hard part is figuring out just what we mean when we say that the life forms here on Earth are “low-entropy.” How exactly do we do the coarse-graining? It is possible to come up with reasonable answers to that question, but it’s complicated. Fortunately, there is a dramatic shortcut we can take. Consider the entire biomass of the Earth – all of the molecules that are found in living organisms of any type. We can easily calculate the maximum entropy that collection of molecules could have, if it were in thermal equilibrium; plugging in the numbers (the biomass is 10¹⁵ kilograms, the temperature of the Earth is 255 Kelvin), we find that its maximum entropy is 10⁴⁴. And we can compare that to the absolute minimum entropy it could have – if it were in an exactly unique state, the entropy would be precisely zero.

So the largest conceivable change in entropy that would be required to take a completely disordered collection of molecules the size of our biomass and turn them into absolutely any configuration at all – including the actual ecosystem we currently have – is 10⁴⁴. If the evolution of life is consistent with the Second Law, it must be the case that the Earth has generated more entropy over the course of life’s evolution by converting high-energy photons into low-energy ones than it has decreased entropy by creating life. The number 10⁴⁴ is certainly an overly generous estimate – we don’t have to generate nearly that much entropy, but if we can generate that much, the Second Law is in good shape.

How long does it take to generate that much entropy by converting useful solar energy into useless radiated heat? The answer, once again plugging in the temperature of the Sun and so forth, is: about one year. Every year, if we were really efficient, we could take an undifferentiated mass as large as the entire biosphere and arrange it in a configuration with as small an entropy as we can imagine. In reality, life has evolved over billions of years, and the total entropy of the “Sun + Earth (including life) + escaping radiation” system has increased by quite a bit. So the Second Law is perfectly consistent with life as we know it; not that you were ever in doubt.

His Brains, anyway. (Which he never talked about himself, but that’s neither here nor there.) Random fluctuations make an appearance in Dilbert. (Hat tip Nick Suntzeff.)

One can only wonder what Calvin and Hobbes could have done with this.

There’s a major event in the life of every young book that marks its progression from mere draft on someone’s computer to a public figure in its own right. No, I’m not thinking about when the book gets published, or even when the final manuscript is sent to the publisher. I’m thinking of when a book gets its own page on amazon.com. (The right analogy is probably to “getting your drivers license” or something along those lines. Feel free to concoct your own details.)

So it’s with a certain parental joy that I can announce From Eternity to Here now has its own amazon page. My baby is all grown up! And, as a gesture of independence, has already chosen a different subtitle: “The Quest for the Ultimate Theory of Time.” The previous version, “The Origin of the Universe and the Arrow of Time,” was judged a bit too dry, and was apparently making the marketing people at Dutton scrunch up their faces in disapproval. I am told that “quests” are very hot right now.

All of which means, of course: you can buy it! For quite a handsome discount, I may add.

It also means: I really should finish writing it. Pretty darn close; the last chapters are finished, and I’m just touching up a couple of the previous ones that were abandoned in my rush to tell the end of the story. The manuscript is coming in at noticeably more words than I had anticipated — I suspect the “320 pages” listed on amazon is an underestimate.

And, yes, there is another book with almost the same title and an eerily similar cover, which just appeared. But very different content inside! Frank Viola’s subtitle is “Rediscovering the Ageless Purpose of God,” which should be a clue to the sharp-eyed shopper that the two works are not the same.

Writing a book is a big undertaking, in case no one before me had never noticed that before. I’m very grateful to my scientific collaborators for putting up with my extended disappearances along the way. It’s also very nerve-wracking to imagine sending it out there into the world all by itself. With blog posts there is immediate feedback in terms of comments and trackbacks; you can get a feel for what the reactions are, and revise and respond accordingly. But the book really has a life of its own. People will read and review it for goodness knows how long, and I won’t always be there to protect it.

Frankly, I’m not sure this “book” technology will ever catch on.

Because of the growth of entropy, we have a very different epistemic access to the past than to the future. In retrodicting the past, we have recourse to “memories” and “records,” which we can take as mostly-reliable indicators of events that actually happened. But when it comes to the future, the best we can do is extrapolate, without nearly the reliability that we have in reconstructing the past.

However — the human brain, as most readers of this blog probably know, was not intelligently designed. It’s doesn’t have the high-level structure of a computer program, where all the processes are carefully planned to achieve some goal. (The lower-level structures share the mechanical features of any other physical system, but that’s of little help here.) Evolution nudges the genome in useful directions, but it can only work with the raw materials it’s given; it doesn’t have the luxury of starting from scratch. So over and over in biological organisms, we find features that were originally developed for one purpose being re-engineered for something else.

As it turns out, the way that the human brain goes about the task of “remembering the past” is actually very similar to how it goes about “imagining the future.” Deep down, these are activities with very different functions and outcomes — predicting the future is a lot less reliable, for one thing. But in both cases, the brain goes through more or less the same routine.

That’s what Daniel Schacter at Harvard and his friends have discovered, by doing functional MRI studies of brains subjected to different kinds of cues. (Science News report, Nature review article, Charlie Rose interview.) Subjects are inserted gently into the giant magnetic field, then asked to either conjure up a memory or imagine a future scenario about some particular cue-word. What you see is that the same sites in the brain light up in both cases. The brain on the left in this image is remembering the past — on the right, it’s concocting an imaginary scenario about the future.

Further confirmation comes from studies of amnesiacs, who famously can’t remember the past. But if you ask the right questions, you find that they also have significant problems imagining their own future.

We tend to assume that the brain must be like a computer — when we want to access a memory, we simply pull up a “file” stored somewhere on the brain’s hard drive, and take a look at its contents. But that’s not it at all. Schacter believes that pieces of data relevant to any particular memory — times, images, sounds — are stored piecemeal in different parts of the brain. When we want to “remember” something, another part of the brain assembles these pieces into a (hopefully) coherent picture. It’s like running a new simulation every time you need a memory, and it’s the same thing we do when we try to imagine some event in the future.

Everyone has heard that memories can be unreliable, but many of us don’t appreciate the extent to which that is true. It’s not the case that “real” memories are stored once and for all deep in the darkest recesses of the brain, and it’s just a matter of digging them up. False memories — conjured from any number of sources, from gradual embellishment to direct suggestion by others — seem precisely as vivid and real to us as accurate memories do. For a good reason: the brain uses the same tools to construct the memory from the available raw materials. A novel and a history book look the same on the printed page.

I’m happy to announce that the first review of From Eternity to Here has appeared, over at Michael Bérubé’s blog. It has also appeared at Crooked Timber, a phenomenon that can ultimately traced to the holographic non-locality inherent in quantum descriptions of space as well as time.

Readers of underdeveloped imagination will wonder how a review could appear when the book has not yet been written. When one has mastered the mysteries of time, should anyone be surprised?

You know what the world really needs? A good book about time. Google tells me there are only about one and a half million such books right now, but I think you’ll agree that one more really good one is called for.

So I’m writing one. From Eternity to Here: The Quest for the Ultimate Theory of Time is a popular-level book on time, entropy, and their connections to cosmology, to be published by Dutton. Hopefully before the end of this year! I’ve been plugging away at it, and have shifted almost into full-time book-writing mode now. (Note to collaborators: I promise not to abandon you entirely.)

I have my own idiosyncratic ideas about how to account for the arrow of time in cosmology, but those are going to be confined to passing mentions in the last chapter. Mostly I’ll be discussing basic ideas that most experts agree are true, or true ideas that everyone should agree on even if perhaps they don’t quite yet, or the implications of those ideas for knotty questions in cosmology. Hopefully we can at least shift the conventional wisdom a little bit.

Naturally there is a web page with some details. Here is the tentative table of contents, although I’ve been cutting and pasting pretty vigorously, so who knows how it will end up looking once all is said and done. One thing is for sure, some of these chapter titles need sprucing up.

0. Prologue

Part One: Time, Experience, and the Universe

1. The Heavy Hand of Entropy
2. The Beginning and End of Time
3. The Past is Present Memory

Part Two: Einstein’s Universe

4. Time is Personal
5. Time is Flexible
6. Looping Through Time

Part Three: Distinguishing the Past from the Future

7. Running Backwards
8. Entropy and Disorder
9. Information and Life
10. Recurrent Nightmares
11. Quantum Time

Part Four: Natural and Unnatural Spacetimes

12. Black Holes
13. The Life of the Universe
14. The Past Through Tomorrow
15. Epilogue: From the Universe to the Kitchen
    Appendix:  Math

If anyone out there is friends with Oprah, maybe drop her a line suggesting that this would make a good book-club choice. I hear that’s helpful when it comes to sales.

Update: And now you can buy it.

The Boltzmann Brain paradox is an argument against the idea that the universe around us, with its incredibly low-entropy early conditions and consequential arrow of time, is simply a statistical fluctuation within some eternal system that spends most of its time in thermal equilibrium. You can get a universe like ours that way, but you’re overwhelmingly more likely to get just a single galaxy, or a single planet, or even just a single brain — so the statistical-fluctuation idea seems to be ruled out by experiment. (With potentially profound consequences.)

The first invocation of an argument along these lines, as far as I know, came from Sir Arthur Eddington in 1931. But it’s a fairly straightforward argument, once you grant the assumptions (although there remain critics). So I’m sure that any number of people have thought along similar lines, without making a big deal about it.

One of those people, I just noticed, was Richard Feynman. At the end of his chapter on entropy in the Feynman Lectures on Physics, he ponders how to get an arrow of time in a universe governed by time-symmetric underlying laws.

So far as we know, all the fundamental laws of physics, such as Newton’s equations, are reversible. Then were does irreversibility come from? It comes from order going to disorder, but we do not understand this until we know the origin of the order. Why is it that the situations we find ourselves in every day are always out of equilibrium?

Feynman, following the same logic as Boltzmann, contemplates the possibility that we’re all just a statistical fluctuation.

One possible explanation is the following. Look again at our box of mixed white and black molecules. Now it is possible, if we wait long enough, by sheer, grossly improbable, but possible, accident, that the distribution of molecules gets to be mostly white on one side and mostly black on the other. After that, as time goes on and accidents continue, they get more mixed up again.

Thus one possible explanation of the high degree of order in the present-day world is that it is just a question of luck. Perhaps our universe happened to have had a fluctuation of some kind in the past, in which things got somewhat separated, and now they are running back together again. This kind of theory is not unsymmetrical, because we can ask what the separated gas looks like either a little in the future or a little in the past. In either case, we see a grey smear at the interface, because the molecules are mixing again. No matter which way we run time, the gas mixes. So this theory would say the irreversibility is just one of the accidents of life.

But, of course, it doesn’t really suffice as an explanation for the real universe in which we live, for the same reasons that Eddington gave — the Boltzmann Brain argument.

We would like to argue that this is not the case. Suppose we do not look at the whole box at once, but only at a piece of the box. Then, at a certain moment, suppose we discover a certain amount of order. In this little piece, white and black are separate. What should we deduce about the condition in places where we have not yet looked? If we really believe that the order arose from complete disorder by a fluctuation, we must surely take the most likely fluctuation which could produce it, and the most likely condition is not that the rest of it has also become disentangled! Therefore, from the hypothesis that the world is a fluctuation, all of the predictions are that if we look at a part of the world we have never seen before, we will find it mixed up, and not like the piece we just looked at. If our order were due to a fluctuation, we would not expect order anywhere but where we have just noticed it.

After pointing out that we do, in fact, see order (low entropy) in new places all the time, he goes on to emphasize the cosmological origin of the Second Law and the arrow of time:

We therefore conclude that the universe is not a fluctuation, and that the order is a memory of conditions when things started. This is not to say that we understand the logic of it. For some reason, the universe at one time had a very low entropy for its energy content, and since then the entropy has increased. So that is the way toward the future. That is the origin of all irreversibility, that is what makes the processes of growth and decay, that makes us remember the past and not the future, remember the things which are closer to that moment in history of the universe when the order was higher than now, and why we are not able to remember things where the disorder is higher than now, which we call the future.

And he closes by noting that our understanding of the early universe will have to improve before we can answer these questions.

This one-wayness is interrelated with the fact that the ratchet [a model irreversible system discussed earlier in the chapter] is part of the universe. It is part of the universe not only in the sense that it obeys the physical laws of the universe, but its one-way behavior is tied to the one-way behavior of the entire universe. It cannot be completely understood until the mystery of the beginnings of the history of the universe are reduced still further from speculation to scientific understanding.

We’re still working on that.

The important event this Dec. 25 isn’t celebrating the birthday of Isaac Newton or other historical figures, it’s the release of The Curious Case of Benjamin Button, a David Fincher film starring Brad Pitt and based on the story by F. Scott Fitzgerald. As you all know, it’s a story based on the device of incompatible arrows of time: Benjamin is born old and ages backwards into youth (physically, not mentally), while the rest of the world behaves normally. Some have pretended that scientific interest in the movie centers on issues of aging and longevity, but of course it’s thermodynamics and entropy that take center stage. While entropy increases and the Second Law is respected in the rest of the world, Benjamin Button’s body seems to be magically decreasing in entropy. (Which does not, strictly speaking, violate the Second Law, since his body isn’t a closed system, but it sure is weird.)

It’s a great opportunity to address an old chestnut: why do arrows of time have to be compatible? Why can’t we imagine ever discovering another galaxy in which entropy increased toward (what we call) the past instead of the future, as in Greg Egan’s story, “The Hundred Light-Year Diary”? Or why can’t a body age backwards in time?

First we need to decide what the hell we mean. Let’s put aside for the moment sticky questions about collapsing wave functions, and presume that the fundamental laws of physics are perfectly reversible. In that case, given the precise state of the entire universe (or any closed system) at any one moment in time, we can use those laws to determine what the state will be at any future time, or what it was at any past time. That’s just how awesome the laws of physics are. (Of course we don’t know the laws, nor the state of the entire universe, nor could we actually carry out the relevant calculation even if we did, but we’re doing thought experiments here.) We usually take that time to be the “initial” time, but in principle we could choose any time — and in the present context, when we’re worried about arrows of time pointing in different directions, there is no time that is initial for everything. So what we mean is: Why is it difficult/impossible to choose a state of the universe with the property that, as we evolve it forward in time, some parts of it have increasing entropy and some parts have decreasing entropy?

Notice that we can choose conditions that reverse the arrow of time for some individual isolated system. Entropy counts the “typicalness” of the system’s microscopic state, from the point of view of macroscopic observers. And it tends to go up, because there are many more ways to be high-entropy than low entropy. Consider a box of gas, in which the gas molecules are (by some means) all bunched together in the middle of the box, in a low-entropy configuration. If we just let it evolve, the molecules will move around, colliding with each other and with the walls of the box, and ending up (with overwhelmingly probability) in a much higher-entropy configuration.

It’s easy to convince ourselves that there exists some configurations from which the entropy would spontaneously go down. For example, take the state of the above box of gas at any moment after it has become high-entropy, and consider the state in which all of the molecules have exactly the same positions but precisely reversed velocities. From there, the motion of the molecules will precisely re-trace the path that they took from the previous low-entropy state. To an external observer, it will look as if the entropy is spontaneously decreasing. (Of course we know that it took a lot of work to so precisely reverse all of those velocities, and the process of doing so increased the entropy of the wider world, so the Second Law is safe.)

But a merely reversed arrow of time is not the point; we want incompatible arrows of time. That means entropy increasing in some part of the universe while it is decreasing in others.

At first it would seem simple enough. Take two boxes, and prepare one of them in the low entropy state with gas in the middle, and the other in the delicately constructed state with reversed velocities. (That is, the two boxes on the left side of the two figures above.) The entropy will go up in one box, and down in the other, right? That’s true, but it’s kind of trivial. We need to have systems that interact — one system can somehow communicate with the other.

And that ruins everything, of course. Imagine we started with these two boxes, one of which had an entropy that was ready to go up and the other ready to go down. But now we introduced a tiny coupling — say, a few photons moving between the boxes, bouncing off a molecule in one before returning to the other. Certainly the interaction of Benjamin Button’s body with the rest of the world is much stronger than that. (Likewise Egan’s time-reversed galaxy, or Martin Amis’s narrator in Time’s Arrow.)

That extra little interaction will slightly alter the velocities of the molecules with which it interacts. (Momentum is conserved, so it has no choice.) That’s no problem for the box that starts with low entropy, as there is no delicate tuning required to make the entropy go up. But it completely ruins our attempt to set up conditions in the other box so that entropy goes down. Just a tiny change in velocity will quickly propagate through the gas, as one affected molecule hits another molecule, and then they hit two more, and so on. It was necessary for all of the velocities to be very precisely aligned to make the gas miraculously conspire to decrease its entropy, and any interaction we might want to introduce will destroy the required conspiracy. The entropy in the first box will very sensibly go up, while the entropy in the other will just stay high. You can’t have incompatible arrows of time among interacting subsystems of the universe.

The Foundational Questions Institute is sponsoring an essay competition on “The Nature of Time.” Needless to say, I’m in. It’s as if they said: “Here, you keep talking about this stuff you are always talking about anyway, except that we will hold out the possibility of substantial cash prizes for doing so.” Hard to resist.

The deadline for submitting an entry is December 1, so there’s still plenty of time (if you will), for anyone out there who is interested and looking for something to do over Thanksgiving. They are asking for essays under 5000 words, on any of various aspects of the nature of time, pitched “between the level of Scientific American and a review article in Science or Nature.” That last part turns out to be the difficult one — you’re allowed to invoke some technical concepts, and in fact the essay might seem a little thin if you kept it strictly popular, but hopefully it should be accessible to a large range of non-experts. Most entries seem to include a few judicious equations while doing their best to tell a story in words.

All of the entries are put online here, and each comes with its own discussion forum where readers can leave comments. A departure from the usual protocols of scientific communication, but that’s a good thing. (Inevitably there is a great deal of chaff along with the wheat among the submitted essays, but that’s the price you pay.) What is more, in addition to a judging by a jury of experts, there is also a community vote, which comes with its own prizes. So feel free to drop by and vote for mine if you like — or vote for someone else’s if you think it’s better. There’s some good stuff there.

My essay is called “What if Time Really Exists?” A lot of people who think about time tend to emerge from their contemplations and declare that time is just an illusion, or (in modern guise) some sort of semi-classical approximation. And that might very well be true. But it also might not be true; from our experiences with duality in string theory, we have explicit examples of models of quantum gravity which are equivalent to conventional quantum-mechanical systems obeying the time-dependent Schrödinger equation with the time parameter right there where Schrödinger put it.

And from that humble beginning — maybe ordinary quantum mechanics is right, and there exists a formulation of the theory of everything that takes the form of a time-independent Hamiltonian acting on a time-dependent quantum state defined in some Hilbert space — you can actually reach some sweeping conclusions. The fulcrum, of course, is the observed arrow of time in our local universe. When thinking about the low-entropy conditions near the Big Bang, we tend to get caught up in the fact that the Bang is a singularity, forming a boundary to spacetime in classical general relativity. But classical general relativity is not right, and it’s perfectly plausible (although far from inevitable) that there was something before the Bang. If the universe really did come into existence out of nothing 14 billion years ago, we can at least imagine that there was something special about that event, and there is some deep reason for the entropy to have been so low. But if the ordinary rules of quantum mechanics are obeyed, there is no such thing as the “beginning of time”; the Big Bang would just be a transitional stage, for which our current theories don’t provide an adequate spacetime interpretation. In that case, the observed arrow of time in our local universe has to arise dynamically according to the laws of physics governing the evolution of a wave function for all eternity.

Interestingly, that has important implications. If the quantum state evolves in a finite-dimensional Hilbert space, it evolves ergodically through a torus of phases, and will exhibit all of the usual problems of Boltzmann brains and the like (as Dyson, Kleban, and Susskind have emphasized). So, at the very least, the Hilbert space (under these assumptions) must be infinite-dimensional. In fact you can go a bit farther than that, and argue that the spectrum of energy eigenvalues must be arbitrarily closely spaced — there must be at least one accumulation point.

Sexy, I know. The remarkable thing is that you can say anything at all about the Hilbert space of the universe just by making a few simple assumptions and observing that eggs always turn into omelets, never the other way around. Turning it into a respectable cosmological model with an explicit spacetime interpretation is, admittedly, more work, and all we have at the moment are some very speculative ideas. But in the course of the essay I got to name-check Parmenides, Heraclitus, Lucretius, Augustine, and Nietzsche, so overall it was well worth the effort.