Time

After the FQXi Essay Contest, I was asked to comment on some of the essays besides my own, but I never did. Mostly because I didn’t take the time to read them all (there were an awful lot), but also because I just don’t know what to say about many of them. In her essay (which I liked), Fotini Markopoulou divides the world in two:

There are two kinds of people in quantum gravity. Those who think that timelessness is the most beautiful and deepest insight in general relativity, if not modern science, and those who simply cannot comprehend what timelessness can mean and see evidence for time in everything in nature. What sets this split of opinions apart form any other disagreement in science is that almost no one ever changes their mind…

That’s just about right (although perhaps there are also other splits with the same quality). Julian Barbour, whose essay finished first in the judging, has famously championed the view that time does not exist, even writing quite a successful book about it. In a recent Bloggingheads discussion with Craig Callender, Barbour talks a bit more about his view.

To which all I can muster is: I don’t get it. There are a set of technical arguments, which for the most part I do get, that can be used to make it seem as if time does not exist. In ordinary classical mechanics, we can perform some formal tricks to remove the time variable from the conventional equations of physics. More dramatically, in general relativity or quantum gravity we can express Einstein’s equation (at least in certain circumstances) in a form where time does not appear. On the other hand, we can usually re-write any of these equations in a form where time does appear (at least, again, in certain circumstances).

But none of these technical arguments are really the point. What I don’t understand — and this is a sincere lack of understanding on my part, not an indirect claim that this perspective is wrong — is what’s supposed to be so great about timelessness. What are we supposed to gain from thinking in this way? What problems is it supposed to solve?

Put it this way: clearly time appears to exist, at first glance. Even the timelessness crowd somehow manages to submit their essay competition entries by the deadline, and finish their Bloggingheads dialogues within an hour. So the claim “time does not exist” certainly doesn’t mean the same kind of thing as “unicorns do not exist.” It must mean (I suppose) that, while we all find time very useful in our everyday lives, there is a deeper level of description in which time doesn’t appear at all; it only emerges in some sort of approximate description of reality. But that approximate description seems extremely valid and useful, including all of the phenomena in the observable universe. Surely it behooves us to take this purportedly-non-fundamental notion seriously, and attempt to understand some of its puzzling features? Moreover, even if “time” doesn’t turn out to be fundamental, why would that tempt you into saying that it doesn’t exist? Protons are made of quarks, but you don’t hear particle physicists going around claiming that protons don’t exist.

The problem is not that I disagree with the timelessness crowd, it’s that I don’t see the point. I am not motivated to make the effort to carefully read what they are writing, because I am very unclear about what is to be gained by doing so. If anyone could spell out straightforwardly what I might be able to understand by thinking of the world in the language of timelessness, I’d be very happy to re-orient my attitude and take these works seriously.

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.

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.

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.