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!

It’s been a mixed bag so far; while I’ve had great fun interacting with people here in Australia, I’ve also been struggling with a nasty cold I picked up on the flight over. Spent yesterday mostly in bed, too fogged up to even work on my talk for Friday. But when I’ve had the strength to be up and about, it’s been a treat. Here’s an iPhone snap of the University of Sydney; that clocktower in the middle houses, appropriately enough, the Centre for Time.

One of the perks of civilization that hasn’t quite caught on in these parts is affordable internet access in hotel rooms, so don’t expect a lot of blogging over the next week or two. Instead, I can point you to a couple of recent videos. One is an extended interview for Edge, entitled Why Does the Universe Look the Way it Does? It is an interview (presented in text and video), not a carefully pre-planned document, so not all thoughts are arranged as elegantly as one might like. Here is some of the flavor:

We are in a very unusual situation in the history of science where physics has become slightly a victim of its own success. We have theories that fit the data, which is a terrible thing to have when you are a theoretical physicist. You want to be the one who invents those theories, but you don’t want to live in a world where those theories have already been invented because then it becomes harder to improve upon them when they just fit the data. What you want are anomalies given to us by the data that we don’t know how to explain.

The other one is a panel discussion on Time Since Einstein, from the World Science Festival. As the description there says, it features Roger Penrose, David Albert, and some other people it would be too exhausting to list individually. Here’s part 1 of 5:

World Science Festival 2009: Time Since Einstein, Part 1 of 5 from World Science Festival on Vimeo.

Now if only my immune system would finish off the little viral buggers inside me, I could get out and see a bit of this interesting country.

Looking online I find basically no research or anything written on this subject, but I am quite certain that just about everyone has some picture of time in their heads. For me, it’s quite a visual one, and past events and for that matter future ones are all attached to my mental picture of the time continuum. My notion of all history, from my own to that of the universe is inextricably linked with my internal mental images of time.

The thing is, as I have reflected on how I actually internally visualize time, I have found it to be somewhat bizarre. Or maybe not – I don’t really know because I haven’t really explored this in one-on-one conversation with others and haven’t learned from anything written out there just how different my picture is from others’. So here goes…I hope those of you out there who are intrigued or inspired by this will share their own images.

The main thing is that my mental picture of time changes depending on the time scale involved, from a microsecond to a minute to an hour, day, week, month, year, or many years. Starting at the largest time scales, those of the cosmos, when I am looking back in time over billions of years I imagine the classical, boring sort of “time as a line” progressing from left to right, straight across my mental image. As we zoom in to more recent cosmological time, though, millions of years, the line becomes more of a curve, and curving toward me. But then, very oddly (and this pattern will repeat itself) when we get to the much more recent past, say the last few thousand years, the curve is revealed to be more of a strip of sorts and moving from down and to the right (that’s the best way I can express it) toward the upper left.

It’s really strange: if I think of a time, say, 20 000 years ago, in my mental field of view it’s definitely off to the right, and as I refer to more recent times, the ribbon is such that more recent times are to the left of earlier times.

But this is not absolute: as we get to the last 2000 or so years, the earlier part is sort of coming straight at me, eventually becoming (you got it) a ribbon coming from the lower left to the upper right again. If I am considering the period from the Renaissance to the present, for example, I see a more distant past as actually more distant, off to the left, coming closer in more recent times an moving left to right. The future, on this time scale, goes off to my right sort of behind me (where I can’t see – duh!)

Okay I have probably lost at least 2/3 of the people who started reading this. Huh? Either this is so alien to how they think of time they don’t really see what I am seeing, or don’t care, or think that this is so off that wall it’s not worth reading further.

So, for the rest of you, the next part is where it gets kind of interesting. My mental timeline/ribbon, which has been snaking from left to right and back across my mental field of view, does a few more twists. As I think of the time scale of my life which began in the early 1960’s (okay, 1959), those early 60’s years are sort of again coming straight at me, becoming a left-to-right ribbon in the 70’s and then definitely right-to-left by the mid 80’s. The years from then to now flow from far away and to the right to nearby toward the left. But they don’t cross the center of my mental picture – that’s the present.

If we zoom in further, say to the past several years, the ribbon is a string of months going back. As I view earlier and earlier months they recede, up and to the right, and merge with the ribbon of the decades. Events, major and minor, are recallable by zooming into my past picture of then-present time. They are all there (the ones I remember, anyway), and freakily often I can remember the exact dates and times they occurred.

Last week to a few months ago is definitely on that ribbon, stretching up and to the right as we go further into the past. But then we get to yesterday, today, and tomorrow. Here the ribbon, which is segmented by lines marking the days, does a weird thing. For a given day, the ribbon starts out straight in front of me, going up, as if I had to climb it, the hours marked off by lines. The ribbon climbs up, into the darkness, reaching a peak and then, after midnight, descending down into the next day, week, month, and year, away from me, off into the distance in the left part of my mental view of time.

The future, the near future anyway (years) is definitely to the left in my mind’s eye. (And no, this whole post is not some sort of allegory of my personal political evolution…) The long term future is unpopulated by memories or images of expectations or hopes, and snakes off to the right.

All this changes when we are talking about smaller time scales. As I zoom into the present hour, to finer and finer scales it becomes more and more a straight line extending from left to right. I can zoom in from here to any micro-time scale and it stays the same. Somehow the left-right snaking curve is attached to particular memories, including my memories of historical events about which I have learned. Micro-time is so non-specific that it doesn’t trigger the snaky ribbon time view.

Another oddity about me in particular is that I actually find it hard to use a standard calendar to keep track of appointments, important meetings etc. I don’t see time on that seven-day table! But with a few anchor dates in the future, gotten from standard calendars, I can quickly calculate intervening dates and their days of the week. If I know I have an appointment on December 4, and an exam to give on December 7, I can see in my head what days they are and I do rather well remembering them. But at this moment, for example, I cannot tell you what day of the week Christmas is (though I know next January 18 is a Monday…)

I know there will be plenty of eye-rolling at this possibly boring description of my mental view of time, but, as I say, I hope it will trigger lots of you out there to share your own. If you really think about it (and I bet you probably have not) you so have *some* sort of picture in your head. What is it?

Yes, that’s a pretty suave picture of me on the image capture. What can I say? I’m just one of those lucky folks with an effortless magic in front of the camera.

If you prefer to get your talks about entropy unadulterated by voice and motion, and don’t mind a more technical presentation, I’ve put the slides from my recent Caltech colloquium online. These are aimed basically at grad students in physics, so there is an equation or two, and the caveats are spelled out more clearly. But the punchline is the same.

NEW YORK — Citing the extremely low level of entropy present before a normal set of football downs, scientists from the NFL’s quantum mechanics and cosmology laboratories spoke Monday of a theoretical proto-down before the first. “Ultimately, we believe there are an infinite number of proto-downs played before the first visible snap,” lead NFL scientist Dr. Oliver Claussen said during a press conference, adding that the very last yocto-down is a by-product of leftover fourth downs from this universe, as well as those from a theoretical universe running along an arrow of time concurrent to our own.

Probably some enthusiastic football coach is going to try to cash in by writing a book about the idea, while others fulminate on the sidelines about how such irresponsible speculation is destroying the game. (Thanks to Ahmet Toker and Tom Fishman.)

“Everything happens to everybody sooner or later if there is time enough.” — George Bernard Shaw, Back to Methuselah

“Time is the longest distance between two places.” — Tennessee Williams, The Glass Menagerie

“The future’s not ours to see.” — Doris Day

“Time rushes toward us with its hospital tray of infinitely varied narcotics, even while it is preparing us for its inevitably fatal operation.” — Tennessee Williams, The Rose Tattoo

“Time, you old gypsy man,
Will you not stay,
Put up your caravan
Just for one day?”
– Ralph Hodgeson

“Time present and time past
Are both perhaps present in time future,
And time future contained in time past.
If all time is eternally present
All time is unredeemable.”
– T.S. Eliot, “Burnt Norton” (Four Quartets)

“Time is the substance from which I am made. Time is a river that carries me along, but I am the river; it is a tiger that devours me, but I am the tiger; it is a fire that consumes me, but I am the fire.” — Jorge Luis Borges, Labyrinths.

Apparently you have to be extremely careful when it comes to poetry; fair use doesn’t necessarily extend very far.

Actually here they are described as “freaky observers,” rather than the more conventional “freak observers.” That description brings to mind Smoove B rather than Ludwig Boltzmann, but who knows? Maybe unlikely thermal fluctuations tend to be pretty kinky.

And yes, before you all start in: we know that Boltzmann Brains don’t really make for a credible alien menace, if you insist on being persnickety about what they supposedly really represent. It’s not that they “perceive” a universe more chaotic than ours — it’s that they would dominate the total number of observers if the universe really were more chaotic than ours. (Which it isn’t!) Also, they would tend to dissolve back into the chaos from which they came, rather than staging a coordinated attack on our homeland. Still! What a novel challenge for the Allies’ greatest hero.

But a solution to the arrow-of-time dilemma would certainly be nice, quantum or otherwise, so the paper has received a bit of attention (Focus, Ars Technica). Unfortunately, I don’t think this paper qualifies.

The arrow-of-time dilemma, you will recall, arises from the tension between the apparent reversibility of the fundamental laws of physics (putting aside collapse of the wave function for the moment) and the obvious irreversibility of the macroscopic world. The latter is manifested by the growth of entropy with time, as codified in the Second Law of Thermodynamics. So a solution to this dilemma would be an explanation of how reversible laws on small scales can give rise to irreversible behavior on large scales.

The answer isn’t actually that mysterious, it’s just unsatisfying. Namely, the early universe was in a state of extremely low entropy. If you accept that, everything else follows from the nineteenth-century work of Boltzmann and others. The problem then is, why should the universe be like that? Why should the state of the universe be so different at one end of time than at the other? Why isn’t the universe just in a high-entropy state almost all the time, as we would expect if its state were chosen randomly? Some of us have ideas, but the problem is certainly unsolved.

So you might like to do better, and that’s what Maccone tries to do in this paper. He forgets about cosmology, and tries to explain the arrow of time using nothing more than ordinary quantum mechanics, plus some ideas from information theory.

I don’t think that there’s anything wrong with the actual technical results in the paper — at a cursory glance, it looks fine to me. What I don’t agree with is the claim that it explains the arrow of time. Let’s just quote the abstract in full:

The arrow of time dilemma: the laws of physics are invariant for time inversion, whereas the familiar phenomena we see everyday are not (i.e. entropy increases). I show that, within a quantum mechanical framework, all phenomena which leave a trail of information behind (and hence can be studied by physics) are those where entropy necessarily increases or remains constant. All phenomena where the entropy decreases must not leave any information of their having happened. This situation is completely indistinguishable from their not having happened at all. In the light of this observation, the second law of thermodynamics is reduced to a mere tautology: physics cannot study those processes where entropy has decreased, even if they were commonplace.

So the claim is that entropy necessarily increases in “all phenomena which leave a trail of information behind” — i.e., any time something happens for which we can possibly have a memory of it happening. So if entropy decreases, we can have no recollection that it happened; therefore we always find that entropy seems to be increasing. Q.E.D.

But that doesn’t really address the problem. The fact that we “remember” the direction of time in which entropy is lower, if any such direction exists, is pretty well-established among people who think about these things, going all the way back to Boltzmann. (Chapter Nine.) But in the real world, we don’t simply see entropy increasing; we see it increase by a lot. The early universe has an entropy of 10⁸⁸ or less; the current universe has an entropy of 10¹⁰¹ or more, for an increase of more than a factor of 10¹³ — a giant number. And it increases in a consistent way throughout our observable universe. It’s not just that we have an arrow of time — it’s that we have an arrow of time that stretches coherently over an enormous region of space and time.

This paper has nothing to say about that. If you don’t have some explanation for why the early universe had a low entropy, you would expect it to have a high entropy. Then you would expect to see small fluctuations around that high-entropy state. And, indeed, if any complex observers were to arise in the course of one of those fluctuations, they would “remember” the direction of time with lower entropy. The problem is that small fluctuations are much more likely than large ones, so you predict with overwhelming confidence that those observers should find themselves in the smallest fluctuations possible, freak observers surrounded by an otherwise high-entropy state. They would be, to coin a pithy phrase, Boltzmann brains. Back to square one.

Again, everything about Maccone’s paper seems right to me, except for the grand claims about the arrow of time. It looks like a perfectly reasonable and interesting result in quantum information theory. But if you assume a low-entropy initial condition for the universe, you don’t really need any such fancy results — everything follows the path set out by Boltzmann years ago. And if you don’t assume that, you don’t really explain our universe. So the dilemma lives on.

But I couldn’t decide between two possible topics, both of which are close to my heart: “The Origin of the Universe” or “The Arrow of Time.” (My original book subtitle was “The Origin of the Universe and the Arrow of Time,” before that was squelched by the marketing department and replaced with “The Quest for the Ultimate Theory of Time.” Quests are big these days, apparently.) So I did the natural thing: I Tweeted the question. And the internet spoke with a fairly unambiguous voice: “Arrow of Time” sounded more interesting. So that’s what I proposed.

And now we’ve just been accepted, so it’s on for San Diego 2010. We have a fantastic line-up of speakers (and also me), spanning quite a range of topics:

• Me, setting the stage about the arrow of time and the Second Law, and drawing some connections to cosmology.
• Huw Price, director of the Centre for Time, Department of Philosophy, University of Sydney, and author of Time’s Arrow and Archimedes’ Point. Huw will be talking about the arrow of time in philosophy.
• Anthony Leggett, winner of the Nobel Prize in 2003 for his work on superfluidity. Tony will be talking about the arrow of time in quantum mechanics and condensed matter physics.
• Michael Lässig, University of Cologne. Michael specializes in statistical physics and quantitative biology, and will be speaking on the arrow of time in biology, in particular in evolution. He recently gave a talk on this topic at the KITP.
• Daniel Schacter, Harvard, author of The Seven Sins of Memory. Dan was the leader of the studies showing that the brain predicts the future in the same way that it remembers the past. He’ll be talking about the arrow of time in psychology.

That’s the fun part about this topic; it ranges naturally from the birth of the universe to the operation of your brain. Should be a good symposium.

Update: Unfortunately, Daniel Schacter won’t be able to make the symposium. Instead, we are very fortunate to have Kathleen McDermott of Washington University in St. Louis. Her research involves how we remember the past and forecast the future.

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.