Here are the slides from the physics colloquium I gave at UC Santa Cruz last week, entitled “Why is the Past Different from the Future? The Origin of the Universe and the Arrow of Time.” (Also in pdf.)
The real reason I’m sharing this with you is because this talk provoked one of the best responses I’ve ever received, which the provokee felt moved to share with me:
Finally, the magnitude of the entropy of the universe as a function of time is a very interesting problem for cosmology, but to suggest that a law of physics depends on it is sheer nonsense. Carroll’s statement that the second law owes its existence to cosmology is one of the dummest [sic] remarks I heard in any of our physics colloquia, apart from [redacted]’s earlier remarks about consciousness in quantum mechanics. I am astounded that physicists in the audience always listen politely to such nonsense. Afterwards, I had dinner with some graduate students who readily understood my objections, but Carroll remained adamant.
My powers of persuasion are apparently not always fully efficacious.
Also, that marvelous illustration of entropy in the bottom right of the above slide? Alan Guth’s office.
Update: Originally added as a comment, but I’m moving it up here–
The point of the “objection” is extremely simple, as is the reason why it is irrelevant. Suppose we had a thermodynamic system, described by certain macroscopic variables, not quite in equilibrium. Suppose further that we chose a random microstate compatible with the macroscopic variables (as you do, for example, in a numerical simulation). Then, following the evolution of that microstate into the future, it is overwhelmingly likely that the entropy will increase. Voila, we have “derived” the Second Law.
However, it is also overwhelmingly likely that evolving that microstate into the past will lead to an increase in entropy. Which is not true of the universe in which we live. So the above exercise, while it gets the right answer for the future, is not actually “right,” if what we care about is describing the real world. Which I do. If we want to understand the distribution function on microstates that is actually true, we need to impose a low-entropy condition in the past; there is no way to get it from purely time-symmetric assumptions.
Boltzmann’s H-theorem, while interesting and important, is even worse. It makes an assumption that is not true (molecular chaos) to reach a conclusion that is not true (the entropy is certain, not just likely, to increase toward the future — and also to the past).
The nice thing about stat mech is that almost any distribution function will work to derive the Second Law, as long as you don’t put some constraints on the future state. That’s why textbook stat mech does a perfectly good job without talking about the Big Bang. But if you want to describe why the Second Law actually works in the real world in which we actually live, cosmology inevitably comes into play.
Ah, I know that office well. What is remarkable is that, although one would think, every time one enters the office, that it must be in the state of maximum entropy, the next time one is in there, one finds that the second law has indeed led to some evolution.
How I wish I could get that kind of audience response! (-:
I attended a talk a few weeks ago by Jack Cowan, who was presenting to the MIT neuroscience crowd some research he and his students had done on a “toy model” of the human cortex. (Announcement and abstract of talk are available here.) Some of his calculational techniques derived from quantum field theory, including something about “Reggeonic fields” I didn’t understand — apparently those have something to do with the states you get from quantizing the bosonic string, which have angular momentum proportional to the square of the energy.
At the beginning of his talk, Prof. Cowan explicitly distanced himself from Penrose, saying that the brain is just too warm for quantum effects to apply. Philosophically, I suppose, his work is analogous to inventing a new and better technique of long division while working on quantum-physics problems, and then applying that long-division technique to other situations.
[To the Esteemed Blog Host: feel free to redact any names mentioned in this post, should discretion so mandate.]
Do tell … what WERE the objections of your provokee to your “dummest remarks”?
Of course, if you think that the quantum wave function is somehow “real” then time is unidirectional: the wave function from an emitter is an expanding spherical shell (or some such, which variations are not relevant.) Then, when it “collapses” the bubble pops in effect and the particle is re-localized. Running that whole picture backwards does not look the same, no matter how reversible the emission and reception events themselves are. Well, any implications to that? Even if you don’t accept much literalism to the WF itself, it is supposed to represent what could really happen there…
BTW, about thermodynamics: Why the heck should unrelated (?) laws like those of optics be forced by nature to serve the interest of preserving a law (Thermo 2) based on jiggling atoms? I mean, for example that you can’t (?) design a mirror or lens system that would focus an image to such short f-ratio that the surface brightness would exceed that of the source, meaning you could heat the target to higher temperature than the source. I had fun arguing about this in Usenet, but no one really answered that question – it was just more of the same unimaginative circular argument that what’s true is true and that’s that.
(PS – With all the strident arguments about whether God is “real” and such lately – of which I am proud to have disseminated many of stupefying grandeur – I hate to break it to you folks just how tricky and fuzzy a “predicate” or whatever that adjective (?!) is anyway… Please look up “modal realism” in Wikipedia and read it while having some stiff drinks or etc.)
tyrannogenius
Good to see you doing something interesting.
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That’s astonishing someone actually made such a blunt remark. Were you completely taken back?
By the way, thanks for the link to your slides. *I* find these ideas fascinating. I hope do do some work myself on these crazy ideas that cosmologists claim.
“Afterwards, I had dinner with some graduate students who readily understood my objections, but Carroll remained adamant.”
LOL! Sane graduate students know enough about political science to avoid telling the king that he is nekkid. That said, I find Sean’s argument weak. I wonder what the quoted objecter wrote before “Finally …”
I can think of a couple of reasons that Sean’s critic might not be impressed, for example the fact that Sean’s origins for low entropy universes seem rather speculative and perhaps also the fact that Sean isn’t really deriving the second law from cosmology – he’s just trying to explain why entropy might have been lower in the past.
What I wonder is whether the fact that the fine-grained entropy doesn’t change is relevant or interesting.
Sean, thank you for your talk! You gave structure to an important question that’s been on everyone’s back shelf. As for that particular professor, well, he does that to nearly everyone – I think everyone else enjoyed the talk.
I’ll second Scott O’s comment: what were the objections? Just curious.
Personally though, I think the best explanation for entropy was one I got from my chemistry professor freshman year, which went something like this: “Think of how whenever you throw a party you make sure everything is nice and neat, but when your friends come over the place gets trashed. It’s not really anyone’s fault, just someone drops a few chips, someone else steps on them, someone else spills a drink, and that’s the way of things.
“Now imagine that instead for a party you started with your apartment completely trashed, and everyone instead decided to come party by cleaning it up, leaving it nicer than when they came. This just doesn’t happen, it’s against the laws of nature!”
Ok, not very scientific, but I promise you there is no better way to explain it to college students! 😉
“Afterwards, I had dinner with some graduate students who readily understood my objections, but Carroll remained adamant.”
lol, I wonder which graduate student(s) he could be referring to. As a graduate student who was at that table, I can speak for myself and at least 3 others who were there when I say that our reaction to said provoker’s “objections” was quite the opposite. An obvious misconception on his part, which Sean very patiently took the time to explain. Incidentally, we often refer to said provoker as the “Santa Cruz heckler”.
If there *were* any graduate students there who agreed with said provoker, they certainly weren’t cosmology or high energy theory students. I find it telling that he doesn’t mention how many professors there agreed with his objections (zero, by my recollection). 🙂
er… provokee, that is. I suppose my own perception of who was doing most of the provoking is backwards from the convention etablished in this post.
This was one of the more enjoyable colloquium talks I’ve heard recently.
I stood around for quite a while after Sean’s talk, listening to his and his Critic’s back-and-forth until Sean finally had to leave for dinner, and then I stood around some more. My impression is that Critic’s overall objections are closest to CapitalistImperialistPig‘s suggestion that
One particular objection (and I hope Sean will redact this if he’d rather it not be posted): Critic argued repeatedly that cosmology is irrelevant because in cosmological N-body simulations, if one runs the simulation under conditions of time reversal — that is, change t for -t — one still obtains the same results, always. Changing t for -t does not have an effect on the evolution seen in the simulation. (This of course assumes that the major physical prescriptions used in simulations are time reversal invariant.)
[This sounds superficially true, except that
1. Our numerical N-body simulations are not equivalent to universes-in-boxes, although they try. They necessarily suffer from information loss relative to the best cosmological “simulation” we have, which is the real universe. They don’t have perfect resolution; and instead of doing (and because we can’t do) discrete particle-by-particle assessment of Everything, some gross analytical recipes meant to reproduce observed phenomena, with their own unconsidered assumptions and consequences, may be used. All of this is a result of computational limitations, human limitations on current understanding (including but not limited to lack of a theory of quantum gravity), and practical limitations (viz., you can’t run a cosmological simulation in less than a Hubble time unless you are willing to sacrifice some information).
2. Even supposing you were able to set up a very large quantity of test universes that did not suffer from some of these limitations, ignoring for a moment the definition that the future is the direction in which entropy increases, and supposing you started your simulations under conditions of a uniform distribution over all microstates compatible with the initial macrostate, naively you would in fact expect some of these universes, startlingly, to experience a decrease in entropy as t increases.]
By way of analogy, Critic argued that if you happened upon a glass of cold water in which ice had melted, and attempted to simulate it under time reversal, you would never derive the prior condition of ice cubes in the glass. [“Rarely” instead of “never” is perhaps a better way to put it, if you have uniform probability of compatible present microstates.] Instead you would derive a glass of progressively warmer water up to equilibrium with the surrounding air. A Santa Cruz cosmologist (whom I hope will correct my record, if he’s reading) pointed out that this derivation would nevertheless be wrong, because ice cubes had indeed been in the glass. You must insist somehow in your simulations that the starting microstates are compatible with the current water in the glass and with some entropy that was lower in the past.
Taking this insistence to an extreme conclusion requires that the universe in the far past also had significantly lower entropy, which I assume is the crux of Sean’s argument that “the growth of entropy is a fundamentally cosmological fact.” (Whether or not it requires the speculative ideas that Sean discussed is a separate argument, obviously.)
I would have liked to have been at that dinner, incidentally, if it was anything like the post-colloquium kerfuffle.
I have never figured out how to convincingly explain to anybody why, a priori, you’d expect entropy to increase in both temporal directions and our usual understanding of thermo depends on the cosmological fact that entropy happened to be a lot greater in the past. Your slide show did a very nice job of explaining things. I’ll try it out on some of the nonbelievers.
I guess I was one of the grad students who “Provokee” (who from now on I’ll just call P) referred to as having understood his objections, given that we talked about them for a little while during the dinner. (Jeff, you were at the wrong end of the table!) The crux of his objection as I understood it was that the Second Law makes no reference to cosmology, was deduced outside cosmology, and is true independent of cosmology. This is a fairly restricted objection. P was not objecting to Sean’s interest in understanding the arrow of time, and wasn’t expressing a opinion about that; he saw the arrow of time as a related but nonetheless separate issue which, in his view, should not be conflated with the Second Law itself. P’s interpretation of some of what Sean said was that Sean was claiming that cosmology is necessary to understand the Second Law (as opposed to the arrow of time), and he felt that if such a claim were true then it would have significant ramifications to the foundations of statistical mechanics and thermodynamics.
I felt I understood P’s point of view and agreed with it as far as it went, but only in the very restricted sense that I think he meant. In a sense, it seemed that P and Sean were not fundamentally disagreeing so much as talking about subtly different issues. But then, I could be wrong. (In defense of P, he is a bright physicist who has made significant contributions that probably most people would be pleased to have made. And he isn’t shy about stating his opinion as others have noted…)
Anyway, Sean, it was a very interesting talk. Thanks!
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I liked the definition of Time that Dr Who gave in the latest episode.
“People think of time as a linear progression of cause and effect, but in fact it’s knotted, wibbly-wobbly and well, …..timey-wimey”
I also liked the concept of the “quantum-locked” Weeping Angels, that had “been around since the dawn of the universe”.
They only move when not being observed , but turn into statues when you look at them.
“The only sociopaths to kill you nicely, by sending you into the past and feeding off the potential energy of your future.”
Great stuff!
“Blink”:
http://www.bbc.co.uk/doctorwho/
Well done, that’s a fairly good presentation! The 2nd law of thermodynamics is linked to cosmology, but you miss out just a few tiny considerations. In a static universe (such as Einstein’s model in 1917 or Hoyles in 1950), entropy (disorder) was supposed to always increase because the temperature becomes more and more uniform.
There are several issues with this idea. Firstly, the lab experiments on chemical reactions which showed that entropy rises (and the theoretical calculations backing them up) applied to instances where the gravitational attraction between the reacting molecules was small, and where the molecules weren’t receding from one another at immense speeds.
So the 2nd law is hardly a good model for the macroscopic universe! Three flaws:
1) Entropy increases are limited due to redshift in an expanding universe: thermal equilibrium (heat death through maximum entropy) between receding bits of well-separated matter would require the uniform exchange of thermal radiation, but in an expanding universe such radiation is always received in a redshifted (lower-energy) state than that emitted. Hence, all matter emits into the outer space more energy than it receives back. This redshift effect prevents thermal equilibrium from being attained while any energy remains, so outer space remains an effective heat sink. (This redshift of incoming radiation is also the solution to Olber’s paradox, i.e. why the sky looks bright and we aren’t scorched to a cinder by the 3000 K infrared cosmic background radiation flash still reaching us from 13,700 million light years away.)
2) Entropy (as temperature disorder) actually falls with time in the universe due to gravitation. When the CBR was emitted at 400,000 years after the BB, the temperature was uniform to within one part in 10,000 or whatever. Now, the temperature is grossly non-uniform, hardly an advert for rising entropy. Space is at 2.7 K and the middle of the sun is at 15,000,000 K. So goodbye 2nd ‘law’. The reason is that the ‘theory’ (that temperatures should become more uniform by diffusion of heat from hot to cool areas) behind the 2nd law of thermodynamics neglects gravitation, which is trivial for molecules in a test-tube in the lab, but is big on cosmic scales.
The universe is 74% hydrogen (by mass), so gravity causes stars to form by inducing nuclear fusion when it pushes this matter together into compressed lumps. The fusion creates the non-uniformity of temperatures because it’s exothermic. This debunks Rudolf Clausius’s definiton of the 2nd law: ‘The entropy of an isolated system not in equilibrium will tend to increase over time, approaching a maximum value at equilibrium.’ The universe is an ‘isolated system’ (there’s no evidence against it being an isolated system), and the universe is ‘not in equilibrium’ because of the redshift phenomena [see poing 1) above]. Hence, however well the 2nd law works in chemistry, it fails spectacularly in cosmology unless redefined.
3) Eddington pontificated in The Nature of the Physical World (1927): ‘The law that entropy always increases, holds, I think, the supreme position among the laws of Nature. If someone points out to you that your pet theory of the universe is in disagreement with Maxwell’s equations — then so much the worse for Maxwell’s equations. If it is found to be contradicted by observation — well, these experimentalists do bungle things sometimes. But if your theory is found to be against the second law of thermodynamics I can give you no hope; there is nothing for it but to collapse in deepest humiliation.’
This kind of scientifically-vacuous but authoritative pontification (which was made before Hubble discovered the redshift relationship) should make any genuine scientist deeply skeptical of the ‘law’. Arthur C. Clarke points out that, historically: ‘When a distinguished but elderly scientist states that something is possible, he is almost certainly right. When he states that something is impossible, he is very probably wrong.’
Please tell me why this doesn’t work…
As the presentation makes very clear, all known proofs of the second law of thermodynamics are model-specific, and consequently “local” in at least some sense. Could the problem be that this “law” isn’t actually globally true?
E.g., suppose the universe is cyclic. As I understand the history of our little piece of the megaverse, one or a few hundred thousand years after the big bang things were in equilibrium, a homogeneous cosmic soup. In a local sense, entropy had already been maximized, and nothin was happenin baby. But the universe expands a little bit, becomes transparent to the dominant wavelengths of the day, and matter starts to CLUMP, opening up vasts new reaches of entropy increases that were hitherto unattainable, resulting in the formation of stars, galaxies, planets, life, GWB, you name it. Before the discovery of dark energy it was easy to imagine the whole thing collapsing on itself, rebigbanging in some (almost certainly) totally disorganized state, and repeating the whole process (hopefully without GWB). This picture seems devoid of mystery except to the extent that physicists cannot reconcile themselves to the SECOND LAW not being a universal immutable global principle.
But if I shuffle a deck of cards repeatedly, is there really some meaningful sense in which each shuffle is “more random” than its predecessor?
In defense of the audience at my alma mater, questioning authority is a grand tradition at Santa Cruz. This naturally extends to high degree of skepticism regarding any and all guest lecturers. I’m actually surprised this didn’t lead to a sit in of some sort at the Chancellor’s office. Or maybe some sort of shanty town built in protest on Science Hill. You’re lucky to get out of there alive
Sean,
Great slides. A question though: You say on p. 22 that you need an infinite-dimensional Hilbert space, but then later you say that you need empty space with a positive cosmological constant so that the de Sitter thermality can drive the production of baby universes. But what of the notion that any de Sitter space has a finite entropy and therefore corresponds to a finite Hilbert space?
Josh, it was a near thing. But I was aware of the notorious Banana Slug reputation, and when I felt them ready to shackle me near the end of dinner, I knocked over a bottle of wine and sneaked off in the confusion. Entropy can be your friend!
(Chatter about the objection promoted to an update to the post itself.)
Matt, that’s of course a good question. But note that “finite entropy” does’t automatically imply “finite-dimensional Hilbert space”; that would only follow if you knew you were in equilibrium, which I’m suggesting that de Sitter is not.
But shouldn’t the question about the dimensionality of the Hilbert space corresponding to de Sitter somehow be an independent statement about de Sitter space in general? That is, if we assume instead a de Sitter space that IS in equilibrium—as would seemingly be the case if we DID assume something that looked approximately like pure de Sitter—we get a finite entropy, and doesn’t that imply in generality that the Hilbert space of de Sitter is finite-dimensional in generality?