The holidays are coming to an end, so expect a return soon to the usual somewhat irregular posting frequency.
Over the past week or two, one thing that I did was get a chance to read new books by two of the most prominent physics bloggers around: Chad Orzel (who has been blogging since 2002, now at Uncertain Principles), and Sean Carroll (since 2004, now at Cosmic Variance).
Orzel’s new book is entitled How to Teach Physics to Your Dog, and he has a website with all sorts of material about the book here. I guess it’s generally agreed that a cute dog improves just about any sort of material. While Brian Greene in his Elegant Universe Nova special introduced general relativity by trying to discuss it with a dog, concluding that “No matter how hard you try, you can’t teach physics to a dog”, Orzel takes a very different tack, structuring his book around conversations with his dog about quantum mechanics. The dog ends up with a solid intuitive understanding of quantum physics and presumably the idea is that the reader should be able to do as well as the dog. The book is a quite good, non-technical, exposition of some of the paradoxical aspects of quantum mechanics, emphasizing the subtleties of the relationship between the quantum and classical views of reality. His expertise in experimental atomic physics gives him an excellent understanding of these issues, and he does a good job of conveying some of this to the reader.
Among the best features of the book are enlightening treatments of the quantum Zeno effect, quantum tunneling, entanglement and quantum teleportation, as well as careful treatment of some crucial subtleties of the subject. If you want to go beyond the usual explanation that the uncertainty principle is about how measurements must change the state of a system, and find out how one can use quantum mechanics to measure a state without changing it, this is a good place to start.
By the end, I observed myself ending up in a linear combination of two possible states describing my feelings about the dog thing: about equal amplitudes for charming and annoying. Even now that we’re in a different decade, I haven’t yet collapsed into one state or the other.
The other new blogger-book is Sean Carroll’s From Eternity to Here, which has its own website here. I confess to being somewhat mystified by this book, and a bit surprised by its contents. Carroll is a very smart guy, with a serious dedication to making the wonderful science of his professional field (cosmology and particle physics) accessible to the general public. Given this, my expectation was that the book would be mainly devoted to telling the conventional scientific story of some part of our current understanding of these subjects, with perhaps a more positive take than mine on the possibility of exciting new discoveries in the near future. I also expected him to include some material on his highly idiosyncratic ideas about the arrow of time.
It turns out though that this rather long book is heavily oriented towards making the case for unconventional claims about physics, with essentially no discussion at all of what is happening on the experimental side of the subject. The LHC appears only in a footnote explaining that it won’t destroy the earth, and there’s virtually nothing about the hot topics of dark matter, gravitational waves, or the cosmic microwave background. In a final footnote, Carroll explains that he decided not to write about these experiments because
it’s very hard to tell ahead of time what we are going to learn from them, especially about a subject as deep and all-encompassing as the arrow of time.
Carroll’s problem is that the questions that he has chosen to highlight in the book may be “deep and all-encompassing”, but they’re of a sort one might describe as “philosophical” rather than scientific. Much of the book is devoted to arguing that in order to understand the local (in time) question of why entropy increases, one must understand the global puzzles pointed out by Roger Penrose associated with gravitational entropy, the Big Bang and inflation. More succinctly, the explanation for why an omelet doesn’t turn into an egg somehow involves understanding the Big Bang. Even after reading the book, I remain unconvinced that the global problem has to be solved to explain the local problem, and unfortunately there’s no scientific way to resolve my difference of opinion with the author. No conceivable experiment can provide evidence one way or another about which of us is correct.
After making the case that one needs to understand the low entropy of the early universe to understand everyday physics, Carroll goes on to propose his own theory, the “Ultimate Theory of Time” of the book’s subtitle. It’s a version of the usual “multiverse” argument: one explains some mysterious distinctive feature of the universe by positing that we live in a multiverse without this distinctive feature, which just occurs as a dynamical accident in our particular universe. The problem is that this particular explanation is not a conventional scientific one, since it is immune to experimental investigation, and, as far as I can tell, few physicists take it seriously. Carroll’s one scientific paper on the subject, (written in 2004 with his graduate student Jennifer Chen) received a lot of publicity on the internet and in Scientific American, but doesn’t seem to have yet been published, despite being listed on his CV as submitted to Phys. Rev. D.
The book seems likely to get a lot of public attention, but I’m not sure this is a good thing for the public understanding of science. It raises fundamental issues in physics, which naturally attracts people’s interest, but then addresses them in a rather post-modern yet pre-scientific manner, avoiding contact with either mathematics or experiment. Probably the best way to think of From Eternity to Here is as an extended essay in the philosophy of science, and as such I’d be curious to hear what philosophers expert in the subject make of it.
Update: Scientific American has an interview with Carroll, in which he addresses objections like mine as follows:
The following statement is very true: To understand the second law of thermodynamics, or how the arrow of time works in our everyday lives, we don’t need to ever talk about cosmology. If you pick up a textbook on statistical mechanics, there will be no talk about cosmology at all. So it would be incorrect to say that we need to understand the big bang in order to use the second law of thermodynamics, to know how it works. The problem is, to understand why it exists at all requires a knowledge of cosmology and what happened at the big bang.
Once you assume that the universe had a low entropy for whatever reason, everything else follows, and that’s all we ever talk about in textbooks. But we’re being a little bit more ambitious than that. We want to understand why it was that way—why was it that the entropy was lower yesterday than it is today?
To understand why the entropy was lower yesterday really requires cosmology. And I think that if you sit down and think about it carefully there is absolutely no question that that is true, yet a lot of people don’t quite accept it yet.
After having sat down to think about it carefully, I still don’t quite accept it…
>> It raises fundamental issues in physics, which naturally attracts people’s interest, but then addresses them in a rather post-modern yet pre-scientific manner
I would think this is true of (almost) all popular books about physics (including your own)? They are not research papers but rather more or less interesting stories about science.
Although I haven’t been through Carroll’s blog posts on arrow of time recently, I do recall them being pretty sensible and agreeing with the general consensus at the time that I read them. That is, it’s general accepted that you need to explain why entropy was low at the beginning of the universe: the Second Law of Thermodynamics alone does not suffice, without the addition of a Past Hypothesis. There’s a neat argument showing this that involves phase space that I’m sure you’ve seen?
Maybe you could explain more what kind of statements you found unlikely? (Apart from the multiverse “ultimate theory,” of course.)
See arXiv:gr-qc/0505037.
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Peter,
thermodynamics books say that entropy is a concept defined for physical systems. A system is a set of matter enclosed in a boundary. But is the universe really a physical system? Many say yes, but is this really so? I remember a friend saying that Weinberg’s opinion is that the concept of entropy is not applicable to the universe. If that is true, all discussions on the topic are not serious. What is the the “official” view on this topic?
I haven’t read Carroll’s book, but I don’t see that the arrow of time enters in explaining why omelettes don’t turn into eggs. That would be going from a larger to a smaller region of phase space, which is improbable unless either the dynamics or the initial conditions are very special, no matter which way one moves in time. (Maybe there’s another idea here I’m not appreciating, though.)
The mystery of the arrow of time (in this context) is rather why there are eggs (very low-entropy objects) in our common experience. Basically, that implies that there must have been still lower entropy in the past. That does indeed lead back to questions about the early Universe. It also inevitably leads to global issues.
In the standard hot big bang, of course, the material degrees of freedom are thermalized. But the degrees of freedom corresponding to gravitational radiation are almost entirely unexcited — in fact, it is precisely this which is required for the homogeneity and isotropy of the Universe. Thus while the matter is in a high-entropy state, potential gravitational radiation is in a very low entropy state, and this very low entropy is moreover what provides the entire Friedmann–Robinson–Walker background (on which the evolution of galaxies, stars, chickens and eggs is described).
Notice that the global character of the conditions — the homogeneity and isotropy — is intimately bound up with the low-entropy character of the gravitational degrees of freedom. This is contrary to what happens in more familiar thermal situations, where a homogeneous system is typically a high-entropy state. The difference is due to the attractive nature of gravity.
(I know this is a bit lengthy, but the question is an involved one.)
“More succinctly, the explanation for why an omelette doesn’t turn into an egg somehow involves understanding the Big Bang.”
I haven’t been able to get hold of the book yet, but I’d be amazed if it contains any such claim, because that would directly contradict SC’s numerous explicit statements to the contrary in his blog postings. There he says that the usual probabilistic arguments explain why high entropy states [almost] never evolve into low entropy states. *But* if you accept this, then you are obliged to explain where low-entropy states observed in our universe came from. The answer, of course, is that they came from something about the big bang that we don’t yet understand.
As for whether physicists take SC’s ideas seriously: you have to take into account the *extremely* mysterious fact that physicists are apt to get very emotional about this issue; and I’m not just talking about cranks like Lubos Motl. Many people get upset when told that something as basic as the second law of thermodynamics is not fully understood. Partly this is due to “cosmology envy” — some people working at the more boring end of physics resent the idea of those pointy-headed cosmologists muscling in on their territory.
Anyway, it is certainly not the case that SC’s ideas are rejected because they challenge some orthodoxy; there *is* no orthodoxy on this matter. Common sense tells us that the second law implies that the universe must have begun in an extremely low-entropy state, and that this has to be explained if we are to make any sense of early-universe cosmology. But most people just don’t want to think about this.
anon,
The preprint you mention is a 5 page non-technical essay for the Gravity Research Foundation essay competition.
Domenic (and others),
I don’t disagree that to understand cosmology you want to explain the low entropy at the Big Bang. I just continue to not see why this explanation, whatever it is, is necessary to explain the 2nd law of thermodynamics. I’m not the only one (the book’s introduction contains another example), and the problem seems to me to be that questions like this inherently can’t be adjudicated by any conceivable experiment. Arguing about them thus tends to be a rather pointless activity. We’re really in the realm of philosophy of science here, not science.
“Tom O’Bulls”,
From your IP address it seems likely you’re one of the people on the very short list of physicists known to have some sympathy for Carroll’s arguments about the multiverse. I really wish you and others would use your real names here, especially if you intend to make arguments about what your colleagues think of all this.
For those asking for an explicit example of a statement from Carroll that I disagree with, a good one is his Facebook summary of the book’s argument:
“You can turn an egg into an omelet, but not an omelet into an egg. This is good evidence that we live in a multiverse. Any questions?’
Hi Peter,
As a mathematician, I am extremely uncomfortable with some of the multiverse claims by Sean Carroll. I think his textbook is marvelous, it was the first textbook I used to learn General Relativity, but I find the multiverse concepts meta-physics at best and it is a bit disheartening to see, let’s face it, one of the more popular physicists so die hard about it.
I find it interesting to lead a discussion in a book rather than scientific papers that are (for one or the other reason) inaccessible for most people. As long as it’s clear to the reader which part is backed up by solid science and which is speculation. It’s a much less constrained medium that offers more freedom. Didn’t read either book though, so can’t say much.
Does it really bother you that the paper didn’t get published?
Btw: Happy New Year 🙂
I look forward to reading Sean’s book, but I am confused by some of these accounts of the issue. Even if the entropy of the universe as a whole can be defined (which I am confused about) and increases over all, the important thing for eggs, chickens and cooks is that nevertheless there are large regions far from equilibrium today.
This is in turn due to the fact that there are stars with cosmological life times, which pour hot photons into cold space. The existence of stars is due to both some fine tuning of the parameters of the standard model and the fact that gravity is universally attractive and long ranged so that gravitationally bound systems have negative specific heat.
The fact that stars exist is likely not due to the extreme homogeneity of the early universe, were the initial density fluctuations quite a bit larger I suspect there still would have been stars, possibly a higher density of them, and sooner.
Nor is there a simple thermodynamic argument that applies to gravitationally bound systems or the gravitational degrees of freedom. The canonical ensemble cannot be applied to systems with negative specific heat such as gravitationally bound systems. It can also be shown, given only that matter has positive energy, that gravitational radiation cannot come to thermal equilibrium within any finite time, nor can it be contained by any material within a finite volume. So it is unclear that equilibrium thermodynamics is ever relevant for the gravitational degrees of freedom.
Thanks,
Lee
Peter,
I think there is an issue which is physics (whatever its implications for philosophy), that is, to explicate the Second Law and its relation to the arrow of time. I also think that while it is wise to be wary of discussions which cannot lead to experimental verification, what we’re doing at this stage is rather trying to clarify our understanding of some of the theory. Hopefully a deeper understanding will suggest experiments.
Let me begin with two possible formulations of the Second Law:
1. Systems tend to move from smaller volumes of phase space to larger ones (or tend to spend more time in larger volumes than smaller ones);
2. Over time, entropy increases.
The point I want to make is that the first one admits a time-symmetric interpretation (indeed, the form in parentheses is explicitly time-symmetric), while the second does not. Thus the first is insensitive to the arrow of time, but not the second; they really reflect slightly different concepts. The second form captures something that the first form misses, precisely because it does implicate the arrow of time.
I would also say that the first statement is plausible and largely an intuitive statement about probabilities. (Of course, subtle questions about issues like coarse-graining are hidden in its implicit assumption that we have selected certain phase volumes.) So I would contend that the thing to be explained about the Second Law is the “something extra” which is added in passing from the first to the second version.
What has been added is brought out most forcefully by viewing the movie backwards: going backwards in time, we find entropy decreases. That is what is puzzling. So the puzzle of the Second Law is why the initial entropy was so low. And this is a cosmological issue.
I appreciate that it seems that there is a considerable leap between everyday thermodynamic phenomena and the early Universe, and I think this is perhaps why their linkage seems hard to accept. However, this is really because we are highly prejudiced about what we consider to be “everyday thermal phenomena.” Had the Universe been a more “random,” average (from the phase-space view) one, it would look nothing like ours. Stars and galaxies would probably not exist (or would be rare). The fact that we can build heat engines and refrigerators (and, more spectacularly, that chickens and eggs — the original points of discussion — exist) is really due to the low entropy we still have available to us to exploit, and this ultimately came from earlier — cosmological — times.
This is too funny. Peter “my credentials don’t matter” Woit is drawing conclusions about a commenters views on physics based on their IP address.
HNY
PH
Bee,
I don’t know why the the paper hasn’t been published, so it’s unclear what the significance of that is. I am curious though what the reaction to it is from experts in the subject. The book does acknowledge that some of what is in it is not widely accepted by other physicists, but doesn’t really explain why.
Lee,
I agree with most of your points. You’ll notice that I have phrased things in terms of phase-space volumes and not (except for small systems, and a reference to the conventional treatment of the hot big bang) in terms of thermodynamic entropy and equilibrium. I acknowledge that this means dodging or postponing certain questions — but that’s often what allows one to make progress.
A rather trivial comment, just for the record. As someone else once pointed out in this blog, turning omelettes into eggs is almost as trivial as the inverse process. Just finely chop the omelettes and feed a hen with them, she will turn them back into eggs, increasing the overall entropy of the barn with heat and waste in the process…
Adam,
I understand the argument, but it just doesn’t seem to me to provide a significant coupling between the global cosmological problem and the local physics problem. According to that argument, whatever the solution to the global problem turns out to be, it’s not going to affect in any way our understanding of the local physics, and no possible local experiment is going to help solve the global problem.
By the way, the contrast to Penrose is interesting. Penrose has been pointing out the big bang entropy problem for a long time, but, unlike Carroll, it leads him to speculative ideas that do directly affect local physics (modifications of quantum theory with potentially observable local consequences).
H-I-G-G-S,
I’ve been repeatedly struck by how much lower the level of discussion is on physics blogs than on mathematics blogs. One major difference is that serious mathematicians participate in blog comments using their own names, and I think this has a lot to do with the problem (and you’re a good example of it….)
What is Carroll’s definition of gravitational entropy? Under which constraints is it extremized?
If one goes back to the very basics of gravitational relaxation from the point of view of statistical mechanics, several issues arise, as mentioned by Smolin, which I fully agree. [ A brief review (with relevant references) can be found, e.g., in section 4.2 of astro-ph/0604544. ] The point is: those issues arise in a very well-studied subject.
[ There are in fact open questions. For instance, if one goes back to the very basics, as my paper above points out, mesoscopic energy constraints may be operating during gravitational relaxation. This has been discussed previously by other authors, like e.g. Kandrup et al. If it turns out that this effect is confirmed in observations, then it is just an example of why one should be careful concerning gravitational entropy and so on. ]
Given that there are still down-to-earth issues that still must be elucidated in this beautiful area of real physics, it is not clear to me the logic to adhere to speculations such multiverses in order to reach whatever conclusions about whatever.
Somewhere, out there in the multiverse, someone or something is turning omelets into eggs, as we speak.
The second law of thermodynamics does not say the entropy (of an isolated system) increases, but the entropy does not decrease.
Peter: Is Sean’s book well written? Like in: worth reading or will catch dust?
Peter wrote:
“I’ve been repeatedly struck by how much lower the level of discussion is on physics blogs than on mathematics blogs.”
Some how almost everyone feels qualified to comment on current physics, but few feel qualified to discuss mathematics. I saw this happen in an undergraduate course on The Philosophy of Science during a discussion of quantum mechanics. After some very wierd comments were made by several members of the class, I asked the class to raise their hands if they had taken a course on QM. Mine was the only hand raised. Not even the instructor had taken QM. But they were more than willing to discuss topics about which they were ignorant.
Peter,
Yes, Penrose deserves a great deal of credit for bringing the cosmological problem forward (and I know what I’ve written here is certainly influenced by his ideas). One used to hear cosmologists talking about the high entropy of the early Universe, with no mention at all of the gravitational degrees of freedom. I haven’t read Carroll’s book, but I believe that in the past he has acknowledged Penrose’s influence.
I agree also that Penrose’s speculations about links to observational physics are very interesting. While I do feel that there is an argument that cosmology does call for some reconsideration of the usual notion of experimentation (one cannot expect to produce, much less reproduce, phenomena on truly cosmic scales), one should approach this very cautiously, since one risks throwing out the foundation for scientific progress. I think something like Penrose’s Weyl Curvature Hypothesis is an excellent example of an idea which could in principle be testable but nonetheless have cosmological implications.
Bee,
You are right, that is the standard formulation; I probably should have phrased it that way to avoid confusion. (But the distinction has no effect on the argument. Also it is arguably mathematical hair-splitting, since: no real system is perfectly reversible; the entropy is perfectly well-defined as a precise real number only under idealized assumptions which do not hold for real systems; etc.)
Bee,
The book is well-written, and people may find lots of the various things discussed useful. My problem is just with the main thesis that the book is structured as an argument for.
Thomas,
That’s part of the problem. But there’s a further problem with physics blogs that a significant number of the informed people with reasonable credentials who post comments have decided to do so anonymously. Cloaked in anonymity, people tend to take a lot less care about what they write…
Adam: In what sense does the whole universe conform to your idea of a “real, not idealized system?”
Peter: Thanks. I think I’ll put it on my reading list. There is a nonvanishing chance I’ll open it before the end of the century.
Bee,
The Universe is certainly a real system. The sense of “idealized” which is relevant here is whether the entropy can be well defined. The Universe is certainly not a system in thermal equilibrium, so it’s certainly very far from “idealized” in the usual sense one wants for such a definition.
The arguments I gave earlier are based on using (logarithms of) phase-space volumes as substitutes for entropy. But that doesn’t really sharply define entropy, because of the question of just where to cut off the phase-space cells (the coarse-graining issue). Only in certain idealized limits does this ambiguity in the phase-space approach contribute zero uncertainty to the definition.
Adam: What I was aiming at is that unlike all other systems the universe is perfectly isolated. Yes, you have to coarse-grain. But is that fundamental?
Bee,
Since we don’t really have a really firm idea of how to define the entropy of the Universe, I don’t think we’re in a position to talk about what is fundamental. For the purposes of the arguments I was giving, some sort of coarse-graining is essential, because one needs to decide when two different states count as macroscopically the same.
It’s true that one might try to consider extending the idea of entropy so as to treat the entire Universe in some “fundamental” sense. However, this is a very big problem, and it’s not clear that it would have a solution. In fact, it’s hard to see how one would define the entropy of an ordinary (say classical mechanical) system which was not in thermal equilibrium.
Adam: If the problem is not fundamental, why is it worrisome? What you say is exactly what I meant: you have to decide what different microstates count for the same macrostate, that determines your entropy (leaving aside all other problems for the moment). This notion stems from thermodynamics and that’s where it has its use, but what’s its use for the whole universe, a system that by definition is all there is and exists once in exactly one microstate?
Bee,
I’m not sure what your point is. If you are arguing that entropy is not a useful concept in its application to the entire Universe, that’s pretty much my point of view. If you are asking about why concerns about the Second Law are fundamental, I’d say that the arrow of time is a fundamental issue — but I’d add that understanding the link between the Second Law and the arrow of time may well take us beyond the bounds of the strict applicability of the concept of entropy and ordinary thermodynamics.
Adam: Yes, is what I’m saying. I think we agree anyway.
Here is, I think, a more precise way of stating Bee’s point.
Entropy, (IMHO) carefully defined, is a property of probability distributions (or, if you prefer) measures.
We can connect it to physics because, for blocks of space containing certain fields and subject to certain boundary conditions, we can construct an argument for what the PDF of the system should be, and we can calculate the entropy of that PDF.
(This requirement, well-defined PDF as a property of a few variables is also why we need thermal equilibrium. If you’re going to have a non-equilibrium system, in theory you COULD define/assume/calculate an associated PDF, and this might even work for something like turbulence, but good luck doing it for a general situation. We can get away with this for the most part because when you’re dealing with a steam engine or whatever, the number of coherent degrees of freedom is so small compared to the number of incoherent degrees that treating the system as in equilibrium basically works OK.)
When you expand this argument to the entire universe it basically falls apart. What is the PDF of states of the universe? What are even the allowed possible states, let alone a claim regarding what probabilities to assign to each possible state?
But if you don’t have a PDF, you don’t have an entropy.