Cosmology and Philosophy at La Pietra

By Sean Carroll | July 26, 2012 5:32 am

I’ve traded off my reasons for not blogging much of late. Last week and before it was The Particle at the End of the Universe (in stores November 13!), but that’s now been handed in and I can kick back and catch up on my martini-drinking. Except that instead of doing that, I instantly hopped on a plane for Europe, where I’m now participating in a workshop on philosophy and cosmology. Not that you should feel sorry for me — the workshop is being held at the La Pietra conference center, a beautiful facility owned by NYU in Florence. I’m not sure why NYU owns a conference center in Florence; it could have been a targeted purchase, but it could easily have just been a gift. (Caltech for a while owned an abandoned gold mine. Universities get all sorts of crazy gifts.) But at least temporarily, martinis have been put aside for Chianti and limoncello.

And work, of course. This is my favorite kind of workshop: less than twenty people, gathered around a table, with no fixed agenda, talking about issues of mutual interest as they come up. This group has both scientists and philosophers, although probably more of the latter. So far each day has featured a scientist — Joel Primack, me, Brian Greene, Scott Aaronson — giving some very general remarks, while everyone else takes turns whacking them with (metaphorical) sticks. My own talk started at 11 a.m. and didn’t finish until 5:30 p.m., with breaks for lunch and coffee. So it’s exhausting both intellectually and physically, but very rewarding to have the chance to dig very deeply into difficult issues.

My talk was about — you guessed it — the arrow of time. Most people in the room are already familiar with the basic story that time’s arrow is (at least mostly) a consequence of the increase of entropy over time, and that our current universe has low entropy, but the entropy was even much lower in the past, and that last fact demands cosmological explanation. The central question concerned what would count as an “explanation.”

One idea might be that whenever you have a simple true statement that has enormously powerful consequence for many different facts about the universe, that statement would qualify as a “law of nature.” Often we think of such laws as patterns that apply individually to each subset of the universe, but one could argue that the statement “the early universe was in a low-entropy state of the kind that would naturally evolve into the universe we see” should also count as a law. If you buy into that, then one shouldn’t necessarily look for a deeper explanation of that fact; maybe that’s just how the universe is.

I think that’s an allowed position, but certainly not the most attractive from the point of view of most cosmologists. We tend to look at the low entropy of the early universe as a clue in our search for a better theory than the one we currently have.

From that perspective, what would count as having explained the low-entropy state? My argument was the following: imagine you have a certain theory of everything, consisting of a space of states (Hilbert space or whatever) and a dynamical evolution law. And imagine that, for almost all solutions to the equations of motion, some certain fact X about the system turn out to be associated with another fact Y almost all the time. (Fact X = our entropy is low, fact Y = it was even lower in the past.) Then, if we do indeed observe that fact X and fact Y are both true, then fact Y is “explained” by this theory. You might still want to explain fact X, but that’s a harder question that I didn’t get into. It’s enough of a challenge to explain the lower-entropy past even if you accept as given the current low-entropy state. (And of course we’re imagining that we have well-defined theories with this feature, which at the moment we really don’t, although there are some rough ideas.)

I won’t claim that I convinced anyone who didn’t already agree, but I do think that there is more mutual understanding now than when we began. And the Chianti has been quite good.

CATEGORIZED UNDER: Philosophy, Science, Top Posts, Travel
  • zetetic25

    No science fiction writers in attendance? They are the ones who need convincing! The notion of time travel is such a recurring theme as to be damaging to the genre. Can we get past the whirlpool?
    (get it?) The rigid arrow of time makes for so much better stories.

    Also: What is up with the evaporation of black holes? If two particles are spontaneously created in the quantum foam at the event horizon why would a preponderance of anti-particles eventually fall in?
    The chances would be 50% for each, thus no net evaporation. I say the inverse is possible with the anti-particle having a greater chance of escaping gravity’s maw. Thus, spontaneous nucleation and matter does not escape the trap.

  • Random Rambler

    Fascinating. Were the discussions filmed and will there be online videos in the near future? Just curious.

    • Sean Carroll

      No filming. There were microphones, but I doubt the quality will be very good; we’ll see.

  • FmsRse12

    maybe the entropy of the universe was lower in the past due to small volume , now the universe has expanded quite a bit so has the entropy….maybe it’s something to do with expansion….like isothermal volume expansion of ions or gas….

  • Phil P

    Try the Brunello di Montelcino – it’s even better than the Chianti.

  • anscal

    As a long-time reader of Cosmic Variance at his first post, as well as a physics student and a person who lives in Florence, may I ask if by any chance the workshop is public?

    I hope you enjoy the site and the food and beverages.


    • Sean Carroll

      anscal– It wasn’t public, and now it’s basically over. It’s good to have a mixture of large public things and small research-oriented things.

  • bob

    It seems La Pietra has an interesting history. It was purchased by the art collector and dealer Arthur Acton, with money from his wife, the American Hortense Mitchell, heiress to a Chicago banking family. They were the parents of Sir Harold Acton, who grew up there, went to Eton and Oxford, and hung out with the likes of Evelyn Waugh. Harold Acton, who died in 1994, bequeathed an estate valued at $500 million, including La Pietra, to NYU. Wikipedia says that an illegitimate half-sister (confirmed by DNA testing) has contested the bequest. Enough interesting stuff to write a book about – in fact, somebody has

  • Chris

    @1 zetetic25
    If two particles are spontaneously created in the quantum foam at the event horizon why would a preponderance of anti-particles eventually fall in?

    I think there is no preponderance of anti-particles falling in. The virtual particles borrow energy from the vacuum so it doesn’t matter which one falls in. As long as one becomes real, energy will be extracted from the black hole. And if you have charged particle pairs you would need to have both positive and negative ones falling in and escaping to maintain charge neutrality of the black hole.

  • John

    Sounds fun. Hope nobody’s using public grant money for this, unless you want the NSF/DOE to get spanked like the GSA was for its Vegas junket.

  • johnq

    I don’t think I’m getting the whole X and Y thing. I suspect it’s been misstated. I believe you’re starting with the premise that Y is true, and then concluding from that premise that you’ve “explained” Y.

    In logical terms, this looks like a tautology: (1) X and Y are generally observed together, (2) X and Y, (3) therefore Y. This is the actual argument you’ve made (I think). Note that the X part is irrelevant. A syllogism that incorporates the truth of Y as a premise cannot possibly explain Y, at least not in any meaningful sense.

    This would work better as a syllogism if it were slightly restated: (1) X and Y are generally observed together; (2) X; (3) therefore Y. I believe that’s what you actually intended to argue (to be sure, the “generally” qualifier means this isn’t actually syllogistic, but it seems close enough that quibbling isn’t warranted).

    As restated, the argument is no longer tautological, but it doesn’t seem to get you very far. As you note, this leaves open the question of why X, which may be just as difficult, or more difficult, to “explain” than Y. Moreover, you’ve opened up a new set of issues, since you now have to explain not only why X, but also why X is correlated with Y. It appears that, as an explanatory framework, you’re actually going backwards, since you now have two unanswered questions rather than one.

    Moreover, the exact same logic can be used to “explain” both X (universe is currently low entropy) and Y (universe was previously in a lower-entropy state). As before, we start with the premise that X and Y are generally observed together. I then note that Y is currently observed, therefore we can conclude that X will also be observed. Thus, the logic you’ve used to “explain” the direction of entropy by invoking the current low-entropy state can simultaneously be used to explain the current low-entropy state by invoking the direction of entropy. I don’t think you need a philosopher to tell you that a logical construct that begins with two unexplained but correlated phenomena, and then “explains” both of them by invoking the other, isn’t really able to explain anything at all.

    I’m finding it somewhat difficult to imagine a roomful of philosophers listening quietly to this without the words “logic chopping” being uttered at regular intervals, so I’m guessing that either you described it differently to them than in this post, or perhaps the inclusion of some physics stuff confused them sufficiently that they couldn’t focus on what you were really saying. Or maybe it was the chianti.

    • Sean Carroll

      johnq– I might not have been clear, so let me try again. We have two things we’ve already observed to be true about the universe, X and Y. We also have a naive set of expectations, according to which X is unlikely, but Y is much more unlikely, and X generally follows from Y. So you think that your greatest burden is explaining Y. But in fact you look at it more carefully in a particular theoretical framework, and you realize your naive expectations were wrong, and appearances of X are generally accompanied by appearances of Y. (So, among other things, Y is not less likely than X after all.) Now you realize that all you really need to explain is X; Y comes along for the ride.

      More specifically: in the Liouville measure on the space of states, our current low-entropy macrostate most often evolves from (and to) higher-entropy macrostates. So the argument is that we have a justification for replacing that measure with one derived from actual occurrences of our data in a multiverse.

      I personally suspect that “the data we currently observe” (i.e., X) isn’t something that needs to be “explained” at all, but that’s a separate debate.

  • Spiros

    There IS a secret society of geniuses that meets in castles in Italy to talk about the future of the universe! Dan Brown, I misjudged you… But now that you whet my appetite for cosmology, Sean, I hope you can clarify something that has been bothering me for some time. If the universe is in a pure state that evolves under a unitary evolution, how can its entropy change? Are we assuming that our universe is entangled with the states of other universes, so tracing them out leaves us in a mixed state with non-zero entropy? Or is the model we use to describe its evolution non-unitary? Of course, if we are discussing subsystems of our universe, then it’s all good. Thanks!

    • Sean Carroll

      Spiros– There are different kinds of entropy, of course. You’re thinking of the von Neumann entropy, which is the QM analogue of the Gibbs entropy, which refers to our subjective information about a state. I’m thinking of the Boltzmann entropy, which is completely objective, once you specify a coarse-graining on the space of states. That’s what increases as the universe evolves (or, for that matter, what increases as an ice cube melts in an otherwise isolated glass of water).

  • Spiros

    Thanks for the clarification Sean. I looked into the Boltzmann entropy and it looks like a simplification of the Gibbs entropy, where particles are assumed to evolve independently (due to the coarse graining you mentioned?) Is that always a good assumption? If not, isn’t the Gibbs entropy (and by generalization to QM, the von Neumann entropy) a tighter measure of uncertainty? I am asking because your prior response reminded me that we also have a Gibbs (thermal) state in QM, whose entropy does change with temperature (even if we assume a time-independent Hamiltonian for the universe). Is this the entropy you are referring to? And if that is the case, what is providing the external heat bath to our universe? My apologies for all these naive questions… I feel like a kid in a candy store and you are buying!

    • Sean Carroll

      Spiros– That’s one thing that Boltzmann did, but not the thing I was referring to. I was thinking of the equation on Boltzmann’s tombstone, S = k log W. That refers to the idea that you have a space of microstates (exact states of the system, phase space in classical mech or Hilbert space in QM) and a coarse-graining of that space into macrostates. Every microstate is inside some macrostate, and W is the volume of the macrostate it is in. So the entropy is an objectively-defined map from microstates to the real numbers, without any assumptions about particle dynamics or an external heat bath. I talk about this a bit more in From Eternity to Here.

  • johnq


    Thanks. A much better explanation. It remains, however, somewhat unsatisfying. If we assume two correlated conditions (X and Y), and then observe X, we can conclude that we will probably (depending on the degree of correlation) observe Y. This is an “explanation” for the observation of Y, but I can’t see that it advances the discussion very much.

    Here’s another example of the same logic: thunder is often followed by rainbows. That being the case, using your logic, the existence of thunder “explains” rainbows. It seems to me that this sort of logic works on a purely predictive basis (if we see X we will probably see Y), but claiming that this in some sense “explains” Y ignores the fact that, even if we accept X as a given (as you are apparently suggesting), we still have to explain the correlation.

    That X and Y are correlated is an interesting fact that may give us a leg up on uncovering why X and Y exist, since it seems likely that the correlation is telling us something about causation of both X and Y. But to claim that the existence of the correlation constitutes some “explanation” of Y in anything other than a purely predictive sense seems an odd use of the word “explain.”

    I will acknowledge the possibility that you have a deeper point here about the correlation of this particular X and Y that I can’t follow because it’s getting into the weeds of theoretical physics in a way that isn’t captured well by the simple explanations you’ve been presenting. If that’s true, then I suppose my point is you need a better way to explain this (assuming you care about explaining entropy to lay-people, as is apparently the case). The relatively simple logical argument isn’t working, at least for me, and apparently for the philosophers as well.


  • Spyridon Michalakis

    Sean, have you ever had to sign an electronic copy of a book you wrote? I am asking because you may have to come up with a way to do that within the next week or so. I am impressed at how clear and engaging your writing is in the book you suggested above. Which makes me think that JohnQ is right about Blog comments not being the best place to explain complex concepts in physics. Still, you clarified my misconception about which entropy the arrow of time was related to. I will keep reading your book before asking more questions like “Is there an arrow of time for microscopic states?” and such… You may already have an answer in From Eternity to Here.

  • Ron

    If X and Y are correlated, but with no causal relationship, it does seem to logically say something about “W”, defined as the (currently hidden) cause of both X and Y. That is, W has a constraint: if W causes X, it must also cause Y, at least under certain conditions. So knowing the correlation says something, if only a little thing, about W.

  • zetetic25

    @ Chris thanks for reply.
    It a puzzler. I’ve thought the lack of charge was caused by the gravity gradient not allowing the charge, or any energy to escape. The spontaneous generation of particles is explained as particle/antiparticle pairs that usually recombine and quickly annihilate. If this occurs at the very intersection of the event horizon, one will fall in and the other fly off. The captured particle falls to the surface and destroys an analog speck. I imagined it would necessarily be an anti-particle to remove mass and it’s inverse would only add more mass. It’s difficult to imagine how mass could be removed simply by the interplay of energy way out at the event horizon.

  • 2012

    Could it be that the initial low entropy of our universe is the result of a high entropy state of a ‘previous universe’ with a different definition of states?

  • John R Ramsden

    @21 Yes, that in so many words is obviously the correct answer, and some of the abstract structures which mathematicians and physicists study even have a corresponding property. For example, many Calabi-Yau manifolds are birationally equivalent over Q to themselves. So in as far as these model reality (in ways still being explored), these “self-equivalence” properties indicate that one universe can have latent dual ones tied up with it, and once the first attains a certain state then the second can become manifest, in parts or all of the former, and so on.

  • Francisco

    Entropy is the disarray state of the Subjects (Object), that at certain Point was in order, how can we determinate the cause of more or less, state of chaos or disarray, if we don’t know the perfect beginning of the Subject into its Harmonious existence. this is to say that chaos was the beginning of the Universe, which at some point in time, will achieved a commencement moving forward to reach some kind of perfection or Harmony, after words, and since when this entropy begins or it has always been? perhaps the less entropy to day means that the harmonious estate hasn’t change at all, But our perception of the ever growing Universe. or have we loose some of our own Powers? and Potentials?.

  • Brett

    I’m so glad you’re putting some emphasis on this Mr. Carroll. When things reduce as far as they can be reduced in physics, we arrive at dimensions with a value attached to them. The fact that we don’t yet really understand Time as a dimension is a major problem that goes overlooked.

  • Shahidur Rahman Sikder

    As a result of the present situation, it became possible to find out the correct solutions to the questions about universe creation or nature through that 21st century of discovered fundamental Universal law and evolution revolution of physics. Possibility, swiftly finds out most important answering of the questions to help people find a place and their role of the Universe. See at The Universe and our place (Details)

  • Thomas Walsh

    Is it possible that the ‘big bang’ is still unfolding beyond our ability to observe? If so, how might such a condition affect entropy? Just a thought – it’s assumed that the big bang executed and ended; but, what if…


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Random samplings from a universe of ideas.

About Sean Carroll

Sean Carroll is a Senior Research Associate in the Department of Physics at the California Institute of Technology. His research interests include theoretical aspects of cosmology, field theory, and gravitation. His most recent book is The Particle at the End of the Universe, about the Large Hadron Collider and the search for the Higgs boson. Here are some of his favorite blog posts, home page, and email: carroll [at] .


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