Egg in a Box

By Sean Carroll | March 18, 2009 9:44 pm

Sure is quiet around here. I can’t blog much, as I’m in the final throes of book-writing. So instead, let’s have some user-generated content!

Here is a figure that I’ve drawn for use in my book.


Your mission, should you choose to accept it, is to figure out what the figure is supposed to be illustrating, and what lesson is purportedly conveyed. (Hint: that’s supposed to be an egg.) How hard can it be?

If it’s a fruitful exercise, we can repeat for other figures, similarly inscrutable.

  • Fermi-Walker Public Transport

    something about entropy ?

  • Dileep

    Hmmm… That entropy just happen to be very low at the big-bang event as a result of a statistical fluctuation, and that the thermodynamic arrow of time is only locally relevant?

  • Anthony A.

    Hi Sean,

    Thanks for the Boltzmann Egg. I think it might have been more fun to let it go through the chicken phase first (and after), which would be a new twist on an old problem.

  • Sean

    It’s kind of remarkable that I managed to avoid “Which came first?” jokes entirely. So far, anyway.

  • Anthony A.

    Sorry to spoil your run.

  • Aaron F.

    This is your Boltzmann brain on drugs… 😉

  • BJM

    Which came first?

    The intact egg ALWAYS comes before the broken egg… right?

  • Not an american

    First one is a Boltzman brain illustration, second is an illustration to your silly idea of different time arrows in same universe, separated by vast time periods – same stuff as in SciAm, methinks.

  • Moth Eyes

    From what I can tell, you’re trying to collapse the wave function of Schrodinger’s breakfast.

  • Not an american

    Actually, scratch that. The bottom sequence is an illustration to cyclic universe. The lesson seems to be that a cyclic universe is more likely than Boltzmann brain. Then you probably go on about how the idea you preach is even more likely.

  • Jason Dick

    It’s an illustration of the fact that a somewhat low entropy fluctuation (a broken egg) is much more likely than a very low entropy fluctuation (all the way to a whole egg that then breaks).

  • emit

    It’s an illustration of what happens when physicists take their theories way too seriously.

  • David Moles

    The second row could be our universe, assuming the arrows are not actually the perceived arrows of time (in which case they would go point from the central low-entropy condition).

    The first row is clearly a Boltzmann Omelet.

  • Fluctuation

    Both are hypothetical fluctuations in a classical phase space, the lower one follows a symmetric evolution in the slices. Both are wrong since classical phase space is only an approximation applicable to macroscopic, large N observations. The above are not possible in the full quantum description relying on einselection.

  • Dennis Towne

    The first thing I thought of when I saw these is “looks like something religious fundamentalists would use to mock the big bang or evolution”.

    “Clearly, these pictures demonstrate the impossibility of particles spontaneously forming a complete egg, much like throwing a bunch of 747 parts into a pile will never form a 747. Therefore, there must be a creator.”

    Then the remainder of my brain kicked in and said, ‘entropy discussions and statistical fluctuation’.

  • lemuel pitkin

    I reckon Jason Dick is right, as far as the book goes.

    As far as the physics goes, way above my pay grade. I do wonder, tho, what is the logical nature of Sean’s objection to the “naive” view that it is simply a fact about the physical world that the universe began in a state of minimum entropy. Is that an empirical issue that could in principle be settled observationally? Is the objection aesthetic? Or is there some fundamental reason why that *could not* be the case?

  • Nick

    I’m sorry, It’s not a fruitful exercise.

    It’s an egg.

  • Ted Bunn

    Others have already said it briefly, so I’ll say it verbosely, because that’s what I do.

    Imagine that our relatively low-entropy universe formed as a chance fluctuation out of a high-entropy background. That’s very unlikely, of course, but given a sufficiently long time it could happen. But that wouldn’t be an acceptable explanation of where our universe came from, for the following reason: our universe is pretty low-entropy today, but we know that it was even lower in entropy in the past. So if it formed via a chance fluctuation, it’d be like the bottom picture: the fluctuation would form first the broken egg (like us today) then keep fluctuating down in entropy to form the whole egg (like us in the distant past) then back. That’s exponentially more unlikely than the top panel, where you fluctuate straight to us today, without producing our past first.

    So the formation-by-chance-fluctuation hypothesis can’t do the trick, because it still leaves what we see as incredibly unlikely.

  • Low Math, Meekly Interacting

    If the roughly isotropic frames are a Boltzmann Omelet, and not just Boltzmann scrambled eggs, there’s the matter of the cheese. And the bacon. I doubt Boltzmann bacon will be a pretty thing to illustrate (I don’t even want to think about Boltzmann cheese), so I’d say stick with scrambled.

  • Matt

    Illustration that there more ways, or states, for an egg to be in brokenness than there are for an egg to be whole. And somehow that’s an explanation for the arrow of time.

  • Sean

    Jason and Ted are right, of course. But we’re always happy to provide others with an opportunity to get their grumpy on.

    lemuel, it’s certainly possible that the universe simply began in a very unlikely state, without any deeper explanation being attached to it. It just seems more fruitful to wonder whether that unlikely state is a clue to the operation of some dynamical process, and try to work out what that might be. At this point we have no way of distinguishing, but we hope to someday do better.

  • Demian


    Sorry about posting a not-so-related-to-the-post question here. Maybe I could have just sent you a private email, but I think your readers are also very informed in this so I will post it here. I am going to teach a class called “Origin” next fall. A part of class is about how the universe began. The class is for general audience and now I have to choose a textbook for it. I will cover standard BB and inflation, but also want to talk about more recent stuffs like string inspired etc. Do you know of any good popularized book for this? I only know of Brian Greene’s “the elegant universe”. If anyone has any suggestion with a bit detail description I would be really appreciate it.

    P.S. For the beginning of the life part, I will probably use Paul Davies “the Fifth miracle.” But, if you have other suggestion, that will be welcomed, too.

    Demian Cho

  • Aaron Sheldon

    Isn’t it a bit misleading to show the early universe as being as disorder?

    Could it be better depicted as a transition from a highly order crystal with global symmetries to a less order crystal that has only local symmetries? With the egg occuring at a scale somewhere around ten orders of magnitude larger then the scale of the existing local symmetries.

    What a Goldilocks coincidence that we occur exactly at the scale where anything bigger is statistical isotropic and anything smaller is symmetrically isotropic, and that this is precisely the same scale that is dominated by electrodynamic interactions. Not too hot, not too cold, not too messy, not too organized.

  • Peter Coles

    Are they screen captures from a cookery programme as seen on a TV with very poor reception?

  • TimG

    Having read your blog (in particular your many posts on Boltzmann’s brain, the arrow of time, the low-entropy conditions of the early universe, etc.) definitely makes this challenge easier. Got any inscrutable pictures you haven’t already blogged about?

    Personally, I like Aaron F.’s answer the best.

  • Theo

    Mumble mumble Boltzman mumble.

    But I’ve read your blog. It’s a nice illustration, but there should be text along with it, and a detailed caption for those of us who buy science books just to look at the pictures.

  • Freiddie

    Boltzmann’s egg. LOL :)

  • dwight

    I was going to say that the pictures look like an excellent illustration that shows how unscrambled eggs can form from a cloud of nebular material, and that the egg is not to scale. I’d probably also say something about the captions being deliberately left off to confuse the matter and imply some sort of massive improbability. But I won’t know whether or not this very speculative material will be accurately labelled as such until the book comes out.

  • Wildflower

    Well, it obviously tells a story about ants encountering an egg and making an omelet using the one they found and a 2nd one.

  • Eugene

    I have an awesome answer to the question “Which came first, the chicken or the egg?”

    It is not PG13 though, so I suspect it won’t be in Sean’s book :(.

    (The answer is : the cock came first).

  • Pope Maledict XVI

    “But I won’t know whether or not this very speculative material will be accurately labelled as such until the book comes out.”

    Just like to correct you there: there is nothing speculative about what Sean is driving at here. The early universe was indisputably in a state of fantastically low entropy, and nowadays very few people would dispute Sean’s claim that a Boltzmann fluctuation can explain that. True, Sean does have some speculative ideas about how to *explain* that extraordinary state of affairs, but that is a different matter. In short: what Sean is pointing to here is neither speculative nor controversial.

    There *is* a sort of pseudo-controversy raised by certain cranks who deny that the origin of the second law of thermodynamics is to be found in cosmology. But that’s a “controversy” of precisely the same kind as the creationist “controversy”.

  • Pope Maledict XVI

    Sorry, “can explain” should of course be “can’t” !!

  • dwight

    Well, no Pope, you’re wrong about the correction. Possibly because you haven’t read all of the thread. Sean claims that just as partially-assembled cracked eggs are much more likely to have formed from a statistical fluctuation than a whole complete egg, so it is that Boltzmanns Brains are more likely – much more likely – than a statistical flucuation that brings our perceived universe into being. He’s been told many times by many people that as formulated, this is just plain incorrect. Or if you prefer, a wild speculation. He’s done things like the above to show his argument, but when people point out that no, make the mass of particles not particularly large and it becomes much more likely that whole eggs form rather than partial eggs, and he shifts the grounds to ‘well, we’re not talking about an undifferentiated mass of particles anyway.’ In which case, his analogy is similarly flawed. There’s a more sophisticated way to put this, of course, and that’s what most of Sean’s fellow physicist believe. The Boltzmann Brain argument really doesn’t have a lot of followers in the mainstream. Again, for pretty clear and easy to explain reasons about how to count states, conditional probabilities, etc.

    That’s not to say that most physicists believe that the universe arose spontaneously as a statistical flucuation, of course. Just that if you don’t believe it did, this argument is not the way to go about proving it.

  • Alan Kellogg

    The sequence in question illustrates viewer experience watching a digitally broadcast cooking program on an analog tv using a cheap converter.

  • TimG

    dwight, you seem to be claiming that given a “large mass of particles” a low entropy state is more likely to arise as a statistical fluctuation than a high entropy state. This makes no sense to me, even after reading the whole thread. If there is a “clear and easy to explain” reason for this, then please explain it rather than simply asserting that such an explanation exists.

  • emit

    Pope Maledict XVI Says: `The early universe was indisputably in a state of fantastically low entropy, and nowadays very few people would dispute Sean’s claim that a Boltzmann fluctuation can explain that.’

    I do not dispute the claim that the early universe was in a state of fantastically low entropy.

    I do dispute the claim that a Boltzmann fluctuation can explain that. Who claims that anyway?

    The whole point of the Boltzmanns Brains argument is that a Boltzmann fluctuation can explain the universe one observes only if solipsism is true. Obviously you should look elsewhere for an explanation.

  • joulesm

    @Eugene: I totally lol-ed at that.

  • existential mime

    Poincare Recurrence

  • Sili

    I’m in the final throes of book-writing

    Just how fast do you work?!!

    Which came first?

    The intact egg ALWAYS comes before the broken egg… right?
    BJM Says:
    March 18th, 2009 at 10:48 pm

    Define “before”.

  • Alan

    Slightly sinosodal interpritation of time ay with the egg joining then breaking again?

  • Qubit

    If a egg can appear then so can a chicken, seen as a there is enough potential information in there to create one? If the chickens mind can reach a low enough state of entropy it can create itself the universe, human beings and then lay the information for the egg in the box for someone to create your experiment then escape and live free range in someone’s back garden. Then seen as it unlikely that it will ever happen again, it will be impossible for the humans to realise that God is fact a free-range chicken and that’s really why chicken taste like everything! :)

  • Qubit
  • CarlN

    Pure stupidity. If this does not tell you that everything comes from nothing, then nothing will.
    Yeah, nothing will :-)

  • Brody Facoum

    Uhm, a stupid question, since the fluctuation answer has already been marked:

    If we read in a few frames where the arrows are, with greater structural density towards the middles of each chain of arrows, do we also have a diagram (of an analogy) of the evolution of two FLRW universes where Omega > 1 and where the bottom one is a conventional “Big Crunch/Big Bang” oscillation while the top one has much more dark energy?

    Stupider question: how would one distinguish between being in the lower type of Universe from being somewhere in a longer chain comprising these two subchains at a time after an expansion from a period where the universe is hot and dense enough for GUT physics and some later period hot and dense enough for BBNS?

    Stupidest question: can they be linked together in a chain in the sort of “extra-universe filled with multiple universes following different arrows of time” model you have been exploring?

    Waaaay out there: is there an equivalence between a fluctuation model where a Boltzmann Brain and its environment appears “ex nihilo” and a continuous model where we only at a few selected points along a timelike axis? (I.e., in your diagrams do we have snapshot at sparsest boundary condition, snapshot at some intermediate point on the order of tens of Gy before the hottest densest boundary condition, a snapshot at the hottest densest boundary, another snapshot at some intermediate point on the order of tens of Gy after the hottest densest boundary condition, and a snapshot at the sparsest boundary; or do we definitely have a diagram as described in Jason and Ted’s comments, and as criticized by “Fluctuation”‘s comment?)

  • Mike

    This is about intelligent design, is it not? I mean, really, creating an egg from nothing? It’s far more likely that you just get scattered yolk than an egg, therefore, there must have been an intelligent designer that formed that beautiful egg. Duh.

  • Loki

    The 2-nd line:

    the egg in the midlle = our present state

    most probable Past and Future to the left and right – should be symmetric!

    the fact that our actual Past is very different represents a puzzle that need to be explained

  • John B

    The top line, “Someone broke an egg”.

    The bottom line, “OK, who’s playing silly buggers?”


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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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