A Universe Out of Chaos

How did the universe come to be? We don’t know yet, of course, but we know enough about cosmology, gravitation, and quantum mechanics to put together models that standing a fighting chance of capturing some of the truth.

Stephen Hawking‘s favorite idea is that the universe came out of “nothing” — it arose (although that’s not really the right word) as a quantum fluctuation with literally no pre-existing state. No space, no time, no anything. But there’s another idea that’s at least as plausible: that the universe arose out of something, but that “something” was simply “chaos,” whatever that means in the context of quantum gravity. Space, time, and energy, yes; but no order, no particular arrangement.

It’s an old idea, going back at least to Lucretius, and contemplated by David Hume as well as by Ludwig Boltzmann. None of those guys, of course, knew very much of our modern understanding of cosmology, gravitation, and quantum mechanics. So what would the modern version look like?

That’s the question that Anthony Aguirre, Matt Johnson and I tackled in a paper that just appeared on arxiv. (Both of my collaborators have also been guest-bloggers here at CV.)

Out of equilibrium: understanding cosmological evolution to lower-entropy states
Anthony Aguirre, Sean M. Carroll, Matthew C. Johnson

Despite the importance of the Second Law of Thermodynamics, it is not absolute. Statistical mechanics implies that, given sufficient time, systems near equilibrium will spontaneously fluctuate into lower-entropy states, locally reversing the thermodynamic arrow of time. We study the time development of such fluctuations, especially the very large fluctuations relevant to cosmology. Under fairly general assumptions, the most likely history of a fluctuation out of equilibrium is simply the CPT conjugate of the most likely way a system relaxes back to equilibrium. We use this idea to elucidate the spacetime structure of various fluctuations in (stable and metastable) de Sitter space and thermal anti-de Sitter space.

It was Boltzmann who long ago realized that the Second Law, which says that the entropy of a closed system never decreases, isn’t quite an absolute “law.” It’s just a statement of overwhelming probability: there are so many more ways to be high-entropy (chaotic, disorderly) than to be low-entropy (arranged, orderly) that almost anything a system might do will move it toward higher entropy. But not absolutely anything; we can imagine very, very unlikely events in which entropy actually goes down.

In fact we can do better than just imagine: this has been observed in the lab. The likelihood that entropy will increase rather than decrease goes up as you consider larger and larger systems. So if you want to do an experiment that is likely to observe such a thing, you want to work with just a handful of particles, which is what experimenters succeeded in doing in 2002. But Boltzmann teaches us than any system, no matter how large, will eventually fluctuate into a lower-entropy state if we wait long enough. So what if we wait forever?

It’s possible that we can’t wait forever, of course; maybe the universe spends only a finite time in a lively condition like we see around us, before settling down to a truly stable equilibrium that never fluctuates. But as far as we currently know, it’s equally reasonable to imagine that it does last forever, and that it is always fluctuating. This is a long story, but a universe dominated by a positive cosmological constant (dark energy that never fades away) behaves a lot like a box of gas at a fixed temperature. Our universe seems to be headed in that direction; if it stays there, we will have fluctuations for all eternity.

Which means that empty space will eventually fluctuate into — well, anything at all, really. Including an entire universe.

This basic story has been known for some time. What Anthony and Matt and I have tried to add is a relatively detailed story of how such a fluctuation actually proceeds — what happens along the way from complete chaos (empty space with vacuum energy) to something organized like a universe. Our answer is simple: the most likely way to go from high-entropy chaos to low-entropy order is exactly like the usual way that systems evolve from low entropy to high-, just played backward in time.

Here is an excerpt from the paper:

The key argument we wish to explore in this paper can be illustrated by a simple example. Consider an ice cube in a glass of water. For thought-experiment purposes, imagine that the glass of water is absolutely isolated from the rest of the universe, lasts for an infinitely long time, and we ignore gravity. Conventional thermodynamics predicts that the ice cube will melt, and in a matter of several minutes we will have a somewhat colder glass of water. But if we wait long enough … statistical mechanics predicts that the ice cube will eventually re-form. If we were to see such a miraculous occurrence, the central claim of this paper is that the time evolution of the process of re-formation of the ice cube will, with high probability, be roughly equivalent to the time-reversal of the process by which it originally melted. (For a related popular-level discussion see From Eternity to Here, ch. 10.) The ice cube will not suddenly reappear, but will gradually emerge over a matter of minutes via unmelting. We would observe, therefore, a series of consecutive statistically unlikely events, rather than one instantaneous very unlikely event. The argument for this conclusion is based on conventional statistical mechanics, with the novel ingredient that we impose a future boundary condition — an unmelted ice cube — instead of a more conventional past boundary condition.

Let’s imagine that you want to wait long enough to see something like the Big Bang fluctuate randomly out of empty space. How will it actually transpire? It will not be a sudden WHAM! in which nothingness turns into the Big Bang. Rather, it will be just like the observed history of our universe — just played backward. A collection of long-wavelength photons will gradually come together; radiation will focus on certain locations in space to create white holes; those white holes will spit out gas and dust that will form into stars and planets; radiation will focus on the stars, which will break down heavy elements into lighter ones; eventually all the matter will disperse as it contracts and smooths out to create a giant Big Crunch. Along the way people will un-die, grow younger, and be un-born; omelets will convert into eggs; artists will painstakingly remove paint from their canvases onto brushes.

Now you might think: that’s really unlikely. And so it is! But that’s because fluctuating into the Big Bang is tremendously unlikely. What we argue in the paper is simply that, once you insist that you are going to examine histories of the universe that start with high-entropy empty space and end with a low-entropy Bang, the most likely way to get there is via an incredible sequence of individually unlikely events. Of course, for every one time this actually happens, there will be countless times that it almost happens, but not quite. The point is that we have infinitely long to wait — eventually the thing we’re waiting for will come to pass.

And so what?, you may very rightly ask. Well for one thing, modern cosmologists often imagine enormously long-lived universes, and events like this will be part of them, so they should be understood. More concretely, we are of course all interested in understanding why our actual universe really does have a low-entropy boundary condition at one end of time (the end we conventionally refer to as “the beginning”). There’s nothing in the laws of physics that distinguishes between the crazy story of the fluctuation into the Big Crunch and the perfectly ordinary story of evolving away from the Big Bang; one is the time-reverse of the other, and the fundamental laws of physics don’t pick out a direction of time. So we might wonder whether processes like these help explain the universe in which we actually live.

So far — not really. If anything, our work drives home (yet again!) how really unusual it is to get a universe that passes through such a low-entropy state. So that puzzle is still there. But if we’re ever going to solve it, it will behoove us to understand how entropy works as well as we can. Hopefully this paper is a step in that direction.

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86 Responses to A Universe Out of Chaos

  1. Mike says:


    In the second to last paragraph on page three the first sentence reads “[t]his story seem surprising not because the net result is unlikely, but because it consists of such a large number of individually unlikely events.”

    I think the third word should be “seems”.

    How’s that for a deep, thoughtful comment on the substance of the paper? 😉

  2. Sean says:

    Oh no! This changes everything!

    Thanks for the catch.

  3. Mike says:

    No problem at all. When the revision is posted, as now it must be, I expect to be listed in the acknowledgments 😉

  4. Tony says:


    During the very long time needed to wait for an ice cube to “unmelt” won’t there be many instances where the ice cube starts to unmelt but the unmelting doesn’t go to completion?

    Similarly, if our Universe was formed in a random fluctuation like you describe, wouldn’t it be more likely that the Universe only proceeded partially toward a big crunch rather all the way to a big crunch?

  5. Sean says:

    Tony, yes, that is exactly right. Which is why the idea that the universe is a fluctuation is very hard to make work — it’s very difficult to see why it would be such a big fluctuation.

    This intuitive notion becomes a little tricky when gravity and curved spacetime are involved; the prospect of inflation in the early universe confuses things a bit. One of our motivations was to un-confuse things as much as we can. And our tentative conclusion is that inflation doesn’t really help in this particular case.

  6. Anthony A. says:

    Tony: yes to both. In fact this is, in essence, the major reason why a fluctuation is not a viable explanation for the universe we see.

  7. Sean Nicholson says:

    Well Sean. I’ve come to the conclusion that your a bit of a one trick pony.
    I’ve read your book from eternity twice. Your your obsession with statistical mechanics and the 2nd law of thermodynamics assumes too much. You make wild leaps from small humps my friend. Waiting forever doesn’t mean every possibility will happen. Entropy is an easy subject to get stuck in and confuse the listener when discussing the origins of the universe and analysing time. Sorry I just distrust your logic.
    Change the record or at least make a better job of your argument.
    Kind regards

  8. george briggs says:

    i think instwad of fluctuations we had a transfer of matter from the preceeding universe. this matter was of E8 symmetry, see papers of lisi et al. this matter had very low entropy

  9. Thanks For Your Comments – Seems Your Proposal Is That The Universe Did NOT Come From “Nothing” – But From “Something” (“Chaos” and/or “Fluctuations”) Instead – Is This Type Of “Somethingness” *Always* Present? – And Related Perhaps – Is True Absolute “Nothingness” *Always* NOT Present? – In Any Case – Thanks For Your Comments – And – Enjoy! 🙂

  10. Ian Ward says:

    It actually might be a good idea to believe in a creator: that way we can leave it up to him/her to figure out how the universe they found themselves in, before they created this one, came to be ie. it puts off all the brain-wracking on them!

  11. William says:


    There has been lots of thought and discussion about how the universe came about and what there was before the Big Bang, but I haven’t seen anything on how the “laws of physics” came about. They seem to be constant and unchanging. We just assume that they have always been so. I know we can see back in time to nearly the beginning (edge?) of the universe and the physical “constants” seem to be constant (taking into accout general relativity), but how do we know that the “laws of physics” remained the same through the Big Crunch?

    Just wondering.

  12. Chris says:

    So if we go along with the idea that the big bang arose from a fluctuation, why do we think that fluctuation actually proceeded all the way to the big bang? Isn’t it more likely that the fluctuation “almost” got there, and then reversed? Or is that even less likely then going all the way to the big bang and proceeding from there? Am I even making sense?

  13. Pingback: Overcoming Bias : Still Scandalous Heat

  14. FmsRse12 says:

    “we impose a future boundary condition — an unmelted ice cube — instead of a more conventional past boundary condition.”

    …doesn’t this mean that future is definetely an unmelted ice cube if this is also the boundary condition….my understanding is that regarding any theory of universe the only interesting parts are the boundary conditions at time zero and approaching infinity, what happens at those points to the universe…. so how can you derive a theory by just assuming certain boundary conditions when its the boundary conditions we are trying to understand in the first place….

  15. David Santo Pietro says:

    I’ve always liked this idea, but what about Boltzmann Brains? If you are going to use the 2nd law to prove anything here you are going to have to use statistics. Don’t the statistics overwhelmingly say that I (as a conscious observer) should be a Boltzmann Brain?

  16. Neal says:

    So … of all histories that include a low-probability bottleneck in the future, the highest probability history is one which gradually approaches that low-probability bottleneck? Reminds me very vaguely of “climbing Mt Improbable.”

  17. BackAlleySUSY says:

    Hi Sean,

    I just have a question regarding this general idea of the universe from a high-entropy state. If the universe is the result of a stochastic fluctuation we would expect this to be the minimal fluctuation, as this is much more probable than anything else. Now we can use anthropic reasoning here to say that it is the minimal fluctuation to create scientist to observe it. However, judging by the vastness of the universe, this fluctuation is much more gratuitous (this is of course the “Boltzmann’s brain paradox”). Does modern cosmology have anything to say about this improbable state of the universe? In other words, is there any reason at all to believe that the universe is a minimal fluctuation?

  18. george briggs says:

    concerning #11: the laws of physics have only one chance to change: at each big bang, and E8 symmetry is involved in setting the rules for the next universe. in this way we can have an evolving
    universe with anthropic characteriistics, which has long been a mystery.

  19. Cutter McCool says:

    “the idea that the universe is a fluctuation is very hard to make work — it’s very difficult to see why it would be such a big fluctuation.”–Sean

    @Sean. Not to get all William-Blakean, but if we’re inside that fluctuation then isn’t that fluctuation only “big” from our perspective? While outside it, within the mother universe that our daughter universe fluctuated from, that fluctuation might be less than a nanoparticle grain of sand?

  20. miller says:

    I was imagining a world in which there are fossils, but the fossils are of creatures that clearly couldn’t have evolved by natural selection. Such a world would be unlikely to come about from a big bang initial state, and would therefore be unlikely to evolve into a big bang state. But then, everything is unlikely to evolve into a big bang state because it’s such low entropy. If we’re already positing a path from chaos to our universe, is it really so unlikely that the path will happen to include fossils of non-evolved animals?

    If I understand your description of the paper, the answer is, “Yes, it is much more unlikely.” Do I understand correctly?

  21. Neal says:

    Been mulling this. You’re arguing that the probability of some history leading up to the Big Bang, conditional upon there being a Big Bang, is maximized when that history looks like a time-reversed Big Bang. Right?

  22. george briggs says:

    i’m saying we may have had millions of big bangs, recycling the same immortal matter over and over again, recycling it thru an E8 symmetry entity each time. the laws of phyics can change only while the E8 symmetry is controlling things. in this way the physical laws could gradually change over time (evolve), resulting in the anthropic universe we observe.

  23. Trevor says:

    So if our current Universe is one of those fluctuations going backward to the Big Bang (but of course we perceive time the other way) AND it is much more likely to not make it all the way back to the Big Bang (a larger fluctuation), doesn’t that mean the creationists might be right?! The Universe was much more likely “created” Just So in order to fool us; it really “started” (ends) at some point well “after” the Big Bang.

  24. Cosmonut says:

    Regarding Hawking’s idea – I fail to understand how the “laws of physics” could “allow” the universe to come into existence from nothing.

    The laws of physics are not transcendent entities – they are just the properties of the various constituents of the universe.

    But nothing would imply no universe and hence no “laws of physics” to allow anything.

  25. Dave says:

    Can a Boltzmann brain be conscious? Who observes the states of the Boltzmann brain? Who observes the observer of the states of the Boltzmann brain?