Against Bounces

By Sean Carroll | July 2, 2007 11:53 am

bigbangbouncegold.jpg Against the languor of the Independence Day weekend, a tiny bit of media attention has managed to focus itself on a new paper by Martin Bojowald. (The paper doesn’t seem to be on the arxiv yet, but is apparently closely related to this one.) It’s about the sexy topic of “What happened before the Big Bang?” Bojowald uses some ideas from loop quantum gravity to try to resolve the initial singularity and follow the quantum state of the universe past the Bang back into a pre-existing universe.

You already know what I think about such ideas, but let me just focus in on one big problem with all such approaches (which I’ve already alluded to in a comment at Bad Astronomy, although I kind of garbled it). If you try to invent a cosmology in which you straightforwardly replace the singular Big Bang by a smooth Big Bounce continuation into a previous spacetime, you have one of two choices: either the entropy continues to decrease as we travel backwards in time through the Bang, or it changes direction and begins to increase. Sadly, neither makes any sense.

If you are imagining that the arrow of time is continuous as you travel back through the Bounce, then you are positing a very strange universe indeed on the other side. It’s one in which the infinite past has an extremely tiny entropy, which increases only very slightly as the universe collapses, so that it can come out the other side in our observed low-entropy state. That requires the state at t=-infinity state of the universe to be infinitely finely tuned, for no apparent reason. (The same holds true for the Steinhardt-Turok cyclic universe.)

On the other hand, if you imagine that the arrow of time reverses direction at the Bounce, you’ve moved your extremely-finely-tuned-for-no-good-reason condition to the Bounce itself. In models where the Big Bang is really the beginning of the universe, one could in principle imagine that some unknown law of physics makes the boundary conditions there very special, and explains the low entropy (a possibility that Roger Penrose, for example, has taken seriously). But if it’s not a boundary, why are the conditions there so special?

Someday we’ll understand how the Big Bang singularity is resolved in quantum gravity. But the real world is going to be more complicated (and more interesting) than these simple models.

  • Pingback: What happened before big bang? « Entertaining Research()

  • urs

    As far as I am aware, Bojowald’s model is “LQG inspired” as opposed to something one can actually derive from first principles.

    So if we’d allow ourselves to ignore, for a moment, the LQG-inherent language in which his equations are developed and just take them at face value, then what Bojowald accomplishes is writing down a difference equation which approximates Einstein’s differential equations, for some highly symmetric cosmological Ansatz, in the usual regime.

    There should be many different difference equations with the same asymptotic behaviour, hence all approximating an ordinary cosmological model.
    So the question then seems to be: how much nontrivial information is encoded in the choice of any one of these difference equations?

    Suppose there were, for some suitable notion of equivalence of these difference equations, just one possible choice, for some reason. Then one could argue, I think, that there might be nontrivial information hidden there. Like: “See, there is, up to equivalence, only one possible discretization of this cosmological model, and, remarkably, it necessarily leads to a continuation through the singularity of this and that form.”

    I am not sufficiently familiar with this work to judge if this is the case. I kind of doubt it, but I have’t really thought about it in detail.

    But naive as I am, I am imagining that there should actually be arbitrarily many essentially different discretizations of a given cosmological model, which show all kinds of behaviour as one continues them through what used to be a singularity in the non-discrete case. If true, that would mean that Bojowald’s model is mainly picked out by the fact that it follows from LQG-motivations. Is that right?

  • B

    so then the conclusion is the total entropy does neither increase nor decrease.

  • hmmm

    There should be many different difference equations with the same asymptotic behaviour, hence all approximating an ordinary cosmological model.

    I bet! I mean, my God, the situation in classical fluid dynamics is a complete mess. I’m not even sure the different difference equations have the same asymptotic behavior. Numerical relativity can only be worse.

  • Scott Aaronson

    Sean, while I don’t have an opinion about Bojowald’s ideas, I find your argument in case (2) unconvincing. As long as we’re going to say that the entropy was tiny at t=0, why not let it increase from there in the negative t direction as well as the positive one? I.e. if you’re allowed to argue that a fine-tuned initial singularity might not be such a problem, since some theory might someday explain the fine-tuning, then why don’t the bouncians get a similar liberty to posit a dynamical mechanism that would explain the low entropy of their singularities?

    (I guess the real question here is what happens to entropy at a Big Crunch, and whether the Second Law is still valid in a situation where the entire observable universe is contracting to the Planck scale. I’m sure people have thought about this, but I don’t know what conclusions they came to, and would love to be enlightened.)

  • Sean

    Scott, it’s just that I’m more willing to contemplate hypothetical ad hoc unjustified special conditions if those conditions are at least boundary conditions, rather than stuck randomly in the middle of the universe. (Neither one is very convincing, of course.) Which is not to say that they are not contemplate-able; but I would put the burden on someone proposing such a model to explain why the conditions there are so special.

    B, the conclusion is that there was not a unique finely-tuned “bounce” through which the entire universe went. (Unless someone comes up with a scheme that explains the fine-tuning, per above.)

  • Watcher

    I also find Sean’s thermodynamic argument contra bounce unconvincing, but for a different reason.

    The bounce picture, as I understand it, does not require an entire universe to collapse, a partial region can suffice.

    If black hole collapse occasionally leads to bounce evolving into a new region with initial inflation, then we have the same growth of entropy (mediated by “baby” universes) that Sean described for us in the slides of his recent talk.

  • aaron s.

    some friend and i have thought about this as well. though we dont haver the mathematical skills to interperate it, maybe someone else does. the way to describe it without pictures would be this:

    imagine a record on a turntable. the axis of the record is super dense but not located in the center so that if you go out from the axis in one direction the distance would be shorter than if you went out in the other. no place a needle on this record and begin it to spinning. from the viewpoint of the needle, there is an expansion and contraction. thats the general idea. if you dont think i am too much of a crack, then i woul be willing to share more of my incomplete idea…

    just an idea though.

  • Watcher

    But naive as I am, I am imagining that there should actually be arbitrarily many essentially different discretizations of a given cosmological model, which show all kinds of behaviour as one continues them through what used to be a singularity in the non-discrete case. If true, that would mean that Bojowald’s model is mainly picked out by the fact that it follows from LQG-motivations. Is that right?

    In answer to your question, I think what you say is probably wrong, Urs.
    Bojowald and co-workers have not limited their attention only to removing the singularity or to the homogeneous-isotropic case. We are not talking about merely one difference equation that accomplishes only one thing (singularity removal) and therefore is picked out from other comparable equations by its LQG motivation.

    It could also be, I guess, that Martin B. has simply been phenomenally *lucky* in his choice of difference equation models. In which case we should all be so lucky. :-)

    Incidentally in another recent paper, he speculates as to a possible explanation for the “dark energy” effect of accelerated expansion, without having to put in a positive cosmological constant or any dark energy. Again he just uses the basic ingredients of his theory without, as Occam said, “multiplying the entities.”
    The Dark Side of a Patchwork Universe
    It looks like a long shot but he might be lucky again.

  • Jason Dick

    Why are we still talking about a big bang singularity? I mean, didn’t cosmic inflation solve this problem quite handily by just proposing that we can’t trust the classical big bang back that far? And don’t cosmic inflation models typically not require there to be any singularity at all?

  • Watcher

    Why are we still talking about a big bang singularity?

    Jason, I think you have to take that up with the editors of Nature or with the APS’s Physical Review D, which published four of Bojowald’s articles in 2006.

    Or ask David Gross’s institute in Santa Barbara, which held a 3 week workshop on ideas for resolving the bigbang and other sigularities just this year, in January. They asked Bojowald to be one of the organizers.

    People just seem to think it’s interesting to consider (in principle) empirically testable ways to resolve singularities.

    What concerns me, rather, is that I think both Sean and Urs have raised objections which are bogus or else need clarification.

  • Jason Dick


    I suppose I can understand the desire among some theorists to examine these things. But it seems to me that one of the very first checks one would want to do is to ensure that the theory predicts a nearly scale-invariant power spectrum on the CMB, i.e. that it mimics inflation during the “bounce”. Has this check been done for Bojowald’s model? Naively it would seem to me to be difficult to produce a model of singularity resolution under quantum gravity that would do this, though granted I know next to nothing about quantum gravity.

  • Archer

    Would it be fair to describe the Carroll-Chen theory as [the upper half of] a “bounce” model in which the low entropy at the “beginning” *is* explained by the nature of the previous state, ie by the low entropy *density* of the previous universe in which the baby nucleates?

  • Joseph Smidt

    Thanks for the post. Does anybody know if very many cosmologists pay much attention to loop quantum gravity? I know “String Cosmology” has a following, but does very many cosmologists take loop quantum gravity seriously?

  • Sean

    Archer, nowhere in our model is there a “bounce,” in the sense of a collapsing universe that then turns around and begins to expand. Of course any good model must contain a piece that expands from a hot dense phase, if you want to look like the observable universe!

    Joseph, the overwhelming majority of cosmologists could care less about loop quantum gravity, string theory, branes, or any of that. You can do an awful lot of cosmology without worrying about what happens at the Planck scale. But among those who do, loop quantum gravity doesn’t have much of a following.

  • Archer

    “Archer, nowhere in our model is there a “bounce,” in the sense of a collapsing universe that then turns around and begins to expand.”

    Right, but do you picture the spacetime inside the bubble as a bounce spacetime from which the contracting half has been amputated? [Clearly not all expanding universes can be interpreted in this way — most of them do not have a distinguished spatial section, for example.] If so, then it might be possible to find a formal link with Bojowald’s work or other work on bounce cosmologies.

  • ArrowQuestion


    if i understand correctly, you are proposing that our observable universe is in fact just a small local section of a much larger universe that underwent a local inflation bang in the distant past thus producing our universe as a cut-off baby universe. but how does this explain your entropy problem?

    in your scenario when our local patch at T=0 underwent a local bang inflation the entropy was some discrete measure E and has been increasing since. so if we rewind from T=0 into the infinite past we’d find E decreasing monotonically forever? isn’t this the very same infinite fine tuning you decry in other theories? trying to understand…

  • Sean

    Archer, our post-bubble-nucleation universe is really just the same as the conventional inflation+Big Bang model; I don’t know of any sense in which it resembles half of a bounce cosmology, other than the senses in which every Big Bang cosmology does. Unlike Bojowald and similar proposals, the focus of our work was never to elucidate a way to resolve the BB singularity; we just assumed that would someday be done, and concentrated on the bigger picture.

    AQ, in our model, the entropy would not be monotonically decreasing prior to the birth of our bubble. The universe was in a meta-stable equilibrium, not changing in any systematic way. The details of the real universe may be different, but I think it’s important to make an effort to avoid any infinitely-finely-tuned moments in the universe’s history. (An effort which we at least make, whether or not we succeed.)

  • evankeane

    Good post on an interesting question. I am inclined to shun the first idea where the universe is infintely tuned at t=-infinty but think the other idea has more merit (if only simply because RP thinks so!). Of course the “why is the bounce point so special” is the question to ask but it is much more agreeable than the other model.

    Evan Keane

  • ArrowQuestion

    if the local patch is in equilibrium with respect to the larger universe for t=-infinity, then you are saying that this local area just happened to vastly lower its entropy immediately prior to the inflation? if this is so, aren’t you falling into the other trap you mentioned and wrapping all of this infinite fine tuning into the moment of the bounce?

    i guess, i understand your problems with such theories, but i don’t understand your proposal or why it is shielded from these very same problems?

  • Sean

    AQ, if you read our paper, you’ll see that the entropy density of the pre-bubble universe was always very low and nearly constant. The patch in which the nucleation occured never lowered its entropy. The feature of GR that allows the whole idea to work is that a high-entropy state can have a very low entropy density.

  • Watcher

    Sean, I’m not sure you responded to my original point.
    Your paper reconciles thermodynamics with a reproductive cosmology scenario in which a universe has lots of “baby” universes. Entropy increases because of the proliferation of offspring.

    You fault the bounce mechanism, however, because according to you it violates thermodynamics!

    But the cosmological bounce can be embedded in the same basic picture of proliferating baby universes. Where you have a fluctuation in empty space, in your scenario, replace that with the formation of an ordinary astrophysical black hole by the usual gravitational collapse. Then suppose at least in some cases the collapse bounces and leads into an inflation episode.

    Then thermodynamics is satisfied in the same way as in your paper.
    So what is sauce for the Carroll-Chen bubble goose is sauce for the Bojowald bounce gander. Your contra-bounce argument of this post must be bogus, I think, unless your paper is (which I hope not!)


  • Sean

    Watcher, in our model, there isn’t anything that collapses, and therefore nothing that “bounces.” One way of stating my objection to bouncing is that there’s no reason why a collapse should be the kind of smooth thing that has a reasonable chance of nicely re-expanding, as Penrose has often emphasized. Our black holes are (admittedly very rare) quantum fluctuations, not the gravitational collapse of any pre-existing matter.

  • Watcher

    Thanks for responding Sean,
    I realize that your (fluctuation) black holes do not involve collapse.

    But your thermodynamics argument in Carroll-Chen is robust and applies more generally. You reconcile a general reproductive consmology picture with the Second Law by counting the entropy of the proliferating number of offspring universes.

    One can, in effect, do a little surgery and replace each of your fluctuation events by a Bojowald bounce event. Then the bounce is embedded in your general scenario and covered by the same thermodynamic justification.

    It seems to me that you can argue on thermodynamic grounds against a cyclic universe scneario that incorporates the bounce mechanism, but that is another issue. We are talking about the mechanism itself (which can appear in various contexts). I would say your objection to the mechanism itself does not hold water, or at least you have not shown that it is valid.

  • Watcher

    One way of stating my objection to bouncing is that there’s no reason why a collapse should be the kind of smooth thing that has a reasonable chance of nicely re-expanding,..

    That’s a separate argument, isn’t it? This is why Bojowald and quite a few others are studying collapse. The jury is still out on what the probability is of re-expansion, whether that is what you would call a “reasonable chance”.
    You surely know of the workshop earlier this year at KITP Santa Barbara on the quantum resolution of spacetime singularities, where this sort of thing was discussed.

    Roger Penrose has, as you say, argued against bounce but in every case I’ve seen he appeals to the Second Law. You have yourself shown a way around Penrose’s thermodynamic objection to the occurrence of a bounce.

    So I would say that the issue of whether a sufficiently “smooth” collapse-re-expansion event can occur is under active study, by folks like those who gathered at Santa Barbara for three weeks or so in January.*

    Perhaps you should spell out more clearly why you think such a thing has no reasonable chance.


    organizers besides Gary Horowitz were Bojowald, Brandenberger, Liu
    interesting videos and slides of some of the talks

  • B

    B, the conclusion is […] Well, I’d say your conclusion is. I don’t know very much about Bojowald’s paper so can’t say anything about it specifically. But if you say with a bounce the total entropy can neither decrease nor increase then I would conclude it remains constant. Whether and why that part of the entropy we observe increases is another question – and the one that you are concerned about. (We do always only observe subsystems, plus the recurring question what is the entropy of the gravitational field?)

  • Count Iblis

    The fine grained entropy stays constant anyway (due to unitary time evolution, information is conserved). The coarse grained entropy of an object can be defined as the number of (extra) bytes you would need in order specify the exact state of the system given the macroscopic state of the system (e.g. pressure, volume etc.).

    So, I don’t see why it is useful to consider the coarse grained entropy when doing theoretical sudies of models. I don’t think it can be defined very well in the conventional way. If you put the entire model universe in a box, then given the macrostate, you would only need the few bytes you need to specify the entire model universe, so the coarse grained entropy and the fine grained entropy would be the same (approximately equal to zero).

  • Lee Smolin

    Dear Sean,

    I think there is a misunderstanding in your formulation of the question. Bojowald et al in LQC do not “try to invent a cosmology in which you straightforwardly replace the singular Big Bang by a smooth Big Bounce continuation into a previous spacetime.” What they do is restrict general relativity to the spatially homogeneous case, with various kinds of matter, and then quantize the resulting dynamical systems. Everything is well defined. They then compute the resulting quantum dynamics, in some cases exactly, in others numerically. In all of the models they study they find that bounces are generic, i.e. they occur in all models, regardless of matter, matter couplings, and initial or final conditions. So bounces were not put in and they are not the result of any fine tuning. They are consequences of these models.

    You cannot raise a thermodynamic argument against the result of such calculations. Within the model, any such argument must be simply wrong, because it disagrees with the results of the calculations. Presumably this could be checked by studying the evolution of a density matrix in these models and verifying the second law follows from an appropriate choice of initial statistical state.

    Given this, I do not see the force of your argument. To begin with there are issues defining the entropy of a whole universe, but even if I ignore these I have no trouble believing in a succession of universes, each of which has slightly more entropy than the last. This could be accomplished just by raising the temperature of the microwave background slightly in each successive universe. Or, in the case that the bounces come from black hole singularities, all that is required is that each new universe have more entropy than the star that collapsed to a black hole that gave rise to the new universe.



  • Hag

    Just a quick note on your comment on the difference between setting a low entropy on a boundary or on the middle of the evolution. If you consider the evolution of the universe as a path in the space of 3-geometries, there is in fact a boundary whenever you encounter more symmetric geometries. It is a stratified space, indexed by (conjugacy classes of the isometry groups of the points(geometries)). In fact I believe it was DeWitt, and Wheeler, who posited some sort of theory where whenever the Universe’s path would reach those boundaries it would “reflect” in some specific way.

    However, as you wisely put, it looks like a collapse doesn’t have any more symmetry than any geometry previuos to it (it should have very high Weyl curvature, as opposed to a Big-Bang singularity for example).

  • Sean

    Lee, I never expressed doubt that the formulation was well defined, only that there’s any reason to expect it to relate to the real world. At least, no such reason is given. You can’t restrict to the spatially homogeneous case, and then claim there is no fine tuning. That is an infinite amount of fine tuning, which needs to be justified.

    I seem to be saying the same thing over and over, but I’ll try one more time. Unlike cosmologies in which the Big Bang is a boundary condition, bounce cosmologies feature a pre-bounce contracting phase. You need to tell me what happens during that phase, and why. Are there perturbations that are in their growing mode as they approach the bounce? If no, why in the world not? Generic gravitational collapse is expected to be highly non-linear and inhomogeneous, what is so special about this? And if yes, why don’t the perturbations grow and destroy the smoothness? Why in the world would we expect a homogeneous expanding cosmology to emerge from the other side?

    These are not annoying technical issues that can be addressed later. They are the Whole Big Problem that must be confronted by any attempt to honestly address the issue of initial conditions.

  • Paul Valletta

    The question of what constitutes SINGULARITY = “Highly Ordered Low Entropy”, has a definate need for re-intepretation?

    If one looks at the thermal temperature of absolute order, the Absolute Zero conjecture, which states that this thermal low-point cannot be achieved?

    The fact is we deem the early Universe as a vast pool of simple volume-like states, that give rise to the comlpex evolution of particle interactions, and consequently time evolutions. Simplistically we expect the Universe to have a decreasing order of simplicity, backwards to the simplest location of one-state, absolute zero, singularity.

    I contend that this “absolute zero”, is actually totally the opposite of what we believe it to be, it is actually the most complex process there can be. Think about it, constrianing every particle and their interactions is really an intricate and highly improbale event, complete order imposed upon everything there is, or to come, is no simple feat.

    A Highly ordered low-entropy begining to the Universe is far, exceedingly far!, more complex than we give it credit, in thermodynamic terms, the Universe Hot evolution is far more simple than the thermodynamic absolute zero beginning?

    The information needed to attain absolute order, is MORE than the information needed to achieve absolute chaos!..order/simplicity is thus actually the most complex function one can imagine.

    As some posting here have raised the notion of constant information, the constriants on Holographic Bounds, have process’s which, in information terms are exponentially complex as one approaches systems with finite temperature, and as Sean clearly pointed out in his last paragraph of the original post, there are expected ultra complex physical process’s when dealing with big-bang singularities.

    The Universe really does take the easy route out of the big-bang, entropic chaos is far more simpler than

  • Paul Valletta

    “The Universe really does take the easy route out of the big-bang, entropic chaos is far more simpler than absoulute order!”

  • Archer

    “I seem to be saying the same thing over and over, but I’ll try one more time.”

    At this point I would like to say that the community owes Sean Carroll a tremendous debt for keeping this issue alive and trying to get people to realize that you simply can’t put together *any* consistent cosmological model until you explain *exactly* how your model solves the problem of the Arrow of Time. The amount of confusion and misunderstanding of this point out there is simply mind-boggling.

    SC: Thanks for your efforts! Just so that you can’t say that your work is *entirely* thankless :-)

  • Sean

    Darn it, now I can only say that my efforts are egregiously underappreciated, not absolutely unappreciated!

  • Lee Smolin

    Dear Sean,

    I agree with you, the LQC models are only models, and the big question is if the singularity is replaced by a bounce also in the full quantum theory. This is under investigation, there are arguments but no firm results yet. And I also agree that it will be very interesting to know what happens to inhomogeneous degrees of freedom during the bounce.

    One should be cautious of reasoning that is too classical. One can see from the LQC models already that near and during the bounce the geometry is quantum and far from classical. There are also arguments, due to Markopoulou, that near Planck temperatures there is a phase transition to a non-geometric phase where locality is lost completely, see gr-qc/0702044 for more on this, hep-th/0611197 for a model of the phase transition and astro-ph/0611695 for possible consequences for CMB spectra. If this is the case then inhomogeneities may be lost during the phase transition for the same reason that you can melt down a sculpture and then get a homogeneous hunk of metal that when it cools again.



  • Moshe

    Sean, I agree with your assessment, but not for the same reasons. Many of the reasons making a bounce very unlikely are specific to gravity- the universal attraction (w/o negative energies) and the fact that inhomogeneous configurations are more likely are both (related) aspects specific to gravity. I’d be more impressed by the existence of bounce in theories that were shown to reduce to conventional gravity in an appropriate classical limit.

    But for your specific objection- doesn’t Price’s “double standard” apply here as well? whatever makes the initial conditions for our universe very unlikely may well be operating the other direction, no?

  • Watcher


    I’d be more impressed by the existence of bounce in theories that were shown to reduce to conventional gravity in an appropriate classical limit.

    Isn’t it common knowledge that LQC converges to classical Friedmann model a few units of planck time away from the singularity?
    So why aren’t you impressed?

    …specific to gravity- the universal attraction

    I guess you know that when matter is put into LQC it turns out that gravity is universally repellent at very high density–a quantum correction becomes important. So whether gravity is permanently attractive at all scales would seem to depend somewhat on the model—I can’t take it as an axiom.


    You can’t restrict to the spatially homogeneous case, and then claim…

    Bojowald’s analysis is not restricted to the spatially homogeneous case, please see for example his latest arxiv paper (and refs)
    Effective equations for isotropic quantum cosmology including matter
    LQC research already involves some perturbative analysis treating inhomogeneities.

    Thanks for hosting such an interesting discussion!

  • Sean

    Moshe, the relevant concern in this case might be a “middle standard.” It’s fine to imagine a trajectory for the universe that both begins and ends in a low-density high-entropy state, but then why are both such states sufficiently finely-tuned to accommodate a phase in the middle with extraordinarily high density and low entropy? (Maybe the ultra-far past is supposed to be even lower entropy than the bounce, but nobody is clear about this, and that possibility seems to make even less sense.)

    Lee, the “melting” analogy could not possibly be less convincing. Melting increases entropy, it doesn’t decrease it. Gravity is different. The idea that “inhomogeneities may be lost” violates everything we know about unitarity and thermodynamics. (Do you really think that gravitational collapse generically smooths things out? Within any trapped surface, or only near the Planck scale? How is the preferred isotropic RW frame established?) Which is not to say that it’s wrong, but you would have to present some pretty amazingly solid arguments before such an idea is taken seriously, given that it flies in the face of so much else that we think is true.

  • Watcher

    Sean, I’m curious about something in this statement

    It’s fine to imagine a trajectory for the universe that both begins and ends in a low-density high-entropy state, but then why … a phase in the middle with extraordinarily high density and low entropy?

    that I wish you’d clarify.

    Entropy requires an observer, does it not. Even to define it you need the an observer from whose standpoint certain sets of microstates look the same, or mean the same macrostate.

    When you talk about the low entropy transition, between a collapsing region and an expanding one, where is the observer standing?

    Maybe the collapsing region is the formation of a black hole, and the observer is outside the event horizon. Then he sees the entropy of the black hole, but he does not see the bounce!

    Martin’s result seems to be that he cannot measure these things only by taking readings in the collapsing region.

    Or suppose he is on the other side, and witnesses the early stages of expansion of a universe. Then, I think, he cannot know the entropy in the prior collapsing region. Martin et al uncovered a kind of uncertainty principle he called cosmological forgetfulness in the course of researching arxiv/0706.1057.

    In a sense there is no violation of the Second Law because no one can measure or observe such a violation.

    Thanks for such a fascinating discussion, and also to Moshe and Lee. Really interesting issues here!

  • Dan

    Can someone explain how Bojowald gets his bounce in the first place?

    If this is really based on gr-qc/0608100, then it seems that the bounce occurs at scales parametrically large compared to the Planck scale (p is much greater than l_p^2 for the entire evolution to the universe, in his language). The model is just a free scalar coupled to gravity so there is really no reason that GR shouldn’t provide the right answer at that scale. So, to rephrase my original question, why should I expect effective field theory to fail at these scales? Or am I missing something?

  • Moshe

    I’m with you on that, Dan. There is no contradiction since it was never demonstrated that the model reduces to a theory of gravity in the appropriate regime, and w/o gravity (say in the form of the Raychaudhuri equation) bounces are easy. One can then go a step further in drawing conclusions from existence of a bounce in a regime where EFT with gravity would forbid it….

  • Chris W.

    Sean, it’s interesting that the overall thrust of your argument is apparently that attempts to write off the singular origin of the Big Bang as merely symptomatic of the breakdown of classical general relativity, analogous to (for example) the “ultraviolet catastrophe” of the classical account of blackbody radiation, are way too facile.

    I’ve long had a feeling that the occurrence of singularities in GR really do indicate that something is deeply singular in a physical sense under the relevant circumstances, and quantum gravity won’t offer any cheap resolution. Analogies with apparently similar predictions in other theories may suggest otherwise, but GR is not just another theory. My sense is that John Wheeler held a similar view.

    [The previous version of this comment can be deleted. It contained a grammatical error that I couldn’t leave alone. :-)]

  • Watcher

    Dan, and Moshe who is with Dan on this,

    If this is really based on gr-qc/0608100, then it seems that the bounce occurs at scales parametrically large compared to the Planck scale (p is much greater than l_p^2 for the entire evolution to the universe, in his language). The model is just a free scalar coupled to gravity so there is really no reason that GR shouldn’t provide the right answer at that scale. So, to rephrase my original question, why should I expect effective field theory to fail at these scales? Or am I missing something?

    Yes, I think you are missing something, Dan.
    Don’t you imagine that the critical quantity to watch would be the ENERGY DENSITY of the collapsing region, and not the size?

    In some of the k=1 numerical simulations that Ashtekar reported at the KITP workshop, the size at bounce was quite large. This would depend on the conditions in the collapsing region that they set up! But in all the different cases the bounce occurred when the energy density reached about 80 percent of Planck.

    If I remember correctly the size of the simulated universe at bounce could (depending on how they set it up) be as large as hundreds of AU—-i.e. solar system size. The scale factor “p” did not matter. What is critical is the energy density (related, as you know, to curvature).

    Forgive me if I don’t go back and check the Summer 2006 papers, including the one you mentioned, and rely on memory.

  • Dan


    Your statement is correct as far as I can tell. This was my impression from the paper. The parameter which is taken to be large is p_{phi}, some momenta associated with the scalar field. This allows for a parametrically large bounce. So, then the conclusion is that taking this quantity to be very large compared to the natural scale is what is needed. Then it is not just a generic gravitational effect but requires tuning some aspect of the matter content as well.

    So, if I try to make this work in loop quantum gravity and not just this truncation, what would I need to do to get that bounce? Do I need a large vev for phi dot, or will any superplanckian energy density do?

    Another stupid question, if space is discrete (in some sense), can I take momenta for particles to be arbitarily large or is there some fundamental cutoff?

  • Lee Smolin

    Dear Sean and Dan,

    I have not worked on loop quantum cosmology, of which there is now a long and technical literature, but I can help with a few points in answer to questions above.

    0) Most of these models are gravity plus some matter fields, massless scalars, scalars with various potentials, with and without inflation etc. have all been studied in detail.

    1) In all the models in question, classical FRW cosmology is always recovered when the curvature of spacetime is small in Planck units. That is the symmetry reduction of the Einstein equations coupled to matter is derived as the low curvature limit of the same dynamics in which singularities are replaced by bounces. So one cannot say that these models do not contain the appropriate form of the Einstein equations. Furthermore, in the full theory that these models are restrictions of, with spin foam dynamics, sufficient components of the graviton propagator have been calculated and Newton’s law is recovered. Hence, LQG in general is a theory of gravity. Granted there are open issues in the relations between the full theory in this form and the models studied in LQC, but it is not correct to say that “these models do not have gravity in them.”

    2) The question of at what scale the bounces take place has been studied in detail, and the conclusion is that bounces happen when the spacetime curvature becomes Planck scale. Once the models are chosen there are no fine tunings. You have the wrong impression from 0608100. To get a correct impression read the review paper arXiv:gr-qc/0601085, or the many papers it cites. For a somewhat different approach to these models that leads to the same conclusions there is the recent paper of Ashtekar et al arXiv:gr-qc/0612104.

    3) Why do bounces happen? Because of quantum corrections to the Einstein’s equations that become of the same order as the classical terms when the curvature approaches Planck scales. This does not contradict the gravitational force dominating at low curvature, as indeed it is shown they do.

    4) The claims that these solutions always bounce are not based on gr-qc/0608100. That has been demonstrated previously in many models and papers, either analytically or numerically. The point of that paper is to set up and study a scenario in which an effective field theory can be derived and used to reproduce some aspects of the exact theories, which have been already solved.

    5) Homogeneous quantum cosmological models have been studied for decades, and most previous results were restricted to the semiclassical level. I am not aware of any test for well definidness, or correspondence with classical GR in appropriate limits, that these models have not passed.



  • Russ Thompson

    Sean said
    Lee, the “melting” analogy could not possibly be less convincing. Melting increases entropy, it doesn’t decrease it. Gravity is different. The idea that “inhomogeneities may be lost” violates everything we know about unitarity and thermodynamics. (Do you really think that gravitational collapse generically smooths things out? Within any trapped surface, or only near the Planck scale? How is the preferred isotropic RW frame established?) Which is not to say that it’s wrong, but you would have to present some pretty amazingly solid arguments before such an idea is taken seriously, given that it flies in the face of so much else that we think is true.

    This statement was given by a very knowledgable fellow on The Physics Forum.
    >>>Smolin’s CNS picture is a MULTIverse picture because it allows the fundamental constants of nature (like 1/137) to change at the pit of a black hole where a new tract of spacetime sprouts off.>>Originally Posted by Tim Thompson
    But there is one more point. It is not true that there is no evidence for multiple universes. Dark matter & dark energy are not observed, but are rather assumed to exist, as a consequence of observation. But how do we know that dark matter & dark energy are the most suitable interpretations? What if the other universes are not so “unobservable” after all? What if we have misinterpreted the observations, and the force we interpret as “dark matter” is really gravity leaking out of the other universes, and into ours? I can readily imagine a multi-universe theory, which includes such an effect, and therefore is not simply “consistent” with observation, but actually predicts the observed effects we call dark matter & dark energy, as consequences of the communication of information between universes.

    I’m not here to make a case one way or the other, but I am here to make the case that observation should constrain theories, but not imaginations. And one should not be overly impressed by the concept of “truth”, or even of “reality”, as it applies to a scientific theory. The one and only constraint that should apply to science at all levels is consistency. Nothing else matters.

  • Russ Thompson

    Much of my last post was cut off.

    So, I’ll just suggest this, and then see what Lee Smolin has to say about it.

    “The universe is not a fractal,” Hogg insists, “and if it were a fractal it would create many more problems that we currently have.” A universe patterned by fractals would throw all of cosmology out the window. Einstein’s cosmic equations would be tossed first, with the big bang and the expansion of the universe following closely behind.

    Hogg’s team feel that until there’s a theory to explain why the galaxy clustering is fractal, there’s no point in taking it seriously. “My view is that there’s no reason to even contemplate a fractal structure for the universe until there is a physical fractal model,” says Hogg. “Until there’s an inhomogeneous fractal model to test, it’s like tilting at windmills.”

    Pietronero is equally insistent. “This is fact,” he says. “It’s not a theory.” He says he is interested only in what he sees in the data and argues that the galaxies are fractal regardless of whether someone can explain why.

    The Laws Of Thermodynamics are being justified as okay to violate in GR when it comes to ‘local energy’ and in all ‘expansion’ cases, so there ‘should’ be NO reason that
    Lisa Randall’s “Leaking Gravity” to our universe, from ‘that other universe’ could not be applied to Lee Smolin’s…[allows the fundamental constants of nature (like 1/137) to change at the pit of a black hole where a new tract of spacetime sprouts off]

    BUT, instead of the a=1/137, it is the Point Particle/Exotic Matter that is coming into our Voids from E-R Bridges of SMBH’s ‘from that other universe’.

  • Moshe

    Thanks Lee, the bounce occurring at the Planck scale makes much more sense (though I am still hesitant to model a violent event like a bounce using a couple of variables only, I’d expect all high energy degrees of freedom to be at play).

  • Anthony A.


    I share your intuition that a gravitational collapse to the planck density is very unlikely to bounce into a homogeneous region. But I think “watcher” has a good point here: don’t you think a very similar objection could be leveled at the nucleation of baby universes? There, we must rely on inflation to take a rare baby universe that is large enough and homogeneous enough to inflate, and turn it into a large or infinite homogeneous region. So I think there are two separate questions:

    1) Might a ‘bojowald bouce’ lead to a universe with one single FRW-region a (perhaps cyclicly repeating) bounce replacing the BB-singularity? (My guess is no, this will not make sense for just the reasons you put forward).

    2) Might some actually realistic version of a ‘bojowald bounce’ take future singularities and allow them (while still increasing entropy) to create no regions that are homogeneous enough to inflate, and thus provide a new mechanism of creating baby universe? (My guess is maybe, who knows?)

    In either case, though, it seems completely clear to me also that until a non-homogeneous analysis has been done, these results don’t really address either question in a meaningful way.

  • Sean

    Anthony, I think there are plenty of reasonable objections to baby-universe nucleation, but the one that I’m raising against bouncing cosmologies is not one of them. The defining feature of a bounce is the existence of a pre-bounce contracting phase. (Otherwise it’s not really a bounce, is it?) And then the problem is that either the entropy is decreasing during that collapse, for no good reason and in contradiction with everything we think we know about gravitational dynamics, or it is increasing during the collapse, yet supposedly gives rise to an extraordinarily low-entropy condition on the other side, for no good reason and in contradiction with everything we think we know about unitarity and thermodynamics.

    My suspicion is that there isn’t any good way out of this dilemma, and bounces of that sort aren’t part of the real world. But I’d be happy to change my mind, if anyone would offer a plausible response to these objections, or even an outline of what such a response might look like. I haven’t heard any, although someone might have one.

  • Anthony A.


    I agree with your concern about the bounces. What I’m getting at is that perhaps in a less contrived version in which there is some sort of bounce, but in a way that increases entropy and leads to an irregular — but expanding — universe, we might have a picture very similar to the baby universe picture.

    In terms of baby inverses, what I meant was that if you proposed baby universes as a way to generate a new universe out of a fluctuation, but made no mention of inflation, I think you would encounter an analogous (but I agree not identical) argument: how would a fluctuation possibly lead to a baby homogeneous universe? The answer is that it would not, but we can appeal to inflation to fix this.

    So again, I also don’t buy the ‘bounce into homogeneity’ either, but I would not rule out that bounces might be a way to lead into some initial state that, say, might inflate. The argument that such an initial state (that will give rise to inflation) is super-low entropy is also a concern for baby universes. It seems to me that in either case the only hope is that we’re only taking a tiny set of the degrees of freedom of the pre-existing space to create the baby (or bounced region). If we take *all* of the d.o.f. and force them into the low-entropy ‘initial’ state, then we run into awful problems in either case.

  • Jacques Distler

    So again, I also don’t buy the ‘bounce into homogeneity’ either…

    If you don’t buy that, then you don’t buy a single word of Bojowald et al’s mini-superspace analysis of bouncing cosmologies.

    If inhomogeneities are not magically suppressed, then there is no way they can be neglected when the universe reaches the Planckian densities characteristic of the bounce. Inflation, you are right, provides a mechanism for erasing primordial inhomogeneities after the fact.

    But it can’t render an otherwise nonsensical mini-superspace analysis sensible.

  • Watcher


    I would not rule out that bounces might be a way to lead into some initial state that, say, might inflate.

    the Bojowald bounce contains inflation without requiring you to put an inflation field in by hand, or make any other adjustments to the model.

    A problem is that the generic inflation you get with this kind of bounce does not last long enough to give the 60 e-foldings people use to explain structure formation. So one might be obliged to assume an inflaton anyway, to get that extent of inflation.

    But the intrinsic inflation should be enough to get you the homogeneity you wanted.
    The LQC papers about this go back to 2003 and 2004 if I remember correctly. there are quite a bunch of papers including one by S. Tsujikawa and Roy Maartens (so you see it got people outside the immediate LQC community interested.) Actually the earliest paper about the intrinsic episode of accelerated expansion was by Bojowald in 2002. If you would like, I will get an arxiv link for you.

    So perhaps, with that proviso, you will buy the “bounce into homogeneity” picture after all :-)


  • Archer

    Anthony A said: “The answer is that it would not, but we can appeal to inflation to fix this.”

    Sean C. has argued *very* persuasively that inflation doesn’t solve problems like this. It only makes them worse! See his previous article about time’s arrow on this blog.

  • Anthony A.


    But this ‘built in inflation’ assumes the minisuperspace analysis that I do not buy in the first place. I’m not saying that it may not occur in a correct inhomogeneous analysis, or be grafted onto a later (and longer) regular inflationary epoch — just that this is not demonstrated.


    Certainly inflation does take a small somewhat homogeneous region and turn it into a large, homogeneous one. Nobody disagrees with that. What Sean (and Penrose, and Hollands & Wald, etc.) have taken issue with is the notion that a small inflating patch is “generic” (and thus high entropy), while at the same time being low-entropy (so that it is an initial state). The ‘baby universe solution’ is an attempt to get around this by positing that a big, high entropy universe can *increase* its entropy by adding on a baby universe (which can then increase its entropy by growing into a big adult universe).

  • Paul Stankus

    Sean, —

    Before tackling the specifics of any particular bounce model, I’d like to ask for your help in clarifying some basic points about the operation of the Second Law in cosmology.

    Let’s consider a plain-vanilla Friedmann closed universe, which expands and then recontracts. If we restrict such a universe to contain _only_ radiation, then its expansion and re-contraction are basically reversible and isentropic (I argued this back in the “Latest Declamations About the Arrow of Time” post, and you more-or-less agreed; see comments #60, 61 and 67 in that thread). Such a universe can bounce as many times as it wants to without increasing its entropy, but is never “interesting” since it remains spatially smooth and no structures ever form.

    Now consider a closed Friedmann universe somewhat closer to our own, with a significant amount of matter. If we arbitrarily disallow the creation of black holes (only temporarily! don’t worry) then we would generically expect this universe to go through four stages: (1) Radiation-dominated early expansion, which is smooth; (2) Matter-dominated later expansion, during which some gravitational clumping occurs; (3) Matter-dominated early re-contraction, when more clumping occurs; and (4) Radiation-dominated final re-contraction, when the CMB (and starlight) have blue-shifted up to where all clumps and structures are evaporated and the universe is smooth again and remains so until the crunch/bounce.

    How do we do our entropy accounting through these stages? During stage (1), the radiation-dominated expansion, the entropy per co-moving volume is conserved (and hence in the entire universe, if you want to be fussy). During stages (2) and (3) we would like to say that entropy increases, since gravitational clumping is spontaneous and irreversible (at least at first blush). But stage (4), the radiation-dominated final contraction looks an awful lot like the mirror image of stage (1). Since the entropy density of a relativistic gas (with negligible chemical potentials) is purely a function of its energy density, then if the energy per co-moving volume is conserved during stages (2) and (3) we would expect the entropy during stage (4) to be exactly the same as during stage (1) at the same scale factor. So, did entropy go up and then down again? What happened to the Second Law? I can see two ways out of this puzzle.

    First we re-allow black holes to form during stages (2) and (3), as we know they should be able to. Black holes are the one kind of clump that will _not_ evaporate in a hot radiation bath [new suggested advertising slogan: “Black holes — they plump when you cook ’em!”] and so their high entropy will be preserved, and only increase, during all stages of the recollapse. So we might be able to preserve the Second Law by including black holes in our accounting. Does this mean we’ve just reasoned black holes into existence on the basis of thermodynamics in cosmology? Cool as that would be, I don’t really believe it since I don’t see how we can guarantee that sufficiently many black holes would necessarily always form in all closed universes. Certainly we can choose parameters to make the matter-dominated phase arbitrarily short, to where we pick up some gravitational clumping entropy but do not form any black holes; and so we’d still be stuck with Second Law problems in such a case.

    The second approach is to recognize that if entropy per co-moving volume is going to be higher during stage (4) than in stage (1), then we somehow have to arrange for the _energy_ per co-moving volume to go up during stages (2) and (3). Is this not correct? I know that energy accounting in GR can be tricky, but if by “energy” I just mean mass-energy and kinetic energy (velocity relative to Hubble flow) of particles then I think the above is true.
    To increase energy per co-moving volume during stages (2) and (3) effectively requires — as I read it — that (i) the universe have a non-zero positive effective pressure during these stages, and that (ii) the pressure is greater during stage (3), early re-contraction, than it is during (2), late expansion. This would all hang together if it were somehow true that a matter-dominated universe can have an effective positive pressure, and that that pressure increases with clumpiness/non-smoothness. This sort of makes sense to me, since during early re-contraction particles will speed up (relative to the local Hubble flow) and gain kinetic energy in a clumpy universe as the clumps fall toward each other. But I have a hard time making this entirely rigorous. Can you advise, and possibly suggest references?

    To sum up, I would re-state your general Second-Law-based objections to continuous bouncing universes in two cases: If black holes do form during one oscillation and are sufficiently massive, then they will have to survive through any continuous “bounce” and so will cause the successor expansion to start in a non-smooth state. After a finite number of bounces basically _all_ the mass-energy of the universe has been absorbed into black holes, which then go on to merge until the Friedmann-Robertson-Walker description must break down (I have no idea what happens then; that’s your department).
    In the case that massive, long-lived black holes do not ever form, then the universe just gets hotter and hotter with each bounce as long as there’s a matter-dominated phase in the middle. This continues until the universe is so hot that there is _no_ matter-dominated phase, after which it just bounces along isentropically but never forms structure again.

    In both these cases the universe lives only a finite time before winding up in some kind of structure-less state, and so I don’t think any bounce model with continuity between bounces is a good candidate for an eternal universe.

    There; does that make sense? Let me know what you think.



  • Qubit

    With bounce, do you mean that the two universes hit each other and then bounce off? Or do you mean that each universe passes through each other and swaps places?

    Obviously both scenarios are possible in a brane model as each brane can still travel forwards through time and collide with each other (and I mean towards each other rather than one catching the other up), but I would say the passing through each other is more likely than any bounce. I say this because if each universe has such low entropy at ground Zero, each would be so finely tuned that they would simply merge into one brane and pass through as long as each brane has evaporated any black holes.
    It just does not look like creation; its just two simple. These things must occur in our universe but I really don’t see where they originally came from, it’s just an explanation of current cycles, like the explaining why sun comes back every morning. Any bounce or ekpyrotic model will not give us an answer to creation?

  • Alejandro

    This is a question that has been worrrying me for years about bounce models. I asked Ashtekar about it at a coffee break in Loops 07, and as far as I understood his answer, he seems to think that the quantum regime has intrinsically low entropy for some reason, so in the collapsing phase entropy is decreasing (Sean´s option 2).

    However, I didn´t press to ask the following natural question: would a generic collapsing spacetime (which has growing entropy, in the classical regime) also become low-entropy as it enters the Planckian regime? This would be very difficult to believe…

  • Watcher

    this is the phase transition that Smolin was talking about
    he used the analogy of a piece of elaborately worked metal becoming more uniform when it melts.

    gravity is different from matter in the sense that a smooth uniform state of the grav. field corresponds to LOW entropy, with lots of potential to evolve structure by clumping.

    so if you think of the grav. field as a chaotically structured piece of metal, that suddenly “melts”, it is a moment when the entropy is set back to zero—the field was elaborately clumped and even crumpled, when it goes into Planck regime it is returned to a uniform condition

    the question, Alejandro, (BTW I like your BLOG very much!) is how can this sudden reduction of entropy be allowed?

    the answer is that nobody can see it happen. there are only two possible observers one in the region before the bounce and one in the region after the bounce. the before man (B) just sees e.g. a black hole event horizon with a lot of entropy, he cannot see into where it goes Planck regime and bounces

    the after man (A) looks back towards the beginning of his universe and observes the CMB and so on, but he also cannot see the Planck regime and the moment when the entropy goes from very high (chaotic crumpled geometry) to low

    Alejandro I have to go, will get back to this later

  • Watcher

    Just to finish what I was writing when interrupted, I think an operationally defined version of the Second Law is that one should likely never be able to measure a decrease of the entropy.

    BTW it is interesting to imagine how things might conspire to protect the Second Law or to conceal its possible failings.

    AFAIK in Bojowald’s Nature Physics paper he talks about a kind of indeterminacy that limits the ability to measure certain pairs of quantities—to know certain things both about the before and after states. I think there is not a complete “forgetfulness”, that would be too dramatic, but some modest limitation of knowlege. In any case, Bojowald’s paper refers to a principle of forgetfulness.
    One might conjecture that this uncertainty about conditions in the other region would also serve to protect the Second Law.

    I think I could agree with what Ashtekar told you about Planck regime being a low entropy state of the gravitational field.

  • A Rivero

    a couple references to the recent talks of Penrose about “Before the big bang”:

    Talk in NI 7 Nov 2005

    Talk in NI Dec 2006

  • Watcher

    A Rivero, thanks so much for those Penrose references. I was thinking very much of a talk about the Second Law and Cosmology that I saw in person.
    A key point is that these two observers A (after) and B(before) have
    different maps of the phase space

    some things which are insignificant microstates for B may turn out to be very important for A in the expanding (even inflating) universe after the bounce.

    In his comment Alej. Satz ASSUMED the continuity of the entropy, so when Ashtekar told him it was LOW at the Planck regime episode, he assumed that it was DECREASING during collapse!
    But this is not true. During classical part of collapse entropy increases a lot because space is being crumpled.
    However at a certain point there is a discontinuity and it jumps to low. This discontinuity happens when there is a CHANGE in the relevant OBSERVER.

    Mr. B can see only high and increasing entropy. He looks at the black hole or collapse of his universe, looking forward in time.
    Mr. A looks backward in time at the beginning of his universe and he sees only a low entropy beginning, and constantly increasing entropy up to his present.
    There is no contradiction and the Second Law is not violated in any operational sense—no one measures a violation.

    I think maybe you see this anyway without explanation but I want to be sure in case others are reading.

  • Paul Valletta

    The scenario pointed out by some posters, can be resolved when the transition phase is:

    If one treats the Bojowald “bounce” as a super critical Bose Einstein Condensate:

    then one can derive the pre/initial state as gravitational flipping? :When the scientists raised the magnetic field strength still further, the condensate suddenly reverted back to attraction, imploded and shrank beyond detection, and then exploded, blowing off about two-thirds of its 10,000 or so atoms. About half of the atoms in the condensate seemed to have disappeared from the experiment altogether, not being seen either in the cold remnant or the expanding gas cloud. Carl Wieman explained that under current atomic theory this characteristic of Bose–Einstein condensate could not be explained because the energy state of an atom near absolute zero should not be enough to cause an implosion; however, subsequent mean-field theories have been proposed to explain it.

    Due to the fact that supernova explosions are implosions, the explosion of a collapsing Bose–Einstein condensate was named “bosenova.”

    The atoms that seem to have disappeared almost certainly still exist in some form, just not in a form that could be detected in that experiment. Two likely possibilities are that they formed molecules consisting of two bonded rubidium atoms, or that they somehow received enough energy to fly away fast enough that they left the observation region before they could be observed.

    Einstein derived/struggled with the gravitational field equations around 1914:

  • Paul Valletta

    Sorry missed a link at hte end:

  • The Celestial Toymaker

    #58 Wouldn’t a contracting Anti-de Sitter space deal with the 2nd law problem anyway? As it’s area approaches zero, so would its number of internal states, according to Bekenstein/Maldacena. As we’re talking about the whole universe what is there to evaporate into? From then on, the only way is up.

    Minor problem being that this doesn’t explain the fact that our universe appears to have a positive cc and there’s no reason for it to contract. Nor exactly why it would bounce.

    You could blame it on the Bosenova.

  • Watcher

    This is the slideshow/audio of a talk Penrose gave in November 2005 at the Newton Institute, Cambridge.
    Alejandro Rivero gave the link in comment #61.

    I saw essentially the same talk and same slides by Penrose in 2006 at MSRI Berkeley, and he had the same thing to day at Perimeter Institute. The message is the Second Law and how to get a reproductive cosmology that somehow gets around the second law.

    I would propose that everybody who wants to discuss here about that should watch the Penrose show if havent already, so all are on the same page. It is very entertaining and visual—he communicates by pictures.

    He illustrates the second law by drawing a map of phase space, corresponding to some particular observer and what he is able to measure and what phasespace points he lumps together as macros.

    Then at the LAST SLIDE or next to last slide he waves his hand and says NOW WE HAVE A NEW MAP OF PHASE SPACE and the second law goes on. He has a reproductive cosmology scheme and at the moment of reproduction there is an abrupt change of perspective on phase space and essentially entropy is discontinuous there. he also says that his idea is crazy. He is very charming about it.

    IMHO this talk is about as good as it gets, if you want deep visual thought about cosmology and I hope everyone has watched or will watch it.

  • Peter Lynds

    Dear Sean,

    “On the other hand, if you imagine that the arrow of time reverses direction at the Bounce, you’ve moved your extremely-finely-tuned-for-no-good-reason condition to the Bounce itself”

    That’s not actually the case – at least, not if one thinks about thermodynamic time reversal in what I would contend is the correct way. At the risk of promoting my own model, you might want to have a look at (although I should say that I have a more gr/math orientated paper on it about to come out). It actually addresses some other problems/paradoxes that other models don’t too.

    If you possibly read this Scott Aaronson, reading your comment about the second law and the big crunch, you might possibly find it interesting too.

    Best wishes


  • Peter Lynds
  • Pingback: Serious News from Outer Space [Uncertain Principles] · Articles()

  • A Rivero

    Watcher, I saw the 2006 talk, where somehow a conjure of twistorial and conformal transformations allows Penrose to ignore the singularity. It is a pity that he does not upload preprints to the web, or at least I am not good to find them. Cosmology is not my main topic. In fact I am not sure if Penrose tricks are relevant to the discussion here. Are they?

  • Watcher

    In fact I am not sure if Penrose tricks are relevant to the discussion here. Are they?

    what he says in the November 2005 talk is very relevant. he draws phasespace, and different size blob regions on it representing the macrostates from perspective of some observer—-the coarse grains of phase space

    then he draws a squiggly line in phasespace and shows how it likely wanders into everlarger blobs (that is entropy likely increases)

    then he goes out to near “time-infinity” and, at the next to last slide, he takes the Reproductive Cosmology step of imagining a new big bang

    and there he says the coarsegraining map of the phase space TOTALLY CHANGES so that we dont have to worry about entropy—-there is a new perspective, as if a new observer with different significant measurments—so basically he assumes a radical discontinuity in entropy

    even though the squiggly line wandering in phapsespace is continuous, because that is moving in a space of fundamental degrees of freedom, which do not change (only the coarsegraining changes, at the moment of reproduction).

    Sean’s scenario seems like an alternative version of Penrose story, except that the detail of reproduction is different. Same argument can basically support both—in rough outline, I think. Have to go, talk more about this later!

  • Watcher

    A Rivero,
    back again. That November 2005 talk at Cambridge that you gave link to

    is the same slides as what I saw him give in March 2006 at Berkeley MSRI and with help from that Penrose talk, I think a good overview is that there are
    THREE reproductive cosmology scenarios that people are offering and they differ in the detail of the imagined reproductive mechanism and all three are covered by the same Second Law insurance policy.

    there’s Penrose’s, there’s Smolin’s, there’s Sean’s.

    in each case when you hop over to the baby universe, the map of macrostates in phase space changes abruptly—–from the new perspective different combinations of fundamental degrees of freedom are significant and measurable.

    So there is a discontinuity in the definition of entropy when you jump to the new point of observation. A new map of phasespace resets the Second Law. There is one absolute correct map of regions in phasespace. So evolution, in terms of fundamental degrees of freedom, can be continuous. But there is this discontinuity in entropy which by definition cannot be observed.

    Schematically all three reproductive cosmology scenarios are so similar that, if we were playing by traditional scholar etiquette, each of the three would be CITING the other two in their references. Maybe they do. Penrose does cite SMOLIN in any case, prominently on one of his early slides. He actually cites it more as “Wheeler-Smolin” because apparently Wheeler had the branching baby universe picture first (or at least the blackhole-to-bigbang part of it). Penrose style here is casual and informal. I like the way he presents the issues visually very much.

    At the end, Penrose makes the point that a large region in one observer’s phasespace can correspond to a small region in another observer’s phasespace
    (so entropy can be reset). He doent acknowledge that the same reconciliation covers the bounce invoked by Wheeler and later by Smolin, but that’s OK it is IMHO just normal scholar tunnelvision when you find a solution you like then you are temporarily blind to other people’s

  • Alejandro Rivero

    Hi Watcher, it seems that our authority appeal has killed the thread :-(

  • Paul Stankus

    Alejandro —

    Don’t despair completely. If you want a little more action, you Big Brains can try gearing down to reply to my Little Brain comment at #56, which asks some basic second law questions before addressing bounce models.

    To make scrolling back up worth your while, here’s a short form of the same question. I’ve seen Penrose’s presentation as well (video of his recent appearance at BNL can be found here ), and recognized many of the diagrams from _The Emperors’s New Mind_ in its outstanding chapter on entropy. Sir Roger starts from the same observation as Sean, namely that since entropy is increasing through the evolution of the universe it must have been very low in the early phases, ie that the universe must have been in a “very special” state at early times. But if the early (post-inflationary) universe was (essentially) dominated by highly relativistic gas spread very smoothly, then how is that state in any way “special”? To put it another way, if you were observing the early, thermal radiation-dominated phase of the universe, what observation could you make that would lead you to say “Gee, this is a low-entropy state.”?

    Let ‘er rip; regards,


  • Sean

    Paul, I would certainly hope such an observer would say “Wow, look at how rapidly this universe is evolving into something quite different. It must be in an extremely low-entropy state.”

    High-entropy states are in thermal equilibrium; they’re static, not evolving. The early universe is rapidly expanding, diluting, and cooling off — as you would expect from a low-entropy state.

  • Paul Stankus

    Hi Sean —

    Thanks for your quick reply; but I’m afraid I don’t buy it. Just because you see a gas expanding/diluting/cooling does _not_ mean that its entropy is increasing. If you move the walls of a gas-filled box to expand its volume, and do it (arbitrarily) slowly enough that the gas remains (arbitrarily) close to equilibrium throughout, then the expansion is isentropic and reversible. If you cycle the volume reversibly, then the entropy does not increase during expansion and neither does it decrease during contraction.

    Is the early thermal universe any different? Recall that we’ve had some of this conversation before, back at #60 and #61 in the “Latest Declamations” thread (see ). I consider the history of a closed Friedmann universe in which only radiation can exist (not our universe, clearly, but I don’t see it as an unreasonable postulate). This universe expands and then re-contracts, and in the absence of matter the two phases should mirror each other (very nearly) perfectly. So a claim that entropy is greatly increasing during the expansion phase must imply that entropy is greatly _decreasing_ during the re-contraction phase, which would be a big violation of the Second Law. The only reasonable conclusion that respects the Second Law is that the expansion of a radiation-only universe is reversible and so isentropic in all phases. Hence, someone observing the early, radiation-dominated expanding phase would _not_ be correct in concluding that entropy is increasing just because there’s a spontaneous expansion in progress.

    In short, spontaneous macroscopic evolution can often be a _sign_ that entropy is increasing, but it is _not_ a sufficient criterion by itself. Some spontaneous macroscopic evolutions are reversible and isentropic, and an expanding radiation-dominated universe is one example.

    What am I missing?



  • Sean

    True, the fact that something is evolving is not by itself evidence that the entropy is increasing; the Second Law says that the entropy won’t go down, not that it can’t stay constant. But it is evidence that you’re not in a maximal entropy state; if you were, you’d really just be sitting there. (The box with moving walls is not an applicable example, because it’s not a closed system; you’re pushing and pulling on those walls.)

    In cosmology, you can set up an evolution that is pretty darn adiabatic, if you are sufficiently careful. Any matter (nonrelativistic) degrees of freedom, for example, would ruin reversibility, as perturbations would grow. And you need to make sure you have a closed universe, not an open one.

    But even then, it’s not perfect. At the nonlinear level, some of those photons are going to come together and make a black hole. And those black holes are just going to grow. The crunch is never going to be precisely as low-entropy as the bang was.

    The whole point, though, is that there is a state that is static, and remains so, without fine-tuning: empty space. That’s the honestly high-entropy state.

  • Dirk Vertigan

    When looking at reproductive cosmology scenarios, you need to realize that `universes’ are not the true replicators. Instead `Self-Replicating Space-Cells’ are the true replicators. `Universes’ are just the `Survival Machines’ for the Space-Cells. Here is the paper:

    By the way, I am certainly not merely postulating the phenomenon of Self-Replicating Space-Cells, nor am I a priori presuming that there should be any kind of replicators nor any other biological analogies. Instead I am arguing that the phenomenon of Self-Replicating Space-Cells must necessarily emerge from a discrete physics model, if it is to successfully model reality.

    Let me know wether you think I am wrong, and why.

  • Paul Stankus

    Sean —

    Picking up from your main points

    “the fact that something is evolving …. is evidence that you’re not in a maximal entropy state”

    “he whole point, though, is that there is a state that is static, and remains so, without fine-tuning: empty space. That’s the honestly high-entropy state.”

    you seem to be taking the hard line, that if any macroscopic evolution is taking place then the state of that universe is not the state of maximum entropy, and hence is a “special” state. This is not an unreasonable view, in my Little-Brained opinion. But, how are we to apply it to non-empty, closed universes?

    Picture any non-empty, closed universe with some matter and no cosmological constant; this is perfectly reasonable, and not at all fine-tuned. Within the FRW description any such universe is _never_ macroscopically static and stable, and hence must _always_ be in a “special” state by your definition. So what is the honest maxium entropy state of a closed, non-empty universe?

    Naturally we have to consider universes outside the family of Robertson-Walker spaces, ie globally non-isotropic/non-homogeneous geometries. I’m not well-versed enough in GR to discuss these geometries in any detail — perhaps after I’ve saved up enough money to buy your book I’ll know more. But what can you, the expert, tell me? Are there closed, non-empty, non-Robertson-Walker, non-fine-tuned, zero cosmological constant universes with a static geometry?

    There’s one arrangement that suggests itself, just by considering what the matter in a static, closed universe would have to look like. As I see it, there is only one non-empty arrangement which could be forever macroscopically static: when all the matter is collected into one, single giant black hole which is in radiation/absorption equilibrium with a thin, cold gas of light particles. Such an arragement is clearly _not_ a Robertson-Walker universe; but could it exist in a static, non-RW geometry? If so, then it seems that that would be the honest maximum entropy state of a non-empty, closed universe.

    If, on the other hand, there is no way to arrange a non-empty closed universe that is also static (and not fine-tuned), then I think your argument and Sir Roger’s loses traction: if all states of a closed universe must evolve macroscopically, then all states of its states are “special” by your definition. Clearly if all possible states are “special” then the word “special” has lost some of its meaning (remember that line from _The Incredibles_:”If everyone is special, then no one is.”) and we have to drop back to “relatively special”.

    In this latter case, it is again fair to ask: is the intial, smooth radiation-dominated phase of a closed universe “relatively special”? How would we judge it to be so? As I see it, the main quality that makes it “relatively special” is the fact that it’s _not_ chock full of black holes. It’s the absence of black holes, not the simple fact of macroscopic evolution, that indicates you’re in a low-entropy state in that early phase. [“Where are all the black holes? The tour brochure specifically said there’d be black holes. I wonder if it’s too late to get my money back…”]

    In short, I think you have to do a little more work to apply your logic consistently to the case of non-empty, closed universes with zero cosmological constant; this is a perfectly respectable class of of universes (isn’t it?) and the Second Law must apply sensibly to them as it does to open universes.

    Best regards,


  • Sean

    The interesting thing about closed radiation-dominated universes in GR is that they are never able to reach their maximum-entropy configurations, because they hit a singularity instead. Because of singularities, classical GR evades some of the standard properties of statistical systems, such as ergodicity. On the other hand, classical GR is not right! Most of us think that quantum gravity will be much better behaved, and the singularities won’t be such an obstacle.

    By starting with a closed universe, you’ve taken a certain set of degrees of freedom and put them on a trajectory for which they will hit a singularity before they reach equilibrium. That doesn’t mean that such an equilibrium doesn’t exist; it’s empty space. (There isn’t any stable and static configuration of a black hole in equilibrium with a radiation bath; the radiation necessarily back-reacts on the geometry, and the universe will expand or contract.)

  • Paul Stankus

    Hi Sean —

    Thanks very much for the clarifications; I really appreciate the help.

    Now, just one more handful of lingering questions and then I promise I’ll let you go (at least on this thread); these are quick, the best one is last:

    1. Reading this statement

    ” closed radiation-dominated universes …. are never able to reach their maximum-entropy configurations”

    I don’t see this as particular to just radiation-filled closed universes; isn’t it also true of matter-dominated closed universes?

    2. In the presence of a positive, non-zero cosmological constant open universes will, and closed universes may, end up as inflationary De Sitter spaces. De Sitter spaces are in many senses static and stable; they even have a temperature! Since it doesn’t appear to evolve, would you consider a De Sitter space to be a maximal entropy configuration?

    3. I’m a bit puzzled by your preference for empty space as a maximum entropy/equilibrium state, ala

    “That doesn’t mean that such an equilibrium doesn’t exist; it’s empty space.”

    I’ll skip the obvious questions (what’s the entropy of empty space? and what’s the temperature of empty space? empty space has no macro evolution, but it also has no micro evolution; it’s only got one allowed state, classically, and so shouldn’t that count as zero, not maximum, entropy?) and ask instead what exactly you mean by “empty”.

    Consider an open, forever-expanding universe with zero cosmological constant that’s filled with pure thermal radiation and no matter. You implied in an earlier comment that this kind of universe would evolve toward being an empty space, and hence (sensibly) toward equilibrium/maximum entropy. But I don’t see in what sense that’s true. Even after it stops self-interacting, a thermal photon gas retains its basic features as the universe expands. For example, thermal photons have a spatial density of (roughly) one per cubic wavelength, and if you think of them as having a size on the order of their wavelength then they’re packed “right next to each other.” This packing remains true even after an arbitrary amount of expansion, and so it is never the case that “empty space” opens up “between” the photons.

    More concretely, we can observe that the entropy per co-moving volume is conserved during any amount of expansion, out to arbitrary scale factors, and so it’s hard to see how this qualifes as getting any closer to maximum entropy. And, while it is true that the energy per co-moving volume is always decreasing, there is no natural threshold scale below which you can declare space to be “empty” or even “relatively empty”. So in the radiation-only universe, even if it’s open, I can’t see how to make any sense of your statement that its true equilibrium is empty space.

    A smattering of non-relativistic matter will complicate this picture, of course, and may lead to more sensible definitions of maximum entropy and empty space. But, do you really want to tell me that a universe has to have matter for the Second Law to be sensible/applicable? (Sir Roger said something like this last time I saw him.) If so, then that’ll be the weirdest thing I’ve heard this week, though it is only Wednesday.

    OK, that’s it for now; thanks again,


  • Archer

    Hi Paul Stankus, you are making some interesting points.

    Let’s go back to your first question: “To put it another way, if you were observing the early, thermal radiation-dominated phase of the universe, what observation could you make that would lead you to say “Gee, this is a low-entropy state.”? ”

    I guess I would answer: wow, look at how smooth the geometry of 3-d space is! How the heck did that happen?

    In the early universe, essentially all forms of entropy were *high*, with the spectacular exception of the entropy associated with geometry. But just having low entropy in the geometry is not enough to ensure that entropy can increase — you need some way of *communicating* the low geometric entropy to other stuff. It seems that what you are saying is that low geometric entropy cannot be exported to a photon gas. In that case, the geometric entropy remains low, the photon gas goes its merry way, and there is no arrow of time of the kind we observe. The universe begins in a state which, *overall*, is extremely special, and it remains that special, in agreement with the second law. I don’t see anything strange in this, because as you admit your universe is nothing like ours anyway — and in what sense could time “pass” for a bunch of photons?

    Now the hard question for me: am I agreeing with you or not? :-)

  • Sean

    Paul– Yes, it would be just as true for matter-dominated universes as for radiation-dominated ones. For the other points, empty space need not be flat; it could have a nonzero cosmological constant. In particular, we appear to be approaching a de Sitter phase, dominated by a cosmological constant. There we have a pretty good estimate of the entropy, from the holographic principle; it’s proportional to the de Sitter horizon area. (So it goes to infinity in the limit as the cosmological constant goes to zero.) Of course our real universe doesn’t reach that phase in any finite time, but it asymptotes to it; more specifically, the energy density becomes less than that of the Gibbons-Hawking radiation in de Sitter, and you are perfectly empty for all intents and purposes.

  • Russ Thompson


    Something we have NEVER ‘seen’, measured, observed, understood in any sense of the word,……

    Anti-Gravity………..wins the battle???

    Lee Smolin…where is your response to #6 and especially # 7?

  • Lee Smolin

    I thought I had addressed them. In the models Bojowald and others study of quantum cosmology bounces are generic. Every pure initial state bounces, this implies that every thermal state will also bounce. So there is no issue of fine tuning to get a bounce.

    There is another issue, which is whether generic states before the bounce result in near homogeneous cosmologies after the bounce, so that the specialness of the big bang is predicted. My understanding is that this is what Sean is querying and I believe it is an open question. It is interesting to note, as someone did, that a small period of inflation is generic in these models. Whether this is enough to set up iniitial conditions which will allow slow roll inflation in a model with an appropriate scalar potential is an interesting question, to my knowledge it is not resolved.

    Besides this I would urge caution using thermodynamic arguments applied to the whole universe, for reasons I did mention above.



  • Russ Thompson

    Thanks Lee, But I was certainly hoping you would have addressed more of the specifics of ‘constants at the pit of black holes’, and realized that instead of ‘Stars’, that the crux of all of that is in the SMBH’s.

    Let’s try it this way…When Einstein and Rosen developed the E-R Bridges, Einstein was definitely considering the ‘electron’ as the ‘base’ element. And was trying to show how that ‘base element’ could get here Via the Bridges from another universe.

    BUT, of course he did NOT know about “Exotic Matter”/Point Particles even existing, NOT did he Know about SMBH’s. Nor did he really know about the Voids as we do today.

    NOW, from there it is actually pretty simple, BUT, you won’t like the result!!! Why, because it will show that “Inadvertantly” science has defined certain things that wound up stacking the deck against finding the answer to how the universe is really working.

    SO, quite simply…NOTHING can COME THROUGH a ‘Naked Singularity’…period, nada, zilch. (They simply cannot exist)

    SO, the ‘base element’ is REALLY the “Point Particle”…BUT I am not going to name it, because as soon as I do, preconceived ideas about all that quantum ‘stuff’comes into play.

    So, the E-R Bridge(s), where ‘something’ can come through, are the SMBH’s from the other universe.

    SO, as Lee is suggesting/saying, the Second Law should NOT apply to ‘initial conditions’of the universe (Because we really don’t know the way it started to even be able to say!), which simply means that ‘something’ CAN go ‘through black holes’. I know…blasphemy.

    SO, whatever goes onto the event horizon of a SMBH in that ‘other universe’ spirals down to r=0=Ring Planck singularity, and comes through to our Voids.

    That is simply where the “Point Particles” are being created. That comes to us as 96% just as Tim Thompson suggested above. AND, is the ‘gravity leaking’ to our universe just as Lisa Randall has shown. BUT, Lisa Randall CANNOT say that it is coming “through SMBH’s”, because that would be Career Suicide, and she may be many different things, BUT dumb is NOT one of them!

    Lee, those “point particles” are the ‘Strings’/gravity and that is actually how String/”M” theory becomes “Background Independent”!

    BUT, see, as soon as I indicated, that ‘those singularities’…ie, the ones in the E-R bridges, which are the SMBH’s rom the other universe to ours, and that there never has been a naked singularity, and therefore the universe started out cold, with the Gravity leaking to us ‘continually’ through the bridges to our Voids to create the expansion, everybody goes goofy…NO it HAD to start off HOT…we know that for sure!!!

  • Paul Stankus

    Hello, Archer (reply — finally — to #82, 83 above)

    I appreciate your homing in on my original question: what’s so special (ie low-entropy) about the way our Universe (probably) started, in a pretty-smooth, thermal radiation-dominated phase? If that’s really a special state, then it should be easy to say how you would change its characteristics so as to raise its entropy.

    Your answer is quite straightforward: spatially smooth geometry is special, and so low-entropy; presumably, then, having a “bumpier” spatial geometry would be a higher-entropy state. At first glance this makes sense, since there are (presumably) more ways for space to be bumpy than there are for it to be smooth.

    Thinking a little farther, though, I’m not so sure that bumpy space is necessarily higher entropy when that space is filled with radiation. We can see this by asking: in a radiation-dominated phase, will a non-smooth spatial geometry tend to grow bumpier or smoother over time? Now, mine is only a Little Brain but I can at least take a swing here.

    Somewhat sloppily, we can divide spatial “bumps” into two kinds: (1) Volume-changing, which follow inhomogeneities in the mass-energy density and (2) Volume-preserving, which propagate on their own, ie gravity waves. The first types will tend to smooth out over time in a radiation-dominated phase, since we know that radiation does not clump gravitationally but instead tends to spread out more evenly in space — you can think of this as the effect of finite viscosity and/or heat conductivity in relativistic gases. The second type will, I think, also tend to damp out at long wavelengths, ie longer than the gas’ inter-particle spacing, as the gravity waves give up energy via dissipative/frictional/viscosity effects in the radiation gas. Short-wavelength gravity waves, ie with wavelengths comparable to the inter-particle spacing, may gain or lose energy randomly and so will tend to come to some sort of equilibrium; but this “graviton gas” does not (I think) represent a lot of entropy.

    Sticking with Sean’s bedrock principle that all spontaneous, irreversible macroscopic evolution represents an increase in entropy, I would then conclude that bumpy space is actually _lower_ entropy than smooth space in a radiation-dominated phase, as in our Universe at early times. So, no: I disagree with your answer that smooth space in the early Universe is “special” or low-entropy, since this smoothness appears spontaneously during radiation domination.



    PS If I can tempt anyone into a reply at this late date, I’ll venture a few words on my own opinion about special early states.

  • Watcher


    Sticking with Sean’s bedrock principle that all spontaneous, irreversible macroscopic evolution represents an increase in entropy, I would then conclude…


    The principle is not rock solid because it leaves out the observer. You could make it plausible by inserting this:

    All spontaneous, irreversible macroscopic evolution seen by a single observer represents an increase in entropy as defined by that observer.

    The definition of entropy has to do with how many microstates are indistinguishable to the observer and therefore constitute a single macrostate. Or is expressed in terms of the volume in phase-space of what the observer sees as a single macrostate. The observer’s MAP of phase space, in other words.

    What you call Sean’s principle, otherwise known as the Second Law, can not be applied to a cosmological bounce simply because there is no observer who sees the Before and After universes and can apply a consistent map to phase space, or who can witness the bounce.

    An observer Before will see increasingly chaotic geometry and (I would imagine measure increasing entropy) while an observer After will look back in time and measure a low entropy state. There is no contradiction and no violence to the Second Law because the two have different maps of phase space and measure entropy differently.

    Thanks for continuing the discussion, Paul. I think it’s extremely interesting.


  • Pingback: Quirks and Quarks: Before the Big Bang | Cosmic Variance()

  • Pingback: Arrow of Time FAQ | Cosmic Variance()


Discover's Newsletter

Sign up to get the latest science news delivered weekly right to your inbox!

Cosmic Variance

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] .


See More

Collapse bottom bar