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.
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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?
so then the conclusion is the total entropy does neither increase nor decrease.
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.
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.)
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.)
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.
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.
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.”
http://arxiv.org/abs/0705.4398
The Dark Side of a Patchwork Universe
It looks like a long shot but he might be lucky again.
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?
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.
Watcher:
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.
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?
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?
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, 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.
sean,
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…
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.)
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
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?
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.
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!)
Thanks.
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.
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.
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.
Thanks
*http://online.kitp.ucsb.edu/online/singular_m07/
organizers besides Gary Horowitz were Bojowald, Brandenberger, Liu
interesting videos and slides of some of the talks