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.
Sean,
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.
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.
Anthony
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 🙂
regards,
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.
Watcher:
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.
Archer:
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).
Sean, et.al. —
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.
Regards,
Paul
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?
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…
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
Alejandro,
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 couple references to the recent talks of Penrose about “Before the big bang”:
Talk in NI 7 Nov 2005
Talk in NI Dec 2006
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.
The scenario pointed out by some posters, can be resolved when the transition phase is: http://en.wikipedia.org/wiki/Bosenova
If one treats the Bojowald “bounce” as a super critical Bose Einstein Condensate:http://en.wikipedia.org/wiki/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:http://www.lorentz.leidenuniv.nl/history/Einstein_archive/
Sorry missed a link at hte end:http://en.wikipedia.org/wiki/Fermbec-Hunt_theory
#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.
http://www.newton.cam.ac.uk/webseminars/pg+ws/2005/gmr/gmrw04/1107/penrose/
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.
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
Sorry. http://arxiv.org/abs/physics/0612053
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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?
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!
A Rivero,
back again. That November 2005 talk at Cambridge that you gave link to
http://www.newton.cam.ac.uk/webseminars/pg+ws/2005/gmr/gmrw04/1107/penrose/
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
Hi Watcher, it seems that our authority appeal has killed the thread 🙁
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 http://www.bnl.gov/video/lectures.asp ), 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,
Paul
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.