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.
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?)
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).
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.
Thanks,
Lee
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).
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.
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
oops:
“The Universe really does take the easy route out of the big-bang, entropic chaos is far more simpler than absoulute order!”
“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 🙂
Darn it, now I can only say that my efforts are egregiously underappreciated, not absolutely unappreciated!
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.
Thanks,
Lee
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?
Moshe
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?
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.
Sean
Bojowald’s analysis is not restricted to the spatially homogeneous case, please see for example his latest arxiv paper (and refs)
http://arxiv.org/abs/0706.1057
Effective equations for isotropic quantum cosmology including matter
LQC research already involves some perturbative analysis treating inhomogeneities.
Thanks for hosting such an interesting discussion!
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.
Sean, I’m curious about something in this statement
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!
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?
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….
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. 🙂]
Dan, and Moshe who is with Dan on this,
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.
Watcher,
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?
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.
thanks,
Lee
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.
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.
http://arxiv.org/abs/astro-ph/9711073
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’.
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).
Sean,
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.
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.