Loop Quantum Gravity

Forestman

In the LQG theory does the universe have to be closed, or can space be infinite in size? What I mean is, is the LQG theory similar to the quasi steady state theory in which the universe does collapse, and then bounces back, but is still infinite in size.

marcus

In loop cosmology (LQC) the bounce is a robust feature---meaning that you get it in pretty much all cases.

Spatial infinite is OK. Spatial finite ("closed" as you say) is also OK. With inflation or without.
In some versions you get the bounce on a one-time basis. In other versions it repeats.

A good recent review paper that covers the various cases is by Ashtekar
http://arxiv.org/abs/0812.4703
It's only 12 pages and written for nonspecialists, and it's up-to-date.

LQC was developed by applying LQG concepts and methods to a simplified situation (isotropic homogeneous --- the usual cosmology assumptions)
There is now a bunch of research aimed at bridging or filling in the gap between the cosmology application and the full LQG theory. Some LQC papers now relax the assumption of isotropy. So there is no longer such a sharp distinction. Both LQC and LQG are evolving. Both have changed radically since 2005. So it's good to consult recent up-to-date survey papers if you want to find out stuff.

Here are some spires searches. I realize you didn't ask and probably don't need spires searches. But since both fields are developing rapidly it's good to be able to glance at an objective snapshot---most highly cited titles and authors at this point in time.

for quantum cosmology (the top QC papers are now mostly Loop):
http://www.slac.stanford.edu/spires/...tecount%28d%29

and for Lqg:
http://www.slac.stanford.edu/spires/...tecount%28d%29

and to make sure nothing falls thru the cracks an extra search for the covariant (spinfoam) version of Lqg:
http://www.slac.stanford.edu/spires/...tecount%28d%29

Forestman

Thanks marcus.

Chalnoth

I thought the bounce was only shown to occur in the case of homogeneity and isotropy? Because if so, that makes it a far from robust result.

marcus

No, it has been shown in other cases. There have been a number of papers about this. Primarily non-isotropic---e.g. Bianchi I.

What you call robust depends on your own ideas, of course. There are always more cases to consider. The researchers themselves use the word robust because from their point of view they have run many different versions of the model in many different cases. And worked out exactly solvable approximate or effective versions as well. And they keep getting the bounce no matter what different things they try. (Including relaxing symmetry assumptions.)

To them, in the LQC context, it feels very robust and solid.

They also acknowledge that the result has not been proven in the context of the full LQG theory. I hear about efforts in that direction. We may hear something about this coming out of the LQG BH workshop that starts this week in Valencia Spain.

Chalnoth

Hmmm, found this paper on the subject:
http://arxiv.org/abs/0707.2548

This sounds really, really screwy, as they claim that the bounce smooths out the anisotropies, which seems to be a violation of the second law of thermodynamics.

marcus

Good for you for finding a paper!

Some of the recent work where the uniformity conditions are relaxed is also in BHs, if I remember correctly. Relaxing the homogeneity assumption as I recall.

But there should be several more like this that focus on the cosmological singularity.

Naive application of the Second Law is of course controversial in this situation as you doubtless realize. There has been some discussion of this even at PF, but not anything conclusive.

Chalnoth

Well, I can just take this system while it's collapsing, and compare it to a later time when it's expanding but reached the same size. There should be a way to write down the entropy of the system such that the system at the later time always has greater or equal entropy to the system at the earlier time. If the later entropy is lower, then something is horribly wrong: if the calculations were done well, and the approximations used did not fail, then this would indicate that some of the assumptions put into the model of the collapsing universe are such that the later, lower-entropy state was encoded in the previous state, and that a general, realistic state would not do the same thing.

But the fact that this model, if I'm reading it correctly, predicts a smoother universe after the bounce, well, that seems to be a rather lower-entropy state than the collapsing universe.

One assumption that I would tend to hope they are not using is that the universe has zero net angular momentum, as any tiny amount of angular momentum gets massively amplified upon collapse, and may well prevent collapse beyond a certain density. But I don't pretend to know anything about Bianchi I models of the universe.

marcus

This is so interesting! Doesn't it remind you of the confusion about energy conservation in GR.
People expect global energy conservation to hold and are surprised when it doesn't.
But conservation laws have to proved in any given context. To apply a law where it cannot be proven mathematically is similar in a way to superstition. Carrying over a belief in something without rational grounds.

Anyway, during the LQG bounce spacetime does not exist and there is no observer to tell you what the macrostates are and how to do the coarse-graining.

All one has, all one can be sure of, are the microstates.

An observer before collapse and an observer in the subsequent expanding universe will have different things they can measure and different macrostates.

On what basis does one calculate entropy?

Without conventional space, in the quantum regime at that moment, how does one prove theorems?

If one cannot prove theorems how can one apply the Second Law? Except as a superstition of course

So it's interesting, there are some good research papers to write on this topic!

BTW Ashtekar has thought a lot about entropy and the Second Law in connection with the LQG bounce. He is probably the main person (with his postdocs and younger faculty) studying it. You might be interested in checking his latest paper on LQG and entropy.

I don't know if your research is theoretical or observational. You might not be interested by I'll fish up a link just in case. What has been published will not, I think, settle the issue of what happens to entropy at the LQG bounce because that is still unresolved. What the available papers can show is the direction Ashtekar is going, how he is thinking about entropy in connection with the LQG early universe. I think there was one in 2008.

apeiron

Alternatively you could take the "QM realm" story of an actual world without observers as the superstition and the second law as the likely more reliable guide for theory framing.

The second law as it is commonly framed in terms of the entropy of an ideal gas is not really up to the task. But within the second law community, other broader definitions might be helpful.

For example, there would be a basic question of whether we should apply the gaussian statistics of a Boltzmann steady-state system or the power-law statistics of an open "far from equilibrium" dissipative structure (the kind of entropy Tsallis, Renyi and others are attempting to model).

As a glimpse of how things might be different, consider the question of microstates and macrostates in a scalefree network. Nodes and hubs are in an open or expanding equilibrium. The "temperature" of the system has a subtly different interpretation.

In an ideal gas, there is one global macrostate (external temperature) and one internal average microstate (a gaussian average lowest scale randomness). But in a scalefree network, there are all scales of action. You cannot pick out the smallest scale and the largest scale as unique as you can with an ideal gas. Instead, there is a scale symmetry across the middle ground of the system.

So you cannot anywhere find a macrostate or a microstate as such. All you see is macro and micro in a certain fractal balance everywhere.

In the ideal gas version of entropy, the second law is taken to say that a system diverges towards a microstate/macrostate split. But in the kind of world we find within phase transitions and other dissipative systems, the system is balanced evenly across all scales. And to persist, it must either expand (grow like a scalefree network, accumulating entropy within itself in effect) or dissipate (export entropy to some external sink).

So the second law would be a powerful guide to cosmological speculation. But you have to now be ready to consider which kind of entropy story should be applied.

marcus

Come on Apeiron, don't confuse the issue. We are talking just about the LQC bounce context. You may have other ideas about a bounce, and other models. But here we are talking about LQG (the topic title on the thread) and the LQC bounce framework.

The "quantum regime" is often referred to in that context as what happens right around the bounce when quantum corrections become dominant and gravity repels. Geometry as we know it stops existing.

Certainly this may be WRONG. The theory has to be tested by what it predicts should be visible in the present. But don't call the conditions deriving from the model "myth". They are mathematically fairly precise. The quantum regime starts when density is a few percent of planck (at which point the classical approximation is no longer good, so quantum geometry takes over.) And it goes up to about 40 percent of planck density.

The question is not whether LQC will test wrong against data. The question is how it handles the entropy issue.
If you have a better bounce theory in mind, please start a thread about it. Or if your theory handles entropy questions differently, again, I urge you to start a thread and talk about it.
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So the point I'm making is that for instance if you want to apply a law, like conservation of energy, in the GR context then you have to prove it in that context. And you cannot naively apply energy conservation in GR, because you can't prove the law.

That doesnt mean GR is wrong, it just means you can't apply global energy conservation when the geometry is dynamic. So this teaches us a lesson or highlights Noether's insight about conservation laws: what is required for them to hold. You know all this.

Same with thermo laws in the LQC case. We have to consider what is required in order to prove a given law, or even what is needed in order for thermodynamic entropy to be defined. We have to think if those conditions pertain closely around the LQC bounce.
Personally I don't know. I'm smply skeptical at this point.

However Ashtekar has clearly been thinking about it. Last year he published a paper on LQC and the Bousso entropy bound.

In classical GR the Bousso bound fails as you go back into the early universe. I'm just paraphrasing, I don't remember why. They show this in the paper. And they show that with LQC you can go back further in time and the Bousso bound holds.
I don't remember how far back it holds, but the bound involves geometry, surfaces, It seems to me that even in LQC the terms of Bousso bound must eventually become meaningless. One stops being able to talk about surfaces and other geomtric stuff. I don't know enough to have a position on this, I'm simply skeptical that the Bousso entropy bound extends back to or beyond the bounce. It involves macroscopic concepts which are emergent from more fundamental degrees of freedom and which I suspect become meaningless (in LQG context) when density reaches a few percent planck.

I'll fetch the link in case you or anyone else wants to think some more about this
http://arxiv.org/abs/0805.3511
The covariant entropy bound and loop quantum cosmology
Abhay Ashtekar, Edward Wilson-Ewing
15 pages, 3 figures; Physical Review D (2008)
(Submitted on 22 May 2008)
"We examine Bousso's covariant entropy bound conjecture in the context of radiation filled, spatially flat, Friedmann-Robertson-Walker models. The bound is violated near the big bang. However, the hope has been that quantum gravity effects would intervene and protect it. Loop quantum cosmology provides a near ideal setting for investigating this issue. For, on the one hand, quantum geometry effects resolve the singularity and, on the other hand, the wave function is sharply peaked at a quantum corrected but smooth geometry which can supply the structure needed to test the bound. We find that the bound is respected..."

marcus

We were talking about LQC papers that deal with non-isotropic cases. There have been a number of LQC papers lately involved with relaxing the homogeneous isotropic assumptions. Too many to hunt them all down. But you found this 2007 one, and I happened just now to see a 2009 one by Ashtekar and Wilson-Ewing. It might interest you. (Partly for the simple reason that it is a good deal more recent than your Chiou-Vandersloot paper on Bianchi I.)

http://arxiv.org/abs/0903.3397
Loop quantum cosmology of Bianchi I models
Abhay Ashtekar, Edward Wilson-Ewing
33 pages, 2 figures
(Submitted on 19 Mar 2009)
"The 'improved dynamics' of loop quantum cosmology is extended to include anisotropies of the Bianchi I model. As in the isotropic case, a massless scalar field serves as a relational time parameter. However, the extension is non-trivial because one has to face several conceptual subtleties as well as technical difficulties. These include: a better understanding of the relatîon between loop quantum gravity (LQG) and loop quantum cosmology (LQC); handling novel features associated with the non-local field strength operator in presence of anisotropies; and finding dynamical variables that make the action of the Hamiltonian constraint manageable. Our analysis provides a conceptually complete description that overcomes limitations of earlier works. We again find that the big bang singularity is resolved by quantum geometry effects but, because of the presence of Weyl curvature, Planck scale physics is now much richer than in the isotropic case. Since the Bianchi I models play a key role in the Belinskii, Khalatnikov, Lifshitz (BKL) conjecture on the nature of generic space-like singularities in general relativity, the quantum dynamics of Bianchi I cosmologies is likely to provide considerable intuition about the fate of generic space-like singularities in quantum gravity. Finally, we show that the quantum dynamics of Bianchi I cosmologies projects down exactly to that of the Friedmann model. This opens a new avenue to relate more complicated models to simpler ones, thereby providing a new tool to relate the quantum dynamics of LQG to that of LQC."

apeiron

Don't mean to get your goat Marcus. But I was addressing the point raised by Chalnoth that LQC would have to be able to handle second law issues (though I feel the dark energy one is even more of a problem for it).

I was saying that there are more ways of viewing entropy than you are considering. This may be "confusing", yet also crucial. Of course, you may reply that it is all the more reason for the LQC-committed to put second law concerns aside for the moment. Fine.

Where did I use the word myth? I would not even begin to be interested in LQC if as a model it was not generating crisp predictions. But my main criticism is that it is an approach that does not include certain known bits of cosmological furniture, such as the second law and dark energy. So naturally I would want to know whether there is even yet a convincing sketch of how they might eventually be included.

A simple way of framing the question is can we legitimately have microstates without a macrostate - can we have entities without a context, figures without a ground?

It is a bit like the complaint we have about the background dependence of string theory. Because it is a model of microstates only, the macro-context has to written in by hand. Loop gravity was better in knotting the micro together to make a macro. It had a systems logic.

In systems theory, micro degrees of freedom would increase as macro constraints are removed. The question for bounce cosmology would seem to be that while it seems no problem winding the universe back to a macro-less foam, so to speak, there seems no intuitive reason why we would keep going back in time (in whatever second law sense you frame time) to pop out the other side and find macro-constraints restored.

Yes, equations run backwards would pass right through the eye of the storm and come out the other side reversed. But the second law is asymmetric, not symmetric. Include it in the models and a restoration of macro becomes somewhat magical.

Again don't take these comments personally. It is just that I find loop approaches to the planck scale intuitively attactive - they fit with the thermodynamic and systems science perspective very nicely. They seem progress in the right direction.

However the bounce cosmology and cyclical universe story of LQC strike me as very ugly and unlikely for the same reason. They run against what I know from systems thinking.

marcus

Thanks for patiently laying out your point of view! It contrasts with mine (may in fact be more focused and well-defined than mine in spots) and seems well worth trying to understand.

Chalnoth

Well, just consider a third state: after the universe starts to collapse again (assuming no cosmological constant, of course), and is the same size a third time around. By the way the equations were written down, this would be a state very similar in character to the initial collapsing state, and should therefore have similar entropy.

However, we know that the entropy has increased dramatically since the early universe.

This alone proves that the collapsing phase cannot be of the same character as the expanding phase's far future. There must be some fundamental differences that make the entropy of the collapsing phase smaller than (or equal to) the entropy of the expanding phase, which in turn means it must be vastly smaller in entropy than the far-future collapsing phase of a zero cosmological constant universe.

Are you talking about this paper?
http://arxiv.org/abs/0805.3511

Well, that definitely provides a hopeful derivation. But it doesn't really answer the question as to how the expanding phase is different such that it is actually higher in entropy than the collapsing phase. Because it should be pretty trivial to show in the simpler case of a homogeneous, isotropic bouncing universe, and even apparent in the Bianchi I case.

My work borders the two, but is generally called theory. And I do admit I know very little about LQG.

apeiron

An analogy that may help explain my intuitive rejection of bounce cosmology....

If you melt ice, you get back to water (a macrostate is shed, resulting in a new level of micro-freedoms). But keep on melting and you do not recover ice. The only logical thing that can happen is a further phase change where further macro-constraints are shed and more micro-freedoms are exposed - so the transition to a vapour phase, for example.

So following a generalised second law way of thinking, if the quantum phase can be "melted" further, it would be expected to lead to a pre-universe with even less structure, not one in which structure was recovered.

This would be more in line with an inflation cosmology. Though I have doubts about that as the inflaton field seems to me still "too structured" to be likely to be something real.

But it would be exactly in line with Wheeler's pregeometry and allied emergent spacetime approaches.

Anyway, a couple of quick points that would seem relevant to evaluation of the issues.

Standard entropy thinking does not account for the free creation of space - all that expansion following the big bang is taken as "a void", and more nothing can be created at no cost, right? I see this as a big hole in cosmology that needs fixing. Entropy modelling has to count all those extra locations as microstates it seems to me. And then the collapse of the void becomes a violent violation of the second law.

Though I can of course see that the free manufacture of the void is a useful simplification for many cosmological modelling purposes. It makes the equations simpler. (Though the discovery that the void is not inertial, but accelerating, is screwing with that simplicity now!)

A second point is the too easy identification of the planck scale with fundamental smallness. The planck scale is also as large as possible in terms of heat, energy density, spacetime curvature, or how ever else you like to measure it.

So we actually have a duality of extremes at the planck scale - both the smallest location and the largest energy. This is of course in the equations, but needs also to be brought out into the intuitive discussions to make sense of the thermodynamics.

A collapsing universe would increase the average heat or energy density of a universe. To allow this as a possibility, we would have to have a way of saying that this recovery of heat was a different kind of heat - more entropic by some measure - than the heat of the big bang.

Penrose tried to do this with his Weyl-Ricci approach of course. I didn't find it convincing, but I may just not yet understand him that well. So that could be an interesting separate discussion.

It is of course a major project in physics to marry GR/QM also to SL - the second law of thermodynamics. Hence all the work on black holes and event horizons. So regardless of whether SL should be an issue for LQC, it is now one for cosmology as a whole.

A good enough reason why it would be (one of) my hobby horses.

marcus

This is intriguing. I have to do something else but will get back to it.
I have seen several Penrose talks on his "outrageous" cosmology idea, either video (like the 2005 one at Cambridge) or in person when he came here---same lecture.
Very impressed and entertained but also I did not find it entirely convincing.
Have to get back to this later