In loop cosmology (LQC) the bounce is a robust feature---meaning that you get it in pretty much all cases.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.
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.In loop cosmology (LQC) the bounce is a robust feature---meaning that you get it in pretty much all cases.
No, it has been shown in other cases. There have been a number of papers about this. Primarily non-isotropic---e.g. Bianchi I.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.
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.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.
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.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.
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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.)Hmmm, found this paper on the subject:
http://arxiv.org/abs/0707.2548 ...
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).Come on Apeiron, don't confuse the issue. We are talking just about the LQC bounce context.
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.But don't call the conditions deriving from the model "myth". They are mathematically fairly precise.
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?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.
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.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?
Are you talking about this paper?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.
My work borders the two, but is generally called theory. And I do admit I know very little about LQG.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.
I'm afraid I can't respond point by point to your post. I like the way you think. It stimulates my imagination and causes new thoughts and gives me something to push against. So I'm happy but probably not holding up my end of the conversation particularly well....
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.
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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...
Neither do I think of them as little discrete specks of existence. Instead, I would take the condensed matter, soliton, perspective of Laughlin, Volvik, etc, which also would be the systems science approach taken more generally in other fields of science.BTW I don't think of locations in space as having physical existence .
Does anyone suggest that these black holes blow all their entropy out the other side - so as white holes, they are spawning other universes? All that created entropy could be exported to balance the books?Say the prior classical continuum (vaguely like ours, but contracting) has evolved a huge number of black holes of all sizes, stellarsize, supermassive etc etc. These BHs represent a huge amount of entropy. An observer before the bounce is witness to all that entropy.
Another alternative out. But if blackholes have a reasonable physical size, then they would all be on top of each other at quite a large scale?Mr Before infers there is a vast complex termite-ridden structure of BHs falling into BHs. Like a fractal, every BH has other BHs falling into it and each of them has still others falling in. When bounce density is reached (estimated around 40 % of Planck) gravity repels and all that structure is invalid.
I think there is a problem here in the idea of the second law being defined from the point of view of a single observer. I know it is a traditional way to talk (Maxwell's demon, etc) but in the systems science approach, the observer would be the global scale of the system. It is not an external observer who becomes ignorant of the microstates to create a macrostate (like a single temperature or pressure reading) but the system itself which forms a macrostate (an ambience, a stable equillibrium).There were amenities available to facilitate earlier proofs (like a single observer throughout, with a single coarse-graining---like conventional geometry and conservation laws) which one may not be able to invoke.
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Say the prior classical continuum (vaguely like ours, but contracting) has evolved a huge number of black holes of all sizes, stellarsize, supermassive etc etc. These BHs represent a huge amount of entropy. An observer before the bounce is witness to all that entropy.
Then at the moment of bounce normal geometry doesn't exist. Quantum corrections make gravity repel. The Schwarzschild BH solution doesn't work. All the black holes must have vanished.
Mr Before infers there is a vast complex termite-ridden structure of BHs falling into BHs. Like a fractal, every BH has other BHs falling into it and each of them has still others falling in. When bounce density is reached (estimated around 40 % of Planck) gravity repels and all that structure is invalid...
Just to clarify, we are not talking about the horizon size. I think we are long past horizons and are talking about the size of whatever entities replace the BH singularity in LQG....But if blackholes have a reasonable physical size, then they would all be on top of each other at quite a large scale? ...