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Loop Quantum Gravity

  1. Mar 23, 2009 #1
    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.
     
    Last edited: Mar 23, 2009
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  3. Mar 23, 2009 #2

    marcus

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    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/find/hep/www?rawcmd=FIND+DK+QUANTUM+COSMOLOGY+AND+DATE+%3E+2006&FORMAT=www&SEQUENCE=citecount%28d%29 [Broken]

    and for Lqg:
    http://www.slac.stanford.edu/spires/find/hep/www?rawcmd=FIND+DK+QUANTUM+GRAVITY+AND+DK+LOOP+SPACE+AND+DATE+%3E+2006&FORMAT=www&SEQUENCE=citecount%28d%29 [Broken]

    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/find/hep/www?rawcmd=FIND++DK+SPIN%2C+FOAM+AND+DATE+%3E+2006&FORMAT=www&SEQUENCE=citecount%28d%29 [Broken]
     
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  4. Mar 23, 2009 #3
    Thanks marcus.
     
  5. Mar 24, 2009 #4

    Chalnoth

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    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.
     
  6. Mar 24, 2009 #5

    marcus

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    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.
     
  7. Mar 24, 2009 #6

    Chalnoth

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    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.
     
  8. Mar 24, 2009 #7

    marcus

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    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.
     
  9. Mar 24, 2009 #8

    Chalnoth

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    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.
     
  10. Mar 24, 2009 #9

    marcus

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    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 :biggrin:

    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.
     
  11. Mar 24, 2009 #10

    apeiron

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    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.
     
    Last edited: Mar 24, 2009
  12. Mar 24, 2009 #11

    marcus

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    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.
    =============

    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..."
     
    Last edited: Mar 24, 2009
  13. Mar 24, 2009 #12

    marcus

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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.)

    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, Lifgarbagez (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."
     
    Last edited: Mar 24, 2009
  14. Mar 24, 2009 #13

    apeiron

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    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.
     
  15. Mar 24, 2009 #14

    marcus

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    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.
     
  16. Mar 24, 2009 #15

    Chalnoth

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    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.
     
  17. Mar 24, 2009 #16

    apeiron

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    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.
     
  18. Mar 24, 2009 #17

    marcus

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    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
     
  19. Mar 25, 2009 #18

    marcus

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    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.

    BTW I don't think of locations in space as having physical existence (as A.E. said, general covariance deprives them of the last shred of objective reality :wink: ) so I wouldn't include them as microstates in an entropy calculation. What seems real to me is the gravitational field and I suppose the entropy should be calculated directly from it and other field(s). But your "void" idea intrigues me and I want to think about it rather than argue at this point.

    To keep on my feet I need to re-iterate the basics of my position. In terms of cosmology what I expect from Loop, and QG in general, is it should break through the big bang barrier and give us testable models of conditions leading up. Once that is achieved, it's a new ballgame.

    Collapse-rebound models are the simplest, don't need to invent new structure, so probably the top priority to work out. And I don't care win or lose. As long as we get testable models that go back further I'm confident people will keep trying until something passes the tests. Loop cosmology is spearheading this development.

    So I don't worry about solving the whole problem of eternity, for now. I don't need to see a model applied into the infinite future or infinite past. What I want to see an empirically confirmed model applicable right around the bang/bounce.

    And I'm skeptical that right around the bounce, in the LQC context, anybody can prove the 2nd Law. If you can't prove it, it makes no sense to apply it. So it's quite possible that entropy is reset from a large figure to near zero, at the time of rebound. I'll give you an intuitive picture, like your ice picture.

    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.

    What does Mr After see, what does he infer? For him, all that prior garbage is irrelevant.
    He has a different set of macroscopic observables, different things that are measurable which matter to him. Different coarse-graining

    So now a mathematician comes along and it is his job to prove that the 2nd Law is valid in this framework. Well, we'd have to inspect previous proofs of the 2nd Law in other situations and see what features of the situation they used, to make the proof work.

    Admittedly I don't know that a proof is impossible, but I'm skeptical. 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.
     
    Last edited: Mar 25, 2009
  20. Mar 25, 2009 #19

    apeiron

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    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.

    In a handwaving description of this downward causality approach, the universe would be a "weight" of constraint bearing down on every location, shaping up its existence. So there is nothing "there" at a locale before the act of "observation" - we could say decoherence even. But something is created "there" as the limit, the event horizon, of this downward constraint.

    So the macro-system creates its micro-state locations. Causality then acts both ways because the accumulation of these locations then constructs the macrosystem. Enough top-down stablised locations can add up to a "constant temperature" ambience, the stable macrostate which is bearing down to create those locations.

    This is the kind of strange loop causality Douglas Hofstadter (Escher, Godel, Bach) was getting at. And which has been applied in mind science by neural networkers such as Stephen Grossberg (Adaptive Resonance Theory nets). And it is being suggested by condensed matter and phase transition guys now.

    So the planck scale in this view would be seen as the limit of resolution for an observing universe - a weight of decohering constraint that cannot resolve its locales into anything smaller, thus creating a countable grain of microstates.

    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?

    I don't like the black holes/spawning universe approach much, but that might be the "out" here.

    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?

    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).

    So as a thought experiment, mr before and mr after would be misleading. My view is that the system is the "mr" and I would be alarmed that mr universe dissolves to a QM foam, disappears as a system, then somehow pops out again in reversed form the other side.

    I have my eye on the macrostate and want to track it back. You perhaps have your eye on the microstates which do not appear to suffer as much trauma - because there seems to be room for them inside the foaminess.

    I would say the safety of those microstates is an illusion because they are in fact being created - soliton-like, via downward constraint - by the macrostate. So in my view, the microstates also get dissolved.

    The only way to cope with this is the idea of vagueness. Instead of anything actually disappearing (either the macro or micro), the two just get squished to a single common scale and thus become a symmetry, indistinguishable. They are both "in there", but you cannot tell them apart.

    So yes, in this view, perhaps they could then grow away (symmetry break) to the other side. But then there are wider reasons, from the systems science and vagueness ontology perspective I am raising, why that would not be the case.

    For one thing, expansion seems "wired in" to my preferred story. That would take a bit of explaining. But anyway, this approach I suggest would give us a somewhat different framing of the second law.

    Traditionally, the second law is talked about as an asymmetric arrow pointing from order to disorder (and even among classical thermodynamicists, it is realised that the idea of order/disorder is very unsatisfactory - loose speak).

    In my story, the arrow of time, the arrow of system development, points from vagueness to crispness. So dissipation is always the dissipation of a potential into crisper (more crisply developed) states of organisation.

    A large cold expanding void, is just such a crisp outcome. Entropic in that everything has been broken down to the same lowest level microstate within the one perfectly expressed macrostate (I love the Davies/Lineweaver tale of blackbox photons - the final fractal residue of a radiation created purely out of ever-expanding event horizons).

    It is disorderly in terms of classical work/heat calculations. But supremely crisply organised from a systems perspective. A broader notion of entropy.

    This idea of a vague-crisp approach to entropy modelling is not standard of course. But I have been working on it with a few other second law, dissipative structure, thinkers. It may come to something one day.
     
  21. Mar 25, 2009 #20

    marcus

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    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.
    In this speculative thought experiment (which I don't feel confident to pursue much further) these would be falling together at a great rate. A hailstorm of backhole pits. Rushing together and merging. Self-destructing.

    But what happens to one of our black hole pits when the stage is reached where gravity repels instead of attracts? Wouldn't it spill its guts?
    Imagine a supermassive BH (billions of solar masses) which because of an abrupt change in the geometric conditions is no longer allowed to remain a BH. What has held it together now releases it.

    I am at sea, Apeiron. The people who have been studying both LQG black hole collapse and cosmological rebound are, besides senior figures like Ashtekar, Corichi, Singh,..., young people like Dah-wei Chiou, Kevin Vandersloot, Lenny Modesto, Christian Boehmer...
    To go any farther I might have to turn to the researchers themselves.
     
    Last edited: Mar 25, 2009
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