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Penrose's argument that q.g. can't remove the Big Bang singularity 
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#37
Nov912, 08:00 AM

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PF Gold
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It seems like all we know fundamentally is that: (1) If there is low entropy in some region, the most likely thing is that it's preceded and followed by higher entropy. (2) Regions of spacetime that are causally connected should have arrows of time that agree. (3) Our universe is nearly flat, so it's probably either spatially infinite or at least much larger than the observable universe. (4) Our own past light cone appears to have had an arrow of time going back to at least the era of big bang nucleosynthesis. This requires extreme finetuning. (5) Our own thermodynamic arrow of time currently points away from the big bang. Based on these observations, it seems to me that the most general picture we can construct is a universe in which nearly all of spacetime is in thermal equilibrium, but there is one or more causally separated islands that are not at equilibrium. In each of these islands, there is some time of minimum entropy, which may or may not coincide with the big bang (or bounce). In our own island, this time seems to have been either at the big bang or before nucleosynthesis. It probably doesn't make sense to explain our island, or any others that exist, as thermal fluctuations, because then it would be overwhelmingly more probable for us to be Boltzmann brains rather than real observers inhabiting a large, nonequilibrium region of spacetime. This means that extreme finetuning is required. We have no physical law or principle that explains this finetuning, so we can't say whether (1) there should be more than one island, (2) an island's minimum entropy should coincide with the big bang, or (3) our own island actually encompasses the whole universe. In principle we can test all three of these empirically, but 1 and 3 can only be tested by waiting for cosmological lengths of time and continuing to make observations. 2 can be tested in our own island by seeing whether cosmological models correctly explain the very early universe with the normal second law of thermodynamics. I don't think a bounce really changes this picture very much. Penrose's argument seems to be based on the assumption that the second law is fundamental and universal, but that doesn't seem to me like a natural point of view. 


#38
Nov912, 01:00 PM

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#39
Nov912, 01:21 PM

Astronomy
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PF Gold
P: 23,235

Infinite dimensional Hilbert space of states. Basically defines the new face of LQC. Anyone at all interested in bounce cosmology (the bulk of that being by the LQC community) should probably memorize the arxiv number 1211.1354 and spend some time reading the paper. It's 50 pages. They have a followup/companion paper in prep. "[2] I. Agullo, A. Ashtekar and W. Nelson, The preinflationary dynamics of loop quantum cosmology: Confronting quantum gravity with observations, (in preparation)" 


#40
Nov912, 01:43 PM

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PF Gold
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#41
Nov912, 02:22 PM

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PF Gold
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I am used to seeing "squeezed" states in the LQC literature, it seems routine to employ mixed states in bounce cosmology analysis. What am I missing? Is there some PHILOSOPHICAL reason you have in mind for why the U should be in a pure state? Correct me if I am wrong but I think the U can ONLY be in a mixed state simply because no observer can see all of it Cosmologists have this distance called "particle horizon" estimated at 46 billion ly which is the distance to the farthest matter which we could in principle have gotten a signal from. But the whole thing (assuming finite) is estimated to be at least several times larger. You know the Bohr proverb about phyiscal science: it's not about what IS but instead what we can SAY about it. In that spirit, all we can say is a mixed state. And that therefore is the state. So your statement that the U must be in a pure state is really interesting to me and I wish you would explain. 


#42
Nov1012, 12:58 AM

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PF Gold
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Loop is transforming and there's a short list research fronts to watch, where the change is happening. Thanks Ben C, Demy, Tom, Finbar for starting and/or contributing to this discussion which has underscored the importance of the hybrid LQC work by Agullo Ashtekar Nelson! I definitely have to add it to the watch list. Several of the following could turn out to be among the most important QG research papers of 2012:
hybrid LQC An Extension of the Quantum Theory of Cosmological Perturbations to the Planck Era (1211.1354) The preinflationary dynamics of loop quantum cosmology: Confronting quantum gravity with observations (in prep) GR Thermo General relativistic statistical mechanics (1209.0065) Horizon entanglement entropy and universality of the graviton coupling (Bianchi's ILQGS talk and 1211.0522) tensorialGFT (Carrozza's ILQGS talk and 1207.6734) holonomySF (Hellmann's ILQGS talk and 1208.3388) twistorLQG (Speziale's ILQGS talk and 1207.6348) dust (Wise's ILQGS talk and 1210.0019) 


#43
Nov1012, 07:40 AM

P: 343

So maybe I'll do a uturn and tentatively buy the "bounce" cosmology. We could think that the state of the universe at the bounce is a pure state. Then the universe evolves to the current day at wich point each observer can only see a finite amount of the universe which will be described as a mixed state. Finally the universe then collapses at which point all the universe comes back together and a pure state is again recovered. Now the issue is why the final pure state would look anything like the initial pure state. 


#44
Nov1012, 07:57 AM

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Demystifier is right that a system in a pure state with finitely (or infinitly many) d.o.f. will remain in a pure state under (unitary) timeevolution and will therefore never have entropy > 0.
Pleae note that the underlined words are not welldefined or not known in general in the case of QG ;) 


#45
Nov1012, 01:47 PM

Astronomy
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PF Gold
P: 23,235

I can only speculate as a nonexpert. My intuition says that a collapsing phase of the U filled with a gas of black holes would reach (assuming the LQC model where gravity becomes repellent at high density) a stage where the horizons of all BH rapidly shrink, releasing Hawking radiation. So what goes into the bounce is a universe full of planckscale gamma photons and planckscale black holes, which can interconvert. The picture is somewhat analogous to a pairinstability supernova where the photons have become so energetic they become indistinguishable from electronpositron pairs. But that is only a crude analogy. I am groping for a picture of what it could be like when radiation and geometry interconvert the one form of energy into the other and back again, very rapidly, at planck scale. Just a speculative picture FWIW. If I were Ivan Agullo or Eugenio Bianchi or Bill Nelson (who has taken a postdoc at Nijmegen in the Netherlands and will be giving talk(s) at Stockholm this month, I gather) I think I would be working towards a model of the bounce of a classical universe which collapses into a planck soup of that kind of stuff (maybe ) and bounces. The one thing that Agullo Ashtekar Nelson say in 1211.1354 is that their followup paper is based on numerical simulations of the bounce (with perturbations) in a hybrid LQCFock picture. They stress the numerical simulations. that rings a bell with me. The results should be very very interesting even if one only tentatively semiaccepts the preliminary model. 


#46
Nov1112, 05:39 AM

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http://arxiv.org/abs/quantph/9803052 for a brief introduction. 


#47
Nov1112, 01:09 PM

Astronomy
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PF Gold
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I'm glad that you find that it is not strictly logically necessary for the U to be in a pure state! I will look at your link. Ah, Claus Kiefer! He had an article just recently about decoherence in LQG, I'll get the link. The quantum state of geometry decoheres through interaction with FERMIONS. The triad variable of LQG chooses an orientation, is forced by the presence of fermions to classicalize. http://arxiv.org/abs/1210.0418 Interpretation of the triad orientations in loop quantum cosmology Claus Kiefer, Christian Schell (Submitted on 1 Oct 2012) Loop quantum cosmology allows for arbitrary superpositions of the triad variable. We show here how these superpositions can become indistinguishable from a classical mixture by the interaction with fermions. We calculate the reduced density matrix for a locally rotationally symmetric Bianchi I model and show that the purity factor for the triads decreases by decoherence. In this way, the Universe assumes a definite orientation. 12 pages, 1 figure I don't remember if you already commented on this paper (it came up in another thread.) If you did I'd like very much to see your comment and would appreciate a link to your post about it. If you haven't yet I hope you will. It's interesting to see Kiefer focusing on one of the outstanding problems in LQG the orientation symmetry of the main variable (not present in theories based on the metric). My take on it is that when Kiefer or others start with the U in a pure state and have it progressively decohere, this does not mean that in reality the U would necessarily have to start pure. The analysis just shows how it could start in a purER state and become LESS pure. The analysis is a fortiori. It is just a convenient simplification to imagine that the system starts in a pure state, the important thing is progressive decoherence starting from whatever level of (im)purity or mixedness. I can imagine you might disagree. 


#48
Nov1112, 01:26 PM

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#49
Nov1112, 01:52 PM

Astronomy
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PF Gold
P: 23,235

What I'm unsure about is the meaning of "squeezed" states. Do you have a good brief explanation, or a link for that? If not, it probably is just a side issue, so no matter. What interested me just now was Demy's mentioning decoherence and the work of Claus Kiefer, a longtime central figure in Quantum Gravity. Just last month Kiefer posted this paper on decoherence in LQG. I'd really appreciate your comments! http://arxiv.org/abs/1210.0418 Interpretation of the triad orientations in loop quantum cosmology Claus Kiefer, Christian Schell (Submitted on 1 Oct 2012) Loop quantum cosmology allows for arbitrary superpositions of the triad variable. We show here how these superpositions can become indistinguishable from a classical mixture by the interaction with fermions. We calculate the reduced density matrix for a locally rotationally symmetric Bianchi I model and show that the purity factor for the triads decreases by decoherence. In this way, the Universe assumes a definite orientation. 12 pages, 1 figure It seems that purity and mixedness are not absolute properties but are on a range. Maybe all states should be thought of as a density matrix rho and the degree of purity would be the trace of the square of rho. ==quote page 7 Kiefer Schell== A measure for the purity of the total state (15) is the trace of ρ_{red}^{2}, which is equal to one for a pure state and smaller than one for a mixed state; it is directly related to the linear entropy S_{lin} = 1 − ρ_{red}^{2} [5]. One could also discuss the von Neumann entropy −k_{B}tr (ρ_{red} ln ρ_{red}), but for the present purpose it is sufficient to restrict to S_{lin}. ==endquote== This seems like a mathematically natural way to go. How does it strike you, Finbar? Does this appeal to you, or is perhaps how you already think of quantum states? On a continuum of mixedness? 


#50
Nov1112, 02:48 PM

P: 343

Not sure what a squeezed state is. Something to do with the saturated uncertainty relation? 


#51
Nov1112, 03:04 PM

Astronomy
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PF Gold
P: 23,235

*trace class operators, to put it more generally 


#52
Nov1112, 03:33 PM

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PF Gold
P: 23,235

The Kiefer Schell paper (as it says in the abstract) is about superpositions gradually becoming indistinguishable from a classical mixture, so it should interest several of us here. there is a nice figure on page 8 which shows the purity factor of a state decline from 1 to zero over the course of "internal time". I'm not sure what internal time means here.
==quote from page 8 of Kiefer Schell== The iteration at each time step starts with the calculation of s_{0} and s_{1}, as described above. As a constraint on the numerical evolution, we normalize s_{0} and s_{1} such that trρ_{red} = 1 is always preserved. Since the initial state is unentangled, trρ_{red}^{2} is initially equal to one. As the inner time variable increases, the total state becomes entangled, and the purity factor decreases—the gravitational variables are in a mixed state, and decoherence becomes more and more efficient. The result can be plotted as a function of the inner time variable φ, see Fig. 1. ==endquote== Figure 1 is what i was just talking about. When I say state (in this discussion, since thread concerns the entropy of quantum states) I mean trace class operator on the Hilbert space. IOW loosely speaking "density matrix". 


#53
Nov1212, 02:46 AM

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#54
Nov1212, 02:51 AM

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