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Reformulation of Loop gravity in progress, comment?

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marcus
#127
Oct31-12, 04:23 PM
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If it turns out (as judging from the interest in Carrozza Oriti Rivasseau's paper it conceivably might) that TGFT (tensorial group field theory) serves as basis for a nearterm reformulation of LQG/SF, then those who wish to follow what is going on in the field could find this tutorial by Krajewski useful:
http://arxiv.org/abs/1210.6257
Group field theories
Thomas Krajewski
(Submitted on 23 Oct 2012)
Group field theories are particular quantum field theories defined on D copies of a group which reproduce spin foam amplitudes on a space-time of dimension D. In these lecture notes, we present the general construction of group field theories, merging ideas from tensor models and loop quantum gravity. This lecture is organized as follows. In the first section, we present basic aspects of quantum field theory and matrix models. The second section is devoted to general aspects of tensor models and group field theory and in the last section we examine properties of the group field formulation of BF theory and the EPRL model. We conclude with a few possible research topics, like the construction of a continuum limit based on the double scaling limit or the relation to loop quantum gravity through Schwinger-Dyson equations
58 pages, Lectures given at the "3rd Quantum Gravity and Quantum Geometry School", March 2011, Zakopane
marcus
#128
Nov16-12, 03:30 PM
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For several reasons I think this paper represents a critical development in the emerging reformulation that I'm trying to understand
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

This is the first paper in which I remember the density matrix and its purity index trace(ρ2) playing a central role in LQC. This is a more general notion of quantum state--the vonNeumann algebra, or C*-algebra approach to QM.

We can see signs of this shift (in how things are formulated) appearing in LQG, in other papers. But this is the first time I'm aware of it's happening in the Cosmology application LQC.
marcus
#129
Nov16-12, 03:35 PM
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As a reminder, here are a half-dozen research areas where this approach to Quantum Gravity is being reshaped. All the ILQGS talks mentioned are now online with the sole exception of Bianca Dittrich's scheduled for 27 November.

twistorLQG (Speziale's ILQGS talk and 1207.6348)
tensorialGFT (Carrozza's ILQGS talk and 1207.6734)
holonomySF (Hellmann's ILQGS talk and 1208.3388)
dust (Wise's ILQGS talk and 1210.0019)
hybrid LQC
An Extension of the Quantum Theory of Cosmological Perturbations to the Planck Era (1211.1354)
The pre-inflationary dynamics of loop quantum cosmology: Confronting quantum gravity with observations (in prep)
GR Thermo and C*-algebra
General relativistic statistical mechanics (1209.0065)
Horizon entanglement entropy and universality of the graviton coupling (Bianchi's ILQGS talk and 1211.0522)
Interpretation of the triad orientations in loop quantum cosmology (1210.0418)

I think the last topic is critical, namely general relativistic thermodynamics (broadly interpreted to include statistical mechanics and the operator algebra formulation).

First it is clear that to be fully successful LQG has to encompass the LQC bounce, with matter and inhomogeneity--we already see that beginning to happen. In encompassing the bounce the model seemingly must include the dissipation or shrinkage of horizons and their vonNeumann entropy, with the emergence of a pure state.

I recently added the Kiefer and Schell paper http://arxiv.org/abs/1210.0418 as an indication of where that is going. Kiefer Schell have the purity/mixedness of quantum states run on a continuum from zero to one. A state is a trace-class operator ρ on the hilbert space, a generalized "density matrix". Pure states are those for which tr(ρ2) = 1, a kind of "purity index". As these gradually decohere, the purity index comes down from 1 to zero. In Kiefer Schell's case the quantum state of geometry does this as it interacts with the matter in the environment. If I'm not mistaken, LQG dynamics will be extended to include states of this density matrix ρ type (as Kiefer and Schell do with LQC) and Rovelli's September paper is a step in this direction. Then the problem will be to understand how the purity index of the state is driven *up* during bounce. Intuitively there is a "release of information" when Planckian density density is approached, and information that had become inaccessible becomes accessible (in the repellent gravity phase of the bounce.) I could of course have this wrong, so I'm looking for other viewpoints.
marcus
#130
Nov17-12, 11:45 AM
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Let's just look at the last 4 of the above LQG initiatives. HSF answers criticism by Alexandrov, so we can disregard the latter.
holonomySF (Hellmann's ILQGS talk and 1208.3388)
See Hellmann's comment here:
http://physicsforums.com/showthread....74#post4162474
(If anyone is new to the discussion, Frank Hellmann posts here as f-h.)
Dittrich may have some more to say about holonomy spin foam models in her ILQGS talk on 27 November.
============
The main thing I have to say right now is that in a certain sense all of the last three are working towards the same goal. The point is that a thermal state automatically breaks Lorentz invariance e.g. page 18 of Connes Rovelli gr-qc/9406019. So it is a no-brainer that any thermal state would have its own inherent notion of time. The challenge is to realize this in GR, what is a thermal state in GR which is timeless?
If one can do that, one finesses "dust". Thermal time and dust are reading from the same page of the book.
dust (Wise's ILQGS talk and 1210.0019)
hybrid LQC
An Extension of the Quantum Theory of Cosmological Perturbations to the Planck Era (1211.1354)
The pre-inflationary dynamics of loop quantum cosmology: Confronting quantum gravity with observations (in prep)
GR Thermo and C*-algebra
General relativistic statistical mechanics (1209.0065)
Horizon entanglement entropy and universality of the graviton coupling (Bianchi's ILQGS talk and 1211.0522)
Interpretation of the triad orientations in loop quantum cosmology (1210.0418)

And hybrid LQC (the breakground work of Agullo Ashtekar Nelson) is a way of putting an infinity of DoF into LQG cosmology, around the time of the bounce before conventional inflation begins. This gives a way to grasp the thermal state. So these three things are, I think, aimed at one goal.
marcus
#131
Nov25-12, 12:31 PM
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In two days Dittrich will give an online ILQGS talk, the last one of the fall semester.

Nov. 27 Coarse graining: towards a cylindrically consistent dynamics Bianca Dittrich Perimeter Institute
http://relativity.phys.lsu.edu/ilqgs/ (online audio and slides PDF)

This will probably be an important talk to hear for anyone wishing to follow developments in LQG (or quantum gravity in general). This will presumably be the second Holonomy Spin Foam (HSF) talk at ILQGS this fall and based on
http://arxiv.org/abs/1208.3388
Holonomy Spin Foam Models: Definition and Coarse Graining

An earlier HSF talk was given Sept. 4 Holonomy Spin Foam Models: Asymptotic Dynamics by Frank Hellmann of Albert Einstein Institute

Other HSF papers which have appeared recently:
http://arxiv.org/abs/1209.4539
Holonomy Spin Foam Models: Boundary Hilbert spaces and Time Evolution Operators
Bianca Dittrich, Frank Hellmann, Wojciech Kaminski

http://arxiv.org/abs/1210.5276
Geometric asymptotics for spin foam lattice gauge gravity on arbitrary triangulations
Frank Hellmann, Wojciech Kaminski

Holonomy spinfoam models are a different kind of spinfoam, similar to lattice connection theories in that they use group element labels living on the 2-complex. Notice that the title of an HSF talk or paper does not necessarily signal that it is HSF by including the word "holonomy". The title of the Hellmann Kaminski paper simply says "spin foam lattice gauge gravity" and you are supposed to understand that it is HSF (a point clearly made in the introduction). I gather from comments made that people working on HSF (coarse graining, asymptotics, dynamics...) have indicated they see the approach as overcoming some obstacles/unresolved questions in the earlier version of spinfoam.

Dittrich is one the main people in charge of organizing next year's Loops conference at PI, and also the senior organizer of the LQG parallel sessions at the GR-20 conference to be held next year in Warsaw.
GR-20 Warsaw (week of 7 July):
http://gr20-amaldi10.edu.pl/index.php?id=18
Loops 2013 Perimeter Institute (week of 21 July):
http://www.perimeterinstitute.ca/conferences/loops-13
__________________

If I had to bet now concerning the future course of LQG development---near future, see where we are in July 2013---I think I would say, as of now, that the two most interesting lines of development are HSF and a nexus of ideas I would call
"GR thermo, C*-algebra, hybrid LQC"
I see these things as coming together and clarifying, among other things, the LQC bounce (which is where the opening to phenomenology seems to be IMHO). Hybrid LQC puts Fock into the bounce picture--lots of particles and geometric fluctuations. (See latest Agullo Ashtekar Nelson.)
The C*-algebra formalism gives a way to do general covariant statistical quantum mechanics. (See new version of http://arxiv.org/abs/1209.0065 that was uploaded 19 November with a new section (Appendix B4) at the end with title something like "GC statistical QM".
marcus
#132
Nov27-12, 08:24 AM
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The slides PDF for Dittrich's talk is already online.
http://relativity.phys.lsu.edu/ilqgs/dittrich112712.pdf
It's about Coarse Graining spinfoam QG and spin net etc. and it is an exceptionally
clear set of slides. Refers to a lot of work in progress (w.i.p.) and recent papers.
Try here http://relativity.phys.lsu.edu/ilqgs/ later in the day to see if audio is online.

You can already learn quite a bit about their approach to coarse graining (and thus the largescale limit) simply by examining the slides. Sample page of computer code. Many diagrams.

EDIT: The audio also is now on line! It's a good talk. Here's the audio.
http://relativity.phys.lsu.edu/ilqgs/dittrich112712.wav
Most of the question time is Dittrich discussing with Ashtekar and Rovelli. Around minute 2, more exactly 2:20, from the end Francesca gets in a question.
Bianca's group is running computer simulations of their coarse-graining strategies. The slide graphics of how the coarsegraining works is well thought out and communicates effectively (when there is the audio explanation along with it).

The type of spinfoam they use is HSF (holonomy sf) and the 2D analog of that is what they call spin net. Both have group element labels rather than some other kind (e.g. spins, twistors). But much of the work involves highly simplified toy models. Not QG. Regular lattices. This does not mean it's trivial or uninteresting! On the contrary, I would say. It looks to me as if an effective method of coarsegraining for 4D spinfoam QG is being developed, and one that can be implemented numerically. If that is the case it will be a substantial advance.
marcus
#133
Nov30-12, 11:05 AM
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I need to elaborate the nexus of ideas mentioned in posts #130 and 131 that seem to be coming to a better understanding of the LQC bounce.
"GR thermo, GC statistical QM, hybrid LQC, pre-inflationary dynamics, matter bounce"
Quote Quote by marcus View Post
Holonomy spinfoam models are a different kind of spinfoam, similar to lattice connection theories in that they use group element labels living on the 2-complex...
...I gather from comments made that people working on HSF (coarse graining, asymptotics, dynamics...) have indicated they see the approach as overcoming some obstacles/unresolved questions in the earlier version of spinfoam.
...
If I had to bet now concerning the future course of LQG development---near future, see where we are in July 2013---I think I would say, as of now, that the two most interesting lines of development are HSF and a nexus of ideas I would call
"GR thermo, C*-algebra, hybrid LQC"
I see these things as coming together and clarifying, among other things, the LQC bounce (which is where the opening to phenomenology seems to be IMHO). Hybrid LQC puts Fock into the bounce picture--lots of particles and geometric fluctuations. (See latest Agullo Ashtekar Nelson.)
The C*-algebra formalism gives a way to do general covariant statistical quantum mechanics. (See new version of http://arxiv.org/abs/1209.0065 that was uploaded 19 November with a new section (Appendix B4) at the end with title something like "GC statistical QM".
Back in post #130 I mentioned the paper Pre-inflationary LQC the PennState people (Agullo Ashtekar Nelson*) have in preparation. Now there's another paper contributing to our understanding of the LQC bounce, this time by Wilson-Ewing (PennState PhD now at Marseille):

The Matter Bounce Scenario in Loop Quantum Cosmology
Edward Wilson-Ewing
(Submitted on 27 Nov 2012)
In the matter bounce scenario, a dust-dominated contracting space-time generates scale-invariant perturbations that, assuming a nonsingular bouncing cosmology, propagate to the expanding branch and set appropriate initial conditions for the radiation-dominated era. Since this scenario depends on the presence of a bounce, it seems appropriate to consider it in the context of loop quantum cosmology where a bouncing universe naturally arises. It turns out that quantum gravity effects play an important role beyond simply providing the bounce. Indeed, quantum gravity corrections to the Mukhanov-Sasaki equations significantly modify some of the results obtained in a purely classical setting: while the predicted spectra of scalar and tensor perturbations are both almost scale-invariant with identical small red tilts in agreement with previous results, the tensor to scalar ratio is now expected to be r≈ 9 x 10-4, which is much smaller than the original classical prediction. Finally, for the predicted amplitude of the scalar perturbations to agree with observations, the critical density in loop quantum cosmology must be of the order ρcrit ~ 10-9 ρPlanck.
8 pages

Francesca's November 2012 review talk at the Stockholm fundamental cosmology conference already discusses the QG corrected Mukhanov-Sasaki equation as per Wilson-Ewing. This Loop matter-bounce paper could have a profound impact. Corrected M-S has the same ρ/ρPl term as the QG corrected Friedmann eqn. Both corrections are "Planck-suppressed", IOW they only take effect as the energy density approaches Planck density. Including the matter-bounce means that the rebound of a collapsing classical phase occurs sooner at much lower density.

*Nelson was at PennState and is now at Nijmegen, he also gave a talk at the Stockholm cosmology conference.
marcus
#134
Dec11-12, 01:33 PM
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New work by Hal Haggard--solo and with Eugenio Bianchi--and by Berndt Müller (10,000 lifetime cites, previous work in nuclear theory and hep-phenomenology) reveals classical physics evidence supporting LQG quantized view of space and the volume gap. This is the idea that the LQG volume operator should have a gap between zero and the first positive eigenvalue.

Intuitively that there should be a lowest volume that you can measure. Space geometry discreteness idea.

What does chaos, a property exhibited by classical dynamics in certain cases, have to do with this?

It seems as if the recent work by Haggard, Bianchi, Müller, Coleman-Smith... could be opening up a new line of LQG research--something we need to notice and try to understand if we're following the field. I'll fetch some links.

http://arxiv.org/abs/1211.7311
Pentahedral volume, chaos, and quantum gravity
Hal M. Haggard
(Submitted on 30 Nov 2012)
We show that chaotic classical dynamics associated to the volume of discrete grains of space leads to quantal spectra that are gapped between zero and nonzero volume. This strengthens the connection between spectral discreteness in the quantum geometry of gravity and tame ultraviolet behavior. We complete a detailed analysis of the geometry of a pentahedron, providing new insights into the volume operator and evidence of classical chaos in the dynamics it generates. These results reveal an unexplored realm of application for chaos in quantum gravity.
5 pages, 4 figures

http://lanl.arxiv.org/abs/1212.1930
A "Helium Atom" of Space: Dynamical Instability of the Isochoric Pentahedron
C. E. Coleman-Smith, B. Muller
(Submitted on 9 Dec 2012)
We present an analysis of the dynamics of the equifacial pentahedron on the Kapovich-Millson phase space under a volume preserving Hamiltonian. The classical dynamics of polyhedra under such a Hamiltonian may arise from the classical limit of the node volume operators in loop quantum gravity. The pentahedron is the simplest nontrivial polyhedron for which the dynamics may be chaotic. We consider the distribution of polyhedral configurations throughout the space and find indications that the borders between certain configurations act as separatrices. We examine the local stability of trajectories within this phase space and find that locally unstable regions dominate although extended stable regions are present. Canonical and microcanonical estimates of the Kolmogorov-Sinai entropy suggest that the pentahedron is a strongly chaotic system. The presence of chaos is further suggested by calculations of intermediate time Lyapunov exponents which saturate to non zero values.
20 Pages, 19 Figures

http://arxiv.org/abs/1102.5439
Discreteness of the volume of space from Bohr-Sommerfeld quantization
Eugenio Bianchi, Hal M. Haggard
(Submitted on 26 Feb 2011 (v1), last revised 6 Jun 2011 (this version, v2))
A major challenge for any theory of quantum gravity is to quantize general relativity while retaining some part of its geometrical character. We present new evidence for the idea that this can be achieved by directly quantizing space itself. We compute the Bohr-Sommerfeld volume spectrum of a tetrahedron and show that it reproduces the quantization of a grain of space found in loop gravity.
4 pages, 4 figures; to appear in PRL

http://arxiv.org/abs/1208.2228
Bohr-Sommerfeld Quantization of Space
Eugenio Bianchi, Hal M. Haggard
(Submitted on 10 Aug 2012)
We introduce semiclassical methods into the study of the volume spectrum in loop gravity. The classical system behind a 4-valent spinnetwork node is a Euclidean tetrahedron. We investigate the tetrahedral volume dynamics on phase space and apply Bohr-Sommerfeld quantization to find the volume spectrum. The analysis shows a remarkable quantitative agreement with the volume spectrum computed in loop gravity. Moreover, it provides new geometrical insights into the degeneracy of this spectrum and the maximum and minimum eigenvalues of the volume on intertwiner space.
32 pages, 10 figures

It was surprising how close the semiclassical numbers were to the numbers computed using the full LQG quantum theory. At that point they were using TETRAHEDRON volume dynamics. Notice the gradual ratcheting up of complexity---now to pentahedron---in the newer papers.

In case anyone is interested in Berndt Müller's earlier research interests http://inspirehep.net/author/B.Muller.1/
marcus
#135
Dec13-12, 11:13 PM
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Yesterday's Pirsa talk on chaos and quantum mechanics:
http://pirsa.org/12120036/ (online video)
Quantum Chaos, Information Gain and Quantum Tomography.
Speaker(s): Vaibhav Madhok
Abstract: Quantum chaos is the study of quantum systems whose classical description is chaotic. How does chaos manifest itself in the quantum world? In recent years, attempts have been made to address this question from the perspective of quantum information theory. It is in this spirit that we study the connection between quantum chaos and information gain in the time series of a measurement record used for quantum tomography...
... We make predictions for the information gain using random matrix theory in the fully chaotic regime and show a remarkable agreement between the two.
Date: 11/12/2012 - 3:30 pm

What I highlighted is the general question that the papers by Hal Haggard and by Berndt Müller also seem to be getting at. Particularly http://arxiv.org/abs/1211.7311
and http://arxiv.org/abs/1212.1930

I continue to be impressed by how many active directions of research in LQG there are at present. I listed some of them a few posts back. I suspect the map of LQG is going to be quite different in July when Loops 2013 is held, from what it was at the previous Loops conference held in 2011 at Madrid.
http://www.perimeterinstitute.ca/conferences/loops-13
marcus
#136
Dec17-12, 12:10 PM
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Is it possible that Mielczarek is on to something? Can we give meaning to what he says here which seems so incomprehensible the first time I read it?
At planck scale, or thereabouts, the spacetime causal structure would be numbed as if by a massive shot of novocaine, into non-existence. All lines of communication go dead?

But he is working in a LQG cosmology context here. Wouldn't there be a bounce well before that density is reached?

http://arxiv.org/abs/1212.3527
Asymptotic silence in loop quantum cosmology
Jakub Mielczarek
(Submitted on 14 Dec 2012)
The state of asymptotic silence, characterized by causal disconnection of the space points, emerges from various approaches aiming to describe gravitational phenomena in the limit of large curvatures. In particular, such behavior was anticipated by Belinsky, Khalatnikov and Lifgarbagez (BKL) in their famous conjecture put forward in the early seventies of the last century. While the BKL conjecture is based on purely classical considerations, one can expect that asymptotic silence should have its quantum counterpart at the level of a more fundamental theory of quantum gravity, which is the relevant description of gravitational phenomena in the limit of large energy densities. Here, we summarize some recent results which give support to such a possibility. More precisely, we discuss occurrence of the asymptotic silence due to polymerization of space at the Planck scale, in the framework of loop quantum cosmology. In the discussed model, the state of asymptotic silence is realized at the energy density ρ = ρc/2, where ρc is the maximal allowed energy density, being of the order of the Planck energy density. At energy densities ρ > ρc/2, the universe becomes 4D Euclidean space without causal structure. Therefore, the asymptotic silence appears to be an intermediate state of space between the Lorentzian and Euclidean phases.
4 pages, 3 figures

I would like to dismiss this as too far-out, but don't feel that I can. LQG research is going in a bewildering variety of different directions right now. I don't remember it ever being so multi pronged in past years.
marcus
#137
Dec20-12, 10:13 PM
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I'll recall post #129 at the top of this page, just so we don't get so intrigued by detail that we lose track of the full spectrum of different ways QG is being reshaped in the runup to the main QG conference (Loops 13 July of next year).
Quote Quote by marcus View Post
As a reminder, here are a half-dozen research areas where this approach to Quantum Gravity is being reshaped.
==quote post #129==
...
twistorLQG (Speziale's ILQGS talk and 1207.6348)
tensorialGFT (Carrozza's ILQGS talk and 1207.6734)
holonomySF (Hellmann's ILQGS talk and 1208.3388)
dust (Wise's ILQGS talk and 1210.0019)
hybrid LQC
An Extension of the Quantum Theory of Cosmological Perturbations to the Planck Era (1211.1354)
The pre-inflationary dynamics of loop quantum cosmology: Confronting quantum gravity with observations (in prep)
GR Thermo and C*-algebra
General relativistic statistical mechanics (1209.0065)
Horizon entanglement entropy and universality of the graviton coupling (Bianchi's ILQGS talk and 1211.0522 and 1212.5183)
Interpretation of the triad orientations in loop quantum cosmology (1210.0418)

I think the last topic is critical, namely general relativistic thermodynamics (broadly interpreted to include statistical mechanics and the operator algebra formulation).

First it is clear that to be fully successful LQG has to encompass the LQC bounce, with matter and inhomogeneity--we already see that beginning to happen. In encompassing the bounce the model seemingly must include the dissipation or shrinkage of horizons and their vonNeumann entropy, with the emergence of a pure state.

I recently added the Kiefer and Schell paper http://arxiv.org/abs/1210.0418 as an indication of where that is going. Kiefer Schell have the purity/mixedness of quantum states run on a continuum from zero to one. A state is a trace-class operator ρ on the hilbert space, a generalized "density matrix". Pure states are those for which tr(ρ2) = 1, a kind of "purity index". As these gradually decohere, the purity index comes down from 1 to zero. In Kiefer Schell's case the quantum state of geometry does this as it interacts with the matter in the environment. If I'm not mistaken, LQG dynamics will be extended to include states of this density matrix ρ type (as Kiefer and Schell do with LQC) and Rovelli's September paper is a step in this direction. ...
==endquote==

Claus Kiefer's recent LQG paper is a step in the direction of the "star algebra" formulation of QG---where the basic mathematical object is (M,ω) an observables algebra M with a state function ρ: M→ℂ which gives the correlations and expectation values.

In the the entanglement entropy part of above post, I added a reference (in red) to a new paper by Bianchi and Myers:
http://arxiv.org/abs/1212.5183
On the Architecture of Spacetime Geometry
Eugenio Bianchi, Robert C. Myers
(Submitted on 20 Dec 2012)
We propose entanglement entropy as a probe of the architecture of spacetime in quantum gravity. We argue that the leading contribution to this entropy satisfies an area law for any sufficiently large region in a smooth spacetime, which, in fact, is given by the Bekenstein-Hawking formula. This conjecture is supported by various lines of evidence from perturbative quantum gravity, simplified models of induced gravity and loop quantum gravity, as well as the AdS/CFT correspondence.
8 pages, 1 figure
marcus
#138
Dec30-12, 01:50 PM
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The idea of this thread is to keep track of the full spectrum of different ways QG is being reshaped in the runup to the main QG conference http://www.perimeterinstitute.ca/conferences/loops-13 (Loops 13 at Perimeter Institute in July 2013).

The Bianchi Myers paper noted in previous post seems remarkably rich in useful ideas--I'm not sure what the right word is, "fertile" maybe? At least to me, it suggests how, if LQG were put in C*-algebra form, one might define 3D REGIONS by subsets of the algebra satisfying an entanglement-area condition. Note the word "architecture" in the title, as indicative of how the authors are thinking.

In any case it adds an exciting motivation to the (M, ω) world format. How can a smooth manifold picture emerge from some instance of (M, ω)? Perhaps one can state a condition in terms of entanglement entropy of certain subsets of the algebra. This is mentioned simply for motivation and I won't speculate further. I will list the various reformulation fronts in a different order.

Loop cosmology is getting into inhomogeneous regimes with multiple degrees of freedom and exploring "pre-inflationary" dynamics in more detail. Provisionally I'm calling that "hybrid loop cosmology" because several recent papers join existing LQC bounce with Fock space in a kind of hybrid. I can't list all the papers developing inhomogeneous LQC, so will just mention a couple.
hybrid LQC
Agullo Ashtekar Nelson—An Extension of the Quantum Theory of Cosmological Perturbations to the Planck Era (http://arxiv.org/abs/1211.1354)
The pre-inflationary dynamics of loop quantum cosmology: Confronting quantum gravity with observations (in prep)

It's hard to know what to call the next development. Perhaps "C*-quantum gravity, T-time, and entanglement entropy".
Work towards general covariant (GC) analysis such as GC-thermo, GC statistical (quantum) mechanics seems to motivate an (M,ω) formulation. This finally solves the time problem because one gets an observer-independent (Tomita) flow on the observables algebra. But how do we recover the regional STRUCTURE of space in the (M,ω) context? I see Bianchi Myers paper in this light. The key word "architecture" in the title is a signal. Also Kiefer Schell paper leans in that direction.
C*-quantum gravity, T-time, entanglement
Rovelli—General relativistic statistical mechanics (http://arxiv.org/abs/1209.0065)
Bianchi—Horizon entanglement entropy and universality of the graviton coupling (ILQGS talk and http://arxiv.org/abs/1211.0522)
Bianchi Myers—On the Architecture of Spacetime Geometry (http://arxiv.org/abs/1212.5183)
Kiefer Schell—Interpretation of the triad orientations in loop quantum cosmology (http://arxiv.org/abs/1210.0418)
Besides the above there are several other clear reformulation initiatives under way.
twistorLQG (Speziale's ILQGS talk and http://arxiv.org/abs/1207.6348)
tensorialGFT (Carrozza's ILQGS talk and http://arxiv.org/abs/1207.6734)
holonomySF (Hellmann's ILQGS talk and http://arxiv.org/abs/1208.3388)
dust (Wise's ILQGS talk and http://arxiv.org/abs/1210.0019)
marcus
#139
Jan2-13, 11:22 AM
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The ILQGS (international LQG seminar) is a good pointer to active areas of QG research---one can see this in the previous post: several of the themes we identified were represented not only by recent papers but also by Fall 2012 semester talks. Jorge Pullin organizes the ILQGS and I think he does a great job.

Part of the Spring 2013 schedule is posted now and we can examine it to help get a clearer picture of current research developments.

Jan 29th Entanglement in loop quantum gravity — Eugenio Bianchi — Perimeter Institute.
Feb 12th Dynamical chaos and the volume gap — Hal Haggard — CPT Marseille
Feb 26th Gravity electroweak unification — Stephon Alexander — Haverford College
Mar 12th ..................
Mar 26th Bianchi I LQC — Brajesh Gupt — LSU

The 26 March talk by Gupt exemplifies the current trend in Loop cosmology towards cosmic models which are less uniform: not homogeneous and isotropic. For many years at the beginning LQC deal with uniform models with a correspondingly small number of degrees of freedom. Now they are running models which achieve a bounce (where the singularity used to be) but involve more complex variation. The socalled "Bianchi I" models are only one example.

Others of the talks are on topics that feature in our 4th quarter MIP poll. I have to go---there's more to say about this.
marcus
#140
Jan2-13, 07:08 PM
Astronomy
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PF Gold
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As suggested in preceding post, we can get an idea of the active directions in Loop research by seeing what the Spring semester ILQGS talks will be about. For instance, I think the 29 January talk by Bianchi will be important and could be based on his November 2012 paper. This I think is a breakthrough paper, as I will explain.
http://arxiv.org/abs/1211.0522
Horizon entanglement entropy and universality of the graviton coupling
Eugenio Bianchi
(Submitted on 2 Nov 2012)
We compute the low-energy variation of the horizon entanglement entropy for matter fields and gravitons in Minkowski space. While the entropy is divergent, the variation under a perturbation of the vacuum state is finite and proportional to the energy flux through the Rindler horizon. Due to the universal coupling of gravitons to the energy-momentum tensor, the variation of the entanglement entropy is universal and equal to the change in area of the event horizon divided by 4 times Newton's constant - independently from the number and type of matter fields. The physical mechanism presented provides an explanation of the microscopic origin of the Bekenstein-Hawking entropy in terms of entanglement entropy.
7 pages

This is a breakthrough because a radical simplification. You can calculate the entanglement entropy, in this case, just from the entanglement entropy of the gravitons alone.
You do not have to put matter fields into the calculation because the gravitons FEEL the matter thoroughly and reflect its entanglements.

Eventually, I suspect, the entropy associated with different regions will be algebraically definable in a C* context, based on correlations between observables. The entropy-area relation will facilitate exploring the geometry in a situation where no manifold is given to start with. This will advance the program of recovering geometric relationships in a C* picture of the world, IMHO. So I think this is an outstanding paper with long-range significance. If someone disagrees with this assessment of 1211.0522, please tell me--I'd be interested in hearing a different opinion.

So later this month, as 29 January approaches, some of us will probably decide to take a look at the November paper to prepare for listening to the online seminar titled:
Entanglement in loop quantum gravity by Eugenio Bianchi.
marcus
#141
Jan16-13, 05:11 PM
Astronomy
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PF Gold
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The idea of this thread is to keep track of the full spectrum of different ways QG is being reshaped in the runup to the main QG conference http://www.perimeterinstitute.ca/conferences/loops-13 (Loops 13 at Perimeter Institute in July 2013).

Now with only 6 months left before conference there has appeared what I think is maybe the MOST ambitious reformulation initiative. This is via GAUGE NETWORK and GAUGE FOAM analogs by Marcolli and van Suijlekom (at Caltech and Nijmegen). These are analogous to the spin networks and spin foams that are already used in the current LQG formulation, except now the chunks of space are equipped with noncommutative geometry.

http://arxiv.org/abs/1301.3480
Gauge networks in noncommutative geometry
Matilde Marcolli, Walter D. van Suijlekom
(Submitted on 15 Jan 2013)
We introduce gauge networks as generalizations of spin networks and lattice gauge fields to almost-commutative manifolds. The configuration space of quiver representations (modulo equivalence) in the category of finite spectral triples is studied; gauge networks appear as an orthonormal basis in a corresponding Hilbert space. We give many examples of gauge networks, also beyond the well-known spin network examples. We find a Hamiltonian operator on this Hilbert space, inducing a time evolution on the C*-algebra of gauge network correspondences...
...
The people:
http://www.its.caltech.edu/~matilde/
http://www.math.ru.nl/~waltervs/index.php?page=home
(Walter Daniel van Suijlekom b. 1978, dual career as professional musician, interesting. PhD 2005 at SISSA Trieste. Since 2007 postdoc at Nijmegen, same place as Renate Loll. Has taught some interesting courses at Nijmegen including NCG, i.e. spectral geometry.)

I think this Marcolli van Suijlekom initiative could lead to a C* algebra formulation of LQG. Already they have a Hamiltonian and time evolution of gauge networks (at least in some case they are considering). At the end of the paper there is a proposal for how to do gauge FOAMS and what the PARTITION FUNCTION should look like, i.e. a PATH INTEGRAL approach coming out. And it looks in a very general way rather like what you see in Zakopane Lectures (2011)

The idea is to have chunks of ALMOST COMMUTATIVE space (represented by finite dimensional spectral triples, spectral polyhedra?) at the vertices of the network, and have the links be morphisms somehow joining the vertices. Almost commutative spectral geometry is how Connes and friends realized the Standard Model. So in spirit very much like current LQG except chunks of almost commutative space at the vertices instead of chunks of ordinary commutative space.

I think these things are all related and am not sure what to call this development. Perhaps "C*-quantum gravity, T-time, entanglement entropy, gauge networks".
I should recall that work towards general covariant (GC) analysis such as GC-thermo, GC statistical (quantum) mechanics seems to motivate a star algebra (M,ω) formulation because this finally solves the time problem. One gets an observer-independent (Tomita) flow on the observables algebra. Then how do we recover the regional STRUCTURE of space in the (M,ω) context? I see Bianchi Myers paper in this light. The key word "architecture" in the title is a signal. Also Kiefer Schell paper leans in that direction.
======================
C*-quantum gravity, T-time, entanglement, gauge networks
Marcolli van Suijlekom—Gauge networks in noncommutative geometry (http://arxiv.org/abs/1301.3480)
Rovelli—General relativistic statistical mechanics (http://arxiv.org/abs/1209.0065)
Bianchi—Horizon entanglement entropy and universality of the graviton coupling (ILQGS talk and http://arxiv.org/abs/1211.0522)
Bianchi Myers—On the Architecture of Spacetime Geometry (http://arxiv.org/abs/1212.5183)
Kiefer Schell—Interpretation of the triad orientations in loop quantum cosmology (http://arxiv.org/abs/1210.0418)

===================
The LQG-LQC bridge, hybrid LQC, matter bounce
Alesci and Cianfrani have established a clear derivation of LQC from the full LQG theory--canonically quantizing first and then reducing to the cosmo case. Loop cosmology is getting into inhomogeneous regimes with multiple degrees of freedom and exploring "pre-inflationary" dynamics in more detail. Provisionally I'm calling that "hybrid loop cosmology" because several recent papers join existing LQC bounce with Fock space in a kind of hybrid. I can't list all the papers developing inhomogeneous LQC, so will just mention a small sample.
Alesci Cianfrani—Quantum-Reduced Loop Gravity: Cosmology (http://arxiv.org/abs/1301.2245)
Agullo Ashtekar Nelson—An Extension of the Quantum Theory of Cosmological Perturbations to the Planck Era (http://arxiv.org/abs/1211.1354)
The pre-inflationary dynamics of loop quantum cosmology: Confronting quantum gravity with observations (in prep)
Wilson-Ewing—The Matter Bounce Scenario in Loop Quantum Cosmology (http://arxiv.org/abs/1211.6269)
====================

Besides the above there are several other clear reformulation initiatives under way.
twistorLQG (Speziale's ILQGS talk and http://arxiv.org/abs/1207.6348)
tensorialGFT (Carrozza's ILQGS talk and http://arxiv.org/abs/1207.6734)
holonomySF (Hellmann's ILQGS talk and http://arxiv.org/abs/1208.3388)
dust (Wise's ILQGS talk and http://arxiv.org/abs/1210.0019)
marcus
#142
Jan25-13, 12:43 PM
Astronomy
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PF Gold
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The twistorial reformulation of LQG has taken a big step forward with:
http://arxiv.org/abs/1301.5859
Hamiltonian spinfoam gravity
Wolfgang M. Wieland
(Submitted on 24 Jan 2013)
This paper presents a Hamiltonian formulation of spinfoam-gravity, which leads to a straight-forward canonical quantisation. To begin with, we derive a continuum action adapted to the simplicial decomposition. The equations of motion admit a Hamiltonian formulation, allowing us to perform the constraint analysis. We do not find any secondary constraints, but only get restrictions on the Lagrange multipliers enforcing the reality conditions. This comes as a surprise. In the continuum theory, the reality conditions are preserved in time, only if the torsionless condition (a secondary constraint) holds true. Studying an additional conservation law for each spinfoam vertex, we discuss the issue of torsion and argue that spinfoam gravity may indeed miss an additional constraint. Next, we canonically quantise. Transition amplitudes match the EPRL (Engle--Pereira--Rovelli--Livine) model, the only difference being the additional torsional constraint affecting the vertex amplitude.
28 pages, 2 figures

To get a sense of Wieland you could watch some of this Perimeter talk (February 2012):
http://pirsa.org/12020129/
marcus
#143
Jan26-13, 02:30 AM
Astronomy
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PF Gold
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P: 23,117
In 3 days, Bianchi's ILQGS talk: Entanglement entropy in LQG
The slides PDF may be posted beforehand (this has happened with ILQGS) and the URL will probably be: http://relativity.phys.lsu.edu/ilqgs/bianchi012913.pdf
After the talk the audio URL will probably be http://relativity.phys.lsu.edu/ilqgs/bianchi012913.wav
He has shown that the BH horizon entropy and the CEH (cosmic event horizon) entropy can both be understood as entanglement.
The state on the accessible side must be MIXED because entangled with the state on the other side. This gives a simple handle on the entropy, as he shows.

The talk will necessarily take as its point of departure his November paper. http://arxiv.org/abs/1211.0522 This is a classic: a major landmark, very short (4 pages), simply worded, and effecting a radical change of perspective.
The November paper was not set in any one theory---e.g. not specifically a LQG paper. It was quite general.
So now we will see what's new since then, what specifically QG development can have grown out of it.

If one is rereading the papers in order to prepare to understand the online talk, there is also Bianchi's December paper with Rob Myers (http://arxiv.org/abs/1212.5183) which I mentioned two posts back.
MTd2
#144
Jan27-13, 10:08 PM
PF Gold
P: 1,960
Quote Quote by marcus View Post
The twistorial reformulation of LQG has taken a big step forward with:
I think it should be remarked that this time time is only a dimension like in GR.


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