Loop-and-allied QG bibliography

[marcus]

Is there any paper that can says when exactly in time the evolution of the universe change to be described by a difference equation to be described by differential equations?

IIRC Ashtekar's paper "Quantum Geometry in Action: Big Bang and Black Holes"
gives an estimate of several hundred steps (of the difference equation) to converge to the semi-classical model

it is the usual sort of limiting process
the quantum regime converges to the semiclassical (after a very short period on the order of 100 Planck time units)
and the semiclassical converges thereafter more gradually to
the ordinary or partial differential equation model
but as with other kinds of convergence one cannot say with precision the exact moment when
the discrete model stops being appropriate and the semiclassical model
begins to apply
there is a transition period when both are giving approximately the same answer

So what one needs is a rough order of magnitude idea of when the transition between models happens. If it is not in that Ashtekar paper then I must be thinking of one by Ashtekar, Bojowald, Lewandowski called
"Mathematical Structure of Loop Quantum Cosmology"

I will try to get a link and page reference for the several hundred Planck time units or DiffEq timesteps---it's in one or the other or both papers. May be other places as well so someone else could come up with yet another link.

------------LONG LAPSE OF TIME-----
I forgot to get the references, however the one I mentioned first has something.
See page 10 of gr-qc/0202008, last paragraph of section 3.1 "Big Bang".
Ashtekar says there that the semiclassical model (Wheeler-DeWitt) is recovered when the scale of the universe is a few hundred Planck lengths. that is, very soon.
Also next to last paragraph on page 8.
I would like to find a more recent and more precise paper, in answer to your question. At the moment I don't have one. Perhaps someone else out there does.

 

[marcus]

"3.3 Chern-Simons perturbation theory.
Setting
$$\frac{3}{4} = \frac{2}{3}$$
our Lagrangian becomes the Chern-Simons-functional..."

there is a mathematician named Dror Bar-Natan
on page 19 of this paper
q-alg/9702009
"The Fundamental Theorem of Vassiliev Invariants"
he claims to prove something
by setting 3/4 equal to 2/3.

His paper is about the "Fundamental Theorem of Vassiliev Invariants"
and it is divided into four sections with four different ways of proving
the fundamental theory and at the end of each section he has
a concluding paragraph entitled
"Why are we not happy?"

This shows a philosophical concern with the problem of human happiness.
Also he proves the theorem by algebra, by physics (the oldest way, already almost 10 years old), by geometry, by topology. and he finds something always unsatisfying or wrong. in the middle of the proof by physics he says
"This is of course silly."

Dror Bar-Natan has an unusual expository style. Or at least I hope that it is unusual.

BTW he calls the topological method "combinatorial-topological" because doubtless he thinks of combinatorics and topology as very close neighbors or almost joined at the hip

He cites V.I.Arnold a russian mathematician. Fairbairn and Rovelli also cited a book by V.I. Arnold. It would be possible to suspect that something is going on with knot theory and Vassiliev invariants. the quirky Bar-Natan tone of voice even encourages this suspicion.

Perhaps it will be necessary to classify knots-with-nodes and I cannot at the moment visualize how this would be done.

I will get the LQG paper by Gambini and Pullin that cites this Bar-Nathan.
Nonunitary gave this link in another thread.

------quote from nonunitary post in "chunkymorphism" thread---
...As far as I know the first paper about the invariants was

gr-qc/9803018

but you are right about the chunkymorphisms. The are a new invention of Rovelli. I haven't read the paper so I can not comment.
-----endquote----

the Gambini/Pullin paper
http://arxiv.org/gr-qc/9803018
is called
"Vassiliev invariants: a new framework for quantum gravity"

 

[selfAdjoint]

How do you get to those q_alg papers in the arxiv? I have been trying every trick in the book for half an hour now and nothing! Click on mathematics and get, but can't ge q-alg or QA. Click on 1997 and search, nothing.

 

[marcus]

How do you get to those q_alg papers in the arxiv? I have been trying every trick in the book for half an hour now and nothing! Click on mathematics and get, but can't ge q-alg or QA. Click on 1997 and search, nothing.

only have a minute to reply but try
http://arxiv.org/PS_cache/q-alg/pdf/9702/9702009.pdf

will get back in a few minutes and check that this works

Im back.
this should get the abstract:
http://arxiv.org/q-alg/9702009

now I understand. the problem is to use the search engine
to find a paper like this one, but hopefully more recent
------------------

go to arxiv
don't click on search immediately
because right beside the button that says "search" there is
a menu box where you can select "math"

select "math" and then click on "search"

you then get a form where you can type in Author and Keyword
I typed in Bar-Natan and knot
and got many QA papers including this sample

3. math.QA/0201043 [abs, ps, pdf, other] :
Title: On Khovanov's categorification of the Jones polynomial
Authors: Dror Bar-Natan
Comments: Published by Algebraic and Geometric Topology at this http URL, 34 pages with many figures, source contains associated program and data file
Subj-class: Quantum Algebra; Geometric Topology
MSC-class: 57M25
Journal-ref: Algebraic and Geometric Topology 2 (2002) 337-370

 

[selfAdjoint]

Thanks. Using your hint, I fooled around and found it with"Vassiliev invariants" which is what I was interested in anyway. Bar-Natan's motive for "why are we not happy" is perfectly clear; he wants to impose on his students a careful understanding of what it means to have a "proved theorem" which you can use to prove other things, and what it does NOT mean - which is the status of what he calls the fundamental theorem of Vassiliev invariants.

 

[marcus]

Hi selfAdjoint, I concur with your description of Bar-Natan's
serious and commendable motive but I also delight immoderately in
his sense of humor
which he uses to the hilt in implementing his serious idea

thanks to nonunitary for this, I never would have seen the paper if
he had not referred to that one by Gambini and Pullin about LQG and
the Vassiliev invariants

you know diff manifolds are in a deep sense just gussied up Rⁿ
and it just shows you what an enormously rich thing Euclidean space is
that you can have all these different variations on that theme
the theme of the continuum
the theme of the coordinate patch and the metric
all fundamentally Rⁿ at the root

can knots and networks be comparably rich
why is there all this interest in them just now
well this is not purely a rhetorical question although it
sounds like it, I was actually wondering, but not expecting to
be able to get an answer

it was clever of you to study algebraic topology in grad school
maybe it will be useful after lo these many years

 

[marcus]

You might be interested to have a look at Frieder Lenz's
lecture notes on
"Topological concepts in gauge theories"

http://arxiv.org./hep-th/0403286

the whole thing is 83 pages

http://arxiv.org./PS_cache/hep-th/pdf/0403/0403286.pdf

They just came out.
he has a good historical sense and begins with a story about something that happened in 1833 involving Carl Gauss and a magnetic monopole :-)

these notes strike me as student-friendly
by someone who is considerate and puts in some nice pictures
Getting ready for a Brahms Req rehearsal tonite.
Up to you to decide if Frieder Lenz's notes are good or not and for what.

 

[selfAdjoint]

Thanks for the links, Marcus.

You know, reading Bar Natan's account of the topological proof of his "fundamental theorem" and its defects, I couldn't help thinking here's a natural arena for spectral sequences. That's only because I'm reading A User's Guide to Spectral Sequences at the same time, but seriously there are his filtered graded algebra and all - by a theorem, there is guaranteed to be a spectral sequence with the 1-page $$E^{p,q}_1$$ isomorphic to the homology of the algebra. But that's no good unless you can compute the limiting page $$E^{p,q}_{\infty}$$. The differentials of the sequence encode non trivial information about the algebra. I can't believe somebody hasn't tried this.

 

[marcus]

Bolen, Bombelli, Corichi
http://arxiv.org./abs/gr-qc/0404004
"Semiclassical States in Quantum Cosmology: Bianchi I Coherent States"

"We study coherent states for Bianchi type I cosmological models, as examples of semiclassical states for time-reparametrization invariant systems. This simple model allows us to study explicitly the relationship between exact semiclassical states in the kinematical Hilbert space and corresponding ones in the physical Hilbert space, which we construct here using the group averaging technique. We find that it is possible to construct good semiclassical physical states by such a procedure in this model; we also discuss the sense in which the original kinematical states may be a good approximation to the physical ones, and the situations in which this is the case. In addition, these models can be deparametrized in a natural way, and we study the effect of time evolution on an "intrinsic" coherent state in the reduced phase space, in order to estimate the time for this state to spread significantly."

 

[john baez]

the great John Baez burnout

Baez has not published in QG for several years, or only negligibly.

Well, I don't think my paper with Christensen and Egan on asymptotics of 10j symbols was negligible - it contained the results of literally billions of calculations, and it was the first detailed analysis of a spin foam model of quantum gravity. And that was back in August of 2002, which isn't several years yet, just a couple! "Several" means at least 3!

But, you're right in perceiving that I'm mainly interested in other things
these days.

I found out about this thread from Carlo Rovelli, who sent me an email teasing me about it. I couldn't resist replying to an article entitled "the great John Baez burnout"! I'll take it as a compliment, since it suggests there was a flame flickering there for a while.

Here's how I replied to Rovelli's email:

Dear Carlo -

Hi! I hadn't seen these... thanks. It's pretty funny.
You know you're getting old when you start getting emails
with subject headers like this.

I am in fact rather fed up with quantum gravity. One reason is that
nobody knows a spin foam model that approximates GR in the classical
limit, and I don't see how to get one, despite a lot of work. But
there's another, equally important *positive* reason: these days, work
on n-categories is really revolutionizing mathematics! The subject
is packed with incredible suprises; it goes all the way down to
the foundations of how we think, and there are huge wide-open fields
of fruit ripe for the picking. I can't help but wanting to spend
my time doing this: it's as cool almost as quantum gravity, but I *know*
it will work.

But I might switch back to quantum gravity if and when spin foam
models seem to start working... because I really love the *physical*
universe, and the most mysterious and exciting aspect of math
to me is how it let's us understand the physical universe.

It will be fun to see everyone in Marseilles and see what their
mood is. Probably rather different from mine!


jb

Just so nobody gets the wrong idea: while I'm tired of trying to find a spin foam model with something like GR as its classical limit, I don't see any reason this should be impossible. Christensen, Egan and I just looked at a few versions of the Barrett-Crane model, and we didn't even succeed in ruling those out, just showing that they were far stranger than anyone expected.

I'm even *more* pessimistic about string theory and M-theory - otherwise I might switch to that.

But really, what got me off quantum gravity was the knowledge that I won't live forever. I have a choice of working on quantum gravity, where nobody knows for sure what's right and what's not, and working on mathematics, where I'm *sure* what I'm doing is right. I spent about a decade working on the former; now I want to do more of the latter.

maybe the term is "mathopause"----it gets mathematicians.

Actually, the idea that mathematicians burn out early is a bit of a myth. Sure, some of them *die* early, like Abel and Galois and Riemann. But the ones who keep living often keep doing good stuff - although lots of them get tired of publishing and spend more time just thinking and talking to people, because it's easier and more fun. For example, take Dennis Sullivan, or Erdos (who got other people to do the writing).

In case anyone is interested, I have a new paper called "Quantum Quandaries: A Category-Theoretic Perspective", in which I argue that a lot of the puzzling things about quantum mechanics will become less puzzling when it becomes part of a theory of quantum gravity, because the category of Hilbert spaces is a lot like a category where the morphisms are spacetimes:

http://math.ucr.edu/home/baez/quantum.ps

This will appear in a volume edited by Steven French, Dean Rickles and Juha Saatsi, probably to be entitled "Structural Foundations of Quantum Gravity".

So, I'm not *completely* fed up with quantum gravity.

I'm also working a lot on the foundations of quantum theory:

http://math.ucr.edu/home/baez/qg-fall2003/
http://math.ucr.edu/home/baez/qg-winter2004/
http://math.ucr.edu/home/baez/qg-spring2004/

So, please don't count me out yet!

But, it's true that there's a nice new crop of people working on loop quantum gravity and spin foam models.

 

[jeff]

I won't live forever

Do you have the proof for that?

 

[marcus]

Background Independent Quantum Gravity---survey paper

http://arxiv.org./abs/gr-qc/0404018

Background Independent Quantum Gravity: a Status Report

125 pages

Ashtekar and Lewandowski

 

[cragwolf]

Just call me a Baez fanboy. I have spent countless hours at his website undergoing significant neural rewiring. Because of him I've been inspired to learn mathematics (I mean really learn it, beyond the "mathematical methods for physics" course I took way back in my undergraduate years). Baez is on the cutting edge of physics and mathematics, but he kindly and humbly devotes some of his time to helping us lesser beings learn something about the wonders of these subjects. His website is a pedagogical paradise.

 

[marcus]

well said!

 

[meteor]

"Flat spacetime vacuum in loop quantum gravity"
http://arxiv.org/abs/gr-qc/0404021

Authors: A. Mikovic
Comments: 20 pages, 6 figures

"We construct a state in the loop quantum gravity theory with zero cosmological constant, which should correspond to the flat spacetime vacuum solution. This is done by defining the loop transform coefficients of a flat connection wavefunction in the holomorphic representation which satisfies all the constraints of quantum General Relativity and it is peaked around the flat space triads. The loop transform coefficients are defined as spin foam state sum invariants of the spin networks embedded in the spatial manifold for the SU(2) quantum group. We also obtain an expression for the vacuum wavefunction in the triad represntation, by defining the corresponding spin networks functional integrals as SU(2) quantum group state sums"

Looking at the text, he mentions something called "spin network invariants". Never heard of this before (though I'm familiar with things like knot invariants or manifold invariants)

 

[john baez]

spin network invariants

Looking at the text, he mentions something called "spin network invariants". Never heard of this before (though I'm familiar with things like knot invariants or manifold invariants)

A spin network invariant is a function that assigns a complex number to each spin network embedded in space, where the number doesn't change when you apply a diffeomorphism of space to your spin network. (Here "space" is some 3-dimensional manifold.)

In loop quantum gravity, quantum states are commonly taken to be spin network invariants. You can think of such a state as a big fat linear combination of spin networks, where the coefficients are the aforementioned complex numbers.

If you attach a spin 0, 1/2, 1,... to a knot, you get a spin network of a specially simple kind. So, any spin network invariant gives an infinite sequence of knot invariants. But it has more information.

 

[selfAdjoint]

By the way Dr. Baez, I have printed of and am studying your new Quantum Quandries paper.. How neat! From a sufficiently high perspective, quantum physics and general relativity are more like each other than either of them is like set theory. I am always glad to see set theory marginalized, because of my prejudice for Tarski's theorem and the BSS-machine results.

 

[Janitor]

I've pretty much decided that there isn't a Santa Claus, but is there really a John Baez?

 

[meteor]

The Bianchi IX model in Loop Quantum Cosmology
Authors: Martin Bojowald, Ghanashyam Date, Golam Mortuza Hossain
Comments: 41 pages, 3 figures, revtex4
Report-no: IMSc/2004/04/16, AEI-2004-028

The Bianchi IX model has been used often to investigate the structure close to singularities of general relativity. Its classical chaos is expected to have, via the BKL scenario, implications even for the approach to general inhomogeneous singularities. Thus, it is a popular model to test consequences of modifications to general relativity suggested by quantum theories of gravity. This paper presents a detailed proof that modifications coming from loop quantum gravity lead to a non-chaotic effective behavior. The way this is realized, independently of quantization ambiguities, suggests a new look at initial and final singularities
http://arxiv.org/abs/gr-qc/0404039

 

[maddy]

The Bianchi IX model in Loop Quantum Cosmology
Authors: Martin Bojowald, Ghanashyam Date, Golam Mortuza Hossain
Comments: 41 pages, 3 figures, revtex4
Report-no: IMSc/2004/04/16, AEI-2004-028

The Bianchi IX model has been used often to investigate the structure close to singularities of general relativity. Its classical chaos is expected to have, via the BKL scenario, implications even for the approach to general inhomogeneous singularities. Thus, it is a popular model to test consequences of modifications to general relativity suggested by quantum theories of gravity. This paper presents a detailed proof that modifications coming from loop quantum gravity lead to a non-chaotic effective behavior. The way this is realized, independently of quantization ambiguities, suggests a new look at initial and final singularities
http://arxiv.org/abs/gr-qc/0404039

How does LQG get rid of cosmological singularities in homogeneous models for e.g. Bianchi V? Any good references to papers?

Is the Belinskii-Khalatnikov-Lifschitz scenario mostly used in analyzing quantum gravity solutions for cosmological singularities?

Thanks for any help (am just a beginner ) .

 

[marcus]

How does LQG get rid of cosmological singularities in homogeneous models for e.g. Bianchi V? Any good references to papers?
.

Maddy, almost all the papers I know of by Bojowald etc have dealt with the isotropic case.

I will find some URL for ones dealing with anisotropic, but it is a comparatively recent effort AFAIK.
I haven't seen anything about Bianchi V. I only recall stuff about Bianchi IX.

People sometimes come here (stingray, nonunitary) who might be able to respond more usefully.

As for papers about the homogenous (but not isotropic) case here are some references:
the most recent review of progress in the field is
"Loop Quantum Cosmology: Recent Progress"
http://arxiv.org/gr-qc/0402053

this contains only two refs that are explicitly to the homogeneous case and they are from last year
"Homogeneous loop quantum cosmology" gr-qc/0303073
"Homogeneous loop quantum cosmology: the role of the spin connection" gr-qc/0311004

maybe you can find more if you look in the references of these

there was also this, which I have not looked at so cannot say if it mentions Bianchi V,
"Quantum suppression of the generic chaotic behavior close to cosmological singularities" gr-qc/0311003

it looks to me as if the homog. case is just barely being scratched at
and that the papers mostly go back only to November of last year
but I am not knowledgeable about homog. case and you might find out things
are different if you take a closer look

most LQC papers involve homogenenous and isotropic simplification and
in effect use a quantized form of the Friedmann equation (which is what most cosmology depends on anyway)---again this is just my limited view and we could hopefully get some expert comment responding to your question

 

[meteor]

http://arxiv.org/abs/gr-qc/0404055


Ln(3) and Black Hole Entropy
Authors: Olaf Dreyer
Comments: Contribution to the Proceedings of the 3rd International Symposium on Quantum Theory and Symmetries, Cincinnati, September 2003

"We review an idea that uses details of the quasinormal mode spectrum of a black hole to obtain the Bekenstein-Hawking entropy of A/4 in Loop Quantum Gravity. We further comment on a recent proposal concerning the quasinormal mode spectrum of rotating black holes. We conclude by remarking on a recent proposal to include supersymmetry. "






This paper try to fix the Immirzi parameter
Give a look to page 2. It contains the formula for the entropy of a Black hole according to Loop Quantum Gravity

 

[marcus]

this thread is serving as a surrogate sticky "reference library". Thanks to all who have contributed so far!

-------Loop Gravity texts--------
Rovelli posted the 30 December 2003 draft of his book "Quantum Gravity", to be published this year by Cambridge University Press.
The PDF file is at his homepage
http://www.cpt.univ-mrs.fr/~rovelli/rovelli.html
The book is around 350 pages long and takes a few (like ten?) minutes to download and convert.
To download the 30 December 2003 draft of the book directly:
http://www.cpt.univ-mrs.fr/~rovelli/book.pdf

Here are Thiemann's Lecture Notes (they have been published in Berlin by Springer Verlag)
"Lectures on Loop Quantum Gravity".
A draft is online at
http://arxiv.org/gr-qc/0210094

-----a recent review article----
http://arxiv.org./abs/gr-qc/0404018

Ashtekar and Lewandowski
"Background Independent Quantum Gravity: a Status Report"
125 pages
many references

---------a newsletter: "Matters of Gravity"----
Jorge Pullin's newsletter "Matters of Gravity"
http://arxiv.org./abs/gr-qc/0403051
this is the Spring 2004 issue

-------Quantum Gravity Phenomenology and DSR---------

some recent phenomenology and DSR papers:

Ted Jacobson, Stefano Liberati, David Mattingly
"Quantum Gravity Phenomenology and Lorentz Violation"
http://arxiv.org./abs/gr-qc/0404067
15 April 2004

Giovanni Amelino-Camelia
"A perspective on quantum gravity phenomenology"
http://www.arxiv.org/abs/gr-qc/0402009
dated 2 February 2004

Giovanni Amelino-Camelia, Jerzy Kowalski-Glikman, Gianlucca Mandanici, and Andrea Procaccini
"Phenomenology of Doubly Special Relativity"
http://arxiv.org/gr-qc/0312124
dated 30 December 2003

Jerzy Kowalski-Glikman
"Doubly Special Relativity and quantum gravity phenomenology"
http://arxiv.org/hep-th/0312140
dated 12 December 2003

Jerzy Lukierski
"Relation between quantum κ-Poincare framework and doubly special relativity"
http://arxiv.org./hep-th/0402117
dated 18 February 2004

other less recent ones:

Jerzy Kowalski-Glikman and Sebastian Nowak
"Doubly Special Relativity and de Sitter space"
http://arxiv.org/hep-th/0304101
dated 11 October 2003

M. Daszkiewicz, K. Imilkowska, J. Kowalski-Glikman
"Velocity of particles in Doubly Special Relativity"
http://arxiv.org/hep-th/0304027
dated 3 April 2003


---------Loop Quantum Cosmology-------

Martin Bojowald
"Loop Quantum Cosmology: Recent Progress"
http://arxiv.org/gr-qc/0402053
One of the invited plenary talks at the January 2004 ICGC
conference (see list of recent conferences)

The Bianchi IX model in Loop Quantum Cosmology
Martin Bojowald, Ghanashyam Date, Golam Mortuza Hossain
41 pages
http://arxiv.org/abs/gr-qc/0404039

"Inflationary Cosmology and Quantization Ambiguities in Semi-Classical Loop Quantum Gravity"
Martin Bojowald, James E. Lidsey, David J. Mulryne, Parampreet Singh, Reza Tavakol
15 pages, 8 figures
http://arxiv.org./abs/gr-qc/0403106

Martin Bojowald and Kevin Vandersloot
"Loop Quantum Cosmology and Boundary Proposals"
http://arxiv.org/gr-qc/0312103
dated 23 December 2003

Martin Bojowald
"Quantum Gravity and the Big Bang"
http://arxiv.org./astro-ph/0309478
dated 17 September 2003, briefly summarizes how
LQG can serve to cure the big bang singularity and
motivate inflationary expansion. Short and less technical
than the other two papers.

Martin Bojowald and Kevin Vandersloot
"Loop Quantum Cosmology, Boundary Proposals, and Inflation"
http://arxiv.org/gr-qc/0303072
dated 19 March 2003

Shinji Tsujikawa, Parampreet Singh, Roy Maartens
"Loop quantum gravity effects on inflation and the CMB"
http://arxiv.org/astro-ph/0311015
from the Tsujikawa/Singh/Maartens abstract:
"In loop quantum cosmology, the universe avoids a big bang singularity and undergoes an early kinetic-dominated super-inflation phase, with a quantum-corrected Friedmann equation. As a result, an inflaton field is driven up its potential hill, thus setting the initial conditions for standard inflation. We show that this effect can raise the inflaton high enough to achieve sufficient e-foldings in the standard inflation era. We analyze the cosmological perturbations and show that loop quantum effects can leave a signature on the largest scales in the CMB, with some loss of power and running of the spectral index."

Viqar Husain and Oliver Winkler "On singularity resolution in quantum gravity"
http://arxiv.org/gr-qc/0312094
this is especially interesting because they duplicate LQC results (for example by Bojowald) using the older version of quantum gravity, ADM variables, quantized metric. Shows that the removal of the big bang singularity is "robust"---doesnt depend on using a particular formalism.

as a background reference for classical (non-quantum) cosmology:
Charles Lineweaver
"Inflation and the Cosmic Microwave Background"
http://arxiv.org/astro-ph/0305179
dated 12 May 2003

-------recent conferences------

Strings meet Loops (Albert Einstein Institute, MPI-Potsdam) October 2003
http://www.aei-potsdam.mpg.de/events/stringloop.html

Loop Gravity Workshop (Mexico City) January 2004
http://www.nuclecu.unam.mx/~corichi/lqg.htm

International Conference on Gravity and Cosmology (India) January 2004
http://www.cusat.ac.in/icgc04/

Quantum Gravity Phenomenology, (40th annual Polish Winterschool in Theoretical Physics) February 2004
http://www.ws2004.ift.uni.wroc.pl/html.html

--------upcoming conferences--------

Loop/SpinFoam Conference (Marseille) May 2004
http://w3.lpm.univ-montp2.fr/~philippe/quantumgravitywebsite/

http://www.maths.qmul.ac.uk/wbin/GRnews/conference?03Aug.1
http://www.maths.qmul.ac.uk/wbin/GRnews/conference?04Feb.2
http://www.maths.qmul.ac.uk/wbin/GRnewsfind/conference?10

General Relativity Conference (Dublin) July 2004
more annoucements at
http://www.maths.qmul.ac.uk/wbin/GRnewsfind/conference?conference

------observational means for testing quantum gravity------

Floyd Stecker
"Cosmic Physics: the High Energy Frontier
http://arxiv.org/astro-ph/0309027
dated September 2003

Stecker discusses the various earth-based and orbital instruments, currently operating, or under construction, or planned, or proposed, and the kind of data becoming available. Among many other things he discusses GLAST, planned to start operating 2007, which, if there are tiny energy-dependent differences in speed among gamma-ray-burst photons, may be able to detect same. Also discusses neutrino observation.


------links to an unselective assortment of current work------

Carlo Rovelli and Winston Fairbairn
"Separable Hilbert space in loop quantum gravity"
http://arxiv.org/abs/gr-qc/0403047

John Baez
"Quantum Quandaries: A Category-Theoretic Perspective"
http://arxiv.org/quant-ph/0404040

Livine's thesis
http://arxiv.org/gr-qc/0309028

Girelli and Livine
"Quantizing speeds with the cosmological constant"
http://arxiv.org/gr-qc/0311032

Oriti's thesis
http://arxiv.org/gr-qc/0311066
"Spin Foam Models of Quantum Spacetime"

Karim Noui and Philippe Roche
"Cosmological Deformation of Lorentzian Spin Foam Models"
http://arxiv.org/gr-qc/0211109
The cosmological constant occurs in a number of recent quantum gravity papers, for instance the one by Girelli/Livine.

Velhinho "On the structure of the space of generalized connections"
http://arxiv.org/math-ph/0402060

Noui and Perez "Three dimensional loop quantum gravity: physical scalar product and spin foam models"
http://arxiv.org/gr-qc/0402110

Noui and Perez "Three dimensional loop quantum gravity: coupling to point particles"
http://arxiv.org/gr-qc/0402111

Noui and Perez "Dynamics of Loop Quantum Gravity and Spin Foam Models in Three Dimensions"
http://arxiv.org/gr-qc/0402112

Noui and Perez "Observability and Geometry in Three Dimensional Quantum Gravity"
http://arxiv.org/gr-qc/0402113

Freidel and Louapre "Ponzano-Regge model revisited, I."
http://arxiv.org/hep-th/0401076

Gambini and Pullin "Canonical Quantum Gravity..."
http://arxiv.org/gr-qc/0402062

Buffenoir, Henneaux, Noui, Roche
Hamiltonian Analysis of Plebanski Theory
http://arxiv.org./gr-qc/0404041
(spin foam, BF)

----------fundamental constants, Planck units, time-keeping-------

Historical source for Planck units, the 1899 paper (thanks arivero!)
http://www.bbaw.de/bibliothek/digital/struktur/10-sitz/1899-1/jpg-0600/00000494.htm

In December 2003, the National Institute of Standards and Technology (NIST) posted new CODATA recommended values for the basic Planck units

http://physics.nist.gov/cuu/Constants/

choose "universal" from the menu to find (among other things) the recommended values of
planck mass
planck length
planck time
planck temperature

A 1997 article on timekeeping, discussing GR effects allowed-for in the GPS
http://www.allanstime.com/Publications/DWA/Science_Timekeeping/TheScienceOfTimekeeping.pdf

-------science journalism----
"The Duel: Strings versus loops"
http://arxiv.org/abs/physics/0403112

A translation of Rudy Vaas' article in the German
science magazine "Bild der Wissenschaft" roughly
comparable to the "Scientific American"

========
simply to have this link on LaTex handy:
https://www.physicsforums.com/misc/howtolatex.pdf

 

[marcus]

Woit's blog:
http://www.math.columbia.edu/~woit/blog/

the responses are getting interesting too
------------------
Recent paper by Olaf Dreyer
http://arxiv.org./gr-qc/0404055
-------------------
this is spillover from the main page of links
which is full
-------------------
a new QG Phenomenology paper
http://arxiv.org./gr-qc/0404113

"On alternative approaches to Lorentz violation invariance in loop quantum gravity inspired models
Jorge Alfaro, Marat Reyes, Hugo A. Morales-Tecotl and L.F. Urrutia
------------

there is also a new Quantum Gravity Phenomenology
paper by Ted Jacobson et al
dealing with QG predictions of Lorentz violation and
their testability

http://arxiv.org/gr-qc/0404067
"Quantum Gravity Phenomenology and Lorentz Violation"
Ted Jacobson, Stefano Liberati, David Mattingly

 

[marcus]

online resources for category theory

looks like some category theory may be needed to do
quantum gravity (e.g. Velhinho, also several Baez papers)

http://www.folli.uva.nl/CD/1999/library/pdf/barrwells.pdf
Barr is at McGill and Wells is at U Virginia
its >100 pages of lecture notes

http://www.dcs.ed.ac.uk/home/dt/CT/categories.pdf
these notes are by Daniele Turi at U. Edinburgh
they are based on Saunders Mac Lane book
"Categories for the working mathematician"

 

[marcus]

Hendryk Pfeiffer has a new preprint on arxiv
called
"Quantum Gravity and the Classification of
Smooth Manifolds"
http://arxiv.org./gr-qc/0404088

"...d = 3 + 1, if it can indeed be constructed, will offer the same potential. This relationship is the main theme of the present article.
The special role of space-time dimension d = 3 + 1 in differential topology is summarized by the following result.

Theorem 1.1. Let M be a topological d-manifold, d = 1, 2, 3, 4,... If M admits an infinite number of pairwise inequivalent differentiable structures, then d = 4.

This is a corollary of several theorems by various authors. We explain in this article why this result is related to the search for a quantum theory of general relativity..."

here is something unique about the dimension 4
It is the only possible dimension for spacetime to be if you want to have
plenty of possible smooth-manifold structures.

In this sense, dim = 5 is not OK, and dim = 6 is not OK.

This is a surprising theorem. I didnt know that d = 3+1 was mathematically so special as that. It is so surprising that I think I must be failing to understand. but Pfeiffer is I think very good and there it is written in black and white as theorem 1.1, so will go back and try to understand.

-------had to do something else and just got back-----
Pfeiffer says, on page 16:

"In d ≥ 3 + 1, no analogous result is available. There exist countably infinite families of (compact) smooth 4-manifolds [13] which are pairwise non-diffeomorphic, but which have homeomorphic underlying topological manifolds. There is therefore a considerable discrepancy between C∞- and C₀-QFTs in d = 3 + 1 space-time dimensions.

The most striking result even concerns the standard space R4 [14, 15].
Theorem 4.1. Consider the topological manifold R^d, d ε N.

• If d < 4, then there exists a differentiable structure for R^d which is unique up to diffeomorphism.
• If d = 4, then there exists an uncountable family of pairwise non diffeomorphic differentiable structure for R^d.

Non-uniqueness of differentiable structures persists in higher dimensions, for example, there are 28 inequivalent differentiable structures on the sphere S⁷, or 992 inequivalent differentiable structures on S¹¹, [16], but in dimension d ≥ 4 + 1 (d ≥ 5 + 1 if the manifold has a non-empty boundary), there never exists more than a finite number of non-diffeomorphic differentiable structures on the same underlying topological manifold.

The space-time dimension d = 3 + 1 is distinguished by the feature that there can exist an infinite number of homeomorphic, but non-diffeomorphic smooth manifolds."

------then on page 19 Pfeiffer says------
"Scenario for quantum gravity.

We have reached a first goal: the diffeomorphism gauge symmetry of general relativity on a closed space-time manifold has been translated into a purely combinatorial problem involving triangulations that consist of only a finite number of simplices, and their manipulation by finite sequences of Pachner moves.

If not only the partition function, but also the full path integral of general relativity in d ≤ 5+1 is given by a PL-QFT, we know that all observables are invariant under Pachner moves.

The partition function of quantum general relativity is an invariant of PL-manifolds, too, and can be computed by purely combinatorial methods for any given combinatorial manifold.

A generic expression of such a partition function is the state sum,
$$Z = \sum_{ colourings } \prod_{ simplices } (amplitudes),$$

where the sum is over all labelings of the simplices with elements of some set of colours, and the integrand is a number that can be computed for each such labeling. In Section 5 below, we give examples and illustrate that the partition function of quantum general relativity in d = 2 + 1 is precisely of this form.

If quantum general relativity in d = 3+1 is indeed a PL-QFT, the following two statements which sound philosophically completely contrary,

• Nature is fundamentally smooth.
• Nature is fundamentally discrete.

are just two different points of view on the same underlying mathematical structure: equivalence classes of smooth manifolds up to diffeomorphism."

also on page 20, right after this, there is a picture which illustrates what are Pachner moves in 2 dimensions and 3 dimensions.

this business on pages 19 and 20 of Pfeiffer paper seems interesting. I never heard talk like this. I have bolded some exerpts for emphasis.

 

[meteor]

http://arxiv.org/abs/gr-qc/0404083

Spectrum of quantized black hole, correspondence principle, and holographic bound
Authors: I.B. Khriplovich
Comments: 9 pages

An equidistant spectrum of the horizon area of a quantized black hole does not follow from the correspondence principle or from general statistical arguments. On the other hand, such a spectrum obtained in loop quantum gravity (LQG) either does not comply with the holographic bound, or demands a special choice of the Barbero-Immirzi parameter for the horizon surface, distinct from its value for other quantized surfaces. The problem of distinguishability of edges in LQG is discussed, with the following conclusion. Only under the assumption of partial distinguishability of the edges, the microcanonical entropy of a black hole can be made both proportional to the horizon area and satisfying the holographic bound

 

[selfAdjoint]

That's a new thought. All edges are equal but some edges are more equal.

 

[Sauron]

I knew long time ago about these peculiarity of 4-dimensional manifolds. I thought it was a mainstream knowledge.

By some stupid reason i have no acces to arwiv for around a week so i couldn´t read the article. So while waitng i´ll ask about other, slighly related, things.

I have a few generic questions/refelxions aobut some of the themes LQG is addressing.


Let´s beging by the question of entropy. My deal is whether the concept of entropy makes sense in GR at all. A lest in the same sense that in ordinay statistichal mehcanics.

I know about two main results. The one, of which i have a reasonable understanding , about the black hole area behaving like entropy. I also have notice about (but no understanding at all) results of Penrose relating the Weyl tensor to entropy, at least in cosmologicla scenarys

The question is that in the microcanonical device the entropy is reltaed to the number of micro-states compatible with an energy. But in GR there is no a good (and less local) definition of the energy of the gravitatory field.

I think these is commonly known. Anyway i would like to know how it has been addressed.

In order to get my own understanding i revised the whole idea (i never have had a deep basics in statistichal mecanics and it was a good exercice for me) of micro-states.

It works fine because it is used mainly for quantum mechanical systems with a discrete spectrum. But i wanted to understand how it could work incontinuous systems, other than the gravitatory field, an dalso in continuous spectrum of quantum systems.

I begined revising the black-body radiation. There the thermal equiibrium is suposed to be achieved by influence of the walls of a cavity.

By general (non rigurous) arguments (kirchov laws and it´s subleties/consecuences) it is assumed that an arbitrary (as far as i know expermintally tested for simply connected) shaped body can be simulated by a box shaped resonant cavity.

Them the number of microstates of the EM field can be charazterized by thre numbers (k1.k2,k3). And by standard manipulations they can be related to the frecuency.

Ok, i will not reexplain all the remaining basic facts. My point is here. We can give a meaning to the number of microstates because we are dealing with a configuration in which the EM field is in a compact region. ALso it is important to note that it seems that we are faced with a topological nature of the black body radiation. It is invariant under topological changes of the shap of the cavity.

So i try to think on the vibration numbers like something with a topologicla meaning. ¿woul the black body reaction could have another behaviour for non topologically trivial shapes of the caity?

Well, i know these hass addresed me far form the original question of the entropy of the gravitatory field. But my gues is that we are triying to aplly blindly a concept which works fine in non relativistic discret spectred hamiltonians. Maybe in some more general situations it needs some refinements.

For example, ¿whay about yang-mills fields?

Of course you will be saying ¿What about at finite temperature field theory?

I have not studied it in deep. But the whole idea seems to me so merely formal that doesn´t convince me as a good way to gain deep understanding of the problems. But of course probably it is my problem.

Well, i have more conceptual issues. But i´ll expose them in another moment.

 

[marcus]

this is interesting
QG has already challenged the Big Bang singularity
quantizing seems to remove it (Bojowald and others say)

maybe there is no black hole singularity, just a very deep well
maybe quantizing GR will remove this singularity also

also even without quantizing GR some alternative models avoid a singularity


http://arxiv.org/astro-ph/9908113
"Alternate Explosions: Collapse and Accretion Events with Red Holes instead of Black Holes"

html version:
http://arxiv.org./html/astro-ph/9908113

http://arxiv.org./astro-ph/9912322
"Red Hole Gamma-Ray Bursts: A New Gravitational Collapse Paradigm
Explains the Peak Energy Distribution And Solves the GRB Energy Crisis"

gammaray bursts are especially interesting and may even now not be
satisfactorily explained---awful lot of energy in them, more than supernovas

what has happened to these 1999 conjectures?

EDIT: by the way the author, Jim Graber, sometimes posts here at PF.
why doesn't someone ask him about this alternative picture of gravitational collapse

 

[marcus]

categories, as they impinge on Quantum Gravity

looks like some category theory may be needed to do
quantum gravity (e.g. Velhinho, also several Baez papers)

http://www.folli.uva.nl/CD/1999/library/pdf/barrwells.pdf
Barr is at McGill and Wells is at U Virginia
its >100 pages of lecture notes

http://www.dcs.ed.ac.uk/home/dt/CT/categories.pdf
these notes are by Daniele Turi at U. Edinburgh
they are based on Saunders Mac Lane book
"Categories for the working mathematician"

not being a whiz with categories or else they're just not very familiar, I'm
a bit bothered by their infiltrating into QG

there was just this paper by John Baez
"Quantum Quandaries: A Category-Theoretic Perspective"
http://arxiv.org/quant-ph/0404040

and this other recent paper by Hendryk Pfeiffer
is categorical in its approach
"Quantum Gravity and the Classification of
Smooth Manifolds"
http://arxiv.org./gr-qc/0404088

and back in February there was this paper by Velhinho
"On the structure of the space of generalized connections"
http://arxiv.org/math-ph/0402060

and now there is a woman mathematician who has published with Louis Crane and lives in New Zealand---her name is Marni Dee Sheppeard.
Her paper is so categorical that it seems the same to me whether I read it front to back or back to front. That is, I see a lot of diagrams with arrows and don't understand anything. but it purports to be about quantum gravity and I like the name Marni Dee so here's the link:

http://arxiv.org/gr-qc/0404121


On state sums, internalisation and unification
M. D. Sheppeard
35 pages

Abstract: "In this mostly expository article, elements of higher category theory essential to the construction of a class of four dimensional quantum geometric models are reviewed. These models improve current state sum models for Quantum Gravity, such as the Barrett-Crane model, in that they appear, for instance to remove degeneracies which swamp the partition function. Much work remains to be done before a complete construction is reached, but the crucial categorical notion of internalisation already illuminates the idea that a full unified model may result from few, albeit as yet poorly understood, additional principles. In particular, a spacetime and matter duality principle is employed through an understanding of the role of pseudomonoidal objects in categorified cohomology."

the good news: these models improve on the Barrett-Crane model which is pretty much the main spin-foam studied and which has some numerical crankiness (Baez published a paper in 2002 about this)

the good news: somehow putting spacetime and matter on the same footing?

the bad news: what the devil is pseudomonoidal objects in categorified cohomology?! it sounds like a new disease and I just hope it's not painful.
well fraid there's something else to learn about in QG

 

[selfAdjoint]

The Sheppeard paper looks good! I am going to read it, and see if I can keep up with it.


I just love the sniffy prose style too, which I associate with Oxbridge and its colonies like The Economist :

"The first and simplest way of regarding a manifold M as a category is to give it, albeit rather trivially, a groupoid structure. That is, the points of the manifold are the objects of the category and each point has attached an identity arrow, which is of course invertible."

Of course!

 

[marcus]

The Sheppeard paper looks good! I am going to read it, and see if I can keep up with it.

I am much cheered by your positive reaction.
I think I might be able to get something out of pages 6 thru 10
as they are a basic expostion of category theory.
although I'm less than confident of getting much of the rest of the paper.

I didnt notice at first that she even had a prose style! when I first looked i was just very impressed: she seemed awesomely intelligent and mainly bewildering. Will try to attribute some of this to her English.

This is a nice efficient way to start talking about categories (maybe it is the standard definition):

"Whereas a set has elements, and a map between sets takes elements to elements, a category has both elements, called objects, and relationships between elements, called arrows. Every object A is equipped with at least an identity arrow 1_A from A to A. Maps between categories, called functors, take objects to objects and arrows to arrows. Arrows may be composed f ◦g..."

 

[marcus]

she makes this point first off that I don't believe I've heard put so clearly by anyone:
background independence is basic to QG, she says, and
if you want background independence
then you have to go categories.

rovelli never told me that, baez only hinted at it, she flatly asserts it.
there is a bold magesterial quality turn to her thinking. Doesnt mince words. Says right out front where she's going. E.g. here is the first of the introduction:


"1 Introduction
The philosophy behind the construction outlined here is that any reasonable
attempt to describe quantum gravity within a unified framework ought to
respect some quantum principle of general covariance. Recall that in coming
to accept general covariance in the first place [37], Einstein needed to rid
himself of the idea that spacetime points had physical meaning outside of
their use in the metric tensor field. Put another way: no gravitational field,
no spacetime.
It is argued here that categorical internalisation is an essential element
required of a successful mathematical description of such a principle. There is mounting support for this point of view from studies of, for instance,..."

 

[selfAdjoint]

Yes. The only problem with doing the first pages is that she front loads the abstract stuff and expects her readers to have some problems with that. Of course with my weird background, that's the part I like!