Loop-and-allied QG bibliography

[marcus]

short exerpt from Smolin article

several people have expressed interest in the SciAm January 2004 article by Lee Smolin, "Atoms of Space and Time"
The complete article is probably worth a visit to your local public library. It is written for general audience but manages to give a fairly clear picture of the field and how it developed. Here is an exerpt, as a sample, from the section where Smolin is describing how he and some others got started:

-------quote page 68----

...In the mid-1980s a few of us...Ashtekar...Jacobson...Rovelli...decided to reexamine the question of whether quantum mechanics could be combined consistently with general relativity using the standard techniques. We knew that the negative results from the 1970s had an important loophole. Those calculations assumed that the geometry of space is continuous and smooth, no matter how minutely we examine it, just as people had expected matter to be before the discovery of atoms.

Some of our teachers and mentors had pointed out that if this assumption was wrong, the old calculation would not be reliable.

So we began searching for a way to do calculations without assuming that space is smooth and continuous. We insisted on not making any assumptions beyond the experimentally well tested principles of general relativity and quantum theory. In particular we kept two key principles of general relativity at the heart of our calculations.

The first is known as background independence. This principle says that the geometry of spacetime is not fixed. Instead the geometry is an evolving, dynamical quantity. To find the geometry, one has to solve certain equations that include all the effects of matter and energy. Incidentally, string theory, as currently formulated, is not background independent; the equations describing the strings are set up in a predetermined classical (that is, nonquantum) spacetime.

The second principle, known by the imposing name of diffeomorphism invariance, is closely related to background independence. This principle implies that, unlike theories prior to general relativity, one is free to choose any set of coordinates to map spacetime and express the equations. A point in spacetime is defined only by what physically happens at it, not by its location according to some special set of coordinates...

...By carefully combining these two principles with the standard techniques of quantum mechanics, we developed...[the means]...to do a calculation...
That calculation revealed, to our delight, that space is quantized. We had laid the foundations of...loop quantum gravity...

------end of exerpt-----

 

[ranyart]

Loop Quantum Cosmology and Boundery Proposals/Bojowald-Vandersloot

Amazing..

http://uk.arxiv.org/PS_cache/gr-qc/pdf/0312/0312103.pdf

 

[marcus]

Originally posted by ranyart
Amazing..

http://uk.arxiv.org/PS_cache/gr-qc/pdf/0312/0312103.pdf

thanks for the lead, ranyart! a Loop Quantum Cosmology
article. I will have a look. In case anyone wants the abstract:

http://uk.arxiv.org./abs/gr-qc/0312103

Martin Bojowald and Kevin Vandersloot
"Loop Quantum Cosmology and Boundary Proposals"
invited talk at the 10th Marcel Grossman meeting July 2003
18 pages, 5 figures

edit: this turned out to be more than the title suggests.
there are 45 references (it's a mini-survey article)
a thumbnail sketch of LQG and quick review of current work
in the general theory, not limited to cosmology
followed by another concise review of current Loop cosmology
developments
then, on pages 10-12, they present their results
relating to cosmological boundary conditions
(citing and comparing work of Hartle/Hawking and of Vilenkin)
finally, pages 12-15, they discuss open questions having to do with behavior around the cosmological singularity or bounce, and graph some results of calculation around the bounce.

it is an interesting paper from several standpoints---
for instance what they choose to emphasize in the overview of the general field: on page 4 at the top, they cite two papers by Sahlmann, another two by Sahlmann/Thiemann, and one by Lewandowski/Okolow.
the view of Loop gravity is on the abstract side, through the window of "representations of the classical algebra"

the paper connects to history by citing Hartle and Hawking "Wave Function of the Universe" (1983) and Vilenkin "Quantum Creation of Universes" (1984) and pointing out the central long-standing concern with cosmological boundary conditions in the Wheeler-DeWitt quantum cosmology model.

they use the algebraic representation-theory raised earlier, carried over and specialized to cosmology, to say how and why Loop quantum cosmology differs from vintage 1980s (Wheeler-DeWitt) quantum cosmology-----different Hilbertspace, different operators, discrete spectra instead of continuous---references to the Bohr compactification and the Stone-von Neumann theorem at bottom of page 6.

then starting on page 7 they focus on the dynamics of loop quantum cosmology---the Hamiltonian constraint and difference equation that determines evolution around the bounce---and
show how the loop model matches up with Wheeler-DeWitt: in effect has the right limiting behavior (see for example Figure 1).
They also discuss ways the modern theory differs from the vintage model
(eliminates the singularity, provides for varying degrees of inflation depending on assumptions, and gives rise to somewhat different boundary conditions, or to similar ones in a different way)

this paper ties a number of threads together.
the other research currents it draws on and connects to
are as significant as the research results
it relates current research in loop cosmology with the historical antecedents (connects it to Wheeler/DeWitt/Hawking/Hartle/Vilenkin) by addressing issues that were traditionally central to earlier work

and it points up linkage between the specialized field of loop cosmology and the algebraic approach to the broader field of LQG associated with Ashtekar/Lewandowski/Thiemann/Sahlmann

the bibliography is extensive and up to date, as you might want from a "mini-survey". For example, the Husain/Winkler "On Singularity Resolution" paper that ranyart just found posted a couple of days ago on arxiv (gr-qc/0312094) is their reference 25.

an earlier brief overview of loop cosmology this year
http://arxiv.org./abs/astro-ph/0309478
is only 6 pages and less abstract
that is Bojowald's
"Quantum Gravity and the Big Bang"
it is less hilbert spacey but gives a quick idea of what
the field is about and how the calculations are done
both papers are good, just different introductions to the same thing

 

[ranyart]

Marcus I know someone asked for a good link for loop Quantum Gravity?

I presume you have this link somewhere?..if so I can always delete it:
http://arxiv.org./abs/gr-qc/0306008

I will post just to the Abstract as I automatically link directly to pre-print papers, but maybe the abstract is more usual practice.

 

[marcus]

Originally posted by ranyart
I presume you have this link somewhere?..if so I can always delete it:
http://arxiv.org./abs/gr-qc/0306008

"Cosmological applications of loop quantum gravity"

I know the paper but I didnt have the link handy, not handy to this thread anyway. Thanks for mentioning it. Bojowald co-authored that with Hugo Morales-Tecotl, in Mexico City. It's good because it is introductory, part of a loop gravity seminar taught for undergrad and grad students. I read somewhere that Rovelli was Morales-Tecotl's thesis advisor, which makes me think that Morales-Tecotl is also a young person too, like Bojowald----recent PhD or recent postdoc.

I will post just to the Abstract as I automatically link directly to pre-print papers, but maybe the abstract is more usual practice.

Whichever you prefer! We can provide links to either abstract and full text. I don't know that one is more useful or usual than the other. I always look at the abstract first because a long PDF download ties up my computer and the abstract tells me how many pages.

Right now I feel a bit to lazy to bother but probably all these links should be gathered in a list-----or two lists: one for the full theory and one for the specific application to cosmology. It gets tedious playing librarian but it is actually easier than having to go through piles of paper on my desk. Thanks again for contributing these good links!

 

[marcus]

New CODATA values of the fundamental constants

Loop gravity is a Planck-scale theory and Planck units have a special place in it. This month the National Institute of Standards and Technology (NIST) posted new values for the basic Planck units

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

choose "universal" from the menu to find (among other things) the 2002 CODATA recommended values of
planck mass
planck length
planck time
planck temperature

the uncertainties have been reduced by an order of magnitude since
the values of Planck units were posted in the 1998 CODATA set.
Maybe this is no big deal but it is nice that the natural units for Loop Gravity are gradually beginning to look more like a recognized system of units

A good article on timekeeping, discussing GR effects on the GPS
http://www.allanstime.com/Publications/DWA/Science_Timekeeping/TheScienceOfTimekeeping.pdf

 

[marcus]

new Amelino-Camelia/Kowalski-Glikman paper

Giovanni Amelino-Camelia, Jerzy Kowalski-Glikman, and two others
"Phenomenology of Doubly Special Relativity"
dated 30 December 2003 (recent)
about 22 pages
http://arxiv.org/gr-qc/0312124

Giovanni A-C is the most eminent person in quantum gravity phenomenology and I believe the fastest riser is Jerzy K-G.
QG Phenomenology is a hot field with a lot of recent papers---both theoretical and observational. The theoretical part says what are the various quantum gravity models and what (in the case of those models that actually predict and can be tested by possible observation) do they predict and how---with planned space observatories etc---can they be tested.

Like pruning a tree, the observationalists can do the loop gravity/spin foam theorists a favor by chopping off the bad branches
(that actually make testable predictions but the predictions are wrong). So there is growing interest and visibility for this QG Phenomenology business.

And so when Giovanni A-C and Jerzy K-G get together on a paper and give the latest word on the subject it is apt to be worth paying some attention. So I posted it. I thought it was.

It is probably time to gather the links in this "surrogate sticky" thread into a single post----there are enough links now so they are too spread out

 

[marcus]

the present state of things in Loop Gravity

Loop Gravity looks like it going to have an active year in 2004,
getting progressively more visible and well-established, with even some recognizeable prospects for testing (phenomenology).

Here are some straws in the wind for 2004.
Smolin's January "Scientific American" article
Rovelli's book "Quantum Gravity" now at Cambridge University Press (but the 30 December 2003 draft is still online)
a spate of conferences and symposia:

Mexico City in January (loop/foam)
Polish Winterschool in February (quantum gravity phenomenology, DSR)
Marseille in May (loop/foam)
Dublin in July (the whole range of gen rel)

How broad a range should "Loop Gravity" cover?
It is actually a fleet of theories being developed which share
two key characteristics
These were underscored in Smolin's article and can be abbreviated DI-BI (diffeomorphism invariance-background independence)
All these formulations of quantum gravity attempt to quantize General Relativity and preserve these two key features of the original 1915 theory. I will quote Smolin's short description of DI and BI in a moment.

The distinction between loop and spin foam approaches has become somewhat artificial. They have always been two parts of a single enterprise, and Livine's 2003 thesis (Boucles et Mousses de Spin en Gravite Quantique) showed how to bridge the formal divide. As can be seen from the titles and programs at the various conferences, one no longer discusses loop as distinct from foam---instead there is apt to be a unified "loop/foam" conference, or loop/foam survey talk, or session of talks.

From a historical perspective, the main thing Loop Gravity does (and and stringy theories do not) is to actually quantize the theory of General Relativity itself and, in doing so, retain the essential features DI and BI, which stringy models lack. Accordingly the main criticism of the Loop Gravity approach(es) by string folk is to insist that attempts to retain the Background Independence and Diffeo-Invariance features of Relativity are doomed to fail (in essence because quantizing GR has so-far proven difficult.) The essential features of the classical 1915 theory are declared to be too radical---General Relativity must be somehow wrong and in need of replacement by a theory which on the one hand predicts the same numbers but on the other hand has room for absolute space and time---a fixed background, a uniform flow of time.

DI and BI actually imply that continuous time does not exist at Planck scale. In Bojowald's Loop Quantum Cosmology papers, for instance, there is no time coordinate. The (quantized) scale-factor of the universe is used as a clock----its eigenvalues are the ticks of the clock---it is meaningless to ask if they are "uniformly spaced"----the progress of the big bang or bounce expansion proceeds in quantized steps--the size of the universe is its own clock.

Quantizing GR means doing physics without time. Or at least with a quantized time as Bojowald does cosmology. This indeed is radical and apparently has many people in a state of denial if not outright horror ("This can't be right!")

As Rovelli says, his book is as much about time as about gravity. The quantization of time (or disappearance of continuous time coordinates at the quantum level) was not something anyone "put in by hand". It arose on its own accord from taking GR seriously and quantizing it by standard approaches.

Well, I should quote Smolin about what DI and BI mean. I will post this now and edit in the quotes later.

---------Smolin SciAm quote----
In particular we kept two key principles of general relativity at the heart of our calculations.

The first is known as background independence. This principle says that the geometry of spacetime is not fixed. Instead the geometry is an evolving, dynamical quantity. To find the geometry, one has to solve certain equations that include all the effects of matter and energy. Incidentally, string theory, as currently formulated, is not background independent; the equations describing the strings are set up in a predetermined classical (that is, nonquantum) spacetime.

The second principle, known by the imposing name of diffeomorphism invariance, is closely related to background independence. This principle implies that, unlike theories prior to general relativity, one is free to choose any set of coordinates to map spacetime and express the equations. A point in spacetime is defined only by what physically happens at it, not by its location according to some special set of coordinates...

...By carefully combining these two principles with the standard techniques of quantum mechanics, we developed...[the means]...to do a calculation...
That calculation revealed, to our delight, that space is quantized. We had laid the foundations of...loop quantum gravity...
------------end quote----------------

 

[marcus]

In an earlier post on this thread I gave the program list for the 40th annual Polish Winterschool of Theoretical Physics, but I apparently didnt give a link

http://www.ws2004.ift.uni.wroc.pl/html.html

The tradition is every winter to choose a topic in Theoretical Physics and get together the world's top people at a Polish ski resort for a couple of weeks of tutorials, seminars, and talks on new research.
It is at Ladek Zdroi, a spa in SW Poland on the Czech border in the Sudeten mountain range.

The first winterschool was in 1964. I guess detente was part of the aim of getting scientists together from east and west, or maybe just good science.

This year the topic chosen is "Quantum Gravity Phenomenology".

That mostly means loop/spin foam/doubly special relativity stuff. Does not seem to be much in way of stringy phenomenology because there doesn't seem to be much testable stringy prediction.

But notice that E. Alvarez is on the program. He is a string theorist who presented a oft-cited wake-up paper "Loops versus Strings" at a conference of string (and other HEP) people a couple of years ago.

Also notice the central role of Jerzy Kowalski-Glikman, who is covering Doubly Special Relativity. Involving a bending of Lorentz symmetry, DSR seems to be taking a prominent place in quantum gravity phenomenology.

What is the key idea in DSR? I will try a separate post on that.

 

[marcus]

the key idea of DSR

The key idea of DSR is to repeat the success of 1905
in an analogous situation

Lorentz transformations of 1905 SR look just like square old Galilean frame transformations but "bent" slightly by a factor which is ordinarily very close to one except at very high speeds.
So you take the block of numbers you would have used in a Galilean and tweak slightly by a factor sqrt(1 - beta²), and then it turns out that a certain physical quantity (c, the Planck unit of speed) is the same in all frames, that is, is unchanged by the new "deformed" Galilean transformations.

In DSR you tweak the transformation matrix even a bit more and you get that TWO physical quantities are unchanged, not only the Planck speed unit, c, is invariant but also the Planck energy unit.

We have to look at the situations in 1905 and now about 100 years later. In 1905 they had square Galilean frame change matrices and they noticed that Maxwell equations predicted a definite speed for EM radiation. So they had two choices
1. there was a preferred frame ("aether") that the equations worked in and they didnt work in other frames ("moving observers")
2. there was no preferred frame ("Galilean relativity") and Maxwell worked in all the frames you could transform to with a straight Galilean framechange. But then there was something that should be traveling the same speed in all frames! Paradox. So they tweaked, or bent, or "deformed" the Galilean symmetries matrices slightly in a way that wouldn't be noticeable at small boosts, in other words with small everyday speed changes.
Lorentz and Poincare saw how, but failed to take it seriously, so Einstein eventually did and gets the credit.

Now in 2004 we have Lorentz framechange matrices---they look like Galilean in the everyday cases and are "deformed" or maybe one should say "subtley adjusted" so that the Planck unit speed is invariant.
And we have realized that there are other natural units BESIDES the natural unit of speed, namely there is a natural unit of energy E_p. This is a gateway to Planck scale where physics is apt to be a good deal different and there is a growing realization that all observers should probably see the same E_p. Or wait, there is still the preferred frame or "aether" possibility.

1. there could be a preferred frame "breaking Lorentz symmetry" as they say, then we don't have to adjust the matrices, and whatever is true is only really true in the universe's preferred frame---what you see from other perspectives deviates more or less from what you would be seeing in the one true frame. This is boring.
(but when people do "observational tests of quantum gravity" it is this Lorentz symmetry breaking hypothesis that they are really testing nowadays)

2. DSR is the other alternative, where there is no preferred frame, no "Lorentz symmetry breaking". You subtley adjust the transformations so they leave TWO rather than only one of the Planck units invariant.

Basically here I am just repeating the account given in this latest DSR paper
"Phenomenology of Doubly Special Relativity"
by Giovanni A-C, Jerzy K-G, and two other people
http://arxiv.org/gr-qc/0312124

 

[marcus]

There is no sticky for links to loop gravity source material. So this thread can serve as a surrogate. This post gathers links from several earlier posts, and shortens the comments. These links include some that I found and some that other PF posters have contributed, to whom thanks!

The term "Loop Gravity" is used for a broad range of background-independent approaches to quantizing general relativity. Rovelli briefly discusses "the name of the theory" on page (xvi) of his new book. The name "loop" is something of an accident because current approaches are not so much concerned with loops. But no one has come up with a designation that includes spin foams and the various models based on spin networks and is any more convenient.

The main things the new approaches seem to have in common is that they emerge from General Relativity (rather than Particle Physics) and that they aren't string/brane theories.

A kind of merging among topological quantum field theory ("TQFT") and non-commutative geometry (especially because of the Cosmological Constant) and spinfoams and (Lorentzian spin network-based) Loop Gravity seems to be in progress. In another direction Loop Gravity seems to be connecting up with Doubly Special Relativity (DSR). A way has been found to do spin network analysis with non-compact groups---using SL(2,C) for gauge instead of SU(2). It seems too early to judge which of these trends are significant in the long term, but it may help to keep some of the links handy for reference.


Rovelli just posted the 30 December 2003 draft of his book "Quantum Gravity". 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

The SPIRES database on citations is often handy. There is a topcited list for the smaller series GR-QG (general relativity and quantum gravity)here:
http://www.slac.stanford.edu/library/topcites/top40.2002.E.html
And the more extensive series HEP-TH here:
http://www.slac.stanford.edu/library/topcites/topcites.review.2002.html

We were discussing stuff from Livine's thesis in this and another thread. Here is Livine's thesis. He does a lot with explicitly covariant---SL(2,C)-style---spin networks and makes an explicit bridge from LQG to Lorentzian spinfoams.
http://arxiv.org/gr-qc/0309028

Girelli and Livine have come out with a paper about quantizing speed.
"Quantizing speeds with the cosmological constant"
http://arxiv.org/gr-qc/0311032

Ichiro Oda has posted "A Relation Between Topological Quantum Field Theory and the Kodama State"
http://arxiv.org/hep-th/0311149

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

Smolin and Starodubtsev
"General Relativity with a topological phase: an action principle"
http://arxiv.org/hep-th/0311163

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.

-------Quantum Gravity Phenomenology---------

two recent papers:
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

other fairly 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-------

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

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

-------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

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


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

Loop/SpinFoam Conference (Marseille) May 2004
http://www.maths.qmul.ac.uk/wbin/GRnews/conference?03Aug.1
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

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

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

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

Floyd Stecker is at the NASA Goddard Laboratory for High Energy Astrophysics and something of a world-class expert on gamma-ray bursts and cosmic ray research. It seems that man-made accelerators are not big or powerful enough to be very effective in providing empirical guidance to quantum gravity theory. So what is apt to take the place of accelerators is high energy astrophysics. 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 2006, 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.

 

[marcus]

sources for Loop Gravity with matter

Loop Gravity is a theory under construction, so Rovelli's
Chapter 7 "Dynamics and Matter", pages 199-212, is describing
work in progress. Section 7.1 discusses the hamiltonian and
7.2 the inclusion of matter.

Table 7,1 on page 208 gives "Quantum numbers of the spin network states for gravity and matter."

The graph $$\Gamma$$ with N nodes and L links, is like a big quantum number describing adjacency. Nodes correspond to regions or chunks of space and links to the surfaces between those volumes

$$\Gamma$$ adjacency
$$i_n$$ volume of node n
$$j_l$$ area of surface l
$$F_n$$ number of fermions at node n
$$S_n$$ number of scalars at node n
$$w_n$$ field strength at node n
$$k_l$$ electric flux across surface l

In section 7.2.4 "The quantum states of space and matter", notation is given for |s> a quantum state of space and matter.

As one has come to expect, quantities like volume/area, fieldstrength/flux appear as irreducible representations/intertwiners.
More details about this on pages 208 and 209.

"thus we can write
$$|s> = |\Gamma,i_n,j_l,F_n,S_n,w_n,k_l>$$
This state describes a quantum excitation of the system that has a simple interpretation as follows. There are N regions n, that have volume and where fermions and Higgs scalars can be located. These are separated by L surfaces l, that have area and are crossed by flux of the (electric) gauge field. The quantum numbers are related to observable quantities as in Table 7.1. This completes the definition of the kinematics of the coupled gravity+matter system."

the next section, 7.3 "Matter: dynamics and finiteness" writes the hamiltonian compounded of four pieces.

$$H = H_{Einstein} + H_{YangMills} + H_{Dirac} + H_{Higgs}$$

One brief exerpt from Section 7.3, "...The fact that the total hamiltonian turns out to be finite is extremely remarkable. It is perhaps the major payoff of the background independent quantization strategy on which LQG is based..."

For the finiteness result Rovelli cites "Lectures on Quantum Gravity"
http://arxiv.org/gr-qc/0210094
these are notes at the grad student level prepared by Thomas Thiemann, which are to appear in a textbook series called
"Lecture Notes in Physics" (Springer, Berlin)

and also "Quantum Gravity as the Natural Regulator of the Hamiltonian Constraint of Matter Quantum Field Theories"
http://arxiv.org/gr-qc/9705019

It is a bit of luck that quantizing space makes the ordinary infinities of QFT go away:"...the ultraviolet divergences of ordinary quantum field theory can be directly interpreted as a consequence of the approximation that disregards the quantized, discrete, nature of quantum geometry..."

 

[marcus]

more confirmation of General Relativity

Labguy posted this in the Astronomy forum, under the heading "Albert is Still Looking Good". It bears on Loop Gravity so I'll copy it and add it to our links.
-----------
Recent release, passed through Ned Wright's Cosmology site:
http://www.astro.ucla.edu/~wright/cosmolog.htm#04Dec03

"A Double Radio Pulsar.
9 Jan 2004 - Lyne et al. (2004, Science in press) gives the details about PSR J0737-3039 A&B, the double radio pulsar binary with a relativistic orbit, previously reported as a single pulsar in a binary system on 4 Dec 2003. The mass of the 23 millisecond pulsar (A) is 1.337+/-0.005 M(sun) while the mass of the 2.8 second pulsar (B) is 1.250+/-0.005 M(sun). There are now 6 measured constraints on (MA,MB) and the values given above are consistent with all 6 constraints, providing a stringent test of General Relativity which GR passes with flying colors".

And:

"An amazing binary pulsar.
4 Dec 03 - Nature today published a paper (Burgay et al. 2003, Nature, 426, 531-533) about a newly announced millisecond pulsar, PSR J0737-3039, in a relativistic binary system. Radio pulsars are neutron stars (NS) which have a mass of about 1.4 solar masses and a radius of 10 km, magnetic fields billions to trillions of times larger than the Earth's magnetic field, and spin periods from 1.6 milliseconds to several seconds. PSR J0737-3039 is orbiting another neutron star every 2.4 hours and the two stars will merge in 85 Myr due to gravitational radiation. Hence LIGO will have many more detectable NS+NS merger events based on the statistics of two objects instead of the previous estimate based solely on the one merging binary pulsar PSR B1913+16 known earlier.

...the relative motion of the two stars is 14,000 km in 22 seconds,..."
-----------

The relevance of continued observational confirmation of GR to Loop Gravity is that the theory is distinguished by treating General Relativity (with its basic assumptions of background independence and diff-invariance) as a fundamental theory to be quantized.

By contrast certain alternatives to Loop Gravity do not treat GR as fundamental. Instead it is treated as the low-energy limit of some hoped-for but still unknown theory not requiring GR's basic assumptions (such as background independence).

The Nature article also points out that having found another binary system due to merge in the (astronomically) near future----85 million years in this case---is suggestive that the merger of a pair of neutron stars (the kind of thing LIGO would like to detect gravity waves from) may be a more frequent event than was estimated earlier. LIGO will itself be testing, and potentially offering further confirmation of, General Relativity.

 

[marcus]

source article for the binary pulsar

The source article for the binary pulsar was posted a couple of
days ago, 7 January 2004.
http://arxiv.org/astro-ph/0401086
it is 21 pages
and discusses the implications for testing GR in detail
the article is information rich, with plenty of
tables (of orbit parameters etc.) and figures.

6 binary pulsars are known
this one was discovered by an Australian dish (Parkes)
in 2003
several different tests (testing several different predictions)
of GR are possible as more observations of the binary system
accumulate
It is a lucky find.

 

[marcus]

current state of things in Loop Gravity research

In another thread the question of demographics came up again.
Numbers of papers, or even numbers of "blockbuster" papers that get lots of follow-up citations, don't necessarily mean all that much but the issue gets raised now and then so we should have some kind of objective data. There is a small and increasing output of papers
in Loop Gravity:

I just went to arxiv.org "Search Physics Archives" page and
put in [ABS = loop quantum gravity]OR[ABS = spin foam]OR[ABS = loop quantum cosmology] since 2000 and it gave me
these numbers of papers:

2000 46
2001 48
2002 64
2003 70

These are the preprints at the archive that have somewhere in their ABSTRACTS either the words loop quantum gravity, or the words spin foam, or the words loop quantum cosmology.
--------------

Although I'm not especially interested in string/brane theories, some people seem interested in comparisons so here's the same numbers for
[ABS = string]OR[ABS = brane]OR[ABS = M-theory]


2000 1457
2001 1496
2002 1500
2003 1265

That is, those where the abstract summary of the paper has in it somewhere the word string, or the word brane, or the word M-theory.

The numbers speak for themselves. There's more to say about the current state of research in Loop Gravity---hope to get back to this later today.

 

[marcus]

The most recent Top Ten listing---GR and Quantum Gravity

A guy at Stanford-SLAC puts out a list of the top-cited papers each year in each archived category. He hasnt done it for 2003 yet, so his most recent list is as of end 2002.
I was interested in the most-cited papers in the category gr-qc
"General Relativity and Quantum Gravity"

http://www.slac.stanford.edu/library/topcites/2002.gr-qc.1.shtml

and, in particular, in RECENT papers (dated 2000, 2001 and 2002) in that category. So here's the "Top Ten" list for that category, with the older (pre-2000) papers winnowed out. Of course most string papers are over in the hep-th, high energy physics-theory, category. I am focussing just on gr-qc here.


---------------------

57 citations
RELATIVITY IN SPACE-TIMES WITH SHORT DISTANCE STRUCTURE GOVERNED BY AN OBSERVER INDEPENDENT (PLANCKIAN) LENGTH SCALE
By Giovanni Amelino-Camelia (Rome U.).
Published in Int.J.Mod.Phys.D11:35-60,2002 [PS file for arXiv: gr-qc/0012051]


54 citations
CLASSICAL BLACK HOLE PRODUCTION IN HIGH-ENERGY COLLISIONS
By Douglas M. Eardley, Steven B. Giddings (UC, Santa Barbara).
Published in Phys.Rev.D66:044011,2002 [PS file for arXiv: gr-qc/0201034]


36 citations
INTRODUCTION TO MODERN CANONICAL QUANTUM GENERAL RELATIVITY
By Thomas Thiemann (Potsdam, Max Planck Inst.). [PS file for arXiv: gr-qc/0110034]


31 citations
THE CONFRONTATION BETWEEN GENERAL RELATIVITY AND EXPERIMENT
By Clifford M. Will (Washington U., St. Louis).
Published in Living Rev.Rel.4:4,2001 [PS file for arXiv: gr-qc/0103036]


28 citations
EXTENDING THE LIFETIME OF 3-D BLACK HOLE COMPUTATIONS WITH A NEW HYPERBOLIC SYSTEM OF EVOLUTION EQUATIONS
By Lawrence E. Kidder, Mark A. Scheel, Saul A. Teukolsky (Cornell U., Radio. Space Res. Ctr.).
Published in Phys.Rev.D64:064017,2001 [PS file for arXiv: gr-qc/0105031]


28 citations
GEOMETRY AND DYNAMICS OF THE BRANE WORLD
By Roy Maartens (Portsmouth U.). [PS file for arXiv: gr-qc/0101059]


27 citations
AN ALTERNATIVE TO QUINTESSENCE
By Alexander Yu. Kamenshchik (Landau Inst. & Landau Network Centro Volta), Ugo Moschella (Insubria U., Como & INFN, Milan), Vincent Pasquier (Saclay).
Published in Phys.Lett.B511:265-268,2001 [PS file for arXiv: gr-qc/0103004]


23 citations
QUANTUM GRAVITY: A PROGRESS REPORT
By S. Carlip (UC, Davis).
Published in Rept.Prog.Phys.64:885,2001 [PS file for arXiv: gr-qc/0108040]


21 citations
QUANTUM GEOMETRY OF ISOLATED HORIZONS AND BLACK HOLE ENTROPY
By A. Ashtekar (Penn State U. & Santa Barbara, KITP), John C. Baez (UC, Riverside & Penn State U.), Kiriil Krasnov (UC, Santa Barbara & Santa Barbara, KITP).
Published in Adv.Theor.Math.Phys.4:1-94,2000 [PS file for arXiv: gr-qc/0005126]

19 citations
GENERALIZED LORENTZ INVARIANCE WITH AN INVARIANT ENERGY SCALE
By Joao Magueijo (Imperial Coll., London), Lee Smolin (Perimeter Inst. Theor. Phys. & Waterloo U.).
Published in Phys.Rev.D67:044017,2003 [PS file for arXiv: gr-qc/0207085]
---------------------

obviously there are different ways of gauging activity and what the
most-cited papers in a field are and what the cut-off should be for "recent" work, but here is one measure: the number of other papers that cited the given paper in their references. At least it gives an idea of who the people are that write the papers that get most often cited in this division of the archive (and some slight indication as to what topics are of lively current interest)

 

[marcus]

Forthcoming LQG papers---Freidel, Louapre, Livine

Loop Gravity-watchers will be familiar with Etera Livine, Laurent Freidel, and David Louapre. David has been a sometimes poster at PF and both Livine and Freidel are among those whose Lorentzian spinfoam papers we discussed. Freidel and Louapre (with help from Livine) are preparing a series of papers on 2+1 dimensional quantum gravity of which the first is now available.

The ancestor of this series is
Laurent Freidel, “ A Ponzano-Regge model of Lorentzian 3-Dimensional gravity ”, Nucl. Phys. Proc. Suppl. 88 (2000) 237-240 , gr-qc/0102098.

The announced series of four papers, of which the first was just posted:

L.Freidel and D. Louapre,"Ponzano-Regge model revisited I: Gauge fixing, observables and interacting spinning particles"
http://arxiv.org./hep-th/0401076

L.Freidel and D. Louapre, “Ponzano-Regge model revisited II: Mathematical aspects; relation with Chern-Simons theory, DSU(2) quantum group and link invariant". To appear.

L.Freidel, E. Livine and D. Louapre, “Ponzano-Regge model revisited III: The Field Theory limit”. To appear.

L.Freidel and D. Louapre, “Ponzano-Regge model revisited IV: Lorentzian 3D Quantum Geometry”. To appear.

------other papers of possible related interest-------

L. Freidel and D. Louapre, “Diffeomorphisms and spin foam models,” Nucl. Phys. B 662, 279
http://arxiv.org/gr-qc/0212001

K. Noui and A. Perez “Three dimensional loop gravity coupled to point particles”, to appear.

----------miscellaneous-----
Links to a couple of things at PF here:

interesting post from "notevenwrong" about testability
https://www.physicsforums.com/showthread.php?s=&postid=128657#post128657

I don't think there's any need for any of us to justify
or explain why we are interested in the kinds of physics that
we're interested in.
So I don't normally bother to explain why I like to
report current developments in Loop Gravity or discuss
new papers with anyone who might be interested. But
here I was being challenged to explain my excitement and
I talked about why it's interesting to me personally
(doesnt have to be to you, but you may be enthused by
some of the same things). It's a ramble though.

https://www.physicsforums.com/showthread.php?s=&postid=128783#post128783

 

[marcus]

The MIT Theoretical Physicist Frank Wilczek
gave the keynote address at a December 2003
Conference on space and particle physics
"SpacePart03"

the text and one slide from his address has just been posted

http://www.arxiv.org/abs/astro-ph/0401347

He sketches the current situation. Wilczek is always
being asked to deliver Particle Physics overviews and keynotes (at the opening of a new accelerator or the closing ceremony for an old one), probably because he is most clearsighted senior theoretician they've got.

His 3 article series "Scaling Mount Planck" in Physics Today
issues back in 2001 and 2002 was a masterful survey of
big questions in theoretical physics (well, I was impressed).

Here he is doing it again, so its worth a look.

Basically it is a simple message. There are now two "standard models"

The one of particle physics and the one of cosmology.

Each has a certain number of exogenous parameters
IIRC he identifies four independent inputs to standard model
comology. And he describes progress and prospects as regards
particle physics explaining certain of the inputs to cosmology.

You can guess a lot of what the elder statesman is going to say
but no other voice has the clarity and authoritiy AFAIK.

I note he puts General Relativity in a good light (something particle physicists may eventually have to believe in on its own terms, in spite of the different underlying spacetime concept). He specifically mentions Diffeomorphism Invariance (calling it by Einstein's name for it: "general covariance")

"General relativity manifestly provides a beautiful, conceptually driven theory of gravity. It has scored many triumphs, both qualitative (big bang cosmology, black hole physics) and quantitative (precession of Mercury, binary pulsar).

The low-energy effective theory of gravity and the other interactions is defined algorithmically by the minimal coupling prescription, or equivalently by restricting to low-dimension operators. In this context, “low” means compared to the Planck energy scale, so this effective theory is very effective indeed.

As in the gauge sector, symmetry---here, general covariance---greatly constrains the possible couplings, bringing us down to just two relevant parameters. Almost all the observed phenomena of gravity are described using only one of these parameters, namely Newton’s gravitational constant. We are just now coming to accept that the other parameter, the value of the cosmological term, plays an important role in describing late-time cosmology..."

This is just a brief exerpt and his forte is his sense of proportion so you have to read the whole thing to get a feel for the relative importance he gives to things.

Earlier articles (June, Novemember 2001, August 2002)
http://www.physicstoday.org/pt/vol-54/iss-6/p12.html
http://www.physicstoday.org/pt/vol-54/iss-11/p12.html
http://www.if.ufrgs.br/~jgallas/wilczek.html

--------marginal note-----
At the same December 2003 space and particle physics conference where Wilczek gave the keynote there were a couple of talks on "Lorentz Symmetry Violation".
a paper on the subject by one of the partcipants
http://arxiv.org/hep-th/0312310
have to follow up on this later, got to run now
(Lorentz violation active research topic, relates to DSR)

 

[marcus]

Kim, Kim, Rim, and Yee---four Koreans are in scoring position

Four Koreans I never heard of before just posted a DSR paper

http://arxiv.org/gr-qc/0401078

"Propagation of Light in Doubly Special Relativity"

It draws a on work by Jerzy Kowalski-Glikman and by Joao Magueijo, in particular on a paper they call KMM (for Kimberly, Magueijo, Medeiros)

http://arxiv.org/gr-qc/0303067

The authors are Kim, Kim, Rim, and Yee.
They are from various universities in Korea.

 

[marcus]

Thiemann's Loop-String gambit

The timing of this is remarkable.
There is a Loop Gravity conference in Mexico City scheduled for next week and Thiemann brings out a Loop-String paper

doing string theory related algebra in the background independent LQG fashion.

Thiemann is scheduled to give a talk at that conference.

Here is the program for the upcoming Mexico City conference

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

Here is the link for Thiemann's new paper, and exerpts from the abstract
http://arxiv.org/hep-th/0401172

The LQG -- String: Loop Quantum Gravity Quantization of String Theory I. Flat Target Space


We combine I. background independent Loop Quantum Gravity (LQG) quantization techniques, II. the mathematically rigorous framework of Algebraic Quantum Field Theory (AQFT) and III. the theory of integrable systems resulting in the invariant Pohlmeyer Charges in order to set up the general representation theory (superselection theory) for the closed bosonic quantum string on flat target space.

...solve some of the major puzzles of string theory such as the cosmological constant problem. The solution presented in this paper exploits the flatness of the target space in several important ways. In a companion paper we treat the more complicated case of curved target spaces.

 

[marcus]

I was not aware until recently that this year Cambridge University Press is expected to bring out two graduate-level LQG texts.

I know Rovelli's 350-page "Quantum Gravity" is at press and expected out this year.

But it also seems Cambridge is publishing a 300+ page book by Thiemann called "Modern Canonical Quantum General Relativity". This is listed as "at press" in the references of a recent paper by the author, with projected publication date 2004.

I believe that a draft of Thiemann's "Modern...Quantum...Relativity" may be online at
http://arxiv.org/gr-qc/0110034
In draft, the title also had the word "Introduction" but that may have now been dropped for the sake of brevity.

Rovelli has an online draft of "Quantum Gravity" at his website---the link was given in several earlier posts.

These two books would together form the basis of a hefty year course in grad school. They complement each other to some extent: Rovelli's is more conceptual and discursive. It discusses philosophical foundations and presents many of the ideas historically. I like the well-chosen graphic examples used to illustrate the ideas. By comparison, the exposition in Thiemann's book is predominantly abstract mathematics, going into mathematical detail with thoroughness and rigor.

I should mention that the Berlin publisher Springer Verlag has also brought out a Loop Gravity textbook as part of its "Lecture Notes" series. This is a shorter, and more introductory, set of notes by Thiemann called
"Lectures on Loop Quantum Gravity".
A draft of this is online at
http://arxiv.org/gr-qc/0210094

As far as I know these three books, all appearing at about the same time, are the first hardcopy textbooks for the new field of Loop Gravity. In that sense 2004 looks like a landmark year in the development of the subject.

 

[marcus]

program for the Mexico City conference

Back in the middle of December I posted the organizer's list of topics (for talks and discussion) for the Loop symposium being held Jan 30 thru Feb 1 in Mexico City.

At that time I did not have a list of the talks or the people giving them. You might be interested. These are most of the people active in Loop Gravity research and many of the talks and the discussion sections center around delicate or key unresolved issues. It is clearly a symposium for people inside the field to share their latest ideas and results, "in house" so to speak. So here is the program:
[I made topics bold or caps for emphasis, so its easier to scan]
--------
friday

Welcome: Alejandro Corichi 1:00-1:10
Session: PHENOMENOLOGY
Chair: Hugo Morales

Sudarsky <End of New Ether>
Discussion
Freidel <Imprints of Planck scale structures and DSR>
Discussion

Session: SEMI-CLASSICAL Issues
Chair: Luca Bombelli

Sahlmann: <Brief survey of available frameworks>
Discussion
Ashtekar:<Physical Applications>

saturday

Session: SPIN FOAMS
Chair: Jose Antonio Zapata

Perez <Status Report>
Discussion
Crane <Beyond Barrett-Crane models>
Discussion

Session: HAMILTONIAN CONSTRAINT
Chair: Karim Noui

Freidel<Relation between spin-foams and canonical gravity>
Discussion
Ashtekar <viability of the Thiemann scheme>
Discussion
Thiemann <The Phoenix project>
Discussion

sunday

Conceptual Issues
Chair: Alejandro Corichi

Jorge Pullin <Future directions that will maximize impact>
Possible topics of discussion:

*Prospects for discrete formulations
*Status of non-compact gauge groups: Integration theory
*Role of supersymmetry
*Observables from particles in 2+1 gravity
*Quantum cosmology and observations
*Where is physics in spin-foams?
*Is Kodama state viable?
*Causality in quantum gravity
* ...
* ...

Abhay Ashtekar <Closing remarks>

LIST OF PARTICIPANTS:
A. Ashtekar (Penn State)

L. Bombelli (Mississippi)

L. Crane (Kansas State U.)

A. Corichi (UNAM. Mexico)

L. Freidel (Perimeter)

J.M. Garcia-Islas (CIMAT, Mexico)

F. Girelli (Perimeter)

E. Livine (Perimeter)

H. Morales-Técotl (UAM-I, México)

K. Nuoi (Penn State)

A. Perez (Penn State)

J. Pullin (Louisiana)

H. Sahlmann (Penn State)

D. Sudarsky (UNAM, Mexico)

T. Thiemann. (Perimeter)

J.A. Zapata (UNAM, Mexico)


---------

 

[meteor]

Given that marcus wants this thread like a sticky for new papers, I will post this one:
"Comparison of area spectra in loop quantum gravity"
http://arxiv.org/abs/gr-qc/0401110
Abstract:
We compare two area spectra proposed in loop quantum gravity in different approaches to compute the entropy of the Schwarzschild black hole. We describe the black hole in general microcanonical and canonical area ensembles for these spectra. For one of these spectra - the equally-spaced spectrum - we show in light of a proposed connection of the black hole area spectrum to the quasinormal mode spectrum that this spectrum is completely consistent with this connection. This follows {\em without} requiring a change in the gauge group of the spin degrees of freedom in this formalism from SU(2) to SO(3).

 

[marcus]

Originally posted by meteor
Given that marcus wants this thread like a sticky for new papers, I will post this one:
"Comparison of area spectra in loop quantum gravity"
http://arxiv.org/abs/gr-qc/0401110

One of the authors, G. Gour, has co-authored with Jacob Bekenstein and the approach to the area spectrum taken here goes back to
a paper of Bekenstein's:

http://arxiv.org/abs/hep-th/0107045
----------quote from abstract------------
The Case for Discrete Energy Levels of a Black Hole
Authors: Jacob D. Bekenstein
Comments: Invited talk at "2001: A Spacetime Odyssey", inaugural conference of the Michigan Center for Theoretical Physics, May 22-25, 2001, 11 pages, to appear in the proceedings published by World Scientific Publishing
Journal-ref: 2001: A Spacetime Odyssey, eds. M. J. Duff and J. T. Liu, (World Scientific Publishing, Singapore 2002), pp. 21-31

The adiabatic invariant nature of black hole horizon area in classical gravity suggests that in quantum theory the corresponding operator has a discrete spectrum. I here develop further an algebraic approach to black hole quantization which starts from very elementary assumptions, and proceeds by exploiting symmetry. It predicts a uniformly spaced area spectrum for all charges and angular momenta. Area eigenvalues are degenerate; correspondence with black hole entropy then dictates a precise value for the interval between eigenvalues.
--------end quote-----

it would be extremely interesting if the equal-spaced area spectrum gains credibility. this is a wonderful paper to have on our
Loop reference shelf "surrogate sticky".

at present measurement cannot distinguish between this version and the unequally-spaced spectrum, it would seem, so theorists can pursue either

if this equal-spaced (ES) notion of the spectrum is right then the Immirzi parameter is

ln 3/3pi

just for fun I will write it in tex.

$$\gamma_{ES} = \frac{ln 3}{3 \pi}$$

this paper by G. Gour and his buddy has potential for stirring up a controversy, I suspect

as you well know, a commonly assumed value is

$$\gamma = \frac{ln 2}{\sqrt{3} \pi}$$

 

[lumidek]

Area spectrum

Dear marcus,

I am not sure why you exactly think that the idea of the discrete area (or even energy) spectrum of the black hole should be gaining credibility. It contradicts all important things that we know about the black hole, for example the thermal character of the radiation and other semiclassical calculations. These well-established insights, initiated by Hawking in the 1970s, have been amazingly confirmed by the developments in string theory in the 1990s, so there is really little doubt that they're correct.

The energy spacing comparable to the Hawking temperature does not sound too reasonable because it would essentially imply that the energy that the black hole must emit must be an integer multiple of the Hawking temperature. The real spectrum copies the nice and smooth curve by Planck.

There is no serious support for the idea of this hugely discretized spectrum - perhaps some children's toy models and many overly speculative papers (which is the polite way to describe the crackpots). The precise numbers that should determine the scaling are totally unscientific, too. You only get a log of an integer in these formulae because some people who propose it are imagining that everything in the physical world is made from bits (or "trits") - simply because their imagination does not go beyond it.

All the best
Luboš

 

[marcus]

Originally posted by lumidek
Dear marcus,

I am not sure why you exactly think that the idea of the discrete area (or even energy) spectrum of the black hole should be gaining credibility.

Dear Lubos, of course I remember what you had to say in your very first QNM paper about evenly spaced area spectrum. Seems a long time ago now.

In a PF context we need to be careful not to say "discrete area spectrum" (which includes the unequal spacing case) when we mean the "evenly spaced spectrum".
There seems to be wide agreement with the notion that discrete area spectrum is compatible with the themal character of the Hawking radiation. (Indeed I had the impression that you were also in agreement with this.)

However you and many other people have argued against the evenly spaced area spectrum for precisely the reason you mention. I believe you are in agreement here with Loop authorities like Ashtekar, Rovelli, Smolin. Back in (when was it?) 1995 when Rovelli and Smolin derived the discrete area spectrum, it was not equally spaced----spacing between eigenv. got closer and closer as area got larger.

No doubt you find it reassuring to be in such good company (on the same side of the fence as Rovelli and Smolin) on this issue

-------
But my personal view is that Jacob Bekenstein is a brilliant and original mind-----he deserves credit at a fundamental level for black hole thermodynamics, Hawking radiation, BH temperature, entropy and all that good stuff that started in the 1970s. He kicked it off.
If he says to keep an open mind and think about equal-spaced (ES) spectrum then I respect him and I am going to keep an open mind about it. Surprises sometimes happen. What if Gilad Gour (also very smart) and Bekenstein are right and there is something nobody has thought of yet that makes it compatible. Have to run, but back later.

 

[lumidek]

Energy spectrum

Dear Marcus,

it's great if we agree that the evenly spaced spectrum does not seem too good.

Concerning the discrete, non-evenly-spaced spectrum, it is not a physical question whether the exponentially dense spectrum of the black hole energy is discrete or not. Of course, if the number of states (exponential of entropy) is finite, it must be discrete "in some sense".

The density of the states is increasing exponentially with a power of the mass. It is naive to think that you can determine the black hole energy with the precision comparable to this expected exponentially small spacing - simply because the width of the black hole itself is exponentially bigger (the width behaves as a power of the mass, without any exponentiating). The width essentially tells you the minimal error with which you can measure the spectrum, and this minimal error is much bigger than the required resolution to determine the character of the exponentially fine spacing.

Once you admit that the gaps in the spectrum are not huge (such as the power law gaps of the evenly spaced spectrum), there is no other physical question to ask about the character of the spectrum.

All the models that give you the super-exact energies must neglect the interactions and Hawking radiation because Hawking radiation makes black holes unstable and energies undetermined (width). Quite generally, you may be worried that neglecting Hawking radiation means neglecting quantum mechanics, and therefore all the conclusions about the quantization are internally inconsistent.

The only exception are extremal, BPS black holes that don't decay (temperature vanishes), and their energy is determined exactly by the BPS bound.

All the best
Luboš

 

[marcus]

Originally posted by lumidek
Dear Marcus,

it's great if we agree that the evenly spaced spectrum does not seem too good...

We don't agree Lubos. You indicate that you have a firm opinion that evenly spaced (ES) area spectrum doesn't seem good.
I am trying to keep an open mind.

 

[marcus]

Originally posted by lumidek


The energy spacing comparable to the Hawking temperature does not sound too reasonable because it would essentially imply that the energy that the black hole must emit must be an integer multiple of the Hawking temperature. The real spectrum copies the nice and smooth curve by Planck.

There is no serious support for the idea of this hugely discretized spectrum -

We were talking about area eigenvalue spacing.
The Gilad Gour paper does not consider "huge" gaps in the area spectrum but, on the contrary, gaps comparable in size to
the Planck area---in other words very tiny.

You may be jumping to conclusions because I mentioned Bekenstein as one who has argued for considering ES area spectrum.

See equation (3) of the Gour Suneeta paper.

Evenly spaced does not imply huge gaps, or gap-size dependent (as you suggest) on the Hawking temp. of the hole.

By your own argument in the your preceeding post if the gaps are
small like in Rovelli-Smolin spectrum (Planck area size) then one would not be able to physically tell the difference from smooth black body. The same applies to Gour-Suneeta because similarly small gaps.

 

[lumidek]

Sorry

Dear Marcus,

I see, sorry. I made a too quick conclusion that you share the only approach that I consider reasonable in this question.

It's great to keep an open mind, but if Hawking is correct, a lot of ideas can evaporate from a mind that is too open.

All the best
Luboš

 

[marcus]

Originally posted by meteor
... I will post this one:
"Comparison of area spectra in loop quantum gravity"
http://arxiv.org/abs/gr-qc/0401110
Abstract:
We compare two area spectra proposed in loop quantum gravity in different approaches to compute the entropy of the Schwarzschild black hole. We describe the black hole in general microcanonical and canonical area ensembles for these spectra. For one of these spectra - the equally-spaced spectrum - we show in light of a proposed connection of the black hole area spectrum to the quasinormal mode spectrum that this spectrum is completely consistent with this connection. This follows without requiring a change in the gauge group of the spin degrees of freedom in this formalism from SU(2) to SO(3).

This is the paper by Gilad Gour and V. Suneeta (both at U Alberta
Edmunton) that Meteor called to our attention.

An objection raised earlier seems not to apply since, while the area spectrum is discrete (as usual in LQG) and evenly spaced, the spacing is microscopic (planck-scale) and not fundamentally very different from the un-evenly spaced. This paper could be important and needs a more careful look. So let's look at Gour/Suneeta equations (2) and (3)

These are the two competing formulas for the area of a surface S.

the first is in the non-evenly spaced (NS) case

$$A_S = 8\pi l_P^2 \gamma \Sigma \sqrt{j_n(j_n + 1)}$$

the second is in the evenly spaced (ES) case

$$A_S = 8\pi l_P^2 \gamma \Sigma (j_n + 1/2)$$

We are talking about a spin network state and a physical surface, S, defined by some material object. The spin network state has N edges which intersect the surface and each edge contributes a bit of area to the sum. The intersecting edges are indexed n = 1,...,N.

Oh yeah, l_P² is the Planck unit of area, the square of the Planck length

Equation (2) is the standard 1994 result of Rovelli and Smolin. A priori one wonders how Gour/Suneeta could possibly be challenging this by proposing a different formula for the area, namely equation (3).

Furthermore their proposal may make some people nervous since it results in a value of ln 3/3pi for the Immirzi parameter. As it happens this doesn't bother me. Some versions of LQG don't even have an Immirzi parameter: Loop theories are under construction and there is still room for variation in the parameters and even some surprises. So I am not going to dismiss this out of hand just because of some number being an unfamiliar ln 3/3 pi instead of the more usual value that has been around longer.

Anyway Meteor posted the link to this a few days ago so let's see what it is about.

 

[marcus]

common sense suggests there may be pitfalls in Gour/Suneeta approach.
the other formula goes back to 1994. why would Rovelli/Smolin have chosen their more complicated formula unless there were some reason?
but so far so good.
anybody (Meteor?) who wants to help read thru this short (7 page)
paper is invited

a couple of more links on the area issue:

Alexios Polychronakos
Area spectrum and quasinormal modes of black holes
http://arxiv.org/hep-th/0304135

Alekseev, Polychronakos, Smedbaeck
On the area and entropy of a black hole
http://arxiv.org/hep-th/0004036

Alexkseev and Smedbaeck are at the Institute for Theoretical Physics, Upsala University, in Sweden
Polychronakos is at the University of Ioannina in Greece and also the
CUNY Physics Department in the USA.

These seem to be the dangerous people we were warned about earlier. They think that, just as an atom while it is in a heat bath in equilibrium at a given temperature can radiate with a black body spectrum but by itself radiates a line spectrum, so a black hole not surrounded by radiation and therefore not in equilibrium with its surroundings may in fact radiate a line spectrum. Over much of the spectrum it would strongly resemble black body but at low frequencies it would deviate and become more obviously liney.

Polychronakos says, in "Area spectrum and...", for instance)

-------quote from page 9----------

We do not feel that this is damning. The high-frequency exponential part of the spectrum is accurately reproduced, the discreteness there being inconsequential. This is the energy range in which the photons (or other emitted particles) behave essentially like classical particles, whose scattering properties are expected to be accurately reproduced by the classical black hole metric. For frequencies close to the thermal frequency, however, the wavelength of the photons becomes comparable to the size of the black hole and they sense global properties of its geometry. Backreaction due to geometry change at emission and absorption of such photons is expected to be important, the energy of these photons being of the same order as
the energy spacing of the black hole. A deviation from ideal black-body spectrum, which assumes a fixed metric and ignores back-reaction, would seem reasonable.

-----end quote----------

 

[meteor]

If my opinion counts, (I'm only an amateur, not a high-level physicist) I don't like the idea of the equally-spaced area spectrum, because it means that practically all the contributions to the black hole area comes from edges carrying a representation of 1. Would be desirable to know why the representations=1/2 are excluded from puncture the black hole area

 

[marcus]

Originally posted by meteor
If my opinion counts..

you found the paper and put it in for discussion
so your opinion doesn't count?

Gour/Suneeta cite Polychronakos (hep-th/0304135)
which I am finding the easiest to read and the
most helpful. (the subject is new to me, maybe to
you as well)

On page 8 Polychronakos says
"To summarize...if the standard counting formula for states (6) is
assumed, then the equidistant area spectrum as proposed in [14]
naturally explains the domination of spin-1 links
and reproduces the ringing mode properties of black holes, without
the need to eliminate half-integer spins..."

You say "...would be desirable to know why spin-1/2" are excluded. It is a good question but, according to him, they are not eliminated arbitrarily or "by hand".
He says there is no need to exclude them, because statistically the spin-1 punctures are more prevalent.
Why? this is what I am wondering. He says there is a natural explanation for why spin-1 is more prevalent and predominates over the other. The explanation is on page 5, I think. Around equations (12) and (13). It is very brief and does not seem hard.
It seems to depend on the semiclassical result of Hod!
Hod made an important contribution to Loop gravity with his number
4ln3, which Motl, fortunately enough, was able to confirm by a direct calculation. It has added interest to the field and given them something to work on, and here it is showing up again on page 5 of Polychronakos.

 

[meteor]

Another paper:
"Beyond space and time"
http://arxiv.org/abs/physics/0401128
Author: Ruediger Vaas
Abstract:
"The secret network of the universe: How quantum geometry might complete Einstein's dream. - An informal introduction to quantum geometry (loop quantum gravity), spin networks, quantum black holes, and the work of Abhay Ashtekar, Carlo Rovelli, Lee Smolin and others."

After a quick inspection, I'm amazed: You will not find a single equation in the text!

An interesting phrase of the text: "If one could observe nature with maximum possible enlargement, space and time would dissolve and the granular mesh of the spin network would come to light ( or more precisely: the quantum physical superposition of all possible configurations of these entities)"