Intuitive content of Loop Gravity--Rovelli's program

meteor

Well, given that my knowledge in differential geometry is rather poor, I've ordered the book "Differential geometry" of Schaum to Amazon. Hope that will be a good book, like all the other Schaum books that I've read
A question: Then the SO(2) connection used like a variable in Ashtekar's general relativity is a real connection or a complex connection? There are papers that say that is real and others that is complex. I'm dying in the doubt
I've just read that loop quantum gravity violates the "weak energy condition" at short distances, when the granularity of spacetime becomes significant. I've don't have the foggiest idea of what is the weak energy condition, so I'm going to read about it right now

marcus

Hi Meteor, I started a thread with your two questions
1. about Ashtekar's new variables
2. about "weak energy condition"
Both could lead to discussion and I am trying to save this thread as a kind of "sticky" for useful links, source material, conference news, and so on. Hope it is OK for me to make a separate thread for what you asked about. You will see it.
I called it "Loop gravity---two questions"

marcus

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

Amazing..

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

marcus

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

"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.

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

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/Publicatio...imekeeping.pdf

marcus

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

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 doesnt 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 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 wouldnt 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 dont 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...40.2002.E.html
And the more extensive series HEP-TH here:
http://www.slac.stanford.edu/library...view.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/GRn...erence?03Aug.1
http://www.maths.qmul.ac.uk/wbin/GRn.../conference?10

General Relativity Conference (Dublin) July 2004
more annoucements at
http://www.maths.qmul.ac.uk/wbin/GRn...nce?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/Publicatio...imekeeping.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

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 [tex]\Gamma[/tex] 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

[tex]\Gamma[/tex] adjacency
[tex]i_n[/tex] volume of node n
[tex]j_l[/tex] area of surface l
[tex]F_n[/tex] number of fermions at node n
[tex]S_n[/tex] number of scalars at node n
[tex]w_n[/tex] field strength at node n
[tex]k_l[/tex] 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
[tex]|s> = |\Gamma,i_n,j_l,F_n,S_n,w_n,k_l>[/tex]
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.

[tex]H = H_{Einstein} + H_{YangMills} + H_{Dirac} + H_{Higgs} [/tex]

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

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

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

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, dont 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.