Marseille workshop on loops and spin foams

[john baez]

I just got back from the Marseille conference on loop quantum gravity and spin foams:

http://w3.lpm.univ-montp2.fr/~philippe/quantumgravitywebsite/

It was really great, so I devoted "week206" of my column This Week's Finds entirely to this conference:

http://math.ucr.edu/home/baez/week206.html

In particular, I spend a lot of time giving a very simple nontechnical introduction to the recent work of Ambjorn, Jurkiewicz and Loll in which they seem to get a 4d spacetime to emerge from a discrete quantum model - something that nobody had succeeded in doing before!

http://www.arXiv.org/abs/hep-th/0404156

I hope this lays to rest certain rumors here that I'd burnt out on quantum gravity.

 

[selfAdjoint]

Thank you professor Baez! So two threads come together here. Marcus posted about the AJL paper yesterday and several questions have been raised. We need to read your essay!


(Added in edit)

Mike2 on the other thread raised the question of whether the quantum gravity model assumed by AJL had been rigorously developed.

Just to clear the air on this I would like to ask this: Has any quantized fully relativistic (1,3)-dimensional theory of any kind been rigorously based? I know of rigorous (1,1)-dimensional theories and maybe some (1,2)-dimensional ones, but I don't know of any fully (1,3) relativistic quantized ones.

 

[marcus]

...certain rumors here...

rumors! here? we must have been kidding
how could anyone get tired of quantum gravity?

 

[marcus]

While we are on possibly important papers (of which e.g. AJL's)
does anyone have any guidance or comment about
Marni Dee Sheppeard's recent
http://arxiv.org/gr-qc/0404121
unless for some reason it is tactless of me to ask.


also I wish we could hear more about the Marseille conference
since Week 206 merely whetted my appetite

[edit: BTW Livine's talk at the conference was called
"Instantons in Gauge Field Theory and the continuum limit"
here is a definition of instanton
http://en.wikipedia.org/wiki/Instanton
in case anyone's curious.]

 

[Mike2]

Thank you professor Baez! So two threads come together here. Marcus posted about the AJL paper yesterday and several questions have been raised. We need to read your essay!

Mike2 on the other thread raised the question of whether the quantum gravity model assumed by AJL had been rigorously developed.

Thanks for the credit. A further question that comes to mind is whether this 4D spacetime is flat or curved. Would it explain the uncurling of space-time from the singularity at the start to the entire universe of today?

 

[Mike2]

I read in a recent Sci Am article that there need not be 10 dimension for a consistent string theory if the curvature of space was large enough. Did I read that right? If so, then perhaps the 4D of the article of this thread may be fundamental and not just an effective theory.

 

[marcus]

recalling the main topic
Baez reported in "Week 206" on the May 2004 Marseille conference
and the main focus of his report was what Renate Loll had to say
about this
http://www.arXiv.org/abs/hep-th/0404156
recent paper by Ambjorn Jurkiewicz and her.

This looks like a landmark paper, judging from remarks on SPR by Baez and Larsson and other reaction, and there are some previous papers by AJL which foreshadow the current one and illuminate what is going on. I think John Baez gave these links to lead-ups.

http://arxiv.org./hep-th/0002050
http://arxiv.org/hep-th/0105267

As far as I can tell the ideas that bear fruit in the recent paper (and generate an extended 4D world) are already three years old. I can't find anything conceptual that wasnt already suggested in the paper dated 27 May 2001:

"A Nonperturbative Lorentzian Path Integral for Gravity"

so right now I'm trying to understand the lead-up papers

BTW Mike2 you mentioned curvature. What they found does not seem to require a high degree of curvature. It does call for a positive cosmological constant, however, which is kind of nice because, as everyone realizes, a positive CC has been deduced from the much celebrated recent supernova observations

 

[Mike2]

Was this paper an attempt to justify or perhaps even derive the very overall topology of space-time?

I wonder if causality is the key to the topology of space-time. For from the simplest logic, causality is one event producing another event. Those events would have to be represented by some region. Even if the events were a single point, one "event" producing another, would require one point to produce another. I suppose that at such a differential state as one or two points that the properties between points or small regions would not change between points, since the changes in these properties cannot be instantaneous at such a differential scale. This causality, one point producing another, would mean that the number of points (or regions) would all increase at the same rate. This would give an expansion of the universe proportional to its size, or an exponential expansion as is predicted in an inflationary universe.

I wonder if the number of dimensions and the metric can be determined from this topology. Since the closes points (or regions) would be responsible for the next point produced, and since all these points in conjunction implies that all are the cause of the others and the next, it would figure that the universe at this scale would be tightly curled up, not elongated into a line for example. This would seem to indicate a tightly curved metric for space-time. The first point would produce a second, and you would have a 1D line, these two, or one of them, would produce a 3 point, and since that next point would have to be about equally close to the other 2, you would have a 2D plane. These three would produce a forth, and since it would have to be about equally as close to the other 3 points, it would be in a 3D volume, etc. Where does this process lead?

I suppose this would conflict with the idea of a specific amount of space-time dispersing as it expands with time. I wonder if the two views can be reconciled

 

[marcus]

again on the subject of the May 2004 Marseille quantum gravity conference, I wonder if anything can be learned from the list of talks. Rovelli was probably the main organizer, so the lineup would reflect somewhat how he sees the field:

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

Monday, May 3rd: Loop quantum gravity
am
Opening remarks
A. Ashtekar (Quantum geometry)
T. Thiemann (Dynamics and low energy)
L. Smolin (Overall results)
T. Jacobson, as devil's advocate (Some questions to loop quantum gravity)

pm
L. Doplicher (Propagation kernel techniques for loop quantum gravity)
W . Fairbairn (Separable Hilbert space in loop quantum gravity)
J. Lewandowski (Quantum group deformations of the holonomy-flux algebra)
B. Dittrich (Master constraint program for loop quantum gravity)
J. Pullin (Consistent discretization)
S. Alexandrov (Lorentz covariant loop quantum gravity)
H. Salhmann (Uniqueness of the Ashtekar-Isham-Lewandowski representation)

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

Tuesday, May 4th: Spinfoam formalism
am
J. Baez (Spinfoams)
L. Freidel (Group field theory and sum over 2-complexes)
J. Barrett (BC models)
R. Loll (Dynamical triangulations)

pm
A. Perez (Spin-foam representation of the physical scalar product in 2+1 gravity)
R. Oeckl (Boundary formulation of quantum mechanics and application to spin foams)
A. Starodubtsev (Definition of particles in 4d quantum gravity)
F. Markopoulou (Quantum information theory and particles in spinfoam)
E. Livine (Instantons in GFT and continuum limit)
H. Pfeiffer (Quantum gravity smooth manifold and triangulation)


18:30 Campus Colloquium (open to external participation)
A Ashtekar (Space and Time: From Antiquity to Einstein and Beyond)

20:00: Lunar eclipses

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

Wednesday, May 5th: Miscellaneous
am
T. Jacobson (Mode creation: quantum field theory on a growing lattice)
L. Bombelli (Statistical framework for the continuum approximation to quantum gravity)
R. Gambini (Relational time in consistent discrete quantum gravity)
G. Mena Marugan (Perturbative and nonperturbative cylindrical gravity)
O. Winkler (Singularity avoidance or how compact is the world?)
J. Swain (Spin-Networks and Approximations of Diffeomorphism Groups)
E. Buffenoir (Quantum radar time in 2+1 dimensions)

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

Thursday, May 6th: Applications of loop quantum gravity, cosmology, black holes and quasinormal modes
am
M. Bojowald (Loop cosmology)
D. Sudarsky (Phenomenology)
A. Corichi (Black holes)
K. Krasnov (Quasi normal modes of black holes)

pm
O. Dreyer (Quasinormal modes)
P. Forgacs (Quasi normal modes of the t'Hooft-Polyakov monopole)
K. Noui (Hamiltonian analysis in Plebansky theory)
S. Parampreet (Some applications of loop cosmology)
K. Vandersloot (A path integral representation of loop quantum cosmology)
S. Major (Observations on a lorentzian model)
P. Majumdar (Universal canonical black hole entropy)

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

Friday, May 7th
am: Related approaches
M. Niedermaier (Asymptotic safety)
R. Percacci (Is Newton's constant essential?)
J. Klauder (Affine Quantum Gravity: An All-Scale Theory)
D. Minic (Modification of quantum mechanics and quantum gravity)
J. Kowalski Gliksman : (DSR as a possible limit of quantum gravity)
F. Girelli (Special Relativity as a non commutative geometry: Lessons)

pm
Panel and general discussion
Conclusion

 

[marcus]

In the thread started earlier about the AJL paper "Emergence of a 4D World" two people (arivero and Mike2) asked about what model of quantum gravity are they using.

I found what I think is a good link. It turns out that it is one John Baez already recommended in "Week 206" when he was talking about the same paper. It is a pedagogical lecture by Renate Loll, with a lot of pictures.
Dated 13 January 2003.
I printed it out. It seemed worth keeping and studying. and to have easy parts.

"A discrete history of the Lorentzian path integral"
http://www.arxiv.org/hep-th/0212340
38 pages

Notice that R. Loll's quantum gravity is not the same as Ashtekar's or Rovelli's or Smolin's, at least on the surface. Here is a brief exerpt from the beginning of the paper:

----exerpt---
In these lecture notes, I describe the motivation behind a recent formulation of a non-perturbative gravitational path integral for Lorentzian (instead of the usual Euclidean) space-times, and give a pedagogical introduction to its main features.

At the regularized, discrete level this approach solves the problems of (i) having a welldefined Wick rotation, (ii) possessing a coordinate-invariant cutoff, and (iii) leading to convergent sums over geometries. Although little is known as yet about the existence and nature of an underlying continuum theory of quantum gravity in four dimensions, there are already a number of beautiful results in d = 2 and d = 3 where continuum
limits have been found.

They include an explicit example of the inequivalence of the Euclidean and Lorentzian path integrals, a non-perturbative mechanism for the cancellation of the conformal factor, and the discovery that causality can act as an
effective regulator of quantum geometry.

1 Introduction
The desire to understand the quantum physics of the gravitational interactions lies at the root of many recent developments in theoretical high-energy physics. By quantum gravity I will mean a consistent fundamental quantum description of space-time geometry whose classical limit is General Relativity...
--------end quote----

what seems to have just changed is that the results for d = 2 and d = 3 begin to extend to d = 4

 

[Mike2]

This causality, one point producing another, would mean that the number of points (or regions) would all increase at the same rate. This would give an expansion of the universe proportional to its size, or an exponential expansion as is predicted in an inflationary universe.
...
I suppose this would conflict with the idea of a specific amount of space-time dispersing as it expands with time. I wonder if the two views can be reconciled

The question becomes how fast do new points appear. I suppose that as long as the rate was not infinite, it would all be just a matter of scale. And since there is nothing else to compare with, it would all seem the same to us.

So can someone tell me how such a scenario would modify the usual point set topology studies?

 

[marcus]

Lollistics: what do you call it?

She and her co-workers have been calling their QG approach various
names and have not quite settled on one.

Recently it is "Causal Quantum Gravity"
(causal denotes Lorentzian rather than Euclidean")

Earlier on it was "Dynamical Triangulations" and "Lorentzian Q.G."
or the "Lorentzian Path Integral" approach to Q.G.

Back in 1992 when Ambjorn and Jurkiewicz were doing it
they called it "Simplicial Quantum Gravity"
as in their 1992 article in Phys Lett B.

It is a commonsense notion and maybe goes back to Regge in the 1950s (?)
or further----you let spacetime build itself out of regular blocks (simplices)
and get the dynamics out of a "partition function" of sorts that tells you how likely some transition is to happen by counting the number of ways it can happen. A rudimentary combinatorics of space.

The new thing is that AJL got it to work and 4D spacetimes started emerging from it
somehow Loll began collaborating with Ambjorn
maybe around 1998, then in 2001 she moved from AEI (MPI-Potsdam) over to
Utrecht,
and they must have decided at some point that the Euclidean approach
to Simplicial QG
wasnt working (despite at least 10 years of trying) and they
would try the Lorentzian approach, where you distinguish time-like legs of the simplex from space-like legs, so there is a past and future idea and the possibility of cause and effect.

Strictly speaking this approach to QG is one of the newest since
the "Lorentzian" or "Causal" simplicial QG papers seem mainly post-2000

I may be wrong about these details---still trying to sort this business out.
Loll is probably the best historian of this approach to QG.
She has an invited LivingReviews article on it which gives the history
going back to 1976 and citing some 200 papers.

http://arxiv.org/gr-qc/9805049

I have been trying to understand Loll's background and looked in spires, where I saw a large number of papers published since 1988 from a series of places:
1988 Imperial College London (postdoc working with Isham?)
1990 Bonn University
1992 Syracuse
1993 Penn State
1995 Florence (and MPI Potsdam)
1996 MPI Potsdam
...
...
2001 move from MPI Potsdam to Utrecht

Baez Week 69 (1995) describes his meeting Loll in 1991 in Seattle and also
meeting Isham and Ashtekar at the same conference----Baez introduction to LQG. Week 69 has thumbnails of the first three LQG researchers Baez encountered
http://math.ucr.edu/home/baez/week69.html

as a wild guess if she was a postdoc in 1988 she could have been born roughly around 1962. that could be way off of course. here's a snapshot:
http://www1.phys.uu.nl/wwwitf/fotopagina's/Medewerkers/Renate.htm
the URL needs to be copy/pasted in

 

[pelastration]

I have been trying to understand Loll's background

Lecture of spring 1999. Lost of graphics.
http://cgpg.gravity.psu.edu/online/Html/Seminars/Spring1999/Loll/Slides/s01.html

 

[meteor]

It is a commonsense notion and maybe goes back to Regge in the 1950s (?)

I think that both dynamical triangulations and Regge calculus are different approaches both encompassed by a wider theory called simplicial quantum gravity. While dynamical triangulations keep the edges of the sinplices fixed and varies the triangulations, Regge calculus do the opposite, varies the edges of the simplices and
maintain fixed the triangulation. Baez 122 explains a bit about all this stuff

http://math.ucr.edu/home/baez/twf.ascii/week122

I've found this review of Regge calculus by Giorgio Immirzi, curiously the same person that the famous/infamous Immirzi parameter takes name from
http://arxiv.org/abs/gr-qc/9701052
"Quantum gravity and Regge calculus"

 

[marcus]

Lecture of spring 1999. Lots of graphics.
http://cgpg.gravity.psu.edu/online/Html/Seminars/Spring1999/Loll/Slides/s01.html

Yes there are a lot of sketches, and it helps. I hadnt seen these lecture slides and am glad you pointed to them.

Meteor thanks! I will look at Week 122---hopefully it will sort simplicial QG out into its various types and I will understand it better

Baez posted again on SPR yesterday about the new simplicial QG work

https://www.physicsforums.com/showthread.php?p=210452#post210452

 

[marcus]

BTW happy 15 May, Kepler Day!

As an aside, by his own account Kepler discovered the third law
on 15 May 1618

a few days later he finished writing "Harmonice Mundi"---the book was published that year

his finding those three laws set a 400 year agenda of figuring out
why gravity acts like that.
why do the planets go in ellipes with sun at focus, sweeping out constant area per unit time, and why does the period-squared vary as the distance-cubed? or why, as he put it, is a planet's period the "sesquipotence" ( 3/2 power) of its average distance from the sun?

 

[marcus]

a day for thoughts concerning the shape of the world
(Kepler's mundus, he too was trying to explain its proportions)
and the hope that starting from those first laws of gravity
mankind may come to grasp the world's geometry.


it would be curious if Ambjorn Jurkiewicz and Loll were on the right track
and that the world's 4D shape including the 1915 Einstein equation
actually does arise from the "causal dynamical triangulation" (referred to in their abstract) which seems merely to be the random sticking together of simplices----with sensible rules that make it possible to simulate in a computer

the fascinating thing is they generate pictures of 4D geometries,
and Baez applied the "a picture is worth..." adage, appropriately

 

[marcus]

... I devoted "week206" of my column This Week's Finds entirely to this conference:

http://math.ucr.edu/home/baez/week206.html

In particular, I spend a lot of time giving a very simple nontechnical introduction to the recent work of Ambjorn, Jurkiewicz and Loll in which they seem to get a 4d spacetime to emerge from a discrete quantum model - something that nobody had succeeded in doing before!

http://www.arXiv.org/abs/hep-th/0404156
...

...I think that both dynamical triangulations and Regge calculus are different approaches both encompassed by a wider theory called simplicial quantum gravity. While dynamical triangulations keep the edges of the simplices fixed and varies the triangulations, Regge calculus do the opposite, varies the edges of the simplices and
maintain fixed the triangulation. Baez 122 explains a bit about all this stuff

http://math.ucr.edu/home/baez/twf.ascii/week122

...

Meteor gives the right perspective. Simplicial Quantum Gravity (SQG?) is the overall line of research and Dynamical Triangulations is one of two or three main approaches within SQG.

Simplicial Quantum Gravity seems to have a lot in common with spinfoam research (Barrett-Crane models could be mentioned). The boundaries of these research areas seem able to shift. Maybe Dynamical Triangulations will turn out to merge with Spinfoams.

At the Marseille conference there was just one DT paper and it was put with the Spinfoam bunch.

In his reply to Larsson on SPR
https://www.physicsforums.com/showthread.php?p=210452#post210452
Baez says he hopes to work on DT with Dan Christensen at UBC
and that he talked to Fotini M. who is also planning some DT
research with a grad student of hers.

The impressive thing to me about DT is that you can put a million identical simplices in a computer and simulate the universe and see it happen:
the whole story---beginning middle and end

since there is a finite number of simplex blocks it has to be a closed universe that bangs, swells up, collapses, and then crunches
but that's a detail
what's nice is the prospect of a 4D spacetime---a history of the geometry of the world---that you can simulate and see

Baez has already done some heavyduty spinfoam computer stuff with Dan Christensen
apparently they have a large computing facility at UBC
so it's a good bet that they will run MonteCarlo DT simulations
and get pictures

I hope they get about it soon, wd very much like to see graphic results
of others besides Ambjorn Jurkiewicz Loll.

 

[marcus]

2D animations at Jan Ambjorn's homepage

Animations

http://www.nbi.dk/~ambjorn/lqg2/

Ambjorn's homepage

http://www.nbi.dk/~ambjorn/

 

[marcus]

What Matt Visser had to say about the Ambjorn/Loll work in 2002

http://www.phys.lsu.edu/mog/mog19/node12.html

this includes a bibliography (mostly on line) of what Visser says are key papers

----exerpts----
Quantum gravity: progress from an unexpected direction

Over the last few of years, a new candidate theory of quantum gravity has been emerging: the so-called ``Lorentzian lattice quantum gravity'' championed by Jan Ambjorn [Niels Bohr Institute], Renate Loll [Utrecht], and co-workers [1]...

...On the one hand, "Lorentzian lattice quantum gravity" has grown out of the lattice community, itself a subset of the particle physics community. In lattice physics spacetime is approximated by a discrete lattice of points spaced a finite distance apart. This "latticization" process is a way of guaranteeing that quantum field theory can be defined in a finite and non-perturbative fashion. (Indeed currently the lattice is the only known non-perturbative regulator for flat-space quantum field theory. This technique is absolutely essential when carrying out computer simulations of quantum field theories, and in particular, computer simulations of quarks, gluons, and the like in QCD.)

In addition to these particle physics notions, "Lorentzian lattice quantum gravity" has strongly adopted the geometric flavour of general relativity; it speaks of surfaces and spaces, of geometries and shapes.

On the other hand, "Lorentzian lattice quantum gravity" has irritated both brane theorists and general relativists (and more than a few lattice physicists as well): It does not have, and does not seem to require, the complicated superstructure of supersymmetry and all the other technical machinery of brane theory/string theory. (A critically important feature of brane theory/ string theory which justifies the amount of time spent on the model is that in an appropriate limit it seems to approximate key aspects of general relativity; and do so without the violent mathematical infinities encountered in most other approaches. Of course, there is always the risk that there might be other less complicated theories out there that might do an equally good job in this regard.) Additionally, "Lorentzian lattice quantum gravity" irritates some members of the relativity community by not including all possible 4-dimensional geometries: The key ingredient that makes this Lorentzian approach different (and successful, at least in a lower-dimensional setting) is that it to some extent enforces a separation between the notions of space and time, so that space-time is really taken as a product of "space" with "time". It then sums over the resulting restricted set of (3+1)-dimensional geometries; not over all 4-dimensional geometries (that being the traditional approach of the so-called Euclidean lattice quantum gravity).

... The result of this topological/ geometrical restriction is that the model produces reasonably large, reasonably smooth patches of spacetime that look like they are good precursors for our observable universe. ...

The good news is that once reasonably large, reasonably flat, patches of spacetime exist, the arguments leading to Sakharov's notion of "induced gravity" almost guarantee the generation of a cosmological constant and an Einstein-Hilbert term in the effective action through one-loop quantum effects [3]; and this would almost automatically guarantee an inverse-square law at very low energies (large distances).

The bad news is that so far the large flat regions have only been demonstrated to exist in 1+1 and 2+1 dimensions -- the (3+1)-dimensional case continues to pose considerable technical difficulties.

All in all, the development of "Lorentzian lattice quantum gravity" is extremely exciting: It is non-perturbative, definitely high-energy (ultraviolet) finite, and has good prospects for an acceptable low-energy (infra-red) limit. It has taken ideas from both the quantum and the relativity camps, though it has not completely satisfied either camp. Keep an eye out for further developments.

References:

Key papers on Lorentzian lattice quantum gravity:
J. Ambjorn, A. Dasgupta, J. Jurkiewicz and R. Loll, ``A Lorentzian cure for Euclidean troubles,'' Nucl. Phys. Proc. Suppl. 106 (2002) 977-979 arXiv:hep-th/0201104

J. Ambjorn, J. Jurkiewicz and R. Loll, ``3d Lorentzian, dynamically triangulated quantum gravity,'' Nucl. Phys. Proc. Suppl. 106 (2002) 980-982 arXiv:hep-lat/0201013.

J. Ambjorn, J. Jurkiewicz, R. Loll and G. Vernizzi, ``Lorentzian 3d gravity with wormholes via matrix models,'' JHEP 0109 (2001) 022 arXiv:hep-th/0106082

J. Ambjorn, J. Jurkiewicz and R. Loll, ``Dynamically triangulating Lorentzian quantum gravity,'' Nucl. Phys. B610 (2001) 347-382 arXiv:hep-th/0105267.

A. Dasgupta and R. Loll, ``A proper-time cure for the conformal sickness in quantum gravity,'' Nucl. Phys. B 606 (2001) 357-379 arXiv:hep-th/0103186.

J. Ambjorn, J. Jurkiewicz and R. Loll, ``Non-perturbative 3d Lorentzian quantum gravity,'' Phys. Rev. D 64 (2001) 044011 arXiv:hep-th/0011276.

R. Loll, ``Discrete Lorentzian quantum gravity,'' Nucl. Phys. Proc. Suppl. 94 (2001) 96-107 arXiv:hep-th/0011194.

J. Ambjorn, J. Jurkiewicz and R. Loll, ``Computer simulations of 3d Lorentzian quantum gravity,'' Nucl. Phys. Proc. Suppl. 94 (2001) 689-692 arXiv:hep-lat/0011055.

J. Ambjorn, J. Jurkiewicz and R. Loll, ``A non-perturbative Lorentzian path integral for gravity,'' Phys. Rev. Lett. 85 (2000) 924-927 arXiv:hep-th/0002050.

[2] A survey of brane theory and quantum geometry:
G. Horowitz, ``Quantum Gravity at the Turn of the Millennium'',
MG9 -- Ninth Marcel Grossmann meeting, Rome, Jul 2000,
arXiv:gr-qc/0011089.

[3] Sakharov's induced gravity:
A.D. Sakharov, ``Vacuum quantum fluctuations in curved space and the theory of gravitation'', Sov. Phys. Dokl. 12 (1968) 1040-1041; Dokl. Akad. Nauk Ser. Fiz. 177 (1967) 70-71.

------end quote from Visser----
this is from Jorge Pullin's newsletter "Matters of Gravity"
Pullin gives this address for the author:
Matt Visser, Washington University visser@wuphys.wustl.edu

The point of the recent AJL paper, where they get extended normal-looking 4D regions, is crumbling of what Visser calls the bad news
("The bad news is that so far the large flat regions have only been demonstrated to exist in 1+1 and 2+1 dimensions -- the (3+1)-dimensional case continues to pose considerable technical difficulties."). This barrier has now to some extent been penetrated by AJL.

This opens the way, if Matt Visser is right about this, to what he calls the good news, namely that the model
"almost automatically guarantees an inverse-square law at very low energies (large distances)."

obviously a breaking story, to be continued

 

[marcus]

my hunch is that the Livine/Oriti paper applies to this
http://arxiv.org/gr-qc/0405085
"About Lorentz invariance in a discrete quantum setting"

Livine and Oriti just posted this, and have also announced two
papers (with Girelli) in preparation:

"Deformed Special Relativity as an effective flat limit of Quantum Gravity"

and

"A quantum clock in a quantum causal set"

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

In the first paper "About Lorentz invariance in a discrete quantum setting"
they set about disposing of an objection that could be raised to any
discrete spacetime geometry model

If it is discrete then it probably has some characteristic length---like Planck length. And what happens to this length when you boost?

Relatively moving observers are all presumed to see this same constant length
and this (naively at least) seems paradoxical.

This objection could conceivably be raised to Ambjorn's and Loll's approach.
And it is also the main cause of the stir over DSR.
So Livine and Oriti are talking about something that applies rather widely: not only to Loop gravity and to Spinfoams, but also to DSR and the lattice-like or simplicial quantum gravity models that interest AJL---the "dynamical triangulation" models that Baez called our attention to in this thread.

 

[marcus]

I'm hoping that looking over the program for the Marseille conference
will give us some ideas of the direction QG is going.
I copied the program of talks here a few posts back.
Loll's talk on Dynamical Triangulations is of course what Baez focussed on
but here are a few others with evocative titles:

J. Kowalski Gliksman (DSR as a possible limit of quantum gravity)
F. Girelli (Special Relativity as a non commutative geometry: Lessons)
E. Livine (Instantons in GFT and continuum limit)

 

[marcus]

some Livine/Oriti quotes:

"Geometric quantities are the observable properties of the gravitational field."


"Gravitation is geometry and measurements of distances are measurements of properties of the gravitational field."


"Does a quantum gravity theory with an invariant length and a discrete spectrum for geometric observables necessarily break Lorentz symmetry or necessarily require some sort of modification/deformation of it? The answer, as we will see, is simply 'no' ”.

 

[marcus]

Larsson: a chance they succeeded in quantizing gravity

key quote from Larsson's most recent post on SPR:

----quote from Thomas Larsson---
Thus, I believe that it is a fair chance that AJL have indeed succeeded in quantizing gravity. They do so not by assuming a lot of experimentally unconfirmed new physics, but rather by strictly implementing the time-honored principles of old physics, especially causality.
---end quote---

My bolding.
Larsson makes important points in this post.
I defer to his judgement and generally agree, but have a couple of
comments to make in the context of this thread.
Here is the text of his post, which was in reply to Baez.

-----Larsson post, for possible comment-----
baez@galaxy.ucr.edu (John Baez) wrote in message news:<c82uao$i34$1@glue.ucr.edu>...
> In article <24a23f36.0405112105.6569f265@posting.google.com>,
> Thomas Larsson <thomas_larsson_01@hotmail.com> wrote:
>
> >baez@math.removethis.ucr.andthis.edu (John Baez) wrote in message
> >news:<c7pbsa$p9$1@glue.ucr.edu>...
>
> >> Given all this, I'm delighted to see some real progress on getting 4d
> >> spacetime to emerge from nonperturbative quantum gravity:
> >>
> >> 3) Jan Ambjorn, Jerzy Jurkiewicz and Renate Loll, Emergence of a 4d world
> >> from causal quantum gravity, available as hep-th/0404156.
>
> >This is pretty exciting.
>
> I'm glad you think so! I sure do!
>
Maybe I was overreacting. It was becoming boring to be negative all the time, so when I realized that somebody had made tangible progress towards some kind of quantum gravity, I got carried away.


Anyway, I would like to discuss to what extent AJL really have succeed in constructing a model of QG in 4D. As I see it, there are three things that could go wrong: that the model isn't quantum, that it isn't gravity, or that the measure is wrong.


1. Is the AJL model really quantum? Some time ago, Urs Schreiber argued that LQG, or at least the LQG string, fails to be a true quantum theory, and I tend to agree. However, the AJL model can be viewed as a statistical lattice model, and if such a model has a good continuum limit, it is AFAIK always described by some kind of QFT. What else could it be?


2. Is the AJL model really gravity? The action is a rather straightforward discretization of the Einstein action with a cosmological term:


\int R => sum over (d-2)-simplices


\int det g = volume => sum over d-simplices.


What is perhaps somewhat unusual is that all edges have the same length, which is different from Regge calculus. Nevertheless, I don't think that this really matters, but one could check if the results look different if you allow for variable edge lengths.


3. Is the measure right? Here is the place where AJL differ significantly from previous simulations. AFAIU, the crux is that AJL insist on a strict form of causality: they exclude spacetimes where the metric is singular, even at isolated points. This may seem like an innocent restriction, but it rules out things like topology change and baby universes, which require that the metric be singular somewhere.


It is not obvious to me whether one should insist on such a strong form of causality or not, but this assumption leads at least to better results, e.g. a reasonably smooth 4D spacetime. Thus, I believe that it is a fair chance that AJL have indeed succeeded in quantizing gravity. They do so not by assuming a lot of experimentally unconfirmed new physics, but rather by strictly implementing the time-honored principles of old physics, especially causality. That is cool.
---------end quote------------
https://www.physicsforums.com/showthread.php?p=212669#post212669

Notice that he says
"What is perhaps somewhat unusual is that all edges have the same length, which is different from Regge calculus."

This is the "dynamical triangulation" approach which has been extensively pursued since around 1985. In the 1990s it has seemingly replaced Regge calculus as the main focus of attention, or so is my impression. Here is a very good historical account from 1992 by Ambjorn Jurkiewicz and Kristjansen

"Quantum gravity, dynamical triangulations and higher derivative regularization"
http://arxiv.org./hep-th/9208032

I have put keywords "dynamical triangulation" in arxiv search and come up with 155 papers mostly since 1995----this includes some search-engine mistakes, not all are dynamical triangulation quantum gravity.

Surveys of quantum gravity typically list DT along with Regge approach on equal footing in the "Discrete Approaches" category. For example in Rovelli's
1998 survey "Strings Loops and Others" (gr-qc/9803024) plenary talk given at the GR15 conference, the approaches are listed:
string, loop, Regge, dynamical triangulation, Ponzano-Regge, euclidean quantum gravity (a Hawking favorite),...,etc,...

the history makes no difference to Larsson's excellent and well-qualified points but I want to know it anyway

DT has been there all along, since 1985 work by David and by Ambjorn, and maybe earlier. But I at least simply did not notice! There is a lot of work, a lot of computer simulations, review papers, interesting graphix including spacetime animation. We should have this stuff assembled and be aware of it. Here are some 1985 papers that I think are DT

[12] F. David, Nucl. Phys. B 257 (1985) 45.
[13] J. Ambjørn, B. Durhuus and J. Froehlich, Nucl. Phys. B 257 (1985) 433.
[14] F. David, Nucl. Phys. B257 (1985) 543.
[15] V. A. Kazakov, I. K. Kostov and A. A. Migdal, Phys. Lett. 157B (1985) 295.

these are from the good survey by Ambjorn, Jurkiewicz, Kristjansen

Renate Loll also has a 2003 introduction
"A discrete history of the Lorentzian path integral"
http://arxiv.org/hep-th/0212340
this is of course DT, but also more----it is foliated
and this goes to another point Larsson made, his point 3, about
the "strict causality"
This has been the variant of the DT approach prevalent since 1998.
Loll gives somewhat of the history of this "Lorentzian" or "causal" DT.
Lots to discuss here

 

[john baez]

New paper by Ambjorn, Loll and Jurkiewicz

[...] there are some previous papers by AJL which foreshadow the current one and illuminate what is going on. I think John Baez gave these links to lead-ups.

http://arxiv.org./hep-th/0002050
http://arxiv.org/hep-th/0105267

As far as I can tell the ideas that bear fruit in the recent paper (and generate an extended 4D world) are already three years old. I can't find anything conceptual that wasn't already suggested in the paper dated 27 May 2001:

"A Nonperturbative Lorentzian Path Integral for Gravity"

so right now I'm trying to understand the lead-up papers.

Good! You're right, the concepts were all there in those earlier papers, and the concepts are simple and elegant. But as you probably know, these earlier papers were just warmup exercises. They tackled quantum gravity in 1+1 and 2+1 dimensions. Lots of approaches work in those low dimensions; the physically realistic 3+1-dimensional case is much harder. So, the first really strong evidence that Ambjorn, Loll and Jurkiewicz are on the right track came from their new calculations in the 3+1-dimensional case. The reason it took them a while to do these new calculations is that they require some heavy-duty computer work.

In case anyone out there doesn't know: classically, in 1+1 dimensions every metric is a solution to the equations of general relativity without matter (with vanishing cosmological constant). In 2+1 dimensions, only flat metrics are solutions to these equations. Only in 3+1 and higher do the equations become interesting... with gravitational waves, black holes and so on.

So, while there are millions of papers on quantum gravity in 1+1 dimensions and 2+1 dimensions, and many of them are actually interesting, it's always incredibly risky to extrapolate any conclusions about higher dimensions from those special cases.

 

[john baez]

new paper by ambjorn, loll and jurkiewicz

Was this paper an attempt to justify or perhaps even derive the very overall topology of space-time?

Not really. The main goal was to get a theory of quantum gravity in 3+1 dimensions that works - meaning that it reduces to general relativity at length scales much larger than the Planck scale. They didn't prove their model works, but they produced some impressive evidence that it might.

But, there is something to say about topology here.

In their model, you can take space at a given time to have any topology you want - any compact 3-dimensional manifold, that is. The model then ensures that the topology of space will remain the same at all other times.

In other words, the model forbids "topology change".

They wanted this, because in very similar models (dynamical triangulation models) that don't forbid topology change, there's a strong tendency for all hell to break loose: typical spacetimes are either "crumpled" or "branched polymers". This problem had afflicted the subject for decades! This is what Ambjorn, Jurkiewicz and Loll seem to have gotten around!

I wonder if causality is the key to the topology of space-time.

I'd prefer to say it's the key to preventing topology change. This is well-known in classical general relativity, where one can prove there's no topology change if spacetime is "globally hyperbolic" - that is, very roughly, if it has a well-behaved concept of causality.

 

[john baez]

new paper by Ambjorn, Loll and Jurkiewicz

Mike2 on the other thread raised the question of whether the quantum gravity model assumed by AJL had been rigorously developed.

As far as I can tell, it's completely rigorous. And I'm a mathematician by training, so I'm more fussy about these things than most.

I know of rigorous (1,1)-dimensional theories and maybe some (1,2)-dimensional ones, but I don't know of any fully (1,3) relativistic quantized ones.

It's easier to make discrete models rigorous than models that assume spacetime is a continuum. That's the main reason I like discrete models.

In particular, all the 3+1-dimensional spin foam models of quantum gravity I've worked on - various versions of the Barrett-Crane model - are mathematically rigorous and background-free.

The problem is, we haven't gotten good evidence that these spin foam models "work" - namely, that they reduce to general relativity in the limit of distance scales that are large compared to the Planck length.

See my Marseille talk for a taste of the problems:

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

Since we don't have any experimental evidence concerning quantum gravity, mathematical rigor is one way to make sure we're not playing tennis with the net down. I will be very happy when we get any rigorously well-defined background-free quantum theory of gravity that works in the sense defined above.

More precisely: I will be very happy if we get numerical evidence that it works, and ecstatic if we can mathematically prove that it works. But since such a model is likely to be nonperturbative, a mathematical proof of this sort might be very difficult. Nobody has even proved confinement in lattice QCD, even though numerical calculations have convinced everyone it's true.

 

[john baez]

Marseille conference, Isham's conference

While we are on possibly important papers (of which e.g. AJL's)
does anyone have any guidance or comment about
Marni Dee Sheppeard's recent
http://arxiv.org/gr-qc/0404121
unless for some reason it is tactless of me to ask.

Hmm, I just see this paper has been withdrawn! Good! I read it while flying to Marseille. She's young, she made a mistake, she's smart, she did the right thing. 'Nuff said.

Read this one, it's much better:

L. Crane, M.D. Sheppeard
2-categorical Poincare Representations and State Sum Applications
http://www.arxiv.org/abs/math.QA/0306440

Also I wish we could hear more about the Marseille conference
since Week 206 merely whetted my appetite.

Well, what can I say? The scenery was great:

http://math.ucr.edu/home/baez/calanque.html

but the wine was awful. Did you know the French Mathematical Society makes their own wine? I'm not sure that's what we were drinking, but it might explain it. At least it got the job done... so even though I was jet-lagged and completely exhausted, I stayed up late every night talking to all my favorite quantum gravity folks: Ashtekar, Barrett, Christensen, Jacobson, Krasnov, Lewandowski, Markopoulou, Loll, Rovelli, Smolin, and others - carefully listed in alphabetical order to avoid any appearance of favoritism.

Seriously, us "old-timers" were all very impressed by the large numbers of bright new young folks moving into the field and doing good things.

We talked about pretty much everything, but I was always trying to get everyone to tell me what calculations Dan Christensen and I should do in the Barrett-Crane model to either get more "physical" results than we've gotten so far, or kill the model dead. Also, a bunch of us were pestering Renate Loll to make sure we understood her model in detail. Ashtekar is doing a lot of work on semiclassical states, so he was talking about that a bunch...

But if you want to see quantum gravity folks in action, it's probably not too late to register for Isham's conference at Imperial College this September - a lot of the same people will be there, too. I'm spending most of the summer in Cambridge, and I'd been planning to go down and spend a week in London starting September 8th, but I may go down a bit early to catch this - or just take the train down for the day a couple of times!

 

[marcus]

your account of the late night conversations and bad homemade wine is heartwarming. thanks for these posts

 

[pelastration]

The scenery was great:

http://math.ucr.edu/home/baez/calanque.html

Indeed beautiful.

You said: I saw these sights, but I didn't take these photographs! I got them off the web, but now I can't find where I got them. If you know, please tell me so I can credit the photographer.

Check George Gollin's website: http://www.hep.uiuc.edu/home/g-gollin/graphics/france.html

 

[marcus]

Indeed beautiful.
...[/URL]

You said it! As long as we are doing pictures, here's the awful truth of what some of these people look like.

http://www.edge.org/3rd_culture/bios/baez.html

Carlo Rovelli:
http://www.cpt.univ-mrs.fr/~rovelli/rovelli.html

Since Ambjorn Loll Jurkiewicz may have finally succeeded in quantizing GR
(necessarily in a Backgr. Indep. fashion since GR's spacetime geometry is B.I.)
we should include a picture of Loll. [edit: this link is courtesy selfAdjoint]



and bring forward the link to the picture of Jan Ambjorn

http://www.nbi.dk/~ambjorn/

More pictures---a graphic realization of the Background Independence of SQG
(Ambjorn has proposed to call the "dynamical triangulations" approach by the name Simplicial Quantum Gravity---yes I know some people think of SQG as a more general term that includes DT as a subfield) can be seen in these computer animations:

http://www.nbi.dk/~ambjorn/lqg2/

clearly these spacetimes have no fixed geometry! they squirm and ripple.

Baez says that Fotini M plans to start some research in this area with a grad student of hers. I would like to find a photo of Fotini. Does anyone have a better link?
http://www.sciam.com/article.cfm?articleID=0007E95C-9597-1DC9-AF71809EC588EEDF
http://www.perimeterinstitute.ca/people/researchers/longterm.cfm


Here's Lee Smolin:
http://www.edge.org/3rd_culture/bios/smolin.html

 

[selfAdjoint]

Why not link to Loll[/URL] ?

 

[marcus]

outstanding question in Simplex Gravity

What is the area spectrum in Simplicial Quantum Gravity?

if Ambjorn and Loll-style "dynamical triangulation" approach to quantum gravity works out (a possibility John Baez seemed to be allowing for) then a major unsolved question concerns the area spectrum

will it come out discrete, as in Loop gravity

will it come out the same as in Loop gravity, the same multiples of the Planck unit area, the same set of numbers for eigenvalues of the operator

how can the area operator in Simplicial Quantum Gravity be constructed

can computer (monte carlo) simulations be used to calculate areas?

 

[jeff]

What is the area spectrum in Simplicial Quantum Gravity?...a major unsolved question concerns the area spectrum

will it come out discrete, as in Loop gravity

will it come out the same as in Loop gravity, the same multiples of the Planck unit area, the same set of numbers for eigenvalues of the operator

how can the area operator in Simplicial Quantum Gravity be constructed

You should think about the fact that the simplicial edges here may be viewed as having been pre-assigned one quantum of length. What we need to know is if GR is produced. Anyway, how seriously should we take quantum theories requiring all but a very special family of quantum fluctuations be ignored? (This may explain why such an obvious idea wasn't previously pursued).

 

[pelastration]

Baez says that Fotini M plans to start some research in this area with a grad student of hers. I would like to find a photo of Fotini. Does anyone have a better link?
http://www.sciam.com/article.cfm?articleID=0007E95C-9597-1DC9-AF71809EC588EEDF

Not a better photo. You can email here and ask.
http://www.perimeterinstitute.ca/people/researchers/view_bio.cfm?id=18 .

Added: I asked here a link to some photo's.

 

[marcus]

maybe we have enough mugshots for the moment

issues about the history of the "dynamical triangulations" line of research
(also Ambjorn calls it SQG simplicial quantum gravity, treating
that as a synonym for DT in one paper I saw) are bound to come up.

so the history of this (1985, 1992, 1998 are important years) is another thing to keep in mind
as a reminder here are some links I posted a while back

https://www.physicsforums.com/showthread.php?p=213245#post213245

for the notes on history, scroll down just past the end of the Larsson quote

 

[john baez]

area spectrum in the AJL model

Indeed beautiful.

[JB] said: I saw these sights, but I didn't take these photographs! I got them off the web, but now I can't find where I got them. If you know, please tell me so I can credit the photographer.

Check George Gollin's website: http://www.hep.uiuc.edu/home/g-gollin/graphics/france.html

Thanks! That's it! I'll credit him.

By the way, Marcus raised an interesting question about the spectrum of the area operator in the Ambjorn-Jurkiewicz-Loll model:

Will it come out the same as in Loop gravity, the same multiples of the Planck unit area, the same set of numbers for eigenvalues of the operator?

That seems very unlikely! The model is based on the assumption that all the tetrahedra of which space is built are regular tetrahedra, all with the same basic edge-length. So, every face of every tetrahedron is an equilateral triangle of the same size. This size is the "quantum of area" in this model - call it a. The model doesn't specify what this number a is, but the obvious area operator - I claim there's an obvious area operator on the Hilbert space of this theory - will have as its spectrum the numbers

0, a, 2a, 3a...

This is more like what Bekenstein and Mukhanov claim in their famous paper on black hole spectroscopy than anything one gets in loop quantum gravity.

How can the area operator in Simplicial Quantum Gravity be constructed?

There are lots of ways, and we could have a fun argument about which one is "right", just like people have had in loop quantum gravity, with the Ashtekar-Lewandowski area operator battling the Rovelli-Smolin area operator. The problem is that we can't tell which area operator is "right" until we find some calculations that only give nice answers with the "right" area operator. Or, do an experiment and measure areas at the Planck scale - not very practical, and this will only work if not only our area operator but also our whole theory is also right!

It seems pretty easy to cook up a nice area operator in the AJL model: there's a Hilbert space whose orthonormal basis consists of all ways of triangulating a given 3-manifold into tetrahedra. Picking a surface for each triangulation, with the surface made of triangles in that triangulation, we get an area operator such that each state in the above basis is an eigenstate with eigenvalue na, where n is the number of triangles in the surface for the given triangulation.

That was a bit terse, but it was a complete description of the "obvious" area operator. It even takes into account the fact that which surface we're talking about can only be specified after we say which state of the universe we've got! In other words, this is a physical observable, not a "kinematical" one.

Can computer (monte carlo) simulations be used to calculate areas?

I don't see the need for this, since the dynamics of the theory don't affect the area spectrum in any obvious way.

(This is what people hope in loop quantum gravity, which is why people dare talk about the area spectrum even before solving the Hamiltonian constraint. In other words, they're computing the spectrum of a kinematical observable and hoping that'll be the spectrum of a physical observable. But the AJL model is gauge-fixed, so there's no Hamiltonian constraint! - so it's much easier to construct physical observables.)

(Where of course "physical" is a technical term that doesn't imply any of this stuff is relevant to the real physical world!)

 

[sol2]

I have a question about topology.

If we accept the ideas of LQG as a basis of of these triangulations in quantum gravity, can we say that these are discrete.

As part of the http://superstringtheory.com/forum/extraboard/messages12/666.html of string theory based on Kaluza and Klein's ordering of geometries this would seem consistent to me, while LQG might be lacking in this discription and less pervasiveness?

Looking at the monte carlo for better comprehension of the energy bending plot, helped to define the structure for me in visualization.s If we can get better pictures then It goes a long way for me:)

I was looking for a consistent geometrical basis. Can this be done?

Also string frequencies can be http://www.superstringtheory.com/forum/stringboard/messages18/1.html why can LQG not?

 

[marcus]

getting back to the main topic of the thread (Simplicial Quantum Gravity---AJL model---Baez comments after the Marseille conference) here are exerpts from JB post from yesterday, 22 May:

... interesting question about the spectrum of the area operator in the Ambjorn-Jurkiewicz-Loll model:

"Will it come out the same as in Loop gravity, the same multiples of the Planck unit area, the same set of numbers for eigenvalues of the operator?"[/color]

That seems very unlikely! The model is based on the assumption
that all the tetrahedra of which space is built are regular tetrahedra, all
with the same basic edge-length. So, every face of every tetrahedron is an equilateral triangle of the same size. This size is the "quantum of area" in this model - call it a. The model doesn't specify what this number a is, but the obvious area operator - I claim there's an obvious area operator on the Hilbert space of this theory - will have as its spectrum the numbers

0, a, 2a, 3a...

This is more like what Bekenstein and Mukhanov claim in their famous paper on black hole spectroscopy than anything one gets in loop quantum gravity.

"How can the area operator in Simplicial Quantum Gravity be constructed?"[/color]

There are lots of ways, and we could have a fun argument about which one is "right", just like people have had in loop quantum gravity, with the Ashtekar-Lewandowski area operator battling the Rovelli-Smolin area operator. The problem is that we can't tell which area operator is "right" until we find some calculations that only give nice answers with the "right" area operator. Or, do an experiment and measure areas at the Planck scale - not very practical, and this will only work if not only our area operator but also our whole theory is also right!

It seems pretty easy to cook up a nice area operator in the AJL model: there's a Hilbert space whose orthonormal basis consists of all ways of triangulating a given 3-manifold into tetrahedra. Picking a surface for each triangulation, with the surface made of triangles in that triangulation, we get an area operator such that each state in the above basis is an eigenstate with eigenvalue na, where n is the number of triangles in the surface for the given triangulation.

That was a bit terse, but it was a complete description of the "obvious" area operator. It even takes into account the fact that which surface we're talking about can only be specified after we say which state of the universe we've got! In other words, this is a physical observable, not a "kinematical" one...

at first sight, at least, it strikes me as strange that there's been no mention of matter participating in defining the surface whose area is to be measured (maybe this would be grist for the "fun arguments" JB says could be possible)

but I am not looking for arguments! I just find it unintuitive that one should have an area operator that measures the area of a perfectly abstract immaterial surface apparently chosen arbitrarily---a different one for each quantum state. I would feel more comfortable if the surface was the surface of my desk or something tangible like that (or at least defined by the gravitational field like a BH horizon would be). Maybe this is qvetching.

 

[sol2]

Marcus I would like to remove my post to preserve continuity between you and JB, Should this be done? I like your questions about what is real as well, but tangibles are not always easy moving to hyperspace realizations and quantum gravity? We'll have to see what JB saids to your response.

 

[selfAdjoint]

getting back to the main topic of the thread (Simplicial Quantum Gravity---AJL model---Baez comments after the Marseille conference) here are exerpts from JB post from yesterday, 22 May:



at first sight, at least, it strikes me as strange that there's been no mention of matter participating in defining the surface whose area is to be measured (maybe this would be grist for the "fun arguments" JB says could be possible)

but I am not looking for arguments! I just find it unintuitive that one should have an area operator that measures the area of a perfectly abstract immaterial surface apparently chosen arbitrarily---a different one for each quantum state. I would feel more comfortable if the surface was the surface of my desk or something tangible like that (or at least defined by the gravitational field like a BH horizon would be). Maybe this is qvetching.

Note that in their work on two and three dimensional "toy models' they did fit them with a toy model of matter, specifically an Ising spin lattice. And they showed that in the continuum limit the parameters of the model which they could derive in their quantum gravity form matched the ones derived in flat Minkowski space. I would presume the next thing they are going to do with their four dimensional mosel is to repeat this calculation.

Note also that this is a "get our claim out there in print" kind of paper, which sets out to do no more than prove their claim to derive four dimensional space from their local quantization. And bells and whistles will come later.

 

[marcus]

Marcus I would like to remove my post.

Sol please don't feel you should remove your "I have a question about topology" post of yesterday. Everyone's (positive) expressions of interest adds to the welcome with which we honor a visiting expert.
It is considerate and sensitive of you to worry about on topic/off topic issues.

the fact is for me I have to focus (which is just my situation relative to this)
but that does not mean you have to do the same!
there is a place for intellectual leaping in these discussions
(and for starting new threads on related tangents too)

however i must say that SQG is still at a rudimentary stage and
dealing with the most basic nuts and bolts
or so it seems to me

and accordingly I think you will find more possibilities for tie-ins with
loop gravity foam and the rest later on when
SQG has been cooking a while longer

 

[john baez]

at first sight, at least, it strikes me as strange that there's been no mention of matter participating in defining the surface whose area is to be measured (maybe this would be grist for the "fun arguments" JB says could be possible).

Actually I don't find this particular type of argument very fun - it's based too much on philosophical taste and not enough on the details of the model being considered. The AJL model has no matter in it, so we can't use matter to locate a surface in spacetime in this model. We can include matter, but then we have a different model.

Some people have strong philosophical objections against models of quantum gravity that don't include matter, but I've never understood these, since classical gravity is a perfectly sensible theory without matter, and nobody ever explains why the philosophical objections are supposed to kick in only when you quantize this theory!

Of course our universe has matter and we're striving for a theory of that. Also of course, there may be technical reasons why a theory of quantum gravity without matter can't possibly work. Nobody knows: this is a big open question. But the vague philosophical argument that "you can't tell where anything is without matter" just seems wrong to me. In curved spacetime, different places are different, so you can tell where features are. The vacuum Einstein equations make perfect sense classically; they don't become ambiguous due to the lack of matter. So, we can try to quantize this theory and see what happens.

The "fun" arguments I was alluding to are those that start with the AJL model, accept the fact that this theory has no matter in it, write down some well-defined operators, and then argue about which one is "the right area operator". Here we are dealing with a tough problem that might actually have a solution.

but I am not looking for arguments!

Don't worry, I'm not really arguing - just explaining why certain arguments don't seem fun to me, while others do.

I just find it unintuitive that one should have an area operator that measures the area of a perfectly abstract immaterial surface apparently chosen arbitrarily---a different one for each quantum state.

It may seem weird, but observables of this sort exist in the classical theory, so it should not really be shocking that they exist in the quantum theory. All we're saying here is that if you have a particular state of quantum gravity, you've got a particular "spacetime" of a quantum sort, and as in a classical spacetime you can talk about surfaces and their area.

I would feel more comfortable if the surface was the surface of my desk or something tangible like that (or at least defined by the gravitational field like a BH horizon would be).

I can see why these make you feel comfortable, but your comfort will turn to terror when you try to do calculations with an operator whose definition relies upon a mathematically precise definition of "the surface of my desk" - or even a "black hole horizon", which is much simpler to define, but still rather complicated. It's easier to first define the area of an arbitrary surface, and worry later about whether it's the surface of your desk. We do this in classical gravity, so I think we should do it in quantum gravity too.

 

[marcus]

very glad to have this lengthier discussion expanding on what you said earlier, which now seems quite reasonable or at least less strange.
so I should now imagine a hilbert space of (linear combinations of) all possible triangulations of a certain 3-manifold using a uniform set of tetrahedra

I have to stop and think if this is separable.

I think so.

for each N, all the possible ways of snapping together a set of N tetrahedra
the union of that has to be countable.

what is the inner product?

selfAdjoint might have an intelligent question (having proceeded ahead a ways), I am still getting my bearings.

 

[pelastration]

It's interesting to see what other people actually do on Elastic Interval Geometry.

Some movies showing dynamical triangulations in 3D: http://www.beautifulcode.nl/fluidiom/index.php?pagename=Main.FluidiomMovies The second mpg-movie (first image) (14Mb) is impressive.

http://www.beautifulcode.nl/gallery/

The server seems a little bit slow. Take your time.

 

[marcus]

what is the inner product?

Would it be nice if the inner product could somehow respect
dual triangulations.

Maybe it says in one of these papers we have links to how one
defines the inner product on a linear space consisting of linear combinations
of trglns of a 3-manifold---and I just missed it---or maybe it is a well-known proceedure I don't know about.

anyone other than JB have a page reference or link for this?

those "moves" that get you from one trgln to another turn into linear operators----possibly fun---any special properties?

 

[marcus]

I have a vague feeling of dejavu that the *star-category (from Q.Quandaries paper) idea could relate to this dynamical triangulations business. Was this spelled out somewhere and i just forgot about seeing it?
Maybe should just drink my coffee and not worry about this.

 

[marcus]

the big kahuna (selfAdjoint comment about AJL etc)

----from sA post on "Rovelli program" linkbasket thread----

...The two great historical exemplars of beauty first were Einstein and Dirac. In each case their approach achieved a great success early but then led them into unproductive wastelands. And it is at least arguable that both string physics and LQG research in the Ashtekar tradition are right now spinning their wheels. Maybe it's time for a younger generation, playing Feynman and Dyson to the Witten - Ashtekar version of Einstein-Dirac to have their say. Which is why I am very interseted in the AJL paper, a possibly rough hewed (remember Feyman's early rep?) but undoubtedly novel approach to the problem of background independent quantum mechanics (and THAT, not just quantum gravity is the big kahuna)...

------end exerpt----

some provocative idea(s) or seeds thereof here

AJL dynamical triangulations approach seems very close in spirit and practice to spinfoam
But also LQG and spinfoam are closely allied lines of research with people moving back and forth between them---even erecting theoretical bridges as in Livine' thesis.

we lack a good general classification-----all these research lines are aiming at a background independent quantum gravity----no official name but could call the goal a quantum general relativity
and there is a tailwagsdog effect that the background independence feature of GR is so massive that when you try to "quantize GR" it begins to look as if you are "bacgroundindependencing quantum mechanics".

two people on the ice, who is pulling whom, that kind of thing

well I didnt quite respond to your point about beauty and the historical parallels, but I want to see where it leads and also this big kahuna idea

BTW here's todays post on SPR by Thomas Larsson about the AJL paper:

https://www.physicsforums.com/showthread.php?p=221756#post221756

-----sample from Larsson----
Dear Zirkus,

Motl has of course completely missed the main point. Distler's
objection from 3 years ago was that he didn't believe in a good
continuum limit in 4D; a "miracle" as he puts it. This may have
been good point at that time; I thought so myself, although I
would have been much less pessimistic if I had known that
Ambjorn and Loll had already succeeded in 2 and 3D.

The new thing is that AJL have presented rather compelling
numerical evidence for a good continuum limit in 4D, thus making
Distler's objection obsolete. It is the fact that AJL have
apparently succeeded in quantizing gravity numerically that
people are so excited about...

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

 

[marcus]

perspective on dynamical triangulation from a 1998 review by Rovelli

In his 1998 review Rovelli says that both spinfoam and dynamical triangulation simplicial QG can be seen as developing from Hawking's "Euclidean QG" which he discusses in the section called "Old Hopes turning into Approximate Theories".

-------quote from Rovelli gr-qc/9803024--------

B. Old hopes --> approximate theories

1. Euclidean quantum gravity
Euclidean quantum gravity is the approach based on a formal sum over Euclidean geometries (6):

Z = N \int D[g] e^{-\int d^4x \sqrt {g} R[g]}

As far as I understand, Hawking and his close collaborators do not anymore view this approach as an attempt to directly define a fundamental theory. The integral is badly ill defined, and does not lead to any known viable perturbation expansion. However, the main ideas of this approach are still alive in several ways.

First, Hawking’s picture of quantum gravity as a sum over spacetimes continues to provide a powerful intuitive reference point for most of the research related to quantum gravity. Indeed, many approaches can be sees as attempts to replace the ill defined and non-renormalizable formal integral (6) with a well defined expression. The dynamical triangulation approach (Section IV-A) and the spin foam approach (Section V-C2) are examples of attempts to realize Hawking’s intuition. Influence of Euclidean quantum gravity can also be found in the Atiyah axioms for TQFT (Section V-C1).

Second, this approach can be used as an approximate method for describing certain regimes of nonperturbative spacetime physics...

------end exerpt----

 

[Mike2]

I hate to be late to the discussion, but I just got through reading Three roads to Quantum Gravity and it amazes me that I still have basic questions such as: how is the discrete spacetime connected in a topologal sense. I mean, does each "cell" of spacetime share a side with adjacent cells? Or are there infinitesimal edges that connect regions together? What are the loops in quantum gravity? And how does this differ from the AJL picture of a spacetime?

Thanks.