Why CDT changes the map of quantum gravity

[Chronos]

I don't think the 2D picture, or even fractional D, is far fetched. Look at all the 2D black hole models that started emerging like 10 years ago. They took different approaches yet somehow arrived at very similar versions of spacetime in the Planckian realm as does CDT. That is what caught my attention when CDT hit the pavement. I see different approaches converging with the same outcome - a smoke and fire thing. CDT may not be dead on, but I think it is scary close.

 

[marcus]

... - a smoke and fire thing. CDT may not be dead on, but I think it is scary close.

my intuitive feeling is in line with yours. I think other people as well (QG folks at AEI who organized the conference, AEI director Hermann Nicolai) must have gotten similar signals because of the way the Loops 05 conference has been set up. the topic list and choice of invited speakers give it a different direction from past Loops conferences. Some influential people must have had a similar impression back when the conference started taking shape and direction

maybe not dead on but scary close is a good way to put it. the other QG people may want to see if they can copy CDT, and what, if any, similar results they can get. in any case some serious openminded consideration will do no harm

MIKE2 I SEE YOUR NEXT POST and to save space I will edit in, and reply here. IMO one CAN think of dimension as the result of measuring and in terms of operators on a hilbert space. With one type of dimension one can think of operators corresponding to measuring distance and to measuring volume. One does a bunch of measurments of radius and volume and compares, to see if the volume is proportional to R^2.5 or R^2.9 or R^3.0 or R^3.1.

the word dimension only has meaning if you say what definition of it you are using and therefore what measurements it is going to depend on, and in this example I mean the concept of dimension that depends on measuring distances and volumes.

in their computer simulations they plot CURVES fitted to DATA about distances and volumes. that is rather like what you were talking about I think-----making measurements (which would correspond in theory to operators on a hilbertspace)

I hope you check out the curves they plot in various figures in their recent paper. it gives a concrete idea of the various meanings of dimension.

 

[Mike2]

my intuitive feeling is in line with yours. I think other people as well (QG folks at AEI who organized the conference, AEI director Hermann Nicolai) must have gotten similar signals because of the way the Loops 05 conference has been set up. the topic list and choice of invited speakers give it a different direction from past Loops conferences. Some influential people must have had a similar impression back when the conference started taking shape and direction

maybe not dead on but scary close is a good way to put it. the other QG people may want to see if they can copy CDT, and what, if any, similar results they can get. in any case some serious openminded consideration will do no harm

So is the dimensionality the result of an operator on the Hilbert space of various geometries in 4D? I can accept changing dimensionality on that basis, maybe. Is there a more common analogy with simple QM that could help visualize what's going on mathematically? Thanks.

 

[marcus]

So is the dimensionality the result of an operator on the Hilbert space of various geometries in 4D?...

Hi Mike, I edited my reply to your post yesterday morning into preceding one (#62) and that may have led to your missing it. the general idea is, I think, right.

in their approach one can make various measurements (which would convenionally correspond to operators), and from these measurements one determines various dimension numbers----for thin spatial slices, for thick slices, for the whole spacetime, for shortrange, for longrange...

there is no one right definition of dimension and no one correct dimension number (because spacetime is not a differentiable manifold with coordinates, where there would be)

I have not seen the construction of a hilbert space of "various geometries in 4D" as you say. With the path integral approach the focus is on the path inegral and not on the hilbert space. But I expect one COULD be constructed for the various spacetime geometries.

these geometries would not be "in 4D" though, I think. they would not be IN any larger space, they would not be embedded in anything, and some of the spacetimes would have dimension greater than 4

for the first 10 years or so that people did dynamical triangulations approach, one of the problems that dogged them was that when you tried building a space of low dimension, like 2 or 3 or 4, it might turn out to have unboundedly high hausdorff dimension. essentially the dimension would go infinite

(even if you were building the space out of 2-simplices and wanted it to be 2D, or when you were building it out of 3-simplices and wanted it to come out 3D--------a kind of crumpling occurred in the computer simulation that led to results of very high dimension)

these possibilities are presumably still there, they just have very small PROBABILITY. so now we have results where the EXPECTATION VALUE, or average value, of the dimension comes out 4, or 3.99 or 4.01
(look at the plots of their data in their paper, it does not come out exactly 4D)

so these geometries are not quite exactly "various geometries in 4D", as you said. But there would be some hilbert space of various geometries that you could construct and define operators on

=====================
Hi Mike just saw your post #65 (which follows) will reply here for compactness. Yes I agree it should be straightforward, but I cannot picture the explicit construction of the Hilbert space for the continuum limit as the simplexes shrink down to nothing. for the path integral corresponding to one fixed size of simplex, I can roughly form an idea of how the Hilbert space could be constructed, maybe also for spacetimes of a fixed volume.
A basis could be made from the discrete set of all possible gluings, which one could try to write down and enumerate combinatorially. I can see the advantage for people who are more familiar with the canonical formulation than with path integrals. But I have not noticed this construction having been done by any of the Triangulations people. Here is your post #65 I am responding to

If there is a path integral, then shouldn't it be an easy matter to convert it to a canonical version with operators on a wave function type of equation? It would probably be easier to understand things in this context, right? Thanks.

 

[Mike2]

so these geometries are not quite exactly "various geometries in 4D", as you said. But there would be some hilbert space of various geometries that you could construct and define operators on

If there is a path integral, then shouldn't it be an easy matter to convert it to a canonical version with operators on a wave function type of equation? It would probably be easier to understand things in this context, right? Thanks.

 

[marcus]

hi Mike, I edited post #64 to include a response to yours.

To get back to the main question----of how CDT changes the QG map:

I think TOPOLOGY CHANGE is a significant issue. the usual version of LQG does not deal with any change in spatial topology. there is a spatial manifold Sigma and the spacetime manifold is simply the cartesian product Sigma x R, that is Sigma plus a time axis. And the Sigma is usually just the 3D sphere S³. So topologically the usual LQG spacetime is S³ x R. LQG is exciting for other reasons than topology.

Loll and Westra have two interesting papers in CDT "Triangulations" gravity about extending the path integral so the sum is over various topologies.

I suspect there is another paper in the works which will come out in time for the October Loops 05 confence.

FAY DOWKER is one of the invited speakers at Loops 05, and she has written at least 5 papers bearing on spacetime topology in QG. Loll and Westra
http://arxiv.org/hep-th/0309012
cite these 5 papers of Dowker.

I have no opinion on Dowker papers cause I haven't looked yet, but one that they cite is
http://arxiv.org/gr-qc/0206020
Topology change in quantum gravity
Fay Dowker
18 pages. Contribution to the proceedings of the Stephen Hawking 60th birthday conference, Cambridge, January 2002

"A particular approach to topology change in quantum gravity is reviewed, showing that several aspects of Stephen's work are intertwined with it in an essential way. Speculations are made on possible implications for the causal set approach to quantum gravity."

Independent of how I like Fay Dowker's reseach, when I have a look later today at it, I can see the theme of topology change emerging in Renate Loll's CDT research and at the Loops 05 conference.

So how is CDT changing the quantum gravity map?

1. putting topology on the table (where Loop has a S³xR spacetime with constant spatial topology)

2. getting away from idea that spacetime is a differentiable manifold (very old idea going back to Riemann 1850)

3. dynamical dimension, able to be different at close range and to change continuously

4. really making the "state sum" or Feynmanian "path integral" work finally.

5. idea of quantum spacetime dynamics---that a microscopic dynamic principle operating down at Planck scale can GENERATE macroscopic spacetime with its wellknown properties.

 

[Mike2]

is a differentiable manifold (very old idea going back to Riemann 1850)

I'm not sure I believe that no manifolds are involved in CDT. For as you shrink the length scale to zero, then you are talking about a continuosly changing metric, a metric field, on what else... but a manifold, right?

 

[Mike2]

=====================
Hi Mike just saw your post #65 (which follows) will reply here for compactness. Yes I agree it should be straightforward, but I cannot picture the explicit construction of the Hilbert space for the continuum limit as the simplexes shrink down to nothing. for the path integral corresponding to one fixed size of simplex, I can roughly form an idea of how the Hilbert space could be constructed, maybe also for spacetimes of a fixed volume.
A basis could be made from the discrete set of all possible gluings, which one could try to write down and enumerate combinatorially. I can see the advantage for people who are more familiar with the canonical formulation than with path integrals. But I have not noticed this construction having been done by any of the Triangulations people. Here is your post #65 I am responding to

It seems to me that you simply replace the measure, x, in the traditional path integral with the metric, g, and convert to canonical form as usual. But I suppose that the detailed nature of the Action integral and the Lagrangian if the CDT path integral prevents knowledge of the Hamiltonian that we would then use in the canonical version. Is that your take on the subject?

 

[marcus]

I'm not sure I believe that no manifolds are involved in CDT. For as you shrink the length scale to zero, then you are talking about a continuosly changing metric, a metric field, on what else... but a manifold, right?

there is something called a "simplicial" manifold which is glued together out of simplexes. it can be a bit craggy and jaggy compared with a "differentiable" manifold. I think you know about this.

when the CDT people take the length scale down to zero they don't necessarily get a differentible manifold. In the first place, altho this is not the main reason let's make explicit that the length scale does not have to go to zero in a smooth way
it could go to zero in spastic jumps
1/17, 3.14x10^-6, (39 billion)^-1,...

A way to picture is that they have a sequence of BLURS made of many simplicial manifolds where in each blur the simplexes are all the same size 'a'. and they take 'a' down. they could, for example, divide 'a' in half each step. so the component simplexes get smaller and smaller

at each step you don't have just one particular collage of simplexes making one particular simplicial manifold, you have a blurry quantum cloud of possible collages

and the 'a' is jumping, maybe spastically, down in size, so the cloud consists of things getting finer and finer. But it is not clear that this process converges to a differentiable manifold, or to any kind of manifold that anyone has yet defined or studied.

BTW Mike you know historically the Greeks resisted the idea of the real numbers for a time, and could only believe in fractions.
nowadays mathematicians define the reals by various equivalent means of which a very common is as LIMITS OF SEQUENCES OF RATIONAL NUMBERS.

that is you only ever get your hands on rational numbers, but you fantasize having an infinite sequence of rationals with larger and larger denominator and the LIMIT of that sequence (which is an abstract thing you never actually get hold of) is the real number

and computers use rational number arithmetic, as an approximation of abstract real number arithmetic which they cannot do because no actual concrete data sequence is ever infinite.

And nevertheless we think of real numbers as REAL, even tho abstractly defined as limits of sequences of rationals.

Well it may be that differentiable manifolds are like the rational numbers were for the Greeks. We can't think of a continuum any other way. But, like, MOST continuums are probably not differentiable manifs!
just like most of the numbers on the real line are not rational---not expressible as fractions----only as limits of sequences.

BTW I believe you are right in saying that manifolds are (at least potentially) INVOLVED in CDT because they always can, for any particular simplicial manifold, coordinatize it and find some way to make a smooth, or mostly smooth, thing out of it. But that is kind of tangential because we are not talking about taking limits of individual manifolds. It is an option, but not part of the main business

 

[wolram]

http://citebase.eprints.org/cgi-bin/fulltext?format=application/pdf&identifier=oai%3AarXiv.org%3Agr-qc%2F0210061

a 2002 paper by Fay Dowker etc.

http://www.imperial.ac.uk/research/theory/research/quantum.htm

A link that may be of interest.

 

[marcus]

http://citebase.eprints.org/cgi-bin/fulltext?format=application/pdf&identifier=oai%3AarXiv.org%3Agr-qc%2F0210061

a 2002 paper by Fay Dowker etc.

http://www.imperial.ac.uk/research/theory/research/quantum.htm

A link that may be of interest.

From where i am, I cannot get the first link to work, but I guess that it is to this paper
http://arxiv.org/abs/gr-qc/0210061
which I can get.

thanks for both links.

I poked around a little at the Imperial College theoretical physics site and noticed that not only is Fay Dowker there but also
Chris Isham.

Renate Loll's degree is from Imperial College. She got her doctorate there in 1989. Could be that her strong interest in quantum gravity was helped by the influence of people like Dowker and Isham.

 

[wolram]

From where i am, I cannot get the first link to work, but I guess that it is to this paper
http://arxiv.org/abs/gr-qc/0210061
which I can get.

Thats the one Marcus.

 

[marcus]

It is an odd coincidence that several of the papers I am currently checking out are by women. I swear it is not me. I am not a philanderer skirt-chaser type at all!

Just got a notion that I'd like to see this. But not only is it in German, so not easy to read, but it is not even posted on arxiv. Will see if there is a Uni Potsdam link.

B. Dittrich: Dynamische Triangulierung von Schwarzloch-Geometrien (in German), Diploma Thesis, Univ. Potsdam (2001).

No luck. Dittrich thesis is not in digital form online anywhere, it seems. Looked several places.

the dittrich-loll paper they just posted, about dynamical triangulation of black holes, says that part of what is in that paper comes from dittrich's thesis.

http://arxiv.org/gr-qc/0506035

the nagging question for me is what happens AFTER the details of this new model of spacetime are worked out. that will take a while. they have substantially done the empty "ground state", and they have made a start with
1. adding some token matter (so far posted work does this only in lower dimension cases)
2. allowing for topology change, like with formation of a macroscopic black hole (so far posted work only in 1+1D)
3. modeling black holes (preliminary)

more is in progress about these than has been posted yet, judging by the mentions in the papers we do have, and citations to unpublished work

But assuming all that gets done. And suppose it continues to check out OK and be at least consistent with what has already been observed. that still leaves the real hard testing with make-or-break predictions about future experiments, but suppose it continues surviving.

then (and that is a lot to assume) we still only have a model of spacetime!

it is a different enough continuum that everything (quantum field theories) built on it will have to be radically different. It is not the rigid framework that field theories are used to. It is not a smooth manifold with differentiable coordinate maps. It is very rough and jagged at small scale, somewhat fractal looking, although conventional looking at large scale.

What will the standard particle model look like when rebuilt on CDT's new spacetime continuum?

AFAIK this continuum only exists as a limit of triangulations, as a limit of a sequence of finer and finer simplicial, jaggy approximations to it. or an idefinite quantum cloud thereof.
(reminiscent of how sqrt2 only exists as limit of closer and closer approximations by a series of wholenumber fractions i.e. rationals) what will field theory look like built on that kind of thing?

I suppose one would have to build the matter field up in stages too, define it on the jaggy triangly approximations and then pass to the limit as the simplexes shrink down finer and finer.

 

[selfAdjoint]

But assuming all that gets done. And suppose it continues to check out OK and be at least consistent with what has already been observed. that still leaves the real hard testing with make-or-break predictions about future experiments, but suppose it continues surviving.

then (and that is a lot to assume) we still only have a model of spacetime!

it is a different enough continuum that everything (quantum field theories) built on it will have to be radically different. It is not the rigid framework that field theories are used to. It is not a smooth manifold with differentiable coordinate maps. It is very rough and jagged at small scale, somewhat fractal looking, although conventional looking at large scale.

What will the standard particle model look like when rebuilt on CDT's new spacetime continuum?

AFAIK this continuum only exists as a limit of triangulations, as a limit of a sequence of finer and finer simplicial, jaggy approximations to it. or an idefinite quantum cloud thereof.
(reminiscent of how sqrt2 only exists as limit of closer and closer approximations by a series of wholenumber fractions i.e. rationals) what will field theory look like built on that kind of thing?

I suppose one would have to build the matter field up in stages too, define it on the jaggy triangly approximations and then pass to the limit as the simplexes shrink down finer and finer.

These are very pertinent concerns, that would apply with only slight rewording to LQG too. The original superstring program was more direct, to uniquely postdict GR-like gravitation AND the standard model at low energies out of the same underlying theory. But that enterprise seems currently not to be working (I don't think it's appropriate to junk string theory yet, though!) Even if Thiemann's Phoenix Program comes through with flying colors, it will still not uniquely determine particle physics, at least I don't see any signs in his papers that it will.

Currently I am looking for a corresponding all-in-one development from some combination of non-commutative geometry, Kea's informational categories, Kneemo's Jordan algebras, and whatever else. It is more and more borne in on me that spacetime is no more to be taken as like what we intuit about it than matter has turned out to be.

 

[marcus]

It is more and more borne in on me that spacetime is no more to be taken as like what we intuit about it than matter has turned out to be.

If you insist that your spacetime model start off by reproducing the Standard (Matter) Model then I wish you luck selfAdjoint

I picture progress as more apt to occur in stages----first getting a quantum dynamics of spacetime, then constructing particle physics on that basis.

It would be a happy surprise if some smart person were to skip the first stage and get an All-In-One, but i don't expect this to happen.

I hope that a good quantum spacetime dynamics (still with only token generic matter, not the full gamut of particles) will inspire changes in how quantum field theory is done and revolutionize the Standard Model by requiring it to be built on the basis of a new continuum.

And so I see the emergence of a new spacetime in CDT as promising, in fact as an important development.

By contrast, you seem to be watching a mixed assortment of bids for an All-In-One, assuming I understand you correctly.

It's certainly wise to diversify one's bets. since you gave a list of your favorite hopefuls, let me fetch a link to a different list----which I would guess include several Hermann Nicolai picks: the topics to be covered in the Loops 05 conference

 

[marcus]

...By contrast, you seem to be watching a mixed assortment of bids for an All-In-One, assuming I understand you correctly.

It's certainly wise to diversify one's bets. since you gave a list of your favorite hopefuls, let me fetch a link to a different list----which I would guess include several Hermann Nicolai picks: the topics to be covered in the Loops 05 conference

responding to selfAdjoint list of prospects, I will list somebody else's list of picks. Keeping open to diverse avenues of progress is essential. The Loops 05 conference

http://loops05.aei.mpg.de/

has these topics:

1. Background Independent Algebraic QFT
2. Causal Sets
3. Dynamical Triangulations
4. Loop Quantum Gravity
5. Non-perturbative Path Integrals
6. String Theory

Thomas Thiemann's Master Constraint Program ("Phoenix") which selfAdjoint referred to is not specifically mentioned and Thiemann is not on the list of invited speakers. (He will surely be speaking and could still be added to the list of plenary invited talks, but as of now has not been.)

I see that the Loops 05 has been added to quite recently! In the past couple of days even. It now has a list of participants who have registered so far---this includes others besides the invited speakers.

What to make of the differences in perspective? selfAdjoint has one list and Hermann Nicolai (director in charge of QG and Unified theories research at AEI) has a different list. Not too much can be made! It is just people's different perspectives.

 

[selfAdjoint]

My point is that a program which merely adds matter to some gravitational theory, like one that merely tacks gravity onto a preexisting particle theory, smacks of epicycles. Surely this is not what Einstein meant by the secrets of the Old One? Sure it's a harder row to hoe, but how can we really be statisfied with less in the end?

 

[marcus]

My point is that a program which merely adds matter to some gravitational theory, .. smacks of epicycles.

and that is a good point! I heartily share your distaste for epicycles.
what I imagine is that QFT and Std Mddle will be fundamentally transformed by the shock of encountering a new kind of spacetime continuum.

(with a completely new structure and even different dimensionality at short range)

these venerable antiques (QFT Std Mddle) were built on Minkowski space. Now if they are to be reconstructed on a foundation that is not even a differentiable manifold it is likely to change them in ways we cannot begin to anticipate.

the image of "tacking on" as one would stick on an epicycle, hardly seems to fit what is under discussion, or?

 

[Kea]

It is more and more borne in on me that spacetime is no more to be taken as like what we intuit about it than matter has turned out to be.

Beautifully put, selfAdjoint!

At present I am working hard, knowing that the Streetfest is only a few weeks away. After that there is a short Categories workshop and then the NCG school is after that. Can't wait!

 

[Chronos]

I realize this is a simplistic view, but I perceive a hierarchical emergence of the macroscopic universe. Spacetime emerged before matter, so it seems logical to try approaching the problem using spacetime as the canvas and matter as the paint.

 

[marcus]

...hierarchical emergence of the macroscopic universe. Spacetime emerged before matter, so it seems logical to try approaching the problem using spacetime as the canvas and matter as the paint.

sure makes sense to me
by analogy in first year calculus you meet functions y = f(x) defined on the x-axis or some other set

the first thing you need to understand about such a thing is its domain of definition. If it is defined on the x-axis or on the real line, then what is that? What are the real numbers and the axis.

Not to get philosophical, you have to know is this function defined on the line or on the plane or a region of xyz space, or what?

After that you can talk about the specific properties of the function---is it positive or negative increasing decreasing, continuous or not, does it have a derivative, does it have some formula or solve some equation.

A MATTER FIELD IS LIKE A FUNCTION y = f(x) defined on some domain of definition which is spacetime.

THE FIRST THING YOU HAVE TO KNOW is about that domain of definition. What is that spacetime continuum that the fields are defined on?

Till now a lot of us thought it was a differentiable manifold with some fixed whole-number dimension. All the matter fields were defined on that sort of thing. Now it looks like it might NOT be.

this is bound to have a deep effect on how matter fields are eventually defined, namely what they are defined on. seems simple enough.

canvas and paint puts it well!

 

[Terry Giblin]

How does one get an invite to an Physics Conf.

Can I start by thanking Marcus, for introducing me to CDT.

Last year, if I had known I would have tried to discuss this topic it when I last visited Utrecht.

It appears that CDT and CFD both use 3 as their primary parameter and produces a shape similar to a diamond shock wave pattern.

So how does one apply to a Physics Conference, the replies I have received todate, is by inivation only, which is fine, but how to I get invited?

Regards

Terry Giblin

 

[marcus]

...
So how does one apply to a Physics Conference, the replies I have received todate, is by inivation only, which is fine, but how to I get invited?
...

Dear Terry, After giving it some seriouss consideration, I would have misgivings about encouraging anyone to attend Loops 05 who hasnt been following the quantum gravity scene for some time as it is likely to be largely technical and scattered around among a number of diverse topics. You are the only one who can judge if it is for you.

Only some (like any talks by Renate Loll) will be sure to be about CDT.
Have you tried reading her papers? I must assume that you have.

In any case if you have decided to try to go then I am puzzled that you could not just register. Did you go to loops05.aei.mpg.de/ and try to register using the registration form provided? I assume that you did, from what you said.

Unfortunately I do not know of anything to do besides the obvious one of filling out and submitting the form.

 

[marcus]

How CDT changes the map of quantum gravity research

... The Loops 05 conference site

http://loops05.aei.mpg.de/

lists these topics:

1. Background Independent Algebraic QFT
2. Causal Sets
3. Dynamical Triangulations
4. Loop Quantum Gravity
5. Non-perturbative Path Integrals
6. String Theory

as a working assumption the Loops 05 conference IS the map of quantum gravity, and these topics suggest how that map looks

and what it looks like to me right now is a trapeze act where Laurent Freidel does an aerial somersault and is caught by Renate Loll who is swinging by her knees upside down.

the topic of this thread is how CDT CHANGES THE MAP OF QG and we should focus back on that and take a fresh look.

it changes it radically and fast. Please have a look at the recent Laurent Freidel paper.

http://arxiv.org/abs/gr-qc/0506067

He basically does spin-foams-with-matter and relates it to other mathematical techniques. Some of the language in this recent paper reminded me of CDT. It was like Freidel was extra aware of how his 3D spin foams work might connect with 3D Loll-type simplex gravity. In both Freidel and Loll's case it has been very important to work things out in 1+1D and 1+2D as a guide for what to do and expect in 1+3.

Freidel co-authors have included people at Perimeter such as Artem Starodubtsev, David Louapre, Etera Livine, Lee Smolin, and others such as Kirill Krasnov, Kowalski-Glikman, Carlo Rovelli (his PhD thesis advisor if I remember right), and now in this latest paper two Cambridge people Daniele Oriti and James Ryan

It will be interesting to see if Loll actually catches Freidel or whether they miss and he falls into the net.