Why CDT changes the map of quantum gravity

[marcus]

I happen to think it does. I will try to say why in this thread.
Other people may very likely disagree, so it is possible to have discussion about this.

you can get most of CDT out of two basic papers
"Dynamically..." and "Reconstructing..."
the links are in my signature. I will copy them in for the convenience of anyone who wants to look over the papers.

I have to go to a choral rehearsal tonight (our dress rehearsal for an upcoming concert!) so I won't be able to do much with this thread. but anyone who wants to say why they think CDT is NOT a significant development---a promising new approach to quantum gravity that changes the map somewhat---they are welcome to get started expressing that opinion already

 

[Kea]

I have to go to a choral rehearsal tonight (our dress rehearsal for an upcoming concert!)

I believe CDT may be significant in convincing people that most, naive approaches to QG are way off target. However, as we are discussing in the other thread, it cannot be fundamental by any stretch of the imagination because it inputs no new fundamental physics. The idea of dynamical dimension is not the sole preserve of CDT.

What are you going to be singing? I once sang in the Bach Mass in B minor - highlight of my brief choral career.

Cheers
Kea

 

[marcus]

Yeah, here are those two links:
"Dynamically..."
http://arxiv.org/hep-th/0105267

"Reconstructing..."
http://arxiv.org/hep-th/0505154

when I say changes the map I partly mean subjectively---my perspective on QG---but I also mean objectively in how agendas of major conferences shape up

I recently compared the list of topic, and speakers, and talks from some recent QG conferences----partly from memory and partly by just looking on line

like there was October 2003 "Loops meets Strings" at Potsdam
and Rovelli's May 2004 conference at Marseille that you could unofficially call "Loops 04"
and there is the upcoming October 2005 conference again at Potsdam, called "Loops 05"

Looking at the list of invited speakers, and the posted list of topics that Loops 05 is to focus on, you can see a much bigger CDT presence. it is a fairly abrupt change. we should try to see why. that is partly what this thread is for in case others might be interested

BTW I went back over those two basic papers and realized that the earlier one is needed in order to understand the later. they didnt repeat very much. so it is very hard to try to read Reconstructing without having Dynamically at hand to look up things in.

maybe i can try doing some explaining if anyone wants to read the two basic papers of CDT and has questions. I certainly don't know everything, only understand a part, but still conceivably may be able to help someone over some stickyplaces (again assuming there is some interest in this)

 

[marcus]

What are you going to be singing? I once sang in the Bach Mass in B minor - highlight of my brief choral career.

highlight of everybody's, the greatest

I've sung it twice, once with Robert Geary of the San Francisco Choral Society (with an orchestra of period instruments but big deal who cares about that, a violin is a violin). Geary is an exciting director.

try it a second time.

I have to practice now. see y'all tomorrow

 

[marcus]

Daniel Boorstin a US historian and writer of books died last year (1914-2004). He was director of the Library of Congress 1975-1987.

He said:

The greatest obstacle to discovery is not ignorance,
but the illusion of knowledge.

Richard Feynman said something to the effect that a physicist doesn't understand anything until he can explain it to his mother. My first topology teacher in grad school was John Kelly, a beautiful man and a wonderful teacher. He said that a mathematician only really understands something if he can explain it to the guy on the street. I think it must be a common folk saying. Maybe some people say that you should be able to explain it to someone waiting with you at a bus stop.

I suspect that here at PF at this moment the most challenging symbolic layman waiting at the bus stop is Spicerack. The bus stops at Spicerack. Well. Well we can always give up. AFAIK Spicerack does not need or want to have CDT explained. But one can imagine doing it, to estimate the challenge.

CDT is rather ordinary. constructed of unpretentious materials with commonplace tools. No big revelations like the universe having extra dimensions that are rolled up. or that we ride on Branes that gravity leaks out of and that crash into each other. People seem to want to wowed, or expect physicists to wow them. CDT doesn't even have anything in it as romantic as the spin networks of Loop quantum gravity!

As the authors say in hepth/0505113 on page 2, CDT "exhibits neither fundmental discreteness nor indication of a minimal length scale." Even those minor headlines are denied us. there is nothing to scream at people.

People seem to like to be told counterintuitive things by scientists, like wow the universe has halfdozen rolled up dimensions that you can't see, like wow who would have thought that! It looks like just 4. It looks to me like CDT is not well furnished with counterintuitive attention-grabbers like that.

The story is more like this: most of physics is based on DiffManifs which is a continuum with smooth coordinate functions, and there is this other kind of continuum called a PL-manifold that has no coordinate functions (you could put ones on by hand but they would have creases and kinks).
A PL-manifold is composed of simple building blocks. Let's call them blox. Blox are roughly speaking triangle or pyramid shape.

In CDT the blox ARE ALL THE SAME SIZE. Let's call a PL manifold that is triangulated with blox all the same size a "triangulated continuum". You study such a continuum, and calculate things about it, and say things about it, by COUNTING THE BLOX. Like, count all the blox that share a certain side or edge. If it is the number you expected then the manif is flat and if it is different then the manif is not flat: it is curved.

Ordinary DiffManifs that most of physics is built on were invented in 1850 by Riemann (or maybe Gauss did, but he was secretive at times).

I don't know when the PL-manifold was invented but in 1950 Tulio Regge discovered how to express Einstein's Gen Rel equation using simplices. But his blox were not all the same size and shape. So he calculated using the lengths of the edges. Later, like in CDT, you calculate stuff just by counting blox because they are all the same size.

for about 20 years people like Ambjorn have been trying (say since 1985) to implement quantum spacetime dynamics using triangulated continuums (to approximate the real spacetime)
because it is mathematically real obvious that you ought to try to do that. But for years it did not work because when you put it in the computer the continuum would crumple up or feather out and be the wrong dimension.

In 1998 Ambjorn got together with Loll and the two figured out that the continuum should be approximated by a LAYERED TRIANGULATED CONTINUUM.

one reason that back in 1998 one might have thought that is if you know any cosmology you know that all cosmologists use the FRW metric to describe the universe and have used virtually nothing but that for 80 years or so (the cliche open and closed universes are just different versions of the FRW metric that solves the Friedmann equations with various settings). And any Friedmann cosmology, any solution of the basic cosm. eqn., with a FRW metric is LAYERED. It has spacelike slices piled up in a causal or timelike ordering.

 

[Mike2]

The story is more like this: most of physics is based on DiffManifs which is a continuum with smooth coordinate functions, and there is this other kind of continuum called a PL-manifold that has no coordinate functions (you could put ones on by hand but they would have creases and kinks).
A PL-manifold is composed of simple building blocks. Let's call them blox. Blox are roughly speaking triangle or pyramid shape.

In CDT the blox ARE ALL THE SAME SIZE. Let's call a PL manifold that is triangulated with blox all the same size a "triangulated continuum". You study such a continuum, and calculate things about it, and say things about it, by COUNTING THE BLOX. Like, count all the blox that share a certain side or edge. If it is the number you expected then the manif is flat and if it is different then the manif is not flat: it is curved.

Ordinary DiffManifs that most of physics is built on were invented in 1850 by Riemann (or maybe Gauss did, but he was secretive at times).

I don't know when the PL-manifold was invented but in 1950 Tulio Regge discovered how to express Einstein's Gen Rel equation using simplices. But his blox were not all the same size and shape. So he calculated using the lengths of the edges. Later, like in CDT, you calculate stuff just by counting blox because they are all the same size.

for about 20 years people like Ambjorn have been trying (say since 1985) to implement quantum spacetime dynamics using triangulated continuum
because it is mathematically real obvious that you ought to try to do that. But for years it did not work because when you put it in the computer the continuum would crumple up or feather out and be the wrong dimension.

In 1998 Ambjorn got together with Loll and the two figured out that the continuum should be a LAYERED TRIANGULATED CONTINUUM.

As I understand it, the "blox" are isomorphic to DiffMorphs. And Ambjorn, et al, are assuming that the blox extend to infinity. But if spacetime is a result of some process, as they suppose, then it also had a beginning that must have been very small, a singularity. I think we should consider what happens as the universe first began. The manifolds that the blox approximate would have curled up, cyclic dimensions. At that scale there could not have existed yet dimensions we could assume to extend to infinity. OK, if that is so, then at the earliest stages, perhaps the blox can be replaced with the original closed manifolds and the integration reduce to global topological concerns, perhaps some index theorm could be used instead of numerical computations. Then we could consider the case as the closed manifolds grow to infinity. Perhaps this would be easier.

 

[marcus]

As I understand it, the "blox" are isomorphic to DiffMorphs. And Ambjorn, et al, are assuming that the blox extend to infinity. But if spacetime is a result of some process, as they suppose, then it also had a beginning that must have been very small, a singularity. I think we should consider what happens as the universe first began...

they do consider it. their computer simulations show a "stem" where the size of the U was minimal, and then the U expands

read the papers, Mike, there is a nice short one called "the emergence of a 4d world" Look at figure 1.

they do not suppose that the simplex building blocks are real but only tools of mathematical analysis
so when the universe is small it does not have to contain "curled up" simplexes ready to open like rose buds ready to blossom or something.

the simplex is not there. you just put it in, as needed, to do the math

 

[Mike2]

they do consider it. their computer simulations show a "stem" where the size of the U was minimal, and then the U expands

read the papers, Mike, there is a nice short one called "the emergence of a 4d world" Look at figure 1.

Yes, I will have to read the paper some day soon. But I think you miss my point. If the integration on closed manifolds can be realated to global topological properties, then the numerical integration can be eliminated in favor of something more analytical. Then perhaps the necessity of a metric to begin with can be derived as being needed to do the integration which is equal to the topological properties.

 

[marcus]

can be replaced with the original closed manifolds and the integration reduce to global topological concerns, perhaps some index theorm could be used instead of numerical computations. Then we could consider the case as the closed manifolds grow to infinity. Perhaps this would be easier.

I did not miss the point of this so much as simply did not respond.
there is no original closed manifold to integrate over
the integral is essentially over the space of all metrics. the integral wants to be taken over an infinite dimensional space of all geometries.

if you simply look at page 2 of hep-th/0105267 you will see this huge integral over the space of all diffeo equivalence classes of metrics. It is a formal integral that one really does not know how to do. so, as you can see on page 2, it is replaced by the analogous sum over all possible triangulations.

however the space of all possible triangulations is also very large.

so we are not integrating over some nice manifold where there are index theorems to use! and known topologies already classified, we are integrating (or summing) over what they call "the mother of all spaces" or the "space of all geometries". it is a bear

the montycarlo approach is a rather elegant, and in this case cleverly implemented, strategy to permit what would not be possible by other known means.

it really is not fair for you to ask questions like that which you would know the answer of if you would just read page 2 of a basic paper.

Yes, I will have to read the paper some day soon. But I think you miss my point. If the integration on closed manifolds can be realated to global topological properties, then the numerical integration can be eliminated in favor of something more analytical. Then perhaps the necessity of a metric to begin with can be derived as being needed to do the integration which is equal to the topological properties.

Yes please do read, even if just the first 4 or 5 pages of these basic papers such as hep-th/0105267.
No I did not miss your point. the integral is over a space of geometries, or (if they are represented as equivalence classes of metrics) over a space of equivalence classes of metrics. or think of it as integrating over a space of spaces. Index theorems and topological properties of closed manifolds don't appear to apply.

 

[marcus]

the basic reason CDT changes the map

the root cause why CDT changes the map of quantum geometry (and therefore quantum gravity)

is that CDT introduces a fundmentally new idea of the continuum as a limit of quantum theories of simplicial manifolds

and this new model continuum is something that YOU CAN CALCULATE WITH and get a computer to crank out and experiment with. so it is a workable hands-on new type of continuum, not a purely abstract la-di-da.

so we here at PF need a convenient name for the CDT continuum and I will try calling it "the quantum continuum" (many layfolk do not like the word manifold, I am told that Einstein himself preferred to say continuum, and the word "manifold" already biases things in favor of stuff with coordinate functions and signature metrics anyway so it is a verbal ball and chain)

the way you calculate stuff with the CDT "quantum continuum" is you fix a length 'a' and you calculate whatever it is you want to know in an APPROXIMATE WORLD that is triangulated with simplex blocks with spatial edge-length 'a'.

and then you reduce 'a' to be a shorter length, and you repeat the calculation and calculate whatever it is you want to know in a better approximation triangulated world, with smaller 'a' length

and then you reduce 'a' some more and repeat----and then you imagine letting 'a' go to zero.

IN PRACTICE, in the CDT computer experiments, this letting 'a' go to zero simply corresponds to running the experiment over again using a larger number of building blocks in the computer. they run things with 100 thousand, and then they run things with 360 thousand and compare results. if the results are nearly the same, then probably using more computer time and running things with 500 thousand blocks is not going to make a dramatic difference. Anyway that is what it means in practice for 'a' to go to zero.

the new CDT "quantum continuum" is not a vintage 1850 differential manifold or some familiar variant of that idea like a pseudo-Riemannian manifold.

the "quantum continuum" is not even a classical thing at all because it has uncertainty built in, not only in it but at the level of each approximation

Let us forget about taking the limit as 'a' goes to zero, which is something of a formality, and just pick one small 'a' where we know that the approximation is going to be good enough for present purposes and the triangulated thing will behave fairly much like the limit. So then we look at that one approximation-----corresponding to, say, putting a third of a million simplex blocks into the computer.

this approximating continuum is already NOT CLASSICAL, because whenever we calculate anything about it we SHUFFLE THE DECK using randomly chosen montecarlo moves
so the spacetime that results is really a piecewise flat PATH INTEGRAL.

the "path" is the spacetime itself, it is not a particle path living inside some larger fixed classical manifold. the "path" is the evolution of space itself, of which there is nothing outside. but otherwise it is pretty analogous to a Feynmannian path integral.

and you can argue all day about details about doing the path integral and how to shuffle the cards and you can compare results of various shuffling methods etc etc. but the basic thing to notice is that THE TRIANGULATED APPROXIMATION TO SPACETIME IS ITSELF A QUANTUM THEORY.

BTW, this is kind of interesting as a detail. The CDT authors use "sweeps" of one million Monte Carlo moves. when they want to get from one configuration to the next they do a "sweep" of one million randomly chosen modification of the simplexes in a random chosen location. this is one shuffling of the deck.

well, that is how they happen to do it. If you were programming it in your school's computer you could decide to make a "sweep" be two million Monty moves or half a million Monty moves. The moves are supposed to be ergodic in the sense that repeating them in random order and location explores the whole world of possible geometries.

the CDT authors sometimes call the world of possible spacetime geometries by the funny name of "the Mother of All Spaces", or sometimes they call it "the space of geometries"----each point in that set is one possible 4D shape of the universe from beginning to end, one possible evolution of geometry from bang to crunch. they show pictures of these things, simplified down to 2D for understandability.

remember we are still working with a fixed small length 'a'
the quantum theory at that level lives in the Mother space of geometries at the level of that 'a'
if we are not satisfied with the precision of the result, we reduce 'a' to a shorter length and repeat, or we "let 'a' go to zero" in our imagination.

so far, because the computer is finite, they can only use a finite number of spacetime simplex blocks, and so the universe must be a finite spacetime volume, which means it cannot continue expanding forever. it has a crunch at the end. I dislike that limitation, but I suppose that ways will be found to work around it.

Anyway, that is what I mean (at least for now) by the "quantum continuum".

it is a model of spacetime. it is not by any stretch of the imagination a differentiable manifold
it is a quantum theory embodying uncertainty about geometry
it is a limit as 'a' goes to zero
it is a limit of quantum theories of triangulated spacetimes that you can calculate with

it is the basic reason that CDT changes the map

(and also it might be wrong. I would not bother with anything that was not predictive enough to eventually be tested and potentially falsified. Models which cannot be wrong are empty and useless. At this point in history, I don't think anybody can say right or wrong about CDT. All I think it is possible to say honestly is that it changes the quantum gravity map and is interesting.)

 

[RandallB]

so we here at PF need a convenient name for the CDT continuum

How about putting a name to "CDT"
(I guessing it's not Central Daylight Time which would be the same as EST)

I've only gotten into to the first few pages of your links - yet the best guess I can come up with for CDT is "Causal-Dynamic-Triangulation"
Could you give us the real name.

 

[marcus]

...
I've only gotten into to the first few pages of your links - yet the best guess I can come up with for CDT is "Causal-Dynamic-Triangulation"
Could you give us the real name.

that is what the authors call it
actually "Causal Dynamical Triangulations"
good inference on your part RandallB


RandallB, you appear well able to look after yourself and read the papers on your own, but in case anyone else is wondering about the terminology, the "Dynamical Triangulations" approach to quantizing General Relativity goes back to early 1990s at least (probably earlier, I just don't know when it started, maybe you could say it started with Tulio Regge in 1950)

the "causal" part was a 1998 innovation by Jan Ambjorn and Renate Loll.

I will try to parse the technical meanings, in case anyone is interested

TRIANGULATION, a triangulation means dividing a space up into simplexes (a simplex is the generalization of a triangle
0-simplex = point
1-simplex = line segment
2-simplex = triangle
3-simplex = tetrahedron, or trianglebase pyramid

a 4-simplex lives in 4D space and has 5 vertices and 10 edges and 10 triangles and 5 faces, each of which is a tetrahedron)

HERE IS SOME TECHNOSPEAK: minkowskian and lorentzian and causal all mean roughly the same thing and refer to the fact that the 4D "minkowski" space of special relativity has "light cones" in it that define all the forwards timelike and backwards timelike directions from a given point.

an event at some point can only CAUSE an event which is inside its forward lightcone, that is: off in a timelike direction from it.

the other directions (not inside the cones) are spacelike. an event cannot cause another event which is spacelike separated from it----that would involve something traveling faster than light.

Euclidean 4D space has no built-in criterion of causality like that. you cannot divide up the directions departing from a point into the timelike and the spacelike directions. Euclidean space does not distinguish. but minkowski or lorentzian space does.

SO IF YOU TRIANGULATE USING SIMPLEXES CUT OUT OF MINKOWSKI SPACE YOU CAN MAKE A CAUSAL TRIANGULATION.

the idea of causal triangulation is to use simplex building blocks what are made of the 4D space of special relativity, and to lay them down with the same orientation, in LAYERS like, so that the timelike spacelike directions are reasonably CONSISTENT

however it is somewhat counterintuitive in the sense that you can build CURVED things. you do not always end up with something that is all over absolutely flat, even though you are using flat building blocks. you are not building inside of familiar flat space, so you are not as limited in how you can put flat building blocks together (more than 6 equilateral triangles might meet at a point, that is a shock I know, but it happens)

DYNAMICAL: we all know that in 1915 General Relativity the spacetime is dynamical. You do not start with a fixed geometry the geometry arises dynamically from the model-----matter tells spacetime how to bend and spacetime tells matter how to flow. 1915 Gen Rel models gravity by the dynamic geometry of spacetime.

There are two ways to IMPLEMENT 1915 Gen Rel using triangulation. One way is you use a fixed layout of simplexes but let EACH SIMPLEX CHANGE proportions. Let their legs get longer and shorter. this way was discovered in 1950 by Tulio Regge. He called it doing Einstein Gen Rel "without coordinates" because instead of needing to coordinatize all of spacetime with t,x,y,z numbers, you just need to use the numbers which are the lengths of the legs, and you can do your calculation with those.

THE OTHER WAY IS TO KEEP ALL SIMPLEXES IDENTICAL BUT LET THE TRIANGULATION LAYOUT CHANGE so that you get different numbers of triangles meeting at a point (not what you would expect if the space was flat) or you get different numbers of tetrahedrons meeting at an edge.
you get different numbers meeting at places than you expect and so some kind of bending and crinkling and jamming and stretching is happening
and it can all be studied and described JUST BY COUNTING the simplexes.

there is a traditional quantum feel to this method because it is based on whole numbers and is a bit like a blur of different mosaics, or different integer-described states.
The appearance of smoothness can come by blurring together many jagged angular discrete possibilities----so you get to work with integer whole numbers, which is nice, but the overall effect can be smooth-looking, which is nice

the DYNAMICAL TRIANGULATION approach uses a small number of types of identical simplexes. the 4-simplexes, for instance, are two kinds depending on how many spacelike and how many timelike edges. Morally they are all identical cut by the same cookiecutter. but there is two types of orientation so you end up with two distinct shapes, which are then duplicated over and over. and they are fitted together

the CAUSAL part is that all the cookies are cut out of minkowski space so they have this idea of causality built into them, of one event being timelike later than another so that it can be causally influenced by it.

so that is my take on what CDT means

 

[Mike2]

that is what the authors call it
actually "Causal Dynamical Triangulations"
good inference on your part RandallB


RandallB, you appear well able to look after yourself and read the papers on your own, but in case anyone else is wondering about the terminology, the "Dynamical Triangulations" approach to quantizing

Well, I finally read the first 4 or 5 pages. Too many prerequisites. Thanks for your explanations. Are you checking your interpretation with the originators?

SO IF YOU TRIANGULATE USING SIMPLEXES CUT OUT OF MINKOWSKI SPACE YOU CAN MAKE A CAUSAL TRIANGULATION.

the idea of causal triangulation is to use simplex building blocks what are made of the 4D space of special relativity, and to lay them down with the same orientation, in LAYERS like, so that the timelike spacelike directions are reasonably CONSISTENT

So it sounds like they are dealing with 4D only. I don't see where they get scale dependent dimension.

however it is somewhat counterintuitive in the sense that you can build CURVED things. you do not always end up with something that is all over absolutely flat, even though you are using flat building blocks. you are not building inside of familiar flat space, so you are not as limited in how you can put flat building blocks together (more than 6 equilateral triangles might meet at a point, that is a shock I know, but it happens)

...

There are two ways to IMPLEMENT 1915 Gen Rel using triangulation. One way is you use a fixed layout of simplexes but let EACH SIMPLEX CHANGE proportions. Let their legs get longer and shorter. this way was discovered in 1950 by Tulio Regge. He called it doing Einstein Gen Rel "without coordinates" because instead of needing to coordinatize all of spacetime with t,x,y,z numbers, you just need to use the numbers which are the lengths of the legs, and you can do your calculation with those.

One thing confuses me. They talk about space of all possible geometries, indicated by various metrics. But they don't talk about the matter required to get those curved geometries approximated by flat simplexes. Is this a flaw in their argument?

 

[marcus]

One thing confuses me. They talk about space of all possible geometries, indicated by various metrics. But they don't talk about the matter required to get those curved geometries approximated by flat simplexes. Is this a flaw in their argument?

in several of their papers they add matter to the model and show how they do it

there get to be extra terms in the Lagrangian, and so different weightings when they add everything up, and so different results

they are having to catch up in 4D now with work they did already in 2D and 3D, so far as I know there is not any 4D paper yet with matter included

AFAIK it is not a flaw because the spacetime path integral can include ANY possible shape
just like a Feynman particle path integral can have the particle going all over the place
the weightings are set up so that when you add it all together the unlikely stuff cancels out

 

[marcus]

So it sounds like they are dealing with 4D only. I don't see where they get scale dependent dimension.

the dimension of the simplexes does not determine the outcome of the resulting spacetime

many people have worked on DT (AJL are noteworthy because of recent breakthroughs) for nearly 20 years, for most of the time a major problem was the resulting dimensionality was not well behaved, no matter what buildingblock dimension the resulting dimension could be all over the place. they finally seem to have it under control

 

[Chronos]

I'm in a kind of wait and see mode for now. I agree with Kea it is not revolutionary. But the approach taken by AL is very interesting and worth following. Lee Smolin was kind enough to comment on a naive question I had about CDT, and said he thought it was promising. That's good enough for me.

 

[marcus]

... Lee Smolin was kind enough to comment ... and said he thought it was promising...

pleasant news, thanks for keeping us in the loop

 

[marcus]

from wolram "where you going" thread

We need a good self-contained CDT thread. I will steal a couple of posts from wolram's thread, as selfAdjoint suggested be done from "third road" to flesh out the new "what NCG is" thread

Where is loop quantum gravity going?...

it is always a mistake to try to predict research, but since you ask I will try

right now it is extremely urgent for LQG to link up with
Renate Loll CDT-----the "triangulations" approach to quantum gravity that uses assemblages of "simplex" building blocks to approximate spacetime

it possibly a year of crisis, and change, in LQG
it will be fascinating to see how things sort out at the October 2005 conference
there are even some fights brewing, or serious rivalries

it has come time now for the full LQG theory to be applied to cosmology.
the LQC of Martin Bojowald was a simplified version of the full theory (assuming the universe is uniform and looks roughly the same in all directions) and LQG got several dramatic results in the period 2001 to 2004.
now they have to drop the simplifying assumptions and apply the full apparatus to cosmology and see if they can duplicate or modify those results. there may be fights (involving Bojowald and Thiemann) about this. but I think that Bojowald is basically a gentle mild personality who will not want to be quarreling, so it may not come out in the open.

I think we can ignore the fracas over cosmology. it will follow well-established lines and come eventually to some satisfactory resolution with more in the way of testable predictions.

What is much more explosive and unpredictable is the collision or merger between LQG and Loll's "triangulations" approach. this is even slightly scary to me.

I think Loop people should make every possible effort to learn and assimilate CDT which I think has some new mathematics contained in it.

sometimes the new mathematics comes from the humble applied grass roots and not from the monumental mathematically topheavy abstract oak trees.
CDT is basically 3 people who found out how to run simulations of the universe.

Bianca Dittrich has been Thomas Thiemann's righthand assistant for 2 years or so and has rendered him very valuable assistance on his Core-LQG program to construct official LQG dynamics. she is very smart. it would be a great blow to Thiemann to lose Dittrich as his assistant. But there are not enough smart people to go around. Suppose Bianca were to go over to the "Triangulations" group at Utrecht? Then there would be 4 CDT people

Wolram, people go back and forth between core-LQG and CDT. The theories involve similar kinds of thinking (but some different symbols or formalism). It might not be too hard for them to assimilate each other. But I absolutely cannot see how this would happen, at the mathematical level. Only at the human level

What is much more explosive and unpredictable is the collision or merger between LQG and Loll's "triangulations" approach. this is even slightly scary to me.

i have tried to follow this, but having just grasped some inkling of what
spinfoams are, the math seems to take a quantum leap in some other
direction, and left me, and I am sure others gasping for breath.

all that means is you are trying to assimilate too much in a hurry.

you already have some grasp of ordinary LQG and (you say) spin foams.


"Triangulations" (Loll style) is a bit like spin foams but here is a difference.

spin foams are mapped or projected or imbedded into some surrounding 4D continuum (technically a differentiable manifold, damn George Riemann for making up such a clumsy name for it)

spinfoams are made of pieces (triangles and stuff) that "live" in some surrounding t,x,y,z space

In Loll-style, the blocks don't live in a surrounding manifold. They ARE it. You use a whole lot of identical building blocks (actually two kinds, slightly different, think of them as male and females, but otherwise identical) and the assemblage of all these block IS the spacetime.

technically there is a topological space R x S³ which the union of this assemblage of half a million blocks is supposed to equal, but the topological space has no differential structure, no calculus to it, just a formality.

morally and intuitively the assemblage of glued together blocks is the space itself.

and then two things happen
1. you consider all the other ways the blocks could be glued together and you get this fantastic blur, this swarm of possible geometries. (they invented a "shuffling" process in the computer that imitates this blur)

2. you imagine reducing the size of each block and increasing the number of blocks, and you make this quantum swarm of geometries, getting finer and finer, APPROXIMATE the real spacetime you want to know about.

that is it,

so the upshot is that WHEN IT COMES TIME TO CALCULATE you can accept a finite degree of approximation and use enough blocks of sufficiently small size and simply don't worry about going to the limit. You just calculate with some finite degree of precsion. And then, all you need to consider is this assemblage of blocks!
And it turns out that Loll and the others figured out how to calculate like demons with that assemblage, they can calculate stuff to beat the Dutch, oh my mistake, they ARE the Dutch.

for this reason it is cannot be permitted for core-LQG not to make contact with this little project they have at Utrecht.

 

[marcus]

What Quantum Gravity is

the question came up in another thread what features should a satisfactory QG have?
or how should QG be defined in the first place, leaving satisfactory to be decided later

in my judgement the clearest QG thinker, the keenest QG mind, of the QG people under 40 years old, that would be Renate Loll

Laurent Freidel, at Perimeter, is also smart and creative and productive, but Renate has the exceptional combination that besides being a fine mathematician she writes extremely clear English. she is the best expository writer in the whole under-40 bunch.

So I am prepared to at least try out what Renate says about QG.

BTW John Baez says he met Renate around 1990 when she was traveling with conferences with Abhay Ashtekar and doing Loop. Not long after that Renate got a neat result about the volume operator of LQG which surprised Smolin and Rovelli. I have enormous respect for both Smolin and Rovelli but she out-mathematixt them both in an elegant and nontrivial way. So Renate does not just do Triangulations. She knows the whole QG field very thoroughly and has researched in several approaches and thought big picture. this is one reason why it shakes me up some to see her going (not with string, not with loop, not with anybody's royal high algebra, but) with triangulations. Renate has the vision and experience and power to do creative work in any department of Quantum Gravity she picks.

So I guess I will take her definition, out of the lecture notes she prepared for her graduate students and prospective research colleagues

http://arxiv.org/hep-th/0212340

She made some lecture notes dated January 2003. Often lecture notes aimed at the grad student level, afford easier entry to a subject than you get with a journal article.

 

[RandallB]

it possibly a year of crisis, and change, in LQG
it will be fascinating to see how things sort out at the
"October 2005 conference"
there are even some fights brewing, or serious rivalries

Referring to "October 2005 conference"
What is it? Where is it? Who is in it?

I don’t suppose they have an area for spectators.
With some serious rivalries going, and the chance for a fight or two brewing, it sounds like an exciting event for some interested amateurs to watch from behind the safety of the sidelines.

RB

 

[marcus]

Referring to "October 2005 conference"
What is it? Where is it? Who is in it?

Hi Randall, there is a thread here about it, called Loops 05. I'll fetch a link

this is a thread about Loops 05
https://www.physicsforums.com/showthread.php?t=74889

here are links to the conference site
http://loops05.aei.mpg.de/index_files/Home.html

http://loops05.aei.mpg.de/index_files/Programme.html

 

[marcus]

I don’t suppose they have an area for spectators.
With some serious rivalries going, and the chance for a fight or two brewing, it sounds like an exciting event for some interested amateurs to watch from behind the safety of the sidelines.

Academics tweak each others noses while maintaining courteous poses.
If you are looking for real fistfights, it will seem lacking
however in a May 2005 paper (leading up now to the conference)
Renate Loll has just referred to Loop Quantum Gravity as
"so-called loop quantum gravity" and stuck her desert-knife between its ribs.

here is from page 2 of hep-th/0505113

"Slow progress in the quest for quantum gravity has not hindered speculation on what kind of mechanism may be responsible for resolving the short-distance singularities. A recurrent idea is the existence of a minimal length scale, often in terms of a characteristic Planck-scale unit of length in scenarios where the spacetime at short distances is fundamentally discrete. An example is that of so-called loop quantum gravity, where the discrete spectra of geometric operators measuring areas and volumes on a kinematical Hilbert space are often taken as evidence for fundamental discreteness in nature [1, 2]. Other quantization programs for gravity, such as the ambitious causal set approach [4], postulate fundamental discreteness at the outset."

the word "speculation" in these circles is a bronx cheer.
Renate's approach (Triangulations) does not suppose a minimal length scale in nature, which however is something of an obsession or cliche or unsubstantiated belief in some other approaches.
All the people she cites here are prominent figures who will be invited speakers at Loop 05. [1] is Lee Smolin, [2] is Abhay Ashtekar, [3] is Jerzy Lewandowski (with Okolow, Sahlmann, Thiemann) and [4] is Rafael Sorkin.

From a strictly logical viewpoint the Loop people she cites are stretching it to suggest a fundamental discreteness to space because there are other ways to interpret the discrete spectrum of LQG area and volume operators.
She has caught them all over-interpreting their results. Except for Sorkin, who just assumes spacetime discreteness.

She hasnt said anything rude, she has just let them know that she COULD.
these are longtime friends I believe, but quite a bit of serious stuff is on the table.

here, on page 2 of another recent paper hep-th/0505154 she touches a sore point---the scarcity of explicit predictions, and some elusiveness about LQG dynamics (its hamiltonian constraint is not finalized):

"At the same time, it becomes a nontrivial test for such nonperturbative theories of quantum gravity whether they can reproduce the correct classical limit at sufficiently large scales. However, using this as a consistency check to discriminate between good and bad candidate theories is in practice complicated by the fact that some explicit results about the quantum dynamics of the proposed quantum gravity theory must be known. For example, this is not yet the case in loop quantum gravity [2, 3, 4] or in four-dimensional spin foam models for gravity [5]."

Here Renate italicized the word some, politely indicating that they have none at all.

If I were lucky enough to be in the visitor gallery, I would be enjoying it.
But I admit it might seem rather tame, if one was expecting something more like a barroom brawl.

well it is still early, maybe things will pick up

 

[RandallB]

Academics tweak each others noses while maintaining courteous poses.
If you are looking for real fistfights, it will seem lacking

Thanks for the links, does look exciting - I found
http://www.panic2005.lanl.gov/
A (particle, nuclear, and astrophysics) conference here in the States during October as well.

I’m guessing Loop vs. CDT might be more exciting, but still need a good commentator to advise the visitor’s gallery the difference between polite seated applause after a speech. Meaning, OK, good job, so you scored a point. Compared to the same polite applause only standing with quite whispers of ‘noble, noble’. That being equal to a two-minute scream of “Goooooooooal” as all stood and stomp on their seats until the bleachers break. Hard to spot the difference at a physics meeting, but wouldn’t it be great to be there for the moment.

I guess to really feel the excitement you’d need to get involved, but oh my, what heavy weights to go up against. So far, I’d lean towards CDT.

RB

 

[marcus]

I’d lean towards CDT.

RB

Definitely, even tho it is 100 researchers against a handful, like 4 or 5.
I will try to find a snapshot of Renate Loll (I'd say she was the forward and Ambjorn the goalie)

Here she is by herself at the 2004 Marseille Loop conference
http://perimeterinstitute.ca/images/marseille/marseille011.JPG

Here she is out for a walk with Julian Barbour, a senior English QG guy.
http://perimeterinstitute.ca/images/marseille/marseille103.JPG

Here she is being a bit doubtful about what Thomas Thiemann is saying
http://perimeterinstitute.ca/images/marseille/marseille028.JPG

 

[Mike2]

Definitely, even tho it is 100 researchers against a handful, like 4 or 5.
I will try to find a snapshot of Renate Loll (I'd say she was the forward and Ambjorn the goalie)

It seems CDT still leaves open the questions: why the path integral, why the action integral, why the Lagrangian, why 4D. These have to come from some more fundamental concerns than simply that they work in particle physics; that's no explanation for something more basic than particle physics. So I don't think CDT can be a candidate for a TOE. It leaves open too many questions.

 

[marcus]

... So I don't think CDT can be a candidate for a TOE. It leaves open too many questions.

you are quite right, I think.

CDT is candidate for modeling the quantum continuum PLATFORM on which a full theory of matter may be built

At the present time there is no quantum theory of spacetime and theories of matter like Std Mddle are built on inadequate substitutes like rigid flat
Minkowski space
or smooth manifolds (so-called C-infinity, infinitely differentiable coordinate charts)

or some may be castle-in-the-air fantasies built upon no foundation spacetime at all, but floating in abstract algebra.

At the present time only comparatively few researchers seem to have focused on the obvious need for an adequate PLATFORM to build "TOE"-like theories on. there needs to be an adequate quantum model of spacetime FIRST and then the structures built on top of it (to describe matter) will not keep falling apart.

Ambjorn and Loll are not so naive that they would be working on a candidate "TOE". By now the TOE dream is a wild goose chase and a bunch of hype. the generation of guys that once seriously thought they could do that in the context of differential geometry, without first re-inventing spacetime, are now old men.

IMHO

 

[marcus]

Mike's post reminds me once more that questing after "TOE"s is no longer cool. Maybe a new watchword could be 'counting the geometries'

Loll has a writer's knack for hitting the essential and her new paper on black holes (to appear) has a title like
"Counting black hole geometries"

It is not that, it is more technical sounding, like "Counting Schwarzschild geometries...etc...etc", but it makes the point that the CDT path integral is basically doing that.

it is a machine to count geometries and it makes sense when you look at it that way

the geometries are weighted with factor exp(iS) where S is the Einstein action-----which makes spacetimes that are too "busy" cancel each other out. Feynman gave an intuitve explanation in the analogous particlepath context in his public lecture "QED" if I remember right, or some other popular thing. It is not hard or arcane or anything.

so leaving aside the business of the weighting factor when you add them up, a path integral (in the case of quantum spacetime dynamics) COUNTS THE GEOMETRIES.

Maybe i will try to expand on that here, in this thread, because if anybody who was interested could only get to the point of seeing that far into the quantum spacetime dynamics path integral then we would definitely be a step ahead

 

[marcus]

It seems CDT still leaves open the questions: why the path integral, why the action integral, why the Lagrangian, why 4D...

the "why" is basically Loll's defintion of what a QG theory should be:

page 1 of "Discrete History" http://arxiv.org/hep-th/0212340
<< By quantum gravity I will mean a consistent fundamental quantum description of space-time geometry (with or without matter) whose classical limit is general relativity...>>

the features of the approach you mentioned are because it is supposed to be a quantum description. so there is a path integral because that is a common type of quantum description (essentially counting the paths except the paths are complete spactimes from beginning of U to the end, or other termini)

the action is the Einstein action because, by her definition, it should have Gen Rel as classical limit.

Keep in mind this is counting is of geometries that have the same topology.
it looks to me that there could eventually be something like an ambjorn-loll index that behaves in a multiplicative way, where if a space combines two topological features like two black holes then you count geometries for each hole and multiply by some kind of product.

but for now let us focus on a very simple case, just one topology which is RxS³----the unit 3sphere moving thru time, and only count different geometries of that one thing

the important thing is to understand counting geometries (not classifying topologies which mathematicians have worked on for a long time already)

heres some quotes from "Discrete History" hep-th/0212340, an introduction to CDT
(lecture notes for grad students that might want to get into it)

from page 11 from "Discrete History" by Loll

<<The point of taking separate sums over the numbers of d- and (d-2)-simplices in (10) is to make explicit that “doing the sum” is tantamount to the combinatorial problem of counting triangulations of a given volume and number of simplices of co-dimension two (corresponding to the last summation in (10)).>>

from page 3 and 4 of "Discrete History"
<< In this approach, “computing the path integral” amounts to a conceptually simple and geometrically transparent “counting of geometries”, with additional weight factors which are determined by the Einstein action. >>

 

[marcus]

... her new paper on black holes (to appear) has a title like
"Counting black hole geometries"

It is not that, it is more technical sounding, like "Counting Schwarzschild geometries...etc...etc", but it makes the point that the CDT path integral is basically doing that.

it is a machine to count geometries and it makes sense when you look at it that way

the geometries are weighted with factor exp(iS) where S is the Einstein action-----which makes spacetimes that are "busy" with much action cancel each other out. ...

I found the correct title of the CDT article on black holes that is supposed to come be coming out:

B. Dittrich and R. Loll: Counting a black hole in Lorentzian product triangulations

this business of counting geometries (which I do not see so clearly realized elsewhere) is one reason that I suspect we have something fundamental and basic in CDT.

(also it is important that the geometries include very jagged rough ones with extreme amounts of curvature, which one does not so much see in ordinary lattice theories-----and that the continuum limit is not even a differentiable manifold)

but other people, especially at PF, have given a different impression of CDT---it is NOT basic, or fundamental. I am not sure what that means because "basic, fundamental" are highly subjective judgemental terms.

for me, one cannot always tell, with some mathematics, how basic it is until later. If a lot of new theorems come out of it, then it was basic. Top mathematicians develop an INTUITION of what new results and new concepts are "deep". I do not think one can assign this based on some standardized rules, it is partly intuitive. MY intuition is that something new is going on with CDT-----it has a continuum, it models spacetime, but it is split off from differential geometry and manifolds. there should be new theorems there.

the business of a scale dependent dimension is very interesting. conventional manifolds do not have this. the CDT continuum is NOT a conventional manifold

also in the mainstream differential geometry basic to pretty much all physics one cannot COUNT the different geometries
to try and do it gets very elaborate, with Ashtekar variables, connections, spin networks. in CDT one cuts immediately to the chase and just outright does it.

there are some other reasons I think we are looking at something basic, and new, maybe i will get to them later

 

[Kea]

...the features of the approach you mentioned are because it is supposed to be a quantum description... so there is a path integral

This is the question: WHY is there a path integral?

 

[marcus]

This is the question: WHY is there a path integral?

Please read my three previous posts, about counting geometries. so then we can talk in terms of counting
https://www.physicsforums.com/showpost.php?p=583395&postcount=27
https://www.physicsforums.com/showpost.php?p=583476&postcount=28
https://www.physicsforums.com/showpost.php?p=583476&postcount=29

I am working towards an answer to that question

 

[Kea]

the "why" is basically Loll's defintion of what a QG theory should be...

Marcus,

We've been reading your posts. The point is that we don't agree with AJL's idea of what QG should be. We think that, if one insists on a 'counting geometries' approach, one should come up with some heavy physical justification for this. What is it?

Cheers
Kea

 

[marcus]

Also, Kea, you may have an idea of why, in Feynman theory of a particle, there is a path integral
IF YOU HAVE ANY IDEAS ABOUT THE FEYNMAN PATH INTEGRAL, PLEASE POST THEM, if they are germane and not too lengthy.

this would be the first question to ask wouldn't it? the "path" integral is originally about the path of a particle

to what extent, and why, is it a valid approach for particles? maybe you have thoughts on that? Feel free to give us your thoughts about particle path integrals

in any case it is a commonplace form that quantum theories can take

CDT is a GENERALIZATION of that where the "path" is a spacetime continuum, say like a cobordism from one spatial geometry to another, or from beginning to end of universe, or some such boundaries. the path is now an evolution of spacetime

one has an action, which classically one would want to minimize, but as Feynman showed us to do, in a quantum theory one uses it to WEIGHT the paths with complex weights exp(iS), then the paths, or spacetimes that are too busy or too crazy tend to cancel out and the effect is LIKE going after the least action path.

historically this has been a lucky approach to quantum theories, so one does not have to JUSTIFY trying out the path integral approach to anything.
one is pragmatic, one sees how it does.
here, with Ambjorn and Loll it suddenly appears to work amazingly well and get some surprising results


so, you see, Loll's easy introduction, the lecture notes "Discrete History" she spends as few pages first discussing the path of an ORDINARY PARTICLE, then she goes on to talk about spacetime where you count geometries

 

[marcus]

... The point is that we don't agree with AJL's idea of what QG should be. We think that, if one insists on a 'counting geometries' approach, one should come up with some heavy physical justification for this. ...

Please tell me who "WE" is and invite them to post here asking this question and saying what they think. I am not sure that you can or do speak for anyone but Kea. It would be nice to hear another questioner and the exact question they ask.

Hi Kea, I just saw the next post and will respond here for conciseness

Marcus

The Feynman path integral works wonderfully for the Standard Model. People have tried for decades to apply this intuition to gravity - but it hasn't worked. I am seriously questioning the validity of this intuition: hence point (1) in my list of QG properties. Maybe I'm the only one that thinks that way, but I get the impression from what others have been saying that I'm not alone in this point of view.

Cheers
Kea

"The Feynman path integral works wonderfully for the Standard Model. People have tried for decades to apply this intuition to gravity - but it hasn't worked."

But now it appears to be working.

 

[Kea]

in any case it is a commonplace form that quantum theories can take...

Marcus

The Feynman path integral works wonderfully for the Standard Model. People have tried for decades to apply this intuition to gravity - but it hasn't worked. I am seriously questioning the validity of this intuition: hence point (1) in my list of QG properties. Maybe I'm the only one that thinks that way, but I get the impression from what others have been saying that I'm not alone in this point of view.

Cheers
Kea

 

[marcus]

the "why" is basically Loll's defintion of what a QG theory should be:

page 1 of "Discrete History" http://arxiv.org/hep-th/0212340
<< By quantum gravity I will mean a consistent fundamental quantum description of space-time geometry (with or without matter) whose classical limit is general relativity...>>

... a path integral because that is a common type of quantum description (essentially counting the paths except the paths are complete spactimes ...

...from page 3 and 4 of "Discrete History"
<< In this approach, “computing the path integral” amounts to a conceptually simple and geometrically transparent “counting of geometries”, with additional weight factors which are determined by the Einstein action. >>

For the purposes of this thread (why CDT changes the map of quantum gravity) we can take Lolls definition of QG. For our purposes here, what a theory should be, to be considered a theory of Quantum Gravity, is what she says in the above.

the use of standard physics tools, such as the real and complex numbers, does not require justification. path integral is one of a couple of traditional methods of building a quantum description and does not require justification

People have been trying to get a theory of quantum spacetime dynamics for a long time, and one of the ways they have been trying for a long time is PATH INTEGRAL quantum spacetime dynamics. And it has not worked so far. But now it seems to be starting to work.

It would be natural, if one was so inclined, to be in denial about this and to be thinking of a million reasons why this cannot possibly be right and why what Renate Loll means by "quantum gravity" cannot REALLY be the REAL quantum gravity, and so on. But I think we might as well listen to her, on her own terms, and try to understand and not be threatened by it.

what it appears to me is like this. Since the 1990s the Loop people have been trying a particular Path Integral approach called SPIN FOAM which was aimed at doing just this what Loll-type Triangulations does and being just this kind of Quantum Gravity theory, and it was not working very well, and no body got to feeling threatened and started redefining the rules so that Spin Foam could not be a REAL QG. People just kept speaking normal professional physics English language-----spin foams, like LQG and many other approaches, was a candidate QG theory.

Now what we are seeing is a particularly clear straight-forward case of a path integral formulation of Quantum Gravity. It has been making very rapid progress for the past two years, and it may come to be, for a while, our PARADIGM of what people mean by a quantum gravity theory.

And it seems to me that a natural reaction to this would be to put one's hands over ones ears, shut one's eyes, and start redefining what people OUGHT to mean when they say "quantum gravity" to be be something completely different from what they have mostly so far. So let's watch out for signs of that happening----not to say it HAS ALREADY been noticeable, but it might happen so let's watch for it.

Cheers

 

[marcus]

Just visited Peter Woit's blog, Not Even Wrong (often interesting posts about string theory there) and was struck by the relevance of this
http://www.math.columbia.edu/~woit/blog/archives/000200.html

it links to an article by Scott Berkun
http://www.scottberkun.com/essays/essay40.htm

that is illustrated, entertainingly enough, by Monty Python episodes

 

[marcus]

parts of the summary section of "Reconstructing the Universe" are worth quoting

---quote from hep-th/0505154---
8 Summary and outlook

This paper describes the currently known geometric properties of the quantum universe generated by the method of causal dynamical triangulations, as well as the general phase structure of the underlying statistical model of four-dimensional random geometries. The main results are as follows. An extended quantum universe exists in one of the three observed phases of the model, which occurs for sufficiently large values of the bare Newton’s constant G and of the asymmetry \Delta, which quantifies the finite relative length scale between the time and spatial directions. In the two other observed phases, the universe disintegrates into a rapid succession of spatial slices of vanishing and nonvanishing spatial volume (small G), or collapses in the time direction to a universe that only exists for an infinitesimal moment in time (large G, vanishing or small \Delta). In either of these two cases, no macroscopically extended spacetime geometry is obtained. By measuring the (Euclidean) geometry of the dynamically generated quantum spacetime *17* in the remaining phase, in which the universe appears to be extended in space and time, we collected strong evidence that it behaves as a four-dimensional quantity on large scales...

...

The most local measurement of quantum geometry so far is that of the spectral dimension of spacetime at short distances, which provides another quantitative measure of the nonclassicality of geometry. As we have seen, the spectral dimension changes smoothly from about 4 on large scales to about 2 on small scales. Not only does this (to our knowledge) constitute the first dynamical derivation of a scale-dependent dimension in quantum gravity, but it may also provide a natural short-distance cut-off by which the nonperturbative formulation evades the ultra-violet infinities of perturbative quantum gravity.

In summary, what emerges from our formulation of nonperturbative quantum gravity as a continuum limit of causal dynamical triangulations is a compelling and rather concrete geometric picture of quantum spacetime. Quantum spacetime possesses a number of large-scale properties expected of a four-dimensional classical universe, but at the same time exhibits a nonclassical and nonsmooth behaviour microscopically, due to large quantum fluctuations of the geometry at small scales. These fluctuations “conspire” to create a quantum geometry that is effectively two-dimensional at short distances...


FOOTNOTE *17*: Since our universe is a weighted quantum superposition of geometries, all “measurements” refer to expectation values of geometric operators in the quantum ground state.
-----end quote---

I think we are looking at a fundmental advance. A concrete picture of quantum spacetime has appeared. It is likely, I suspect, to become the paradigm for what the words "quantum spacetime" come to mean in our discussions.

 

[marcus]

We are talking about Reconstructing the Universe hep-th/0505154, a landmark CDT paper.

the phase diagram relevant to the discussion in foregoing post is Figure 3 on page 10,

the kappa here is the reciprocal of G, and region C of the phase diagram is the good phase where the universe has its familiar spatial and temporal extension.

what we see immediately is that the Newtonian gravitational constant G, the coupling constant, has to be sufficiently strong for spacetime to exist.

I am interested in understanding the other parameter, \Delta
which they call the "asymmetry parameter"

Delta = 0 corresponds to the simplexes being equilateral
You can see that in Figure 3 if Delta is near zero we get out of the good phase C and again the familiar spacetime fails to materialize. I'm wondering what this tells us---what the significance of Delta is. I can see that it affects the angles of simplexes and thus how one compares purely spatial curvature with curvature involving timelike lengths.

Visually the asymmetry parameter tells us "squatness" of the simplex in standard position. (by simplex I mean 4D simplex, the 5 pointed thing a little 4D pyramid-like thing sitting on a tetrahedron base--should I call it "pentamid"?)

each simplex has equal spacelike lengths and equal timelike lengths, but the spacelike and timelike lengths don't have to be equal, there is this positive number alpha with

alpha =- timelength²/spacelength²

if alpha were equal to one then we have the "equilateral" case, but the CDT people want to make alpha smaller than one, like 7/12, say. around one half but maybe a little over one half. they find what works good. it is not so critical, the Figure 3 shows as wide range works. But alpha should not be ONE, it should be somewhat less

this "asymmetry parameter" Delta is a measure of how much it is less than one. it is not simply the straight difference but it is an indicator of that. IIRC Delta occurs in angle formulas and in measuring curvature. IIRC its meaning has to do with how purely spatial curvature relates to other kinds.

 

[Kea]

It would be natural, if one was so inclined, to be in denial about this and to be thinking of a million reasons why this cannot possibly be right and why what Renate Loll means by "quantum gravity" cannot REALLY be the REAL quantum gravity...

Sigh.

Is that it? Are we supposed to accept path integrals because that seems to be the best thing around? The third road isn't hand waving - it has alternatives. These alternatives can explain, for example, quark confinement in a mathematically rigorous description of elements of the Standard Model. There are alternative cosmologies that suggest that there may be no cosmological constant, and which agree with the supernovae data. What evidence does CDT have to support it?

Oh well. I'm quite used to people thinking I'm crazy. Sigh.
Kea

 

[Kea]

the use of standard physics tools, such as the real and complex numbers, does not require justification

Oh. Do AJL use real numbers? I was under the impression they were doing p-adic geometry.

Kea

 

[marcus]

---quote from http://arxiv.org/hep-th/0505154 ---

...In summary, what emerges from our formulation of nonperturbative quantum gravity as a continuum limit of causal dynamical triangulations is a compelling and rather concrete geometric picture of quantum spacetime. Quantum spacetime possesses a number of large-scale properties expected of a four-dimensional classical universe, but at the same time exhibits a nonclassical and nonsmooth behaviour microscopically,...

the topic of the thread here is, of course, "Why CDT changes the map of quantum gravity". Also I want to do some introductory explaining about what CDT is----how the approach works and how spacetime is modeled as the quantum spacetime just mentioned.

for my working definition of what QUANTUM GRAVITY theories are, i am using Renate Loll's own concise description of a QG theory:

page 1 of "Discrete History" http://arxiv.org/hep-th/0212340
<< By quantum gravity I will mean a consistent fundamental quantum description of space-time geometry (with or without matter) whose classical limit is general relativity...>>

THE CLEAREST OBJECTIVE SIGNAL that CDT is changing the map of QG research is what we already know about the programme of this year's main QG conference.

this is the October 2005 "Loops 05" conference.

http://loops05.aei.mpg.de/index_files/Home.html
http://loops05.aei.mpg.de/index_files/Programme.html

the prominence of CDT in the October programme is greater than at any similar conference in the past. CDT is not only listed on the Loop 05 Homepage as a topic in its own right but it exemplifies another focus of the conference that was listed there, namely
Non-perturbative Path Integrals

CDT is one of the leading path integral approaches to QG. So there are clear signs that people at this year's main QG conference will be hearing a lot about CDT.

And my guess is that people in other branches of QG research will be devoting considerable effort to MAKE CONTACT with CDT. There will probably be some convergence of the approaches, with people in other departments of QG deriving analogous results to those found in CDT, or inspired by what has been discovered in CDT computer simulations of quantum spacetime.

 

[marcus]

IMHO Loll-type triangulations is the most important new development in quantum gravity for some years

and partly for that reason I think it is essential that a good description and explanation of the CDT authors' methods be devised that can work for laypeople. it is a landmark new development and interested non-technical people should be able to follow what's happening

another reason for working up some clear non-technical explanation is that it is so interesting! the CDT quantum spacetime is simple enough to grasp, very concrete (not floating ectoplasmically in some abstract algebra-land), and well-furnished with attractive novelty. so there are other good reasons for developing good explanations of it for laypeople.

also IMHO this PF forum can serve as an "explanation-lab" or "explanation-workshop" to try out ways of presenting new theoretical physics----quantum gravity physics----and see what works.

I am going to take some risks here, and i think I'll try calling the simplest 4D object (analog of triangle, conventionally called "4-simplex") by some made-up names. this may not work and I may have to go back to calling it by the conventional name of 4-simplex.

in CDT method, spacetime is assembled out of TWO TYPES of 4D building blocks. and all those of a given type are IDENTICAL
we (any possible readers and I) need to get to the point of visualizing the layered assemblage of spacetime made from some halfmillion building blocks of this type (roughly half of each type)

 

[marcus]

working with building blocks is good for several reasons. when you approximate quantum spacetime by assemblages of these 4-simplex blocks then

1. you can totally get rid of coordinate functions, the blocks are identical (by type) and you can gauge curvature by COUNTING because the geometry of spacetime is COMPLETELY EXPRESSED BY HOW THEY ARE GLUED TOGETHER. You don't have to futz around with drivatives and bundles and connections and diffeomorphisms and all that hardware that is based on coordinate charts. you have a directory in the computer memory that keeps track of how the blocks are glued together, and the different numbers in each type, and that directory is the geometry.

2. these tiny little blocklets are all cut out of Minkowski space, the space of special relativity, which is kind of sweet, isn't it? So they have two kinds of edges: spacelike edges and timelike edges. BTW a block has 10 edges in all. Think of a tetrahedron with 6 edges, and use that as the base of a pyramid, so there is an apex above the tetrahedron connected to its 4 corners by 4 additional edges

3. I was going to think of reasons it is good to approximate quantum spacetime by random assemblages of blocks. Well it makes everything finite so you can COUNT GEOMETRIES. essentially different geometries are equivalent to essentially different ways of assembling and gluing the blocks! and you can count those combinatorially.

4. you can also make formulas for curvature and volume and the Einstein action (measuring how "busy" a spacetime is) which ONLY INVOLVE COUNTING different kinds of simplexes. so it makes setting up a the usual physicist-gear kind of straightforward.

instead of doing a lot of calculus with drivatives and integrals most of which are purely theoretical because no one ever gets down in the mud and solves them. instead of all that, you just tell the computer to COUNT stuff

5. it is kind of a readymade situation for quantum mechanics---one of the standard tools is path integral!

have to go back later

 

[Mike2]

By now the TOE dream is a wild goose chase and a bunch of hype. the generation of guys that once seriously thought they could do that in the context of differential geometry, without first re-inventing spacetime, are now old men. IMHO

Just a second. How close are we, and what needs to be done? It seems to me that since everything is described by coordinates, etc, that a TOE would have to explain the emergence of a manifold from a singularity. But isn't this pretty close to what CDT is trying to do? Then it would have to explain how particles emerge from spacetime. So why does that seem such a fanciful endeavor? We seem to be touching on it already. I suppose one issue would be that even if we came up with a situation where particles emerged from spacetime through some symmetry breaking process, how would we know if it were the particles we are familiar with in the standard model or if they were some more fundamental particle that we will never connect with the standard model? Isn't there some reason to suspect that there can be no more fundamental particle beside quarks?

Also, if everything emerges from a singularity in a reasonable and traceable way, then it seems that it must have emerged in a continuous fashion. Otherwise, instantaneous changes would by nature defy any attempt at explanation. So I have my doubts that non-commutative geometry is truly fundamental, since it allows for spontaneous, unexplanable changes in the spacetime itself, IIRC. Comments welcome, thanks.

 

[setAI]

CDT is a very interesting computational formalism [as is LQG/ M-theory/ etc]- but I'm more interested in the "computer" itself (^_-)

that is why computationalism/ causal sets/ categories/ and the like are more promising IMO-

 

[marcus]

How close are we, and what needs to be done?...

Mike, I think we are very close (to a model of quantum spacetime)

and when we have a good concrete model of spacetime to build the fields of matter, and its forces, on top of, then the whole picture will change
how the fields are built will depend on what the spacetime foundations are like

so it seems illogical and unproductive to pursue the matter business now when you are still working with outdated models of the continuum---building fields on classical Minkowski space and the like. that has gone about as far as it can without remodeling the spacetime foundations

I gather that SetAI has a rather similar view, since he has also focused his attention on progress being made towards a model of quantum spacetime

 

[marcus]

...
that is why computationalism/ causal sets/ categories/ and the like are more promising IMO-

Look at the focus topics for the October "Loops 05" conference.
Rafael Sorkin (father or at least godfather of causal sets) is on the
invited speakers list and causal sets is one of the topics

Fay Dowker is also an invited speaker, if you know causal sets then you may know of her too.

quote: "The topics of this conference will include:

Background Independent Algebraic QFT
Causal Sets
Dynamical Triangulations
Loop Quantum Gravity
Non-perturbative Path Integrals
String Theory"

for more information see
http://loops05.aei.mpg.de/index_files/Home.html

for the list of speakers for the October conference see
http://loops05.aei.mpg.de/index_files/Programme.html

 

[marcus]

CDT is a very interesting computational formalism ...

setAI I am glad you find it interesting! that is a good sign.
but i think it is more (or perhaps you might say less) than a computational formalism

it is a concrete model of the continuum which may turn out to actually be the RIGHT model----that is become the new paradigm (replacing the differentiable manifold) for how we think of spacetime

the CDT continuum is NOT discrete
however the 4D simplex, cut out of Minkowski space (the space of special relativity) is a kind of "atom of relationship"

and these simplexes are assembled, and the arrangement of them randomly shuffled, in accordance with General Relativity

(so you have elements of both SR and GR)

spacetime becomes a PATH in the "path integral" quantization approach.

but in CDT one does not stop there, with a random assemblage made of a finite number of simplex building blocks, one goes to the limit of small blocks-----so in the end there is no discreteness, no minimal length like Planck length, no atoms of spacetime----there is a continuum

 

[marcus]

I will quote from the conclusion of the latest CDT paper because it is relevant to this response to setAI:


http://arxiv.org/hep-th/0505154
Reconstructing the Universe
J. Ambjorn, J. Jurkiewicz, R. Loll

<<...This paper describes the currently known geometric properties of the quantum universe generated by the method of causal dynamical triangulations, as well as the general phase structure of the underlying statistical model of four-dimensional random geometries. The main results are as follows. An extended quantum universe exists in one of the three observed phases of the model,...
...In summary, what emerges from our formulation of nonperturbative quantum gravity as a continuum limit of causal dynamical triangulations is a compelling and rather concrete geometric picture of quantum spacetime. Quantum spacetime possesses a number of large-scale properties expected of a four-dimensional classical universe, but at the same time exhibits a nonclassical and nonsmooth behaviour microscopically, due to large quantum fluctuations of the geometry at small scales. These fluctuations “conspire” to create a quantum geometry that is effectively two-dimensional at short distances...>>