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Why CDT changes the map of quantum gravity

  1. May 23, 2005 #1

    marcus

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    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 wont 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 :smile:
     
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  3. May 23, 2005 #2

    Kea

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    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 :smile:
     
  4. May 23, 2005 #3

    marcus

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    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 dont 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)
     
    Last edited: May 23, 2005
  5. May 23, 2005 #4

    marcus

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    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
     
  6. May 24, 2005 #5

    marcus

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    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 doesnt 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 doesnt 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 cant 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. Lets 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 dont 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.
     
    Last edited: May 25, 2005
  7. May 24, 2005 #6
    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.
     
  8. May 24, 2005 #7

    marcus

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    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
     
  9. May 24, 2005 #8
    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.
     
  10. May 25, 2005 #9

    marcus

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    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 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 dont appear to apply.
     
  11. May 25, 2005 #10

    marcus

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    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 :smile:
    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 dont 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.)
     
    Last edited: May 25, 2005
  12. May 25, 2005 #11
    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.
     
  13. May 25, 2005 #12

    marcus

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    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
     
    Last edited: May 25, 2005
  14. May 25, 2005 #13
    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 it sounds like they are dealing with 4D only. I don't see where they get scale dependent dimension.

    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?
     
  15. May 25, 2005 #14

    marcus

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    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
     
  16. May 25, 2005 #15

    marcus

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    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
     
  17. May 26, 2005 #16

    Chronos

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    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.
     
  18. May 26, 2005 #17

    marcus

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    pleasant news, thanks for keeping us in the loop
     
  19. May 26, 2005 #18

    marcus

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    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

    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

    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 dont 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 dont 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.
     
  20. May 26, 2005 #19

    marcus

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    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.
     
  21. May 27, 2005 #20
    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
     
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