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Jerzy Kowalski-Glikman weighs in at Woit's

  1. Jan 20, 2006 #1

    marcus

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  3. Jan 22, 2006 #2

    marcus

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    I want to emphasize this new thread at Woit's

    http://www.math.columbia.edu/~woit/wordpress/?p=330

    the thread has lots of interesting topics and expert disagreement.

    Jerzy K-G says he does not think DSR needs to have an energydependent speed of massless particles (light), and he cites a 2004 paper of his own.
    http://www.math.columbia.edu/~woit/wordpress/?p=330#comment-7788
    (21Jan6:36P)

    there are indications that LQG is going to predict some form of DSR, so then it becomes critical to determine what KIND of DSR, because this affects whether or not GLAST provides a test of LQG.

    Anonymous(22Jan4:25A) has asked:
    "Lee, how do you expect the matter degrees of freedom to emerge [from LQG]?"
    http://www.math.columbia.edu/~woit/wordpress/?p=330#comment-7793

    Lee says he expects matter to emerge from the quantum treatment of spacetime---essentially from the geometry of LQG. He referred Anonymous to his Loops '05 talk. And mentioned work in progress which I think includes collaboration with Bilson-Thompson, who has devised a topological preon model based on braids. Actually people are investigating a bunch of ways that matter could emerge from QG, not just one way, I don't think it is time to pick a front-runner and I don't think Lee's reply to Anonymous does more than indicate some possibilities he has in mind.

    Lubos has asked for clarification about DSR and speed of light
    22Jan1:43 pm
    http://www.math.columbia.edu/~woit/wordpress/?p=330#comment-7804

    "...I am confused how Prof. Kowalski-Glikman and Prof. Smolin and others may disagree about the basic question whether DSR predicts an energy-dependent speed of light. Is it just a terminological disagreement or a physical one? My understanding is that DSR violates the constancy of speed of light and it simultaneously violates locality in a brutal way, by any distance, because locality requires a linear representation of the energy-momentum vector transforming under the Lorentz group.

    (DSR is deformed special relativity whose symmetry group is the contraction of the q-deformation of the (anti) de Sitter group, which introduces nonlinearities to the [J,P] commutators.)

    But do you agree that GLAST should detect something that will look like energy-dependent speed of light? DSR is all about the speed of light..."

    there are lots of goodies in this thread---it's one of Woit's best.
     
  4. Jan 22, 2006 #3

    marcus

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    Samples from the Woit thread

    http://www.math.columbia.edu/~woit/wordpress/?p=330#comment-7812
    -------LS quote-------
    Lubos, I am afraid I can’t understand your comments, they do not reflect any detailed understanding of how the actual calculations and proofs are done. Let me just start with the first line of one of your lengthy comments: “Preference over the way to regulate infinities - lattice instead of dim. reg. or Pauli-Villars or other regulators.”

    For the millionth time, LQG does NOT USE LATTICE methods. It is not a matter of “preference”, the methods of background dependent theories such as dim reg or Pauli Villars CANNOT BE USED, because if the whole metric is an operator there is no background metric, which is needed to define them. Nor can lattice regularization be used as that also depends on a background metric. We had to invent NEW METHODS for regularization, suitable for gauge theories whose dynamics is defined on a manifold with no metric and we did so (This was why it took some years of careful work to develop LQG). They are roughly like point splitting regularization but somewhat more complicated because one has to ensure that in the limit in which the regulator is removed the resulting states, inner products and operators are spatially diffeo invariant. This is more intricate and constraining than the regularizations defined by background metrics.

    I could continue to correct each comment you make line by line, but as almost nothing written there corresponds to what is actually done it would take a book. I would ask you once again to please study the details and understand them. There are valid criticisms and limitations to LQG which are worth discussing, but its hard to argue with someone who is unwilling to understand the actual results and claims.
    ----end quote---

    more in a later post
    Here LS is responding to the kind of questions which nonspecialists in QG may often ask. His remarks might possibly serve as a basis for a kind of FAQ or beginners or string theorists worried by some new-physics facet or unfamiliar feature. I don't know for certain, but it could be that the same questions and comment come up repeatedly so some of the Smolin material could have further use.

    http://www.math.columbia.edu/~woit/wordpress/?p=330#comment-7821

    ----LS quote----
    Hi everyone, thanks, again Ill do my best to answer clearly.

    First to Zorq: You assert: “There are an infinite number of polynomials in the Riemann curvature and its covariant derivatives that can be added to the spin-foam action.” No, we don’t know this because the spin foam amplitude is not expressed in terms of polynomials of the Riemann curvature. It is expressed in terms of invariants of quantum groups, such as q-15j symbols. I would not be surprised if there are an infinite number of such possible amplitudes, but I know of no result that shows so.

    Further, as I thought I emphasized, there are conditions to be imposed. One, for sure, is the uv finiteness (in the sense that sums and integrals converge) of the sums over labels in a spin foam amplitude. This is quite restrictive. Only a few solutions are known, (see as usual hep-th/0408048 for exact references to the finiteness proofs for spin foams). We just do not know how large is the space of spin foam amplitudes that have this property. So I am making no claim here, either way. But you asked for restrictive conditions and this is an important one. OK?

    You also say: “A similar infinite set of couplings exists, also, in the LQG Hamiltonian”-to which similar remarks apply. The LQG quantum Hamiltonian constraint is not expressed in terms of classical quantities and it has to satisfy some quite non-trivial consistency conditions coming from the operator constraint algebra. We do not know how large is the space of solutions to these. As I mentioned we know of only a few.

    (Also, I thought I was using the language of the Wilsonian RG, and I agree I was using it to make a trivial point.)

    Now, to Anonomous. Thanks for your helpful attitude. You ask, “In ordinary QFT we know that there are numerous irrelevant operators involving gravity that one can add to the Lagrangian….so why are there not infinitely many choices of theory in your cutoff theory?” I hope the above answers you clearly. The point is that the spin foam action is NOT made by writing classical spacetime diffeo invariant expressions in the continuum and then subjecting them to a regularization. Once you are in the spin foam or group field theory language the amplitudes are expressed in a different framework-that of quantum group invariants. This is consistent with the idea that there is no continuum below the Planck scale. And there are conditions imposed. The conditions of finiteness of sums over labels of spin foam amplitudes is pretty restrictive, so there could easily be only a finite space of solutions to it. But this has not been shown so I am not claiming it is true.

    Now about 2+1: “You stress that these theories reduce not to usual QFTs but to some kappa-deformed theories, but it doesn’t seem that that resolves the problem either. Such a deformation doesn’t make gravity renormalizable.” First, the point of the argument was to directly show that an argument given by someone was wrong because, again, none of the DSR theories are in the class of perturbative QFT’s on Minkowski spacetime. Second, DSR theories can be uv finite because there are maximum energies in sums over momenta.

    You want a heuristic explanation for why a diffeo invariant regularization procedure results in finite operator products. OK, here is one that was very helpful to us originally. (again see 0408048). In the absence of a background metric all operators are distributions and all distributions are densities. So when defining an operator product in the absence of a background metric you have to carefully keep track of density weights.

    We regulate by point splitting, which means we introduce an auxiliary background metric q_0 just for the purpose of defining the distance between points. We have to define the product of two operator valued distributions to be one operator valued distribution. In general the result has inverse powers of the distance measured in units of q_0 times determinants of q_0 to soak up the density weights. If the resulting operator is to be diffeo invariant (under actions on the quantum fields) it cannot depend on q_0 because q_0 is not acted on by the operator that generates diffeos. It turns out this means it cannot depend either on the distance measured in units of q_0 (this is seen by an argument where q_0 is scaled.) Thus, a diffeo invariant operator extracted from the limit in which the regulator is removed cannot depend on q_0. Hence because all divergences are measured in units of q_0 there can be no divergences. This is borne out by the detailed calculations. But what kind of operator can appear? Only one that is a natural integral over an operator of density of weight one-as the density weight can in the limit only come from the operators. Since local field operators have density weight one, this can come from an n’th root of the product of n operators, each of density weight one. This is exactly how area and volume operators are defined.

    There is another trick which is to represent the inverse of the determinant of the operator metric as a commutator of operators that can be defined in the regulated theory. This allows us to construct further finite operators including the Hamiltonian constraint.

    To Aaron, about the limit G to zero in 2+1 see Freidel and Livine for how it works in detail. Remember I am talking here about a spin foam calculation, so the result comes from a path integral and not the Hamiltonian theory. You can ask, could this have been seen in the Hilbert space and how would the limit G to zero look there? I don’t know (I hope that is ok as these are new results.) It seems like a good research problem, perhaps you would like to work on it...
    ---endquote---
     
  5. Jan 22, 2006 #4

    marcus

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    http://www.math.columbia.edu/~woit/wordpress/?p=330#comment-7827

    These replies by Lee Smolin, on the Woit thread, seem really apt as material for a FAQ, except that it would be a
    FREQUENT OBJECTIONS BY STRINGTHINKERS or "FOS" instead of FAQ.

    Another one came in this evening.

    =======LS quote========

    January 22nd, 2006 at 8:44 pm
    Hi, I hope the following is useful.

    First, with respect to strong coupling limit of quantum gravity in the context of LQG, see THE G (NEWTON) —> INFINITY LIMIT OF QUANTUM GRAVITY, Viqar Husain , Class.Quant.Grav.5:575,1988. This was early days, probably the results Viqar got on the strong coupling limit could be much improved with what we have learned since.

    I am very happy to talk about effective field theories, “I assume we all believe in effective field theories…” Yes, BUT we must be careful to remember that the class of effective field theories are labeled by the symmetries and gauge symmetries of the ground state. There are separate classes of effective field theories for Poincare invariant, kappa-Poincare invariant and broken Poincare invariant theories. This is an elementary fact, but it is the key point I have been trying to make. If you have two theories and one describes perturbations around a ground state that has symmetry P and the other has a ground state with symmetry Q and P is not equal to Q then they are not described by the same class of effective field theories. Becauuse each term in the effective action should be separately invariant under either P or Q and they are not the same. Is that clear?

    Having said this I don’t understand what we are arguing about. I agree there is some set of possible amplitudes of spin foam models. I mention that it is likely that these will be restricted by the condition of finiteness of sums over labels. I mention that we do not know how large the space of such good spin foam models is. Some of you would have bet there were no such theories, so I’m surprised if you are now cavelierly insisting there are infintie numbers of them.

    I do not deny it is possible it may be infinite, but I also will not be surprised if the condition of finiteness is restrictive and there are only a few parameters. But the bottom line is we don’t know. I also agree that these will map to effective field theories. I only insist that if Poincare invariance is q-deformed, or the geometry is non-commutative as is the case in 2+1 this is NOT the same class of effective field theories that are constructed by perturbation theory around flat Minkowski spacetime. I agree it would be very interesting to know how the parameters of the finite spin foam models map to the parameters of the effective field theory with the appropriate ground state symmetry. I don’t say more because as I’ve said already, we don’t know the answer for 3+1. It is only very recently we know the answer for 2+1 with matter. What is not clear about this?

    If someone thinks it is known or obvious that the space of spin foam amplitudes which lead to convergent sums or integrals over labels for any spin foam diagram is infinite dimensional, please provide details as this would constitute an important new result. Otherwise, do not presume to know the answer to an open question. By the way, let me stress sincerely it would be very important to characterize the space of finite spin foam amplitudes, and I hope someone will take this on...

    =========endquote=========
     
  6. Jan 23, 2006 #5

    Chronos

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    Typical Lubos flaming, in my opinion. No substance, just fairy wings.
     
  7. Jan 23, 2006 #6

    marcus

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  8. Jan 23, 2006 #7

    marcus

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    Continuation of the Smolin quotes from that thread

    these quotes might be useful material for a FOS ("frequent objections by stringthinkers") page. here is a continuation

    http://www.math.columbia.edu/~woit/wordpress/?p=330#comment-7852

    ---quote LS at Woit blog---
    January 23rd, 2006 at 10:02 am
    To Boreds,

    You ” presume that if you try to perturbatively quantize GR around this
    background (kappa-Minkowski that it will be non-renormalizable, and that there will be an infinite set of counter-terms.” -To my knowledge its not known if this is true or not, perhaps someone else knows. Otherwise it would make a good research project. The reason it may be false is that some DSR theories incorporate maximum energies and momenta.

    To Zorq, “Will the effective field theory, at least, be writable as a generally-covariant local functional of the metric?” Again, not known, but a good research project. One conjecture is it will be writable as a function of an energy dependent metric as in our work on rainbow gravity with Magueijo.

    btw by uv finiteness we mean you sum over the labels on intermediate states and, rather then diverging as is the case in perturbaive QFT when the labels are momenta and the sums are unbounded, the sums are convergent. The fact that this doesn’t coincide with textbook meanings in perturbative background dependent QFT is obvious, but again, our point is you have to learn a new kind of QFT.

    If i can make a remark, the questions being raised are good ones, what is confusing is the adversarial tone. The discovery by Freidel and Livine that in 2+1 quantum gravity with matter there is an effective field theory on kappa-Minkowski is very recent. We don’t know that this is the case in 3+1, although we know how to try to show it and it is in progress. We don’t know whether there will be any version of effective field theory besides this one, which describes the excitations of a ground state with deformed poincare invariance. Since the fundamental theory is not formulated in spacetime and spacetime geometry is emergent, it is not obvious or known whether there will be a diffeo invariant effective field theory of the kind which is assumed to exist in formal treatments of the path integral. Why isn’t it good-and exciting-when research indicates a new way of thinking about things that might succeed in a case where the older approaches have been unproductive?...

    ---endquote---
     
  9. Jan 23, 2006 #8

    marcus

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    If L is the Lone Ranger then Etera Livine is Tonto

    we should also consider mining what "L" says in the same thread. He's clearly an expert in spinfoam research.
    http://www.math.columbia.edu/~woit/wordpress/?p=330#comment-7840
    http://www.math.columbia.edu/~woit/wordpress/?p=330#comment-7848


    -------quote------

    L. Says:
    January 23rd, 2006 at 12:59 am
    Surely mr. motl is joking when he promotes Nicolai et al. to quantum gravity experts, with no offense intended to them.
    Sure it is fun to do physics but it doesn’t mean that this is not a serious activity where it takes much more to become an expert in a field than writting an incomplete review on a field as it was a few years ago, writting a research paper that address and solve a problem is for instance an example of what it at least takes. I hope the next paper of Nicolai will be a resarch paper addressing some of the issues he cares about and i am sure knowing his capability that it will be interesting.

    I will try to answer peter’s initial request hoping but not feeling totally sure that it might help the debate at this point.

    The latest review of Nicolai et al. is much more satisfactory than the previous one, which essentially was describing the field as it was circa 1998 ignoring most of the work that was done since namely on spin foams exactly with the motivation to address some of the issues he mentioned there.

    He tries in the new review to include some of the more recent material and some of the problems he points out are problems recognised in the community for some time---some being already addressed in the literature. I don’t think that was their intention (Nicolai is a genuine skeptic i think, and we need skepticism in science, it's healthy) but sometimes in the presentation it looks like they are dicovering the issues they talk about and it verges on giving the impression that people working on this are not aware of the issues or concerned. Yes, making a deeper relationship between spin foam and LQG is important (see the recent work by perez on this and on ambiguity in LQG, the recent work of Thiemann on the master constraint and some older and important work by Livine and alexandrov who made key progresses in this direction) and Yes addressing the semi-classical limit is a necessary and key step (more remarks on that later).

    There is however a certain number of imprecisions, omissions and misconceptions in their review. I will talk only about the spin foam section.
    For instance when they present the riemannian spin foams they confused what is done in the literature, namely a quantisation of riemanian quantum gravity, with some hypothetical and to-be-defined hawking-like wick rotated version of Lorentzian gravity.
    The purpose of spin foam is to construct the physical scalar product, and this means that we sum over history with exp i S. No direct relation is therefore a priori expected between Lorentzian and Euclidean theories. That’s why both Lorentzian and Euclidean model are studied, lots of the techniques are similar---the Lorentzian case involving non compact groups is technically more challenging.
    When they discuss the Barrett-Crane weight they confused the 15j symbol prescription (which describes a topological field theory) with the 10j symbol prescription which deals with gravity and present this as an ambiguity.
    They also make the wrong statement that the spin foam approach is plagued with the same amount of ambiguity as LQG. This is not correct, the ambiguity in LQG amounts to ambiguities in the choice of the vertex amplitude (like different spin regularisation) whereas there is a large consensus on the form of the 10j symbol (in fact the intertwiners that need to be chosen are shown to be unique).
    There is an ambiguity in the choice of edge-amplitudes but this amounts to a different choice of normalisation of spin network vertices.
    If one chooses the canonical normalisation that comes from LQG this edge amplitude is fixed uniquely. The possibility to have less natural normalisation was introduced later as an exploration of these models especially in order to have finite spin foam models when loop correction (bubbles) are included (gr-qc/0006107). This attractive possibility was later dismissed by showing that if one insists on preserving spacetime diffeomorphism invariance at the fundamental level---as it was argued---the spurious divergence that arises in these higher loop amplitudes is a residual diffeomorphism signature (gr-qc/0212001).
    They forgot to mention that the Hilbert space of LQG and the Barrett-Crane model are isomorphic in the Riemannian case---they also forgot to mention that there are many different and independent derivations of this weight from the dynamic of GR.
    They present as another ambiguity the restriction to tetrahedral weight. This restriction is perfectly consistent with the fact that 4-valent spin network are enough to construct states with non zero volume and that any LQG dynamics act within this subspace which should be thought of as a superselection sector of the theory.
    So this means that the line of thought that starts from a classical action and construct a quantum gravity weight has singled out one prefered possibility---assuming one chooses the canonical normalisation.
    This doesn’t mean that this model is definitely the right one and having the correct semi-classical dynamic is the key issue, but it shows that
    by addressing the problem of the dynamic in a covariant way and focusing on the implementation of space-time diffeo, one proposal stands out from microscopic derivation and addresses in a satisfactory way some of the LQG issues, which is by itself an important result.

    I don’t want to give the wrong impression and claim that everything is settled for this model, there are still some study and questionning going on about this proposal which is not totally free of potential problems which are not really the ones presenting in NP (except that we are still lacking a strong physical argument for the canonical choice of edge amplitude ), but clearly the presentation NP is very far from fair and accurate.

    They mention some problems with 2D Regge triangulations having to do with spiky configurations without mentioning and knowing (even if they cite the relevant paper in a footnote) that this problem is now fully understood in the more relevant and interesting 3D case (these spiky configuration are just an overcounting due to redundant gauge degrees of freedom, an issue which was overlooked in the first works).

    Also they completley miss the point about how we reached triangulation independence and the fact that there is a auxiliary field theory called group field theory which naturally gives the prescription allowing to compute triangulation independent spin foam amplitude. This is one of the main line of developpement of spin foam model: it started a while ago now ( hep-th/9907154). Ignoring this line of work which explicitly addresses and solves one of the issue they worry about is not a small omission.

    For instance they say `A third proposal is to take a fixed spin foam and sum over all spin’ and cite ( hep-th/0505016) which exactly show on the contrary how to consistently sum over spin foam in order to get a finite triangulation independent positive semi-definite physical scalar product and allows for the first time computation of dynamical amplitudes. This proposal is uniquely fixed by the microscopical model and if one sticks to Barrett-Crane with canonical normalisation this gives a uniquely defined scalar product (so far for Riemannian gravity).

    This is very far away from the picture they draw. The best I can do understand how they came up with this false understanding, is that they haven’t read the paper because it's pretty clear that what is done there is not what they describe.

    Concerning the semiclassical issue they don’t mention at all the new line of development which consist of coupling quantum gravity to matter and integrating out the quantum gravity field in order to read out what is the effective dynamics of matter in the presence of quantum gravity.
    This allowed solving this issue in 3D in a completly unambiguous way.
    They don’t mention all the other work in this directions involving coupling to matter field which were presented at Loop2005 (work of Lee, Starodubtsev, Baratin …)

    I could continue but i think i can stop here for some detail criticism of their work. If I were a referee of this paper I would at least suggest them to go back to their drawing board before submitting it.


    L. Says:
    January 23rd, 2006 at 9:14 am
    Concerning renormalisation group issues i am not sure that all the experts that covered this subject always have in mind that we are talking about quantum gravity and that some of the major results in this fields needs qualification when applied to this subject ( the notion of scale, scaling in background independent theory is way more subtle).
    It doesn’t mean that this cannot apply of course and there are beautiful news results and research going along this line recently, namely in the work of Reuter et al. and Percacci et al. Niedermaier et al. etc… they have by the way revived (not proven, there is a difference) the asymptotic scenario which is another way to go around non renormalisability.
    This is not free of difficulty either (being sure that the statements made are really diffeo invariant being one of the major one).
    An other key and special point about renormalisation group in GR is the fact that G_{N} is at the same time a coupling constant and a wave function normalisation which can be used to fixed your set of unit. The natural unit we work with in quantum gravity is planck unit, in this setting the notion of fixed point is not well defined because the renormalisation group flow vector field (the beta function) depends on the cut-off. If you try to work in cut-off unit (which is the usual scheme but much more delicate concerning diff invariance) a very important subtltety arise that the change of unit is not really invertible, as an introduction see for instance \hept-th0401071.

    By the way an interesting concidence is that having asymptotic safety is realised then in Planck unit the cut-off parameter have a finite value and the effective anomalous dimension at the non gaussian fiexed point is two dimensional. These renormalisation facts resonates strickingly with the picture arising from background independent approaches, wether its LQG, dynamical triang or spin foams.
    I don’t know if this is just accidental or something deeper is going on, one should be careful but it is interesting. I just wanted to make sure that our local experts on the renormalisation are really tune up to apply it to gravity.

    Also 2+1 gravity when treated as a perturbation theory around flat space is non renormalisable but however finite and unambiguously defined. Of course i don’t want to imply that what happens there apply to the 4D case, but this exemple should be applied to most of the statement made here in order to make sure that it doesn’t provide a counterexample
    Concerning the very nice work of Carlip and the potential ambiguities in 2+1 (did you know that the world revolved since then?), lets recall that the ambiguities that are described in the work of Carlip refer to the quantisation of pure three d gravity on the torus. A case that we can now do in the back of the envelopp.
    This case is far too simple and especially singular (it is a non stable RSurface)to be generic, in order to chose the right quantisation you have to show that it is possible to consistently quantised the theory on all types of background while respecting the symmetry. This means that you have to give the prescription to glue amplitudes and extend the quantisation to higher genus surfaces and include topology changes while respecting the diffeomorphism symmetry of the theory.
    The Ponzano-Regge model properly understood does exactly the job and pick one particular candidate available (Maas operator of weight 1/2 if i remenber correctly) in the torus as being consistent and anomaly free, I don’t know of any proof or evidence that an other inequivalent but consistent quantisation scheme exists.
    I don’t have a proof either that that the other possibility are necessarilly inconsistent an interesting but difficult open problem. The bottom line is that there is only one full quantisation of three d gravity known today where everything can be computed: the spin foam quantisation, which is also shown to reduce to the t’hooft quantisatisation of the theory when the later apply and to the hamiltonian chern-simons quantisation, when the later apply namely if you restrict to cylinder.


    -------endquote------
     
    Last edited: Jan 23, 2006
  10. Jan 23, 2006 #9

    selfAdjoint

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    I don't know who "L" is, but he/she seems to be a non-native English speaker, which I conclude from his/her use of "omition" for omission and "attracting" for attractive. I don't think even a poor speller among anglophones would use those locutions. His first response, which you quoted, needs to be highlighted and I hope will find its way into the arxiv. Lubos' persistence in the face of that reasoned and well supported assault shows, I think, desperation.

    BTW Marcus, I have never been a great fan of Kuhn's Structure of Scientific Revolutions, but doesn't it strike you that these debates are reminiscent of his description of the confusion that accompanies a paradigm-shift (in his technical use of the phrase). I am reminded of the bitter and humanly destructive debates over atomism vs. energetics which took place toward the end of the nineteenth century, just beore Planck's and Einstein's breakthroughs.
     
  11. Jan 23, 2006 #10

    marcus

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    I think you are right. It does resonate that way.
    Never been a fan of Kuhnery myself, but it has its grain of truth and may apply here.

    there is something in Newthink that the faithful practitioners of Oldthink just don't seem to "get" no matter how often it is explained
     
  12. Jan 23, 2006 #11
    This is disappointing. Perhaps you could be more specific?
     
  13. Jan 23, 2006 #12

    marcus

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    hi josh,
    I think what selfAdjoint said was just a side remark about the discussion going on at Woit's.
    The topic of this thread is not Lubos obviously.
    Personally I'd rather we not let discussing that individual supplant the main topic.
    if you want to discuss Lubos maybe you could make a new thread, for that express purpose, and maybe lots of people will want to discuss him and it will be popular!
     
    Last edited: Jan 23, 2006
  14. Jan 24, 2006 #13

    selfAdjoint

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    Yes, I was just exhasperated that after "L" had clearly shown how those authors had thoroughly misunderstood LQG, Lubos replied that he still considered them experts on it. My reaction was just that. a reaction, not something I can justify.
     
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