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Don't mess with the pass integral

  1. Oct 25, 2010 #1
  2. jcsd
  3. Oct 25, 2010 #2


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    I do like very much many of Motl's physics posts, but Causal Dynamical Triangulations is not intended to be a discrete theory of gravity. It is hoped to be the low energy limit of some continuum theory. It is of course unclear if this is the case, but some candidates are Asymptotic Safety, scale invariant gravity, or Horava-Lifgarbagez gravity (it's also not clear that any of those are UV complete quantum theories of gravity), but none of those are discrete. In fact, the second paper below cautions comparing their results with spin foams because they assume a continuum limit, whereas the most common spin foam formulations are discrete. Nonetheless, I think Lubos is right that the censoring in CDT is not properly derived, and this is pointed out in the CDT papers too. But basically, they have an interesting computational result, whose meaning is intriguing but unclear.

  4. Oct 25, 2010 #3


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    Of course Lubos is always right in his blogs b/c he never writes down the issues where he is wrong.

    It is not the case that one can always start with a classical action on a smooth manifold and then "derive" the PI or simply use this action to write down the PI. There are two problems:
    1) I don't think that one can derive the PI containing the action from the Hamiltonian PI if the Hamiltonian is not a Gaussian in the momenta b/c then the p-integral can't be done.
    2) I don't even think it's always necessary to derive the PI

    Look at classical mechanics: you do not "derive" the action. You just write down an action and derive some predictions; if they fit to the experiments you found the correct action. Fine.
    You can do the same thing in QM. You simply write down a PI. If it works you found the correct one. You need not care about the derivation (of course in most cases you will start with a classical action but that's not required by the formalism).

    Ontologically it might even be nonsense to start with a classical theory and quantize it. Perhaps one should turn things round, write down a quantum mechanical PI and "classicalize" it.

    Of course CDT (and many other theories) are somehow ad hoc. Most theories are not proved (nor disproved) mathematically but physically via experiments. As soon as this happens nobody cares about the derivation, the axioms and the proofs (the QCD PI is ill defined but it works in the perturbative regime; there it has produced reasonable physical results plus some Nobel prizes; funny, isn't it?)

    One should ask Lubos to write down the full PI for string theory; afaik this is not known so far.
  5. Oct 25, 2010 #4


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    BTW some people seem to think there is only one kind of discreteness in QG and that it always means the same thing, but as Atyy just showed us there are different kinds. In CDT the triangulation is regularization discreteness. It is like doing the conventional particle path integral, with paths divided into piecewise linear segments.

    The test of a good regularization for the path integral is (I think) pragmatic. The piecewise linear paths are a tiny, perhaps quite unrepresentative, subset of all paths---and the triangulated geometries are a small jagged subset of all geometries. The proof of the pudding is in the eating, as the saying goes---the important question is do you get interesting results.

    With LQG (I think, tell me if you disagree) there is inferential discreteness. One imagines making finite measurements and inferring from them some predictions and then making more finite measurements of what was predicted. The information is discrete.

    One is not interested in what space "IS" or what it is "made of". One is interested in how geometry responds to measurements---and how measurements are correlated. So in this sense, Lqg is an inferential theory (in the making). It is information centered.

    There is no reason, for example, that its schemata cannot be locally Lorentz invariant.

    I was watching the second Causets lecture (Fay Dowker and Rafael Sorkin) and I was struck by the fact that in Causets there is even a third kind of discreteness. Or seems to be. It seems not to be entirely analogous to the other two---the discreteness here seems to be more literal than in Lqg and Cdt. And yet the theory also has Lorentz invariance.

    Well, that may be just a side comment--not immediately related to the path integral topic.
    Last edited: Oct 25, 2010
  6. Oct 25, 2010 #5
    I'm in no position to judge Luboš' post on the merits but his tone certainly doesn't make me inclined to bother trying to figure out what he is saying.

    I've run across his type in various arenas over the years and it has never been accompanied by actual deep expertise. I suppose he could be the exception but I find the bluster usually covers over some inadequacies or insecurities at the very minimum. People like him don't help their cause they harm it.
    Last edited by a moderator: Oct 25, 2010
  7. Oct 25, 2010 #6


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  8. Oct 25, 2010 #7


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    I just found out Zohren's supervisor was Dowker, even though his work was with Ambjorn and colleagues. http://arxiv.org/abs/0905.0213
  9. Oct 26, 2010 #8
    How do the CDT people ensure that their path integral is unitary and does not contain
    superluminal effects?
    If these conditions are not met there is no hope that the theory is confirmed by experiment.
  10. Oct 26, 2010 #9


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    I think they do not calculate anything that "propagates"; therefore there is no "speed" on these triangulations. Look at spacetime e.g. during inflation: it can expand with superluminal speed w/o causing any problems; speed of light applies only if something is propagating _on_ a predefined spacetime, but this is not what they are interested in (not yet)
  11. Oct 26, 2010 #10
    What about gravitational waves?

    What about the even more fundamental requirement of unitarity?
  12. Oct 26, 2010 #11


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    They do not look at gravitational waves. A gravitational wave is an artificial object b/c it splits the geomeztry into a background (defining a metric and a light cone) and a wave that propagates on it. The strength of CDT is that it does not introduce this split.

    Regarding unitarity I am not sure. Usually you need unitarity if you want to calculate something like <out|U|in>; then U must be unitary. But I do not know how CDT defines these states |..> and how these matrix elements are related with the path integral Z.
  13. Oct 26, 2010 #12


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    To expand on your comment, there is a lot of sharing between Causets and CDT. After Joe Henson had done Causets for some years and co-authored with Sorkin and with Dowker, he took a postdoc with Renate Loll at Utrecht. Then moved on to Perimeter where he has done both. Loll has had Dowker come to Utrecht to give seminars. David Rideout has programmed cluster/supercomputer tools for several QG models including both of these (so I understand from Steve Carlip). Perhaps Causets and CDT have the kinship of both being "path integral" or sum over histories (SoH) approaches.

    Zohren certainly has co-authored a lot on CDT with Loll, Ambjorn et al. I hadn't realized that he was a Dowker PhD. You've probably noticed how Loll PhDs and former postdocs have crossed over into Asymptotic Safety too.
  14. Oct 26, 2010 #13
    Great, so these guys do quantum gravity but they don't calculate the properties of gravitons. Regarding background independence have these guys ever heard of pertubation theory?

    Unitary is a basic requirement of any theory which claims to be quantum mechanical. It just means that probabilities add up to 1. So it has to be there no matter how you write things down.
  15. Oct 26, 2010 #14


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    It is a common misconception that in order to study quantum gravity one needs gravitons; neither gravitons nor perturbation theory is required. It's just the other way round: especially CDT and LQG try to avoid using gravitons as perturbative degrees of freedom defined on a background; that is the core message of background independence!

    I think "these guys" know perfectly well what they are doing; I only said that "I am not sure ..." and that "I don't know ..."; please note the difference :-)
  16. Oct 26, 2010 #15
    Right, background independence is the new religion.

    300 years of successful pertubation theory are thrown out of the window.

    That's ok but I think it is not only a problem with you. :-)

    I am following the blog of Lubos Motl for quite a while and I am convinced he is a top
    shot physicist. You can check by scanning the archive what and with whom he has published. If you are really interested in fundamental physics I can only give you the advice to read his blog carefully and you will start to see things differently.
  17. Oct 26, 2010 #16


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    I studied QCD for years and I learned that perturbation theory is only valid in a certain regime; it is neither helpful to study the low-energy limit (confinement, bound states, hadron masses, form factors, ...) nor to study conceptual issues (gauge fixing ambiguities, ...). Unfortunately reading standard text books one could get a different impression :-(

    Regarding Lubos: I agree that he is a very talented physicist, but I think he is rather arrogant and even he has certain blind spots. He knows a lot but he is certainly not Doctor Know. Regarding conceptual discussions I usually trust the experts in a certain field; as Lubos is not an expert in CDT ...
  18. Oct 26, 2010 #17


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    What I'm about to say isn't in defense of CDT specifically, it's rather a strong objection against the simplicity of reasoning, and in particular IMO confusing confidence in current QM formalism with the more important foundations of QM - that we don't yet understand - that may survive even into QG.

    I was about to comment earlier when I skimmed Lubos text but decided not to as I've done it before to no good. IMHO he misses the most important and difficult questions in his analysis, and confuses the success of QM formalism for particle physics, with the success of QM formalism for a generic general measurement theory (general inference), that applies also to observer/system scenarious that we are forced into when discussing unification and cosmological models.

    Well probability adds up to one by definition, but the question is more complicated than that IMO. That's not even an argument.

    The question is what the physical meaning of "probability" is in nature! Or rather what purpose the measure we call "probability" is supposed to have, and wether the mathematics of classical logic, QM logic is even properly understood?

    Now, there are some people that just don't care. They don't understnad or see why this is a relevant question.

    But, some people may think that probability is really just a way to count evidence, or rate an expectation. In particular ina way that is subjective = observer dependent. Furthermore this process of counting evidence, seens as processing and storing information, and noting that these are physical processes, certainly suggests that the measures we THINK that probability answers to as per it's axiomatiation, MAY not be quite the most general.

    And in the light in such reconsiderations, violation of unitarity really is not so strange, if with it you mean that the set of possibilities does not fact change at a significant rate relative to the input processing during the COURSE of the processing of data and computation of the measures.

    Sure Lubos is knowledgable but from my perspective his overly exaggerated confidence in current QM formalism without considering what it's supposed to mean, comes out silly.

    Like Marcus mentioned with causets, there are much deeper ideas on discreteness, whos ambition is to even derive QM logic (rather than just "play with the PI"). And these are the things I find interesting, but in that context Lubos comments just makes it entirely clear to me who it is that is misunderstanding something - and it's not the guys Lubos thinks is trying to "rape and distort the basic principles of physics".

    (I do agree that CDT is simple in the sense that a deeper attack could and should also explain the PI.) But Lubos comments generealizes his critique beyond sense.

  19. Oct 26, 2010 #18
    The problem with "trust the experts in a certain field" is that it won't work if the whole field is flawed. That it is what Lubos claims and I would like to encourage you to seriously consider the possibility.

    I agree Lubos is not an easy character. But I claim you would get pretty much the same answers from another top shot, but very polite physicist, which is Nima Arkani-Hamed.
  20. Oct 26, 2010 #19


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    as usual - unfortunately. I think he is blind in a certain sense: he is not willing to see that others are much more open minded regarding weaknesses of their approaches than HE is with HIS approach. I bet asking Loll regarding open issues in CDT you will get a list of questions; try the same with Lubos and strings ... (this could be an interesting experiment; who is willing to start?)
  21. Oct 26, 2010 #20
    I know a little bit of QFT too. Of course if you study it in the regime where the coupling is of order one like the low energy regime of QCD then pertubation theory breaks down pretty much by definition.

    It works well in QED where the low energy coupling is week. As we all know gravity is weak in the low energy limit as well so pertubation theory should work here too.

    In fact every textbook about GR derives gravitational waves as pertubations of the metric tensor around the flat space Minkowksi metric.
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