|Oct13-04, 10:52 AM||#1|
Various Critiques of Loop and String
Various critiques have gained prominence lately---or maybe it is not so lately and they just now got my attention. for example there is the controversy at Wiki over Lubos polemic and there is Thomas Larsson SPR thread about representing diffeos. maybe we should have a thread to comment.
Larsson's POV puzzles me and maybe someone here can help me by explaining
---post 4 of his diffeo thread---
Helling-Policastro showed that canonical quantization a la LQG is
strange. However, it might be worth pointing out that string theory
admits no canonical quantization at all in more than two dimensions.
Everything is done using path integrals. Usually one justifies formal
manipulations with path integrals by referring to the well-defined
Hamiltonian formalism. This seems somewhat dubious if no Hamiltonian
This puts some perspective on LQG's achievements. It is not obvious
to me that strange canonical quantization is so much worse than no
canonical quantization at all.
The secret reason why canonical quantization of diff-invariant
theories in more than 2D fails is that the relevant diffeomorphism
group anomaly is little known. The diffeomorphism generators should
be represented by unitary operators on a conventional Hilbert space,
and all non-trivial such representations are anomalous. Since neither
the string theory nor LQG camps care about these anomalies in 4D,
they cannot do canonical quantization.
He seems to have a special idea of what is canonical quantization, requiring that there be a unitary rep of the diffeo group. then he shows why Loop (or String, whatever) cannot have a unitary rep of the diffeo group.
then he concludes that they cannot have (his idea of) canonical quantization.
but when I read mainstream LQG people they do not say they have a unitary rep of the diffeos, and they have been saying for over 10 years that the LQG approach is canonical quantization of GR. they obviously MEAN something different from Larsson when they say canonical. His requirement for what it means is more stringent, apparently.
Larsson applies his demands even-handedly, I must say. Here is a recent post at NEW. This is yesterday (12 October) on the Witten thread
---quote from Larsson---
response to: If you were Witten, what would you do to "fix up" string theory as it's known today (besides fixing up diffeomorphism anomalies)?
What would convince you to change your mind and be in support of string theory?
In the unlikely event that string theory acquired massive experimental support, I guess that I would have to believe in it. But the present situation is rather the opposite.
The construction of a quantum theory with some prescribed symmetries is, from my perspective, the same thing a constructing the representation theory of the group of symmetries. There is really a 1-1 correspondence:
1. Given a quantum theory, its symmetry group acts by a unitary representation on the Hilbert space.
2. Given a unitary representation of some group, the Hilbert space on which it acts is the Hilbert space of some quantum theory.
In particular, the Hilbert spaces of the fully interacting gauge-invariant or diff-invariant theories carry unitary representation of the groups of gauge transformations and diffeomorphisms. Perhaps one should factor out gauge symmetries, although I don't see why - it is definitely not necessary for consistency (unitarity). But this is really irrelevant for the argument. The anomalies must be there at least before factoring them out, so if you cannot write down the anomalies in the first place, you lose.
I am pretty sure that there is no way to fix string theory. The representations look the way they do, and their Hilbert spaces look rather like fixed versions of field theory. I don't see any way to "fix" SU(2) to allow for unitary spin-1/4 representations either.
I don't have a clue what I would do if I were Witten, and I don't really care. It's not my problem.
Posted by: Thomas Larsson at October 12, 2004 12:20 PM
|Oct13-04, 11:14 AM||#2|
then there is this diatribe of Lubos over at Wiki
Lubos originally inserted in the regular LQG article
(it has questionable and misleading statements as I'll discuss later, so doesnt really fit in regular encyclo type article, but anyway)
and they have now tagged it as controversial and are having a pow-wow in the "talk" section---but no one over there seems to know enough LQG to put the finger on Lubos troubles!
here is their tag at the top line:
"The neutrality of this article is disputed. See the article's talk page for more information."
It is interesting to see how they handle this kind of thing at Wiki. It is a lot of work for them, I reckon regretfully. Short of simply disqualifying Lubos from contributing to Wiki, I dont see anything but blood sweat and tears for them. So they are embroiled in their "talk" section about it.
Anyway, i will point out some misleading things in Lubos Loop crit.
but my attitude is that no one who knows anything about LQG would take his article seriously and that his article is on balance beneficial because it draws attention and stirs up interest---as beating the drum and ringing the alarm bell will do---and so is a kind of Theatrical Entertainment. even a little charming (as Lubos often is)
All good fun, if a little hard on Wiki.
|Oct13-04, 11:23 AM||#3|
practically the first thing Lubos says, in his point #1, gives the
impression that LQG insists on dimension 4
Lubos: The spacetime dimensionality (four) is another assumption that cannot be questioned, much like the field content.
but that is wrong. LQG standard treatment, like the little Rovelli Upadhya primer, develops the theory generally for any number of dimensions.
Loop has even been studied in various other dimensions like 2+1, as well as the normal 3+1. It works. You can do it with N dimensions.
So what is Lubos talking about?
|Oct13-04, 11:38 AM||#4|
Various Critiques of Loop and String
In his recent "Invitation" Smolin makes the point that Loop is not wedded to the Einstein-Hilbert action and is free to include correction terms or whatever other terms. Indeed this kind of thing is being explored because it offers some interesting possibilities.
But Lubos alread in point 1 is giving the impression that Loop is rigidly fixed on one action and he expands on that in point 2.
in point 1. he says:
It even assumes that Einstein's equations are more or less exact in the Planckian regime. this is really too vague, Loop does not need to assume that E. eqns are exact anywhere, what does "more or less" mean, and what is wrong with Loop having the option of modifying E. eqns in whatever regime?
but then he gets more definite about it in point 2.
According to the logic of the renormalization group, the Einstein-Hilbert action is just an effective description at long distances; and it is guaranteed that it receives corrections at shorter distances
because this is presented as a criticism of Loop it gives the misleading impression that Loop is restricted to the Einstein-Hilbert action---not true---and that String is superior because it allows for correction terms.
|Oct13-04, 11:57 AM||#5|
my feeling is that Lubos performance Wiki is self-discrediting and in the long run must be an embarrassment to Harvard physics dept.
However no Loop person that I know has wanted to point this out. Fraid I just count as a spectator.
I did not see anyone who does LQG research reply to Lubos. He has stuff that is wrong or misleading but it does not seem to do any harm (unless Wiki readers believe it, and they must look out for themselves I guess)
My attention was caught by Lubos point 13 which doesnt take account of recent papers.
Smolin "Invitation" says Loop Hilbertspace is separable and cites Rovelli and Fairbairn recent article to that effect. But Lubos says:
While all useful quantum theories in physics are based on a separable Hilbert space, i.e. a Hilbert space with a countable basis, loop quantum gravity naturally leads to a non-separable Hilbert space, even after the states related by diffeomorphisms are identified. This space can be interpreted as a very large, uncountable set of superselection sectors that do not talk to each other and prevent physical observables from being changed continuously. All known procedures to derive a different, separable Hilbert space are physically unjustified.
No one has shown that Rovelli/Fairbairn is "physically unjustified". It just comes from Gen Rel which is pretty damn physically justified. GR is invariant under extended diffeos. So if you make LQG follow GR in this you get a separable hilbertspace----that is at the kinetic states level before any further reduction involving constraints.
Lubos writes as if he is the arbiter of what is "physically justified" and he apparently dismisses Rovelli/Fairbairn, and Smolin ( and now according to personal communication Ashtekar/Lewandowski; see R/F paper's notes) without citing them or giving reasons.
|Oct13-04, 12:26 PM||#6|
Loop quantum gravity is not a predictive theory. It does not offer any possibility to predict new particles, forces and phenomena at shorter distances: all these objects must be added to the theory by hand. Loop quantum gravity therefore also makes it impossible to explain any relations between the known physical objects and laws.
I am trying to understand the reasoning and it seems to me the main drift is to take criticisms being made of String (by physics community in general, not by LQG'ists who have mostly been staying out of the argument business)
and apply them to Loop.
String has been being beaten by the stick of its not being predictive (the famous 10^100 vacua, one now hears 10^200 or even more, the much deplored appeals to Anthropism)
so I guess Lubos thinks the best defense is offense and he takes the stick and starts beating on the little guy next to him.
thing is, Loop is doing rather well at getting to the predictive stage
(see the Polish winterschool lecture notes, a ten day symposium on Quantum Gravity Phenomenology)
See Amelino-camelia latest (october 2004) article, he is so to say the leading expert on QG phenomenology---chairs the sessions on it.
See Smolin's recent "Invitation" with its "Near term experimental prospects" section. That side is coming along great.
and testing is not such a big deal because Loop has a narrower aim. It is not expected to go on record as to whether (A) SUSY and/or (B) electroweak symmetry breaking will or will not be seen at upcoming LHC energy. These are things string theorists are under pressure to give their theory's prediction about, because its broader scope includes it. But havent as yet offered unambiguous prediction.
Acid test of whether theory is predictive, and all that.
predictivity is a String Theory problem at present, and getting a lot of attention, so Lubos projects that on Loop where it doesnt really fit!
Progress towards testability is actually a Loop strong point and one of the
most exciting parts of the story.
|Oct13-04, 01:26 PM||#7|
I was looking down the list and beginning to wonder if one really needs to reply. the points seem strained as to be self-discrediting
this point 7, for example.
Spin networks do not actually pick out a preferred frame.
they do not actually constitute a return to the "19th Century luminiferous aether"
the talk about Background Independence is symptomatic. Gen Rel is B.I. and Loop gravitists have made a point of preserving this basic feature---String theorists not---so BI is a Loop strong point.
It has gotten so people mean different things by BI. In case of Loop it is that the theory is built on a plain manifold without preconceived geometry, no prior stipulated metric. the metric, or geometry, is supposed to arise in a dynamic way, to be a quantum geometry state, in effect.
the author will not be satisfied, it seems, until he completely turns the tables (at least in his own realm of discourse)----for him Loop must "really" be background DEpendent and it must be String that has the virtue of Background Independence. concepts must be redefined somehow, which I do not understand, to make that true.
BTW pretty much every proposed kind of Quantum Gravity has some kind of scale, like Planck scale, and Loop is no exception. Incorporating Planck (or other fundamental) scale has led to versions of DSR---which means special relativity modified to include some other invariant scale in addition to speed of light. the upcoming opportunities to test quantum gravity are essentially about this.
this is what Lubos critique calls "Clash with Special Relativity"
well, that is one way to phrase it.
main thing is that QG involves some testable modifications of SR.
|Oct13-04, 01:37 PM||#8|
after looking some more at Lubos Wiki critique of Loop
i am thinking more and more that it does not need any response
it is Wiki's problem, and they can deal with it however
their institutional culture handles these things
But there are other critiques of both string and loop making the rounds!
so I think we should be up for discussing them.
Especially that of Thomas Larsson.
One reason for focusing on Larsson's critique because selfAdjoint
brought it up, and he generally has good ideas. May be something to it. would be great if we could get Larsson to come here. I would like
to understand the substance of T.L. critiques both of string and loop better.
|Oct13-04, 06:25 PM||#9|
Sean Carroll, in his blog Preposterous Universe has picked up on Lubos embroilment in a P.O.V. controversy at Wiki.
it is the 13 October entry (today) and kind of funny. he lists all the other controversial issues (bigfoot, religious prostitution, canibalism, whatever) that Wiki has had to quarantine and hash out and wonders publically how Loop Quantum Gravity ever got into such company.
here is the specific link
though just going to the blog gets you the same while it is current.
|Oct13-04, 07:57 PM||#10|
I loved the term "internets", slyly picking up the President's usage from the last debate. And just the list of topics is a hoot. Just about everything there is controversy about. And I guess as he says, that does include LQG. I wonder why string theory isn't there, though.
|Oct14-04, 10:00 AM||#11|
---quote from Serenus---
Amusing comment I heard [from a grad student]: LM's rabid hatred of Loop Quantum Gravity reminds one of some of those campaigners against child pornography --- they seem to be a little *too* interested. You never know, it might even turn out that LM's home computer is full of Lee Smolin's papers, for "research" purposes only of course...
serenus zeitblom| Wed, October 13, 2004 @ 9:19 pm
I suspected it was something like this last year when I first saw Lubos great paper on Quasinormal Modes. It has become an important part of the LQG canon! And tho Lubos has made this important and helpful contribution to LQG he always emphasizes that his paper, and the followup with Andy, shows the theory's flaws.
I'll bet Lubos has more citations on that one QNM paper than on all his string writings combined. Intricacies.
Oh, the answer to your question. It must be that String just isnt sexy enough----(joke)----you could always start something at Wiki about the Anthropic Principle.
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