A new preprint by Michael Douglas indicates that, at least this week, the latest “predictions” from string theory are for:
1. No large extra dimensions.
2. No low scale supersymmetry.
So it looks like the “prediction” of the string theory “Landscape” will be that no physics related to string theory beyond that of the standard model will ever be observable. Thus the only “prediction” of string theory will be that you can never see any physics related to it. This kind of “prediction” is great since it proves string theory must be true. Either you don’t ever see any effects of string theory in which case you have confirmed its predictions so it must be true, or you do see effects of string theory, in which case string theory is even more true.
Nothing really new at Brian’s physics colloquium today. About 300 people showed up, which I think is probably a record for a physics colloquium. Brian doesn’t like Susskind’s “anthropic” arguments, which shows good sense. He still hopes that some new form of non-perturbative string theory will explain the standard model by picking out the right Calabi-Yau, but admits there’s no known reason for this to happen.
Good to hear that Brian remains a believer in the task to find the *right* string-theoretical description for the world around us.
On September 25, 2004 03:56 PM Simplex said:
…But if you have some articles by LQG people criticising string (besides Rovelli’s Dialog) please let us know!…
I don’t know of any articles. I don’t even read the archives regularly. I do however know several of the LQG principals and I’ve heard my share of “string theory is a horribly idea” tirades.
Ironically, one of the most persecuted LQGists, Lee Smolin, is some one I’ve heard make comments similar to, “we have to take string theory seriously…”.
I am still not following your conclusions. For 2-d gravity string theory has the correct canonical quantization. That’s what we talked about so far.
I agree.
When canonically quantizing gravity in 3+1 dimensions one finds that the commutator of the generators has divergences and hence cannot be well defined. LQG circumvents that by using a singular GNS representation where the generators themselves are not represented at all. By comparison with the 2d case one see that this step is not backed by ordinray QM. So the conclusion is that the LQG way to make canonical quantization of 3+1 D gravity work (work for the spatial diffeos that is -even with that trick the Hamiltonian constraint remains a problem) is using some very unusual notion of ‘quantum’.
One comment: the full Dirac algebra of ADM constraints is physically equivalent to the 4-diffeomorphism algebra. As emphasized by Rovelli, phase space is a covariant concept – the space of solutions to the classical field equations. We may label a solution by its positions and momenta at t = 0, but this is just one way to coordinatize phase space. However, some 4-diffeos do not preserve the standard coordinatization, so if we insist on keeping it, we must add compensating transformations, and we wind up with the Dirac algebra. But conceptually we are still dealing with 4-diffeomorphisms, and if we canonically quantize in the covariant phase space instead, that is our constaint algebra.
So in conclusion we find that no way at all is known to apply canonical Dirac-like/inspired quantization to 3+1d gravity.
Because there are additional anomalies which the standard formalism cannot handle.
Although I don’t know much about Liouville field theory, it seems to be some sort of archetype of an anomalously broken gauge symmetry. There is an extra mode, the Liouville mode, which becomes physical when D != 26. Analogously, we may expect that there are extra modes, which are passive in the classical theory, become physical when the diffeomorphism constraints are quantized.
In fact, it is easy to describe these modes. To build representations of the diffeo algebra, we first of all need to expand all fields in a Taylor series around “the observer’s trajectory” q(t), viz.
f(x) = \sum_m f_m(t) (x-q(t))^m
(We need some conditions on the Taylor functions f_m(t) to ensure that f(x) is independent of t). Classically, we can reformulate the field equations for f(x) as a hierarchy of equations for the Taylor coefficients – awkward but in principle straightforward. Upon quantization, the passive modes q(t) become physical – they have canonical momenta and are represented on the Hilbert space – in pretty much the same way as the Liouville mode.
This is necessary in order to quantize a general-covariant theory in a way that represents the diffeomorphism constraints unitarily, because this is the way to build anomalous (and thus potentially unitary) representations of the diffeomorphism algebra. The need for such an expansion is clear since the anomaly is a functional of q(t). In string or field theory, where one never introduces this reference curve, the anomaly is invisible.
In string theory the answer to this problem seems to be that the action for 3+1 d gravity is really embedded into a ‘UV completion’ whose path integral (namely the SFT path integral) can perturbatively be computed or which, for certain asymptotic backgrounds, can be computed non-perturbatively.
If this means if and/or that the canonical Dirac constraints of gravity ever appear here is something that I don’t see. You seem to think so but you haven’t provided evidence for it.
One thing that can nicely be seen in the toy example of 1+1d gravity is that the Dirac prescription for quantizing constraints is just a first guess. The next best guess is Gupta-Bleuler quantization, which tells you that indeed not all states need to be annihilate by the constraints.
These may be regarded as different Virasoro representations. So from my point of view, the right way to quantize is to build unitary Virasoro representations.
But even that is based on ad-hoc assumptions. In the end it is the path integral that counts.
This is a bold statement – let’s just ditch canonical quantization. It is nice that you make this assumption of string theory explicit.
Do you really believe that string field theory or M field theory will not have any canonical formulation?
I believe that before one can draw any conclusions from the results on diffeo algebras that you have in mind, one would have to understand if and in which way they are actually connected to a process called ‘quantization’. Currently it seems that there is no such thing as Dirac constraints for gravity in more than 2-d.
I have previously claimed to have quantized general covariance, and associated quantum reps with any general-covariant theory. However, after having looked into the covariant phase space, I’m leaning towards the opinion that the construction in math-ph/0210023 is really an honest quantization of gravity, although the nomenclature in the paper is not quite right. Here what I do:
1. Start with some general-covariant theory, containing gravity and other fields.
2. Regularize the theory by expanding all fields in a Taylor series and truncate at some finite order p. This is the unique regularization compatible with diffeomorphisms.
3. Construct the space of functions over the covariant phase space, as cohomology spaces. The diffeo algebra acts on these functions spaces by Poisson brackets.
4. Replace Poisson brackets by commutators and represent the Heisenberg algebra on a Fock space. The diffeo algebra acquires an anomaly, so this must be quantization.
5. To remove the regulator, the anomalies must not diverge in the p -> infinity limit. Check and solve the conditions for this.
The cool thing is that these finiteness condition naturally require that spacetime has four dimensions.
There is a catch, though. I need twice as many variables as one would expect, so I really construct the ring of differential operators over phase space in point 3. But this is really the only way that my prescription differs from ordinary QM. In particular, since the regularized theories live in 1D, they don’t need any renormalization beyond normal ordering.
Hi Thomas –
I am still not following your conclusions. For 2-d gravity string theory has the correct canonical quantization. That’s what we talked about so far.
When canonically quantizing gravity in 3+1 dimensions one finds that the commutator of the generators has divergences and hence cannot be well defined. LQG circumvents that by using a singular GNS representation where the generators themselves are not represented at all. By comparison with the 2d case one see that this step is not backed by ordinray QM. So the conclusion is that the LQG way to make canonical quantization of 3+1 D gravity work (work for the spatial diffeos that is -even with that trick the Hamiltonian constraint remains a problem) is using some very unusual notion of ‘quantum’.
So in conclusion we find that no way at all is known to apply canonical Dirac-like/inspired quantization to 3+1d gravity.
In string theory the answer to this problem seems to be that the action for 3+1 d gravity is really embedded into a ‘UV completion’ whose path integral (namely the SFT path integral) can perturbatively be computed or which, for certain asymptotic backgrounds, can be computed non-perturbatively.
If this means if and/or that the canonical Dirac constraints of gravity ever appear here is something that I don’t see. You seem to think so but you haven’t provided evidence for it.
One thing that can nicely be seen in the toy example of 1+1d gravity is that the Dirac prescription for quantizing constraints is just a first guess. The next best guess is Gupta-Bleuler quantization, which tells you that indeed not all states need to be annihilate by the constraints. But even that is based on ad-hoc assumptions. In the end it is the path integral that counts. Evaluating the path-integral of 1+1d gravity correctly yields the BRST quantization, and this finally shows when and in which sense Dirac and Gupta-Bleuler apply. Since already in 2d the BRST quantization highlights a couple of subtleties that are missed with Dirac/Gupta-Bleuler, this teaches us to be careful with applying these methods to higher dimensions.
I believe that before one can draw any conclusions from the results on diffeo algebras that you have in mind, one would have to understand if and in which way they are actually connected to a process called ‘quantization’. Currently it seems that there is no such thing as Dirac constraints for gravity in more than 2-d.
It seems to me that Urs Schreiber, Helling, and Policastro have shown that LQG seems to have made a wrong turn, in making an unphysical construction. Can LQG be rescued?
I think not. However, the substance of my critique of string theory (apart from the overselling and lack of experimental support, which everybody sees) is essentially the Helling-Policastro argument transcribed to 4D:
H-P: Any unitary representation of the conformal algebra in 2D on a conventional Hilbert space is necessarily anomalous. LQG does not admit such anomalies. Hence LQG is wrong.
Me: Any unitary representation of the diffeomorphism algebra in 4D on a conventional Hilbert space is necessarily anomalous. String theory does not admit such anomalies. Hence string theory is wrong.
Urs Schreiber claims that this argument does not apply to string theory, because only the perturbative definition is understood. This only reflects our limited understanding of a complicated theory and is no problem. However, if string theory does not admit a formulation in a conventional Hilbert space with a unitary action of the diffeomorphism group even in principle, then it breaks with conventional quantum theory far more than LQG. And if it does admit such a hypothetical formulation, then the 4D Helling-Policastro argument applies to it.
It seems to me that Urs Schreiber, Helling, and Policastro have shown that LQG seems to have made a wrong turn, in making an unphysical construction. Can LQG be rescued?
I added this because it was important to dig deep for the positions Smolin has assume and for the general public this might not be apparent, so I of course went looking.
Sol2
A case in point, is the understanding of Smolin’s position.
I have followed his thinking as a example of the rigourous, and summations, although at a much generalized level. I do not think I should have been faulted on this as a crank( an overall generalization) of those who have not developed fully from the roads GR has taught us. Including those who wish to try and make a discription of the gravity waves fit some gravitonic expression?
Smolin tells us that General Relativity is not about adding to those structures or even about substituting those structures for possible new structures. Of course, we must understand what he is refering to here .
The basis of Smolins position rejects the idea, that space and time are fixed. He believes it evolves dynamically. He then subcribes, in my way of thinking, to the value of using this structure( it is contradictory to me as I stated up in previous post about photon intersections[Glast limitations] and the intersection of gravtonic considerations.
In the methods explained in terms of Glast’s experimental standing we see where this can be taken further? Smolin calls it a set of relationships between events that take place.
To place such attempts at rediscribing the nature of the spacetime fabric disturbs him?
http://www.physicsforums.com/showpost.php?s=5c7da106e4775f720f0aefeedf9be54e&p=308810&postcount=8
Are we to deny some method to geometrical expression classically defined and not consider this at the quantum levels?
What is Quantum geometry if we cannot linearly describe the action that is taking place at the most suttles levels of existance?
I would appreciate any corrections in my thinking.
ksh95 at September 25, 2004 01:02 PM says:
“In my opinion, both camps could benefit by worrying more about getting their own houses in order and paying less attentions to these petty squables.”
Please point me to some criticisms of String by Loop Gravitists.
I see plenty of criticism of String but almost none from LQG researchers.
there was Carlo Rovelli’s entertaining Dialog (between a junior researcher and a senior) but that was some months back and comparatively light reading.
Lee Smolin has joined in the widespread criticism of the Anthropic Principle but that is not String per se. Thomas Thiemann tried to bridge the gap inspired by a senior string theorist (Hermann Nicolai). I did not think his attempted bridge was at all hostile, though it did not get a very favorable response from string theorists.
What I hear in the way of “squabbling” is very one-sided. String folk like Lubos Motl giving many reasons why LQG cannot possibly be right.
I see little evidence to suggest that Loop people are wasting any effort on squabbling or on criticizing String. Their field is undergoing rapid change and growth, the production of papers has shot up in the past couple of years (although still very small by comparison with more established lines of research) and I do not imagine they have much extra time to devote to controversy.
But if you have some articles by LQG people criticising string (besides Rovelli’s Dialog) please let us know!
In all fairness, looking at how the history developed helps to shape the perspective in regards to the history of strings as it unfolds.
http://xxx.lanl.gov/PS_cache/hep-th/pdf/9909/9909016.pdf
For those inclined to developement a resource for continued reference to hold the higher road to edcuational value, I would draw your attention to the following post.
http://superstringtheory.org:8080/forum/edonline/discussion.jsp?thread=16
Regardless of the demeanor each discussion forum holds, this is an attempt to get minds to further embrace a place that would develope the conceptions beyond personal perspectives.
I defintiely need this spirit of cooperation to draw from.
Regards
As a condensed matter theorist I have no horse in this race so I feel I can offer an non-expert but unbiased opinion. Frankly, it seems like this whole quantum gravty enterprise could be headed south. String Theory’s short comings are will documented. This website being an excellent example. Loop Quantum Gravity is facing some serious criticisms. Examples can be found in Urs’s post below or in http://www.arxiv.org/abs/hep-th/0409182.
In my opinion, both camps could benefit by worrying more about getting their own houses in order and paying less attentions to these petty squables. Funding sources have neither infinite resources or patience. I hear there have been some great advances in AIDS research these days. Similarly, nano sized complex molecules seem poised to usher in the next era of ultra small electronic devices. If you people aren’t careful you’ll find the technologically relevent areas of physics moving into the engineering building, while all the high end theorists adjust to their new offices next to the philosophers.
Chris W. wrote:
This is not quite true. There has been some input to LQG from string theory recently.
A while ago Edward Witten himself demonstrated that the Kodama state which Lee Smolin is so fond of is not normalizable and hence not really a physical state after all.
Then Hod and Dreyer and some other people became quite excited about a numerical coincidence between quasinormal mode spectra of black holes and BH entropy calculations in LQG. Motl and Neitzke published a paper (which is by now TopCited 50) showing that it is indeed just a numerical coincidence. Shortly afterwards it turned out that the entire entropy calculation in LQG was based on a wrong assumption.
H. Nicolai emphasized that LQG people should try to apply their methods to 1+1 dimensional gravity and see if any of the well known results could be reproduced. Shortly afterwards Thomas Thimemann did exactly that and found that the LQG method misses all the standard results. He used the GNS construction as well as Pohlmeyer invariants to do so.
I showed that the Pohlmeyer invariants that he used and could not quite quantize are quantizable in the standard non-LQG-like context. A while later it turned out that this result was already found in the 80s by Isaev, but apparently forgotten. A few days ago Helling and Policastro demonstrated how the GNS construction that Thiemann used leads to the ordinary non-LQG-like quantization when one uses a continuous GNS state instead of the highly singular one used by Thiemann, which is also used in full LQG.
There is a very simple argument that the standard LQG prescription to first solve the spatial diffeos and then impose the Hamiltonian constraint cannot work in principle in 1+1 dimensions. Thiemann circumvented this by including the Hamiltonian constraint in the GNS construction. It was clear that his singular construction has nothing to do with known physics, and indeed he admitted that it is motivated only by the speculation that such ‘unusual quantum mechanics’ might turn out to be correct at the Planck scale.
After enduring LM’s sermon I perused some other recent sci.physics.strings threads and found one of the most lucid and informative discussions (by Urs Schreiber) of "background independence" in string theory that I’ve come across. Its relevance to the topic of this post is conveyed in the following remarks:
I wonder if anyone in the string theory community would bother to articulate this if they weren’t being pressed by the LQG’ers. By the way, I doubt that the present inability to identify a sensible classical limit in LQG will ultimately prove to be an insoluble problem; see hep-th/0404156. The string theorists who disagree should roll up their sleeves, grit their teeth, and demonstrate its insolubility. This would be an extremely interesting result. Unfortunately they apparently think it’s so obviously true as to be not worth the effort.
This one by LM is another in the crusade to rid the world of LQG.
Um, so, if there is no observable, how can the theory be–um–verified?
It strikes me that they are getting more and more into pseudo-physics
blablabla
really good comments on problems that everyone sees.
however, not really constructive in any way.
Well, the “non-perturbative string theory will make everything work” line has been used for nearly twenty years, and has been a huge success for string theorists. I don’t think they’ll drop it anytime soon.
Witten’s most important contributions to mathematics just use QFT, not string theory (Chern-Simons-Witten invariants of 3-manifolds, Seiberg-Witten invariants of 4-manifolds). Much of what people think of as string theory contributions to math are really 2d CFT, not string theory. Seems to me that if you’re just doing CFT, you’re doing 2d QFT, not string theory. You’re only really doing string theory if you try and sum up contributions from different genus calculations. Some of the recent work in topological string theory does give things like Gromov-Witten invariants for all genera simultaneously, so seems to really be string theory.
I think the string theorists are entering very dangerous territory by the constant over-selling of what string theory can or cannot do. The hype over the supposed `Theory of Everything’ is going to backfire and be detrimental to the lay public’s perception of what physicists do.
I contrast the claims of string theorists with QED (anomalous moment of electron, etc), the ‘standard model of strong and electro-weak interactions’ (rho parameter test, etc). Pretty much everone thought (and knew) they were effective theories—hence the modest term ‘model’. Considering what constitutes a model, much more is expected of a ‘theory’, let alone a ‘theory of everything’.
Of course, the problem is the lack of dearth of unexplainable experimental data. So just say that strings/susy etc are one of the possible alternatives—nothing more.
Otherwise, string theory will be viewed as mathematical theology.
The only interesting results in string theory are those that are of interest to mathematicians. BTW, could anyone tell us how many of the new results of interests to mathematicians are of string theory in particular, not QFT? My understanding is that most (all?) of work of Witten of profound mathemtical importance are really based on applications of QFT. So Witten’s work is of lasting importance in terms of his role in progress of mathematical physics, even if string theory does not work out; others, such as those based on ‘string phenomenology’ and the like, I am not so sure.
Seems like “non-perturbative” is everybody’s favorite buzzword and faint hope whenever they have run up against a brick wall and/or ran out of good ideas to work on in particle and/or string theory research. I wonder what they will think up of next, when the “non-perturbative” buzzword starts to wear thin and becomes too much like an excuse of “crying wolf”. (That is without entering into the anthropic stupidity).