Why I am REALLY disappointed about string theory

[atyy]

Thanks Marcus!

So let's come back to Gross' question - and to my last two topics (again slightly modified) -

• what string theory really is
• what the fundamental principles are and how the final theory will look like (in terms of strings or other fundamental degrees of freedom)
• what the major obstacles (inherent to string theory) are preventing us from identifying these underlying principles and constructing this unique framework or theory

I think there are people looking for these answers, but it's hard.

http://motls.blogspot.com/2009/09/murray-gell-mann-80th-birthday-and.html reporting on Gell-Mann's comments:
"I am puzzled by what seems to me the paucity of effort to find the underlying principle of superstring theory-based unified theory. Einstein didn’t just cobble together his general relativistic theory of gravitation. Instead he found the principle, which was general relativity, general invariance under change of coordinate system. Very deep result. And all that was necessary then to write down the equation was to contact Einstein’s classmate Marcel Grossmann, who knew about Riemannian geometry and ask him what was the equation, and he gave Einstein the formula. Once you find the principle, the theory is not that far behind. And that principle is in some sense a symmetry principle always.

Well, why isn’t there more effort on the part of theorists in this field to uncover that principle? Also, back in the days when the superstring theory was thought to be connected with hadrons rather than all the particles and all the forces, back in that day the underlying theory for hadrons was thought to be capable of being formulated as a bootstrap theory, where all the hadrons were made up of one another in a self-consistent bootstrap scheme. And that’s where superstring theory originated, in that bootstrap situation. Well, why not investigate that further? Why not look further into the notion of the bootstrap and see if there is some sort of modern symmetry principle that would underlie the superstring-based theory of all the forces and all the particles. Some modern equivalent of the bootstrap idea, perhaps related to something that they call modular invariance. Whenever I talk with wonderful brilliant people who work on this stuff, I ask what don’t you look more at the bootstrap and why don’t you look more at the underlying principle..."

http://physics.aps.org/viewpoint-for/10.1103/PhysRevLett.103.081301 "In a wider perspective, what do these results mean for superstring theory and its claim to be the sole pretender to the throne of a perturbatively consistent extension of Einstein’s theory? String theory differs from field theory in that, on top of its pointlike excitations, it has an infinite tower of massive states corresponding to the quantized vibrational modes of the string. However, a closer look reveals that its (still conjectural) finiteness hinges not so much on the presence of these extra states, but rather on a new type of symmetry (called modular invariance), which has no field theory analog. This suggests that the new symmetry that may ultimately explain finiteness must act in a way very different from known realizations of spacetime and internal symmetries. Accordingly, we should view the coexistence of several possibly finite candidate theories only as a first step towards the future construction of an underlying theory of quantum gravity, where classical space and time are only emergent concepts, and which would also be viable nonperturbatively."

Nicolai and collaborators have a very interesting line of work - actually, it's not clear to me if this symmetry is just some there in some special limit, or a more general principle - I find it interesting for its relation to quantum chaos - and the Riemann hypothesis:
http://arxiv.org/abs/hep-th/0207267
http://arxiv.org/abs/hep-th/0212256
http://arxiv.org/abs/0912.0854

 

[marcus]

I promised to get a couple of links.
Atyy jogged my memory about one of them.

But there seems to be a lot of free-floating defensiveness. I'd like to understand that better. Who is supposed to be the enemy?

One has to distinguish between criticisms of the mathematics itself, and criticisms of the program (direction, emphasis...)

The most trenchant criticisms I can remember from recent times were from Nima Arkani-Hamed (November 2008) and from Murray Gell-Mann (I will try to find the links).

Gell-Mann was talking about the direction of the program (avoiding hard fundamental questions of principle in favor of increasing elaboration) and Nima was talking about what he suspects are mathematical limitations (not to expect it to say anything new about high energy physics, but maybe about gravity). ...

But we are told repeatedly about imagined bogeymen. "Armchair experts" who apparently were calling for a complete halt ...

Here is the ScienceNews link to that Gell-Mann interview:
http://www.sciencenews.org/view/feature/id/47280/title/Interview_Murray_Gell-Mann

It is not about the creative potential of the mathematics, but is rather critical of the direction of the program---the (inadequate) vision and priorities of senior people who guide the research effort by the projects within the string community which they support.

This is the ScienceNews Murray birthday interview Atyy just quoted where he refers to the "paucity of effort to find the underlying principle."

 

[BenTheMan]

What is *the* theory of quantum gravity?

Are you single?

THE theory of quantum gravity is string theory, of course.

All kidding aside, though:

THE theory of quantum gravity is that microscopic description of Nature whose low energy limit is consistent with both GR and the standard model. While it is true that the low energy physics can not uniquely specify the UV completion, it is true that the low energy physics implies certain constraints on the microscopic physics.

Haelfix was making very general statements about the constraints that any theory of quantum gravity must satisfy if it is to be consistent with what we currently understand about gravity. If things are drastically different, as they may be (but probably aren't), then we have a lot of re-thinking to do.

But personally I'm of the opinion that most people are more or less on the right track.

 

[BenTheMan]

And no, I'm not single.

But if you play your cards right, I'll send you a pair of my used underwear.

 

[negru]

By the way. Whatever other theory you find would still have to explain all the features string theory uncovered so far (like the relation between gluons and gravitons) as well as why adding some extra symmetry (susy) gives stuff like ads/cft. Since we know all these things have to be true and explained (whether real or not - they're consistency checks which have to hold), it seems to me very likely that any other theory will just be a particular solution (or face) of string theory.

 

[MTd2]

What if there are no gravitons?

 

[negru]

I don't think you can avoid gravitons in any quantum theory of gravity. Plus you can always just stick to the effective quantum gravity, which is fine by any standard and has gravitons.

I mean, you have gravitational waves (think a nobel or some went to that). What's the quanta of the gravitational wave then?

 

[MTd2]

Curiously, denying gravitons, at least at fundamental level, ended being what Erik Verlinde means by emerging gravity. He is now saying that the only fundamental string is the open string.

 

[BenTheMan]

What if there are no gravitons?

Then you have to understand Quantum Mechanics as emergent, which is (as far as I can tell) what the loop quantum gravity people are interested in.

 

[atyy]

Curiously, denying gravitons, at least at fundamental level, ended being what Erik Verlinde means by emerging gravity. He is now saying that the only fundamental string is the open string.

So back to where he started?

 

[atyy]

Then you have to understand Quantum Mechanics as emergent, which is (as far as I can tell) what the loop quantum gravity people are interested in.

Nah, Carlo Rovelli has been trying to get gravitons. How can gravitons not exist - I mean quantum GR is a good effective theory at low energies. The only questions is whether the gravityon is fundamental or emergent, isn't it?

 

[MTd2]

Then you have to understand Quantum Mechanics as emergent, which is (as far as I can tell) what the loop quantum gravity people are interested in.

Quantum Mechanics as emergent is something from t'Hooft's dissipative mechanics. Don't you mean GR?

 

[negru]

If it's emergent or not (and I wouldn't trust Verlinde at all on this one) the graviton still exists. For effective gravity it wouldn't really matter. If you don't like the graviton, you'd have to change the basic QM principles.

 

[MTd2]

Why changing QM? The 2-form of Einstein tensor would be reinterpreted as a gauss law entity, it is not a field therm. You might think of gravitons as something like phonons in a lattice, because you mean effective. But I am not sure if space is cold enough so that there are coherency effects on whatever exists as a fundamental lattice.

 

[tom.stoer]

As long as they are not observed experimentally gravitons are purely mathematical entities. There's no physical reason except for analogy (which is not a bad reason!) to expect them to exist.

In LQG there are NO gravitons at the fundamental level.

 

[tom.stoer]

How much has all this todo with string theory?

 

[negru]

They might be just mathematical entities, but consistency is pretty important for any theory. Because an inconsistent theory can predict pretty much anything you want.

Just like any other theory of quantum mechanics you find would have to explain why the hilbert spaces work.

It doesn't matter if gravitons are not at the fundamental level in LQG. It would still have to explain effective quantum gravity.

 

[MTd2]

What if there is no effective quantum gravity?

 

[negru]

Then quantum mechanics is wrong.

 

[suprised]

In LQG there are NO gravitons at the fundamental level.

Because there is no gravity either. And as far as I know, it hasn't been proven to reproduce gravity in 4d at the effective level either - despite they'd been hoping for years.

 

[marcus]

In LQG there are NO gravitons at the fundamental level.

Current status of the LQG graviton propagator:
http://arxiv.org/abs/0905.4082
You know the story at least as well as I do. The graviton is a mathematical concept primarily at home in a stable flat geometric setting. High energy means curved unstable geometry. No question of gravitons being "fundamental", in the usual sense of a high energy regime. The graviton propagator for then-current LQG was derived around 2006, then a new spinfoam vertex got established around 2008 and the calculations are being repeated.
Corrections welcome if anyone has more up-to-date information about the LQG, or a better way to summarize the situation.

 

[negru]

Looks like they get something similar in a particular limit and a particular gauge. In any case, there are two options now:
1)they get the correct answer to all orders etc
2)they don't

1)they'll have to explain the KLT relations. oops, they can't because they don't have any gauge theory do they?
2)they'll say that gravitons aren't real anyway so who cares

Btw I also noticed some susy LQG papers? What's up with that? If susy can be incorporated into LQG, I'll be anxiously awaiting their interpretation of ads/cft.

So at this time I really don't think we should keep getting LQG in this discussion, when we're talking about consistency, predictions, or basically anything like that. We're getting too off-topic with LQG speculations.

 

[MTd2]

Then quantum mechanics is wrong.

This is like saying that a water flux must be quantized otherwise quantum mechanics must be wrong. Only very special cases of fluxes, like He4, have some sort of quantization. Water is quantized in H2O molecules, He3 at 1K has an effective quantization as a "quantum liquid", superfluid. Hmm, and I am not really talking about LQG here. Just saying what is happening with Erik Verlinde, so that you can already be aware when other people come to you and say these things.

 

[tom.stoer]

So at this time I really don't think we should keep getting LQG in this discussion, when we're talking about consistency, predictions, or basically anything like that. We're getting too off-topic with LQG speculations.

I fully agree; it's a nice detour, but does neither help to understand gravity in the context of string theory nor unification of other forces with gravity which is not the focus of LQG.

So again I would like to come back to the list of questions

• what string theory really is
• what the fundamental principles are and how the final theory will look like (in terms of strings or other fundamental degrees of freedom)
• what the major obstacles (inherent to string theory) are preventing us from identifying these underlying principles and constructing this unique framework or theory

and I would like to ask if one should add the nature of fully dynamical gravity and/or geometry as another deep question. I would say "no", perhaps as one example of an onstacle, but not as a fourth question.

Gravitons in string theory - fine; some sorts of black hole calculations - fine; but what I still do not understand in all details is how one can argue that string theory fully incorporates gravity as dynamical background independet geometry. Looking at the string theory action it uses a fixed metric in target space; there is no way how a propagating string can affect this geometry. Of course string theory contains all fixed geometries somehow, but it does not allow one to change from one to the other and to describe this via dynamical evolution. By that I mean that I cannot see how to formulate the collaps of a black hole in string theory; I cannot start with some geometry and then looks what will happen later. As far as I can see this is not due to technical problems, but due to conceptual one; I simply cannot formulate this question in the context of strings.

Afaik one can get around this problem in AdS/CFT (I do not understand the details here) because one is able to translate gravity into CFT w/o gravity such that dynamical geometry is represented by dynamical fields on a background. In that sense the theory is fully background independent except for the AdS which is more a topological superselection sector (due to its boundary conditions), but within AdS geometry is allowed to fluctuate freely.

If this is true (that means if I understood correctly) the problem of background independence has been solved in the AdS/CFT context (on the CFT side), so all what remains to be done is to allow for other spacetimes like dS etc.

And if this is true gravitons ceased to exist since we a) do no longer study gravity in AdS with the help of "perturbative gravitons" but we b) we translated it to CFT where there are simply no gravitons :-)

 

[ccdantas]

http://egregium.wordpress.com/2007/05/24/is-there-more-to-gravity-than-gravitons/"

 

[MTd2]

Let me quote the above paper:

http://arxiv.org/abs/gr-qc/0409089

From Gravitons to Gravity: Myths and Reality

T.Padmanabhan
(Submitted on 23 Sep 2004)
There is a general belief, reinforced by statements in standard textbooks, that: (i) one can obtain the full non-linear Einstein's theory of gravity by coupling a massless, spin-2 field $h_{ab}$ self-consistently to the total energy momentum tensor, including its own; (ii) this procedure is unique and leads to Einstein-Hilbert action and (iii) it only uses standard concepts in Lorentz invariant field theory and does not involve any geometrical assumptions. After providing several reasons why such beliefs are suspect -- and critically re-examining several previous attempts -- we provide a detailed analysis aimed at clarifying the situation. First, we prove that it is \textit{impossible} to obtain the Einstein-Hilbert (EH) action, starting from the standard action for gravitons in linear theory and iterating repeatedly. Second, we use the Taylor series expansion of the action for Einstein's theory, to identify the tensor $\mathcal{S}^{ab}$, to which the graviton field $h_{ab}$ couples to the lowest order. We show that the second rank tensor $\mathcal{S}^{ab}$ is {\it not} the conventional energy momentum tensor $T^{ab}$ of the graviton and provide an explanation for this feature. Third, we construct the full nonlinear Einstein's theory with the source being spin-0 field, spin-1 field or relativistic particles by explicitly coupling the spin-2 field to this second rank tensor $\mathcal{S}^{ab}$ order by order and summing up the infinite series. Finally, we construct the theory obtained by self consistently coupling $h_{ab}$ to the conventional energy momentum tensor $T^{ab}$ order by order and show that this does {\it not} lead to Einstein's theory. (condensed).

*************

Padmanabhan is the guy who Verlinde bases his holography, without gravity, ideas.

 

[atyy]

I have pretty much all the same questions as a layman as tom.stoer's long post #129 (except I think of it as "what's exciting in string theory?").

But regarding the question of background independence in perturbative string theory, is it really that a propagating string cannot change the background geometry? After all, the string contains the graviton, and the graviton is geometry. Like in perturbative classical GR, where the full metric g=background+h. The theory is still at least somewhat background independent, since actually only g will turn out to be observable, and it will get its dynamics from h. The problem with perturbative classical GR seems to be that it is perturbative, I think, more than that it is background dependent (but am not sure about this, since the attempt to get a non-perturbative equation for background+h with dynamics restricted to h can get you to almost the full equations, but not quite, since it requires that spacetime can be covered by harmonic coordinates, Eq 62 and following discussion in http://relativity.livingreviews.org/Articles/lrr-2006-3/ )

 

[suprised]

So again I would like to come back to the list of questions

• what string theory really is
• what the fundamental principles are and how the final theory will look like (in terms of strings or other fundamental degrees of freedom)

Obviously no one can answer these for sure, this is an unfinished theory, and all what one can do is inspired speculations. I had outlined mine above.

• what the major obstacles (inherent to string theory) are preventing us from identifying these underlying principles and constructing this unique framework or theory

I think the following is not inherent to string theory except the last one:

Computational difficulty… lack of human intelligence...armchair experts who try undermine the effort


It is simply not so that one is able to compute anything, even for a completely well-defined theory (try to analytically compute the hadron spectrum from the QCD langrangian, eg. And anything having to do with gravity is going to be much more complicated). So that's why supersymmetric toy models are so useful - as many things can be computed, sometimes even exactly. This is a quite non-trivial feat and source of a lot of excitement, as well as of many conceptual insights. Whether one would ever be able to get beyond studying toy models.. I don't know, but I doubt it.

; but what I still do not understand in all details is how one can argue that string theory fully incorporates gravity as dynamical background independet geometry.

I don't think that anyone claims this!

Looking at the string theory action it uses a fixed metric in target space; there is no way how a propagating string can affect this geometry. Of course string theory contains all fixed geometries somehow, but it does not allow one to change from one to the other and to describe this via dynamical evolution. By that I mean that I cannot see how to formulate the collaps of a black hole in string theory; I cannot start with some geometry and then looks what will happen later. As far as I can see this is not due to technical problems, but due to conceptual one; I simply cannot formulate this question in the context of strings.

This is very true; at least for the on-shell formulation of string that we know. There is simply no known formulation which would allow to "compare" different backgrounds, describe tunnelings, etc, as all this would require an off-shell formulation that we don't have. Some limited toy models exist here and there, eg some insights can be gained by considering tachyon condensation, which is a model for relaxing to a ground state. Some other toy models for going off-shell are topological strings where one can identify on-shell vacua as critical points of off-shell superpotentials. AdS/CFT provides a background-independent setup in a certain sense, for a specific situation, but this also doesn't allow to address questions of vacuum selection or Calabi-Yau's, etc.

Obviously one of the major missing points in string theory is the lack of an off-shell, perhaps background independent formulation; I guess no one would contest this statement… it's hardly a point of disagreement for string physicists!

And if this is true gravitons ceased to exist since we a) do no longer study gravity in AdS with the help of "perturbative gravitons" but we b) we translated it to CFT where there are simply no gravitons :-)

In would say if gravitons turn out not to exist, string theory is dead (in the sense of unification with gravity); it still would be relevant for gauge theories, and describe QCD strings etc.

 

[Haelfix]

The geometry definitely can change (and in fact the topology can too) in a dynamic way, then there are backreactions and consistency checks that can be performed to ensure that you were in fact correct. Of course if the geometry change is too violent, the higher orders of perturbation series do become important and then for lack of a calculational scheme to compute them, you either have to guess the answer, invent a new nonperturbative method or look for some sort of duality.

However the only problem that I am aware off is that explicit examples of calculations are horribly messy and unlovely and its hard to do in full generality, but then that shouldn't be so surprising. ADM calculations are often messy as well.

 

[MTd2]

Would a non perturbative formulation of string theory help with an off shell formulation?

BTW, I think it is strange to talk about even about the existence of a background for a string theory, right?. Anything in string theory is about string interactions, even dimensions are fields on the worldsheet.

 

[MTd2]

The thing I don't like in string theory is really, really, very simple. LQG, Asymptotic Safety, GR, Quantum Mechanics, String Theory are very beautiful theories, all of them with a degree of non-intuitiveness. This part of not being non intuitive, and making us change our perception is really cool, but what bother's me is how spin is taken for granted whereas all other quantum numbers can be obtained from something else.

I mean, It really bothers me is that there is no justification for the origin of spin.

 

[marcus]

I have to say this exchange impresses me by its modesty forthrightness and absence of obfuscation. "Surprised" gives a professional perspective on his own branch of research which allows room for other approaches. Congratulations to both parties here:

It is simply not so that one is able to compute anything, even for a completely well-defined theory (try to analytically compute the hadron spectrum from the QCD langrangian, eg. And anything having to do with gravity is going to be much more complicated). So that's why supersymmetric toy models are so useful - as many things can be computed, sometimes even exactly. This is a quite non-trivial feat and source of a lot of excitement, as well as of many conceptual insights. Whether one would ever be able to get beyond studying toy models.. I don't know, but I doubt it.

Originally Posted by tom.stoer
; but what I still do not understand in all details is how one can argue that string theory fully incorporates gravity as dynamical background independent geometry.​

I don't think that anyone claims this!

Originally Posted by tom.stoer
Looking at the string theory action it uses a fixed metric in target space; there is no way how a propagating string can affect this geometry. Of course string theory contains all fixed geometries somehow, but it does not allow one to change from one to the other and to describe this via dynamical evolution. By that I mean that I cannot see how to formulate the collapse of a black hole in string theory; I cannot start with some geometry and then looks what will happen later. As far as I can see this is not due to technical problems, but due to conceptual one; I simply cannot formulate this question in the context of strings.
​

This is very true; at least for the on-shell formulation of string that we know. There is simply no known formulation which would allow to "compare" different backgrounds, describe tunnelings, etc, as all this would require an off-shell formulation that we don't have. Some limited toy models exist here and there, eg some insights can be gained by considering tachyon condensation, which is a model for relaxing to a ground state. Some other toy models for going off-shell are topological strings where one can identify on-shell vacua as critical points of off-shell superpotentials. AdS/CFT provides a background-independent setup in a certain sense, for a specific situation, but this also doesn't allow to address questions of vacuum selection or Calabi-Yau's, etc.

Obviously one of the major missing points in string theory is the lack of an off-shell, perhaps background independent formulation; I guess no one would contest this statement… it's hardly a point of disagreement for string physicists!

Originally Posted by tom.stoer
And if this is true gravitons ceased to exist since we a) do no longer study gravity in AdS with the help of "perturbative gravitons" but we b) we translated it to CFT where there are simply no gravitons :-)​

I would say if gravitons turn out not to exist, string theory is dead (in the sense of unification with gravity); it still would be relevant for gauge theories, and describe QCD strings etc.

 

[element4]

I mean, It really bothers me is that there is no justification for the origin of spin.

How about the unitary (projective) representations of the Poincare group? For particles with mass $$m^2>0$$, the little group is $$SU(2)$$ aka. spin. Thus spin is a consequence of relativistic symmetries.
Maybe you have something more subtle in mind?

 

[petergreat]

I mean, It really bothers me is that there is no justification for the origin of spin.

Even an un-quantized classical Dirac field has spin, i.e. the conserved Noether charge associated with rotations is a sum of orbital angular momentum and intrinsic angular momentum. A classical Dirac field is nothing but a system of linear PDEs! If spin is a valid concept in something as elementary as a system of linear PDEs, why is there any mystery about it? What I'm trying to say is that although spin is discovered in the weird quantum world, the notion of (unquantized) intrinsic angular momentum is possible even classically. (Although a classical Driac field is irrelevant to physics.)

 

[MTd2]

Maybe you have something more subtle in mind?

More subtle in mind. Every quantum number on a low energy effective theory can be related to a specific compactification of branes to where string attach. So, you have an explanation from more fundamental objects. Except for the spin. Note here that we are talking about a surface, so I keep wondering why not looking for some kind of vorticity quantization because of topological considerations.