Why I am REALLY disappointed about string theory

[tom.stoer]

Sorry for interrupting this discussion.

Thanks a lot for your patience and you continuing interest - but I have to step out for a while. I will stay in the mountains (alps, Europe) for hiking and climbing. Hope I'l be back in a while and still find this thread active.

Best regrads
Tom

 

[marcus]

Hope I'll be back in a while and still find this thread active.

I don't know if one can expect steady continued activity. But even if it is quiet for a few days I still expect that the activity will start back up when you return. Have a a great time in the mountains!

 

[tom.stoer]

Bad wheather, so I will stay for another day :-)

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.

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.

Regaring background independence: the problem is rather simple and one can see it already it 26-dim. bosonic string. The fundamental variable is X^a(s,t), with a=0..25 and s,t are the worldsheet coordinates. The string action contains X^aX_a so one contracts a in 26-dim. using a metric. It's exactly this metric that is not dynamical.

 

[tom.stoer]

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.

What I know is that the CY topology can change. The "global topology" will not change due to "superselection rules" or something like that; I guess it's like a topological conservation law, something that forbids e.g. tunneling from a kink to an anti-kink in the Sine-Gordon model due to the potential barrier.

What I don't inderstand is how (e.g. in the classical world sheet formulation) you can either plug in or get out a dynamical target space metric.

What I see is that if you map gravity => CFT then via changing something in CFT dynamically you automatically change the geometry after the inverse mapping CFT => gravity.

Nevertheless in the original formulation you still have the problem that all strings ("gravitons") are not able to change the background geometry. That means (as you say) that it's horribly complicated to do or understand these calculations. But this is exactly the point: if you start with the FRW k=+1 metric in GR you will by no means be able to find FRW K=-1 or Kerr by perturbation series. So in order to get the big bicture I think one must address this weak point of the theory.

One question: I asked for string field theory, but it was said (by Witten) that this is too messy to be true; then you are talking about an off-shell formulation which is missing. But isn't this string field theory?

 

[Haelfix]

Well, going from K=1 FRW to K = -1 FRW I think is probably something you wouldn't want String theory to show, since it is classically forbidden (then again who knows what quantum mechanics can do). But I think the gist of your post is correct.

Its worth recalling a few terminology points for the readers. A background in string theory has considerably more information than a background in GR. That is to say, the metric is only one field amongst many.

Also its worth emphasizing what can be shown in principle, vs what can be shown explicitly.

The fact that you have gravitons and a target space that satisfies einsteins equations exists does tell you a few things. It tells you that in principle a coherent state of many of these gravitons can and will form a gravitational wave that will change the target space metric dynamically. However, just like in the case of QED, you don't see many people working out explicit details of how a coherent state of QED photons changes the classical EM field. Instead you simply work with Maxwell's equations when doing classical calculations directly for most practical purposes.

So I think the point is that we are less interested in how the classical metric changes in isolation, and more with how the generalized quantum background changes in string theory, and that is important. Unfortunately as Surprised explained, there you really do need an offshell formalism to work it out in generality as opposed to a few explicit examples (usually discovered with dualities) or a few toy models where you have to bend over backwards via many picture changing operations to finally arrive at a result.

 

[tom.stoer]

I don't want to go from k=+1 to k=-1. I only want to say that if you would use k*1 as background, that you can't construct k=-1 simply by using perturbation theory.

So a background dependend formalism with perturbation expansion hides certain aspects of the theory, namely (if you start with k=+1) that k=-1 exists and that there is a very easy connection, namely simplychanging K=+1 to k=-1. If you start with only one background and if you only nw this background, you have no chance to explore the whole space of solutions.

That's what happened in string theory. There is no global picture that allows you to look at the whole theory. You can only look at individual pieces and hope to be able to constuct dualities or something like that.

I was thinking that string field theory would provide something like this global picture.

Summarizing this discussion I would say that we have identified some obstacles, namely
- background independence
- off-shell formalism

 

[atyy]

I was thinking that string field theory would provide something like this global picture.

Summarizing this discussion I would say that we have identified some obstacles, namely
- background independence
- off-shell formalism

I think these have been known for many years as major questions that many would like to have solved. Polchinski wrote very similarly to you, suprised and Haelfix http://blogs.discovermagazine.com/c...t-post-joe-polchinski-on-science-or-sociology "If you have the flat spacetime S-matrix, you actually know a lot about curved spacetime, since you can form a very complicated geometry by throwing together a lot of gravitons in a coherent state. From a particle physics perspective, where the goal is to measure the underlying Lagrangian, this is enough: the S-matrix encodes all local physics in curved spacetime. Further, with this effective Lagrangian one can study processes in a fully curved spacetime, as long as the curvature stays below the string scale. One can then list things that are not covered by this: first, cosmological questions like initial conditions and spacetime singularities, and these are indeed open questions and the subject of active research"

I too would like to know: what is the current thinking on string field theory? 5 years back, Taylor's review http://arxiv.org/abs/hep-th/0605202 speculated that "String field theory is the only string formalism developed so far which, in principle, has the potential to systematically address questions involving multiple asymptotically distinct string backgrounds. Thus, although it is not yet well defined as a quantum theory, string field theory may eventually be helpful for understanding questions related to cosmology in string theory."

Is development slow because it is difficult, or is now thought not to be the way forward any more (just like matrix models like BFSS or IKKT are no longer thought to be completely general non-perturbative formulations, compared to 10 years ago)?

 

[marcus]

Summarizing this discussion I would say that we have identified some obstacles, namely
- background independence
- off-shell formalism

As a footnote, here's the first paragraph of a 1993 paper by Edward Witten:
==quote==
Finding the right framework for an intrinsic, background independent formulation of string theory is one of the main problems in the subject, and so far has remained out of reach. Moreover, some highly simplified special cases or analogs of the problem, which look like they might be studied for practice, have also resisted understanding.
==endquote==
http://arxiv.org/pdf/hep-th/9306122

 

[marcus]

The standard textbook "Gravitation" by Misner Thorne Wheeler ("MTW") calls background independence "no prior geometry."

The idea of "no prior geometry" can get confused with a another notion: that a theory might encompass a lot of different posssible prior geometric backgrounds. It is probably worth making a clear distinction.

 

[petergreat]

Sorry for interrupting with a very simple question. How is it possible that string theory can calculate black hole entropy without an off-shell formalism? Black holes are intrinsically non-perturbative objects. There are no black holes in the out-states of an S-matrix because they evaporate in the far future.

 

[tom.stoer]

I know that these issues have already been identified and discussed since years. Nevertheless it was intersting to re-derive them in our discussion and to agree on them.

You can hear (quite frequently) statements like "string theory is the only theory of quantum gravity we currently have" and "string theory is fully background independent". So there was some value in our detour.

That brings me back to my question regarding the intrinsic obstabcles (I think I would add "mathematical complexity") and to atyy's question what the most promising research programs addressing these issues are.

 

[marcus]

Nevertheless it was intersting to re-derive them in our discussion and to agree on them.

Definitely!

 

[tom.stoer]

So before leaving I'll try to summarize the string theory internal obstacles

• background independence
• off-shell formalism
• mathematical complexity

 

[atyy]

http://arxiv.org/abs/1002.1120
String Theory and Water Waves
Ramakrishnan Iyer, Clifford V. Johnson, Jeffrey S. Pennington
"While string theory has had remarkable successes over the last several years, accelerated by the revolutions in understanding its non-perturbative properties, it is still very much the case that we do not yet know what the theory is. ... For the problems outlined above, it would be rather excellent to have the simplest possible string theories that still contain some of the marvellous non-perturbative physics we know and love, and be able to follow them as they connect to each other in ways that are entirely invisible in perturbation theory. Further icing on the cake would be to have the physics all captured in terms of relatively familiar structures for which there is an existing technology for its study. This is the subject of this paper (and a follow-up to appear later[4]), at least in part."

 

[Fra]

Tom, thanks for starting and interesting thread with many good posts. I've been in Rome for a week and just got back.

I'll just add a comment on one of the later disussed topics, from my own perspective (which aims for an intrinsic inference model; and physical interactions ~ inferences between observers; and that no interactions without context(observer) is possible).

I share a lot of what several have said but I just want to add a nuance in the discussion of B/I. A point where I disagree with some typical critics against ST background dependence. My point is to try to understand this in terms of measurements, and that what we are talking about here is not just mathematics, it's the quest for observer independence. And the real question is to what extent the belief in observer independence is rational and scientifically justified, and what it even MEANS? I don't think this is just a philosophical point.

If you start with only one background and if you only nw this background, you have no chance to explore the whole space of solutions.

That's what happened in string theory. There is no global picture that allows you to look at the whole theory. You can only look at individual pieces and hope to be able to constuct dualities or something like that.

I was thinking that string field theory would provide something like this global picture.

If we associate background ~ the context of an observer, the choice of background or vacuum etc, is physiclly the problem of specifying the observer.

(Anyone object to this association?)

I sense that you ask for a global observer independent picture? But does that make sense and resonate with the scientific idea of a measurement theory that information should be infered?

If inferrable/abducable "theories" require an inference context ~ an observer ~ background (in some general sense) then the observer invariant "supertheory" just wouldn't be inferrable, computable or representable? If this is the case, isn't the quest for observer invariant gods view, just a remnant desired from structural realism? is it scientifically justified?

I'm just raising the question, of what scientific status - in terms of measurement, computation and representation - such a supertheory or space of all theories would have?

My opinon is that the landscape in ST is a problem, but that I think the solution is not to seek some universal static observer independent view. Another solution may be to instead consider the physical world as interacting evolving observers with incomplete views, WITHOUT background (meaning also NO inferrable transformations that transforms deterministically between the set of observers).

This doesn't support string theory, I just want to add a different version of the critique against the lack of BI suggesting that BI in the sense of strucutral realist observer independence is hard to justify scientifically, since there is no way for any single observer to infer, compute, decided this. And that it may suggest a different way of looking at the "BI problem"?

/Fredrik

 

[atyy]

And the real question is to what extent the belief in observer independence is rational and scientifically justified, and what it even MEANS? I don't think this is just a philosophical point.

Smolin, http://arxiv.org/abs/gr-qc/9508064
Thus, our goal is not to eliminate the observer, it is instead, to relativize him. We would like a formalism that allows us to divide the universe arbitrarily into two parts, and call one part of it the observer and the other the system. We would like there to be something like a gauge symmetry, that expresses the arbitrariness of the split. And, most importantly, to satisfy the principle, we must do this in such a way that it is impossible to construct a single state space that would allow us the possibility of speaking in terms of a description of the whole system by an external observer. ... Thus, our slogan is “Not one state space and many worlds, but one world, described consistently by many state spaces.”

Van Raamsdonk, http://arxiv.org/abs/0907.2939
"we will argue that the “glue” connecting various parts of spacetime together is quantum entanglement between the corresponding degrees of freedom in the non-perturbative description. ... The mathematical structure that we observe in section 2 shares some features with an approach to quantum gravity called “relational quantum cosmology” [11], which also involves associating quantum states in a number of different systems with a single quantum spacetime. The association of specific Hilbert spaces to particular causal patches is also implicit in Bousso’s discussion of holography in general spacetimes [17, 18], and it is central to the holographic space-time proposal of Banks and Fischler [8]. "

 

[atyy]

It was me, see: https://www.physicsforums.com/showpost.php?p=2386391&postcount=9
This expresses my personal view, and the view of other colleagues but certainly not of all of them. And I am very glad that at least one can remember a statement over threads.

What did you have in mind here? I know you were being very speculative, but a few pointers to directions in the research literature for lay outsiders would be much appreciated.

 

[Fra]

Thanks Atyy, those views highlights one part of the problem - they reject the objective quantum state of the entires universe, in favour of sets of relative/subjective states.

So far so good and I agree.

But the next, more tricky question which was my main point is to know the structure of this "set of sets", and what transformations or evolution relations that exists within this set, and what inference status we have on this.

As far as I know, there aren't much published at all, in the more radical direction I have in mind, but the one coming closests is probably Smolin, in particular leaning towards the Unger angle, although they didn't publish anything beyond philosophical talks.

Some comments

And the real question is to what extent the belief in observer independence is rational and scientifically justified, and what it even MEANS? I don't think this is just a philosophical point

Smolin, http://arxiv.org/abs/gr-qc/9508064
Thus, our goal is not to eliminate the observer, it is instead, to relativize him. We would like a formalism that allows us to divide the universe arbitrarily into two parts, and call one part of it the observer and the other the system. We would like there to be something like a gauge symmetry, that expresses the arbitrariness of the split. And, most importantly, to satisfy the principle, we must do this in such a way that it is impossible to construct a single state space that would allow us the possibility of speaking in terms of a description of the whole system by an external observer. ... Thus, our slogan is “Not one state space and many worlds, but one world, described consistently by many state spaces.”

With one reservation I agree with their main message here, and it's in line with what I think. The problem is here

We would like there to be something like a gauge symmetry, that expresses the arbitrariness of the split. And, most importantly, to satisfy the principle, we must do this in such a way that it is impossible to construct a single state space that would allow us the possibility of speaking in terms of a description of the whole system by an external observer. ... Thus, our slogan is “Not one state space and many worlds, but one world, described consistently by many state spaces.”

It's clear what they mean here, and the first step is to my liking, but, the problem is that the "symmetry" that provides/defines consistency is not an inferrable/observable structure.

Edit: A clarification what I mean. The correct statement should be that the symmetry is inferrable as in inducable (ie it remains uncertain), but it's not deducable in the logical mathematical (non-uncertain) sense. For most practical purposes there is no difference, but it is a big different to the way you view this, and what implications it may have on the framework. So the emergence of the symmetry should be more like a statistical process, except there is no global objective probability space.

This is the point where rovelli resorts to structural realism. The idea to "relativize the observer" is of course right, but the problem is how: they implicitly assume that there MUST EXIST a representable mathematical transformation or symmetry that defines this consistency. This expectation is not justified - this is my objection. Instead I think the existence of an objective consistency condition only makes sense if you consider equiblirium, where a local group of observers are reasonably equilibrated.

So what they say makes good sense to me in the equilibrium approximation. As long as we keep that in mind, it's a good start.

The non-equilibrium problem them becomes that of how to infer these consistency transformations from the inside. They say that no observer can hold a complete view, and this is true. But each observer can still hold a reasonably complete view of the symmetry that exists in it's closest environment (where there is causal contact), and that this should yield an evolving symmetry, where consistency is violated off equilibrium. I think this requires some new mathematical framwork though, and I'm not aware of anything cleanly published in this direction. Conceptually, I think Roberto Ungers "social law" analogy is good.

Van Raamsdonk, http://arxiv.org/abs/0907.2939
"we will argue that the “glue” connecting various parts of spacetime together is quantum entanglement between the corresponding degrees of freedom in the non-perturbative description. ... The mathematical structure that we observe in section 2 shares some features with an approach to quantum gravity called “relational quantum cosmology” [11], which also involves associating quantum states in a number of different systems with a single quantum spacetime. The association of specific Hilbert spaces to particular causal patches is also implicit in Bousso’s discussion of holography in general spacetimes [17, 18], and it is central to the holographic space-time proposal of Banks and Fischler [8]. "

As far as I see, this suffers from the same structural realism. They resolve part of the point, but the problem of "relativize" the observer in a physical way, and not just mathematical way is missing.

It seems they are trying more or less the same trick we konw from SR, GR and gauge theories. The problem is that they seem to put in manually the choice of symmetry transformation. I think that the "abducable" symmetry, has to be emergent by means of a physical process and it's this physical process we need to describe (in terms of probably a new mathematical framework). The relativity defined by means of fixed transformation groups doesn't seem to have the right traits?

Edit: When picking on the fixed transformations, I also expect a solution to unification of forces, this is where Ithink the evolving symmetries will be useful. The unification could be accomplished in principle by scaling the observer complexity to zero. During this scaling various "phase" transitions will occurse that merges interactions into indistinguishable ones.

/Fredrik

 

[tom.stoer]

I am sure that observer-dependence (or -independence) is an interesting problem, but I don't think that it's at the heart of the string theory issues. If you look at the string theory Lagrangian it's nothing else but a Langrangian (spiced with some supersymmetry etc.). The problem is that treating it mathematically always requires a) to break somehow it's invariances and b) to check that nevertheless the invariance survives somehow.

The problem with background invariance seems to be that by introducing a background means to break the theory in different sectors or even in different theories. To check background invariance is much harder than to prove e.g. "gauge symmetry after gauge fixing" (BRST or something like that) because you have still one theory.

To me background invariance is not necessarily an ontological issue; it could very well be an issue regarding mathematical complexity only. It seems to be likely that we still do not have (or understand) the mathematical tools.

 

[Fra]

I am sure that observer-dependence (or -independence) is an interesting problem, but I don't think that it's at the heart of the string theory issues. If you look at the string theory Lagrangian it's nothing else but a Langrangian (spiced with some supersymmetry etc.). The problem is that treating it mathematically always requires a) to break somehow it's invariances and b) to check that nevertheless the invariance survives somehow.

Yes, I like that way of putting it.

If I may transcode what you sa into how I'd like to put it:

by introducing a background (ie by enforcing that the THEORY itself is abducable or in a generalized sense "measureable - ie by "introducing an observer" that implements this inference), we genereally might break any objective theory.

But this is exactly why my conclusion is that the theory itself evolves. Ie. there IS no objective theory in the strict sense. All objective theories are merely effective.

The timeless eternal picture of a mathematical fixed theory of everything is not compliant with the inference model since no inference machinery can establish such a picture for several reasons. If the theory is to be the result of an inference process from inside observes, the entire notion of "observer invariance" really needs new understanding. There is no objective fixed symmetry or set of transformations that defines this (which is what you would need to "check that invariance survives"), the "observer invariance" is perhaps better replaced by "observer DEMOCRACY", where a quasi-objective consensus is emergent just like social laws are.

So in the evolving pictures, the invariance may in fact not survive, but then what happens is that the population defining the observer democracy is changed, so that a new invariance is establish as a new steady state.

I like the analogy here to Einsteins static universe. I think the that nature of relations here, means that static laws of the universe are no more sensible than is Einsteins original quest for a static universe.

To me background invariance is not necessarily an ontological issue

Maybe to me, it's a bit also of an epistemological issue: since I question the nature of the process wherby the background invariance or non-invariance is established - processes in nature are not deductive by nature; they are inductive as there are always uncertainties. This is not reflected in our mathematical models of today.

It seems to be likely that we still do not have (or understand) the mathematical tools.

Yes that's a possibility, I agree. I too think that we need a new mathematical framework, but something that replaces partly the deductive approach with an inductive more flexible approach. Maybe we even need to unify not only forces, but also mathematics (or the abstraction of all computational and representation processes). In this sense one would marry math and physics more, and not just study the mathematics of physical systems but also study the physics of the actual realisations of mathematical systems and computation devices. Only then does things like fitness of algortihms and datacompression enter the picture due to finite resources. Compression ratio is always competing with decoding speed etc.

/Fredrik

 

[tom.stoer]

Maybe you are right - but your post is not regarding string theory, it's regarding ALL physical theories we have constructed so far ...

 

[Fra]

Maybe you are right - but your post is not regarding string theory, it's regarding ALL physical theories we have constructed so far ...

That's true.

But to get back to your focus, I guess what I tried to say (a little bit in defense of string theory) in the first post of mine in this thread does relate all this to the

Landscape problem and the lack of B/I formulation of ST.

My opinon is that sometimes the critique against hte lack of B/I in ST, is a little bit simple minded in that it ignores some of the issues I tried to illustrate. Namely that the nature of that B/I means, and how it can or can not fit into an measurement/inference perspective is not trivial.

There is somewhat of a paradox there; to required that we talk only about measurable things, and to required that we are independent of the measurement machinery. The two traits don't add upp consistently - thereof the quest for new ideas.

So maybe the landscape is just the set of observers, defining the democracy? Then maybe an evolutionary picture might help ST there.

That's the only small point I wanted to add, that has to do with ST.

(Still I don't want to give the impression that I like ST; I don't)

/Fredrik

 

[marcus]

I don't know if TomS and others actively want to continue this thread. It has been a very interesting thread and the main body of it may have reached a natural conclusion. The last post by Surprised contained a frank exchange of views worth quoting.
Since our system does not handle two levels of quotes, if I quote Surprised in the conventional automatic way the questions to which he responded will drop out! To avoid that form of incoherence I will just do it manually, with indent:

==excerpt from Surprised post #133==
...
...
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.
==endquote post==

Here is the link to post #133

...
...
It is simply not so that one is able to compute anything, ...

Perhaps i could add my personal view that although I might find string publicity and behavior of individual theorists at times disappointing, I consider string to be a splendid extension of the great edifice of mathematics called differential geometry (the mathematics of smooth manifolds) and, as such, a valuable investigation in its own right even absent any definite expectation of relevance to physics. Since I look on stringy mathematics without any physics expectations, I do not find it disappointing. Many people do, but I do not, so my own thoughts don't fit in exactly with the stated topic of the thread.

 

[marcus]

In the light of what I just quoted, and the comment at the end, it is not actually disappointing to observe that stringy math depends to a large extent on an intensive use of manifolds---smooth continua---many different dimensions.
Manifolds come in any dimension, there are of course one dimensional manifolds. "Strings" (which come in several different dimensions) and their worldsheets are manifolds. The "branes" to which some strings must be attached are also manifolds. The whole works lives, in turn, in some larger "target" manifold of still higher dimension. Such a target manifold normally has a fixed metric geometry unable to respond to what is going on inside!
As retired mathematician, instead of being disappointed by such signs of the remarkable fecundity of differential geometry, I'm inclined to find them mildly satisfying. It's nice to see string mathematics give diff-geom and its manifolds such an extensive elaborate workout! (Not that I expect it to have anything special to do with the fundamental physical nature of space and matter. The signs are that manifoldless approaches are likely to take the lead there.)

 

[Fra]

I'll try keep the focus a little better. But to expand a little on the same point I already tried to make, relating to what surprised said that Marcus put forward in the light again.

I still have no ready solution, but I have some conceptual points that may guide the thinking.

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.

They vision I have, does have a similar "problem", and by projecting ST to that, I would say that the missing "comparasion between different backgrounds" is the missing interaction or communication with different observers. This means that, given my personal association here that the "background" is part of specifying the observer (if I forget for a second about my objections to the continuum etc), what ST does is to describe the expected evolution of the environment with respect to an ny given observer (background), but that this background is fixed.

The sort of "B/I formulation" would correspond to how, TWO such observer interact with EACH OTHER. The exact same problem I see with what I think of as observer complexes. (The difference is that my picture of observer complexes are not "strings" but there are other similarities)

My thinking of this has come to the standpoint that, as rovelli puts it, the only way for two observer to LEVEL anything, is by a real physical interaction/communication. The problem is of course, how do you describe communication without a communication CHANNEL?

From the point of view of the two involved observers, there exists no description, and they have to resort to true evolution (darwin style). This means that part of the evolutio nis simply unpredictable, but it also means that the observers backgrounds are changed.

What can be, is that a third observer can give a partial prediction of how two observer complexes does interact, and how their actions CHANGE, and how this (but the connection between background~prior and their entropic actions) also how their backgrounds change.

This is in fact, exactly what we do already when one observer, observes how two particles interact in a lab. IT's just that we need to see, that the situation is the same, and that if we only could sort this out, also THOSE already known standard actions, should also follow from the same construction.

But I'm not suggesting some anthropic lame argument, I'm suggesting that maybe this could be made precise, and that the physical landscape, is MUCH smaller than the mathematical landscape AND that although there is no deductive scheme to navigate inthe landscape, there MAY be a inductive scheme.

The main problem I see is, that with the proposed conceptual model here, the continuum baggage makes it harder. But that leads to my other objections I already made here and hte other thread.

/Fredrik

 

[tom.stoer]

Marcus, all!

I think it's not up to us to close this thread as others may want to continue. But I agree with you that we have reached a "natural conclusion".

As a final comment from my side I would like to come back to my post #1: It was about disappointment and promises ...

One central statement was that the greatest achievement of string theory is that string theory turns most (all?) possible theories including gravity from theories into solutions derived from a (unique?) theory. Another central statement was that string theory comes with an enormous mathematical and physical apparatus, w/o being able to give us a hint why we should believe in this apparatus (10/11 dim., SUSY, CY, ...).

We identified central obstacles and problems which I would like to list again: lack of (full) background independence and off-shell formalism; mathematical complexity. No find is really new, so the discussion was more interesting than the final result :-)
Nevertheless we identified some good reasons why to believe in the theory even so it has this enormous complexity.

Regarding my personal impression: I think not so much has changed with my disappointment with the theory - but we (you!) established a much better understanding of the true nature of the achievements, problems and obstacles. So besides the problems I see (new) options for research programs in order to overcome these difficulties.

A last remark: Even so I am still (a little) disappointed with the theory I am not at all disappointed with this forum and this discussion! Thanks to all for their contribution and their patience!

Regards & Thanks
Tom

 

[suprised]

In the light of what I just quoted, and the comment at the end, it is not actually disappointing to observe that stringy math depends to a large extent on an intensive use of manifolds---smooth continua---many different dimensions.
Manifolds come in any dimension, there are of course one dimensional manifolds. "Strings" (which come in several different dimensions) and their worldsheets are manifolds. The "branes" to which some strings must be attached are also manifolds.

Well, no. Unfortunately this is confused by many string physicists as well. Whenever people talk about manifolds and strings, that applies only at a particualar region of parameter space (large radii, weak coupling). In other words, that amounts to the supergravity limit, where usual geometrical notions apply. But this is just a very small piece of the full parameter space, perhaps a subset of measure zero.

But away from this limit, these notions break down, and some kind of stringy quantum geometry emerges. For example, the notion of a D-brane wrapped around a p-dimensional cycle becomes ill-defined. What replaces this notion, is an object in some appropriate (derived, Fukaya etc) category. There is no other good way to describe a D-brane than in these abstract mathematical terms, generically (away from the geometrical regime).

I think that the thinking in terms of manifolds has a lot of merits, mostly technical, but has also done a lot of conceptual damage to the understanding of strings, eg in terms of "compactifications" of some higher dimensional theories. As I keep repeating, this picture is not generic and applies only to a very small corner of all possible string "backgrounds".

 

[MTd2]

I must agree with suprised. If one looks at the action of superstring sigma model, there is nothing there that hints the SUSY fields, which yields the dimensions, will organize with any specific pattern except for general restrictions (branes) on the degrees of freedom of the worldsheet.

I wonder if there are any good arguments, besides string gas cosmology ( review here http://arxiv.org/abs/hep-th/0510022 ), to the emergence of any geometrical pattern on strings.

 

[suprised]

Perhaps I should add: I wrote this to emphasize that there is no simple notion to characterize string theory in one sentence, like the geometry of manifolds. Because it is so rich - depending on in which corner one looks, one finds interesting physical or mathematical structures, but none of them capture the whole thing in any seizable way.

Yes, one may say that geometrical string compactitications have shed a lot of light onto the algebraic geometry of Calabi-Yau's, for example, but as I said, this pertains only to some corner of the space of theories. Yes, one may say that string theory is background independent, in the sense of AdS/CFT; but that's again only a corner. Or that strings give insights to gauge theory; black holes and heavy ion physics. Or that it offers a playground for conformal field theory, and mathematical applications of it, like the theory of modular forms and variations on the monstrous moonshine, division algebras, loop groups, categories, K-theory, and <whatever>.

So there is no simple way to say that string theory is just "this" or "that", "purely mathematical" , or whatever. It is a very complex web of aspects and relationships that confuses many people, including experts. I see this here with amusement, where so many people try to guess in simple terms what it is. Well, there is no simple answer!

 

[Finbar]

String theory is more of a fame work than a theory. In fact its probably best to think of all of modern particle physics as a collection of models which use different frame works e.g. the standard model is a model in the frame work of QFT etc.

Maybe a theory should then be something like quantum theory which is based on a set of principles or maybe special relativity. These have a more universal meaning in that all models should be approximated by them in some limit.

QFT in flat spacetime then consists of a framework in which all models will naturally obey the principles of quantum theory and special relativity. However String theory also seems to be theory that its relativistic and quantum mechanical so it also is a frame work in which models maybe be built.

 

[tom.stoer]

So there is no simple way to say that string theory is just "this" or "that", ... It is a very complex web of aspects and relationships that confuses many people, ... I see this here with amusement, where so many people try to guess in simple terms what it is. Well, there is no simple answer!

This is similar to the situation in the early days of quantum mechanics = before Heisenberg and Schrödinger. There were magic numbers and magic formulas; there were hints regarding spectra, angular momentum and selection rules, half integer spin, Compton scattering, quanta of fields like photons etc. But there was no simple statement what quantum mechanics "is".

Nevertheless some clever people were able to work this out in detail, so today there is a complex web of aspects but with an underlying clear concept what qm "is". What we are discussing is what qm "means", how it can by applied to gravity, to the universe, ... But the basic rules are clear!

My hope is that this can be achieved within string theory as well. That does not mean that problems like the landscape will go away, that one can calculate (uniquely) the spectrum of elementary particles, ... But it means that there is a mathematical framework with a small set of formulas, guiding principles or even axioms which sets the rules how to apply the theory. Within such a framework certain dualities or the "web of axpects" should become as clear as the relation between the Heisenberg and the Schrödinger picture.

 

[Fra]

This is similar to the situation in the early days of quantum mechanics = before Heisenberg and Schrödinger. There were magic numbers and magic formulas; there were hints regarding spectra, angular momentum and selection rules, half integer spin, Compton scattering, quanta of fields like photons etc. But there was no simple statement what quantum mechanics "is".

Interesting analogy but maybe a key difference I see is that the birth of QM was driven by real physics (ie. unexpected experimental results that was unexplained). So the patchwork of magic relatins was backed up by real data, and the "logic" and "reasoning" essentially ending up with the idea of a "measurement theory" exemplified by Bohrs mantra etc came afterwards, as a result of processing and adapting to real data.

String theory seems to be different. The logic and reasoning came first, some some ideas to replace points with strings etc. And then the web of relations and dualites in ST certainly doesn't have the same epistemological status as did the web of magic relations that drove the development of quantum theory.

This is why I think all one can judge, is not a concrete result, but the plausability of the choice of reasoning, set of premises and abstractions that guiding string theory research.

But same same is true for LQG. This is why I try to abstract the basic constructing principles and methodology of theory building, specific to LQG vs ST, and try to in some intellectual spirit assess their soundness, beacuse that's all there is to judge or discuss until explicit connections to experiment is made. And who knows if that takes another 20 years.

/Fredrik

 

[suprised]

This is why I think all one can judge, is not a concrete result, but the plausability of the choice of reasoning, set of premises and abstractions that guiding string theory research.

Well there is more than armchair philosophy - there are plenty of very non-trivial computational results; hard facts, so to say, which _do_ mean something!

For example, counting states in black holes. What does it tell? It tells string theory provides just the right number of degrees of freedom that makes this work - unlike an ordinary QFT.

So string theory makes a lot of sense, and just this by itself is extremely non-trivial! This sets it apart from zillions of other possible, random ideas, which on an armchair philosophical level would seem plausible too.

 

[Fra]

Well there is more than armchair philosophy - there are plenty of very non-trivial computational results; hard facts, so to say, which _do_ mean something!

For example, counting states in black holes. What does it tell? It tells string theory provides just the right number of degrees of freedom that makes this work - unlike an ordinary QFT.

So string theory makes a lot of sense, and just this by itself is extremely non-trivial! This sets it apart from zillions of other possible, random ideas, which on an armchair philosophical level would seem plausible too.

Yes, I know there are a lot of hard results withing ST; various theorems etc. But that is something that is as I see it mainly physically significant withing the string framework, or if we just discuss the mathematics of string theory - to the mathematics. Nothing wrong with that of course, if you study mathematics itself. Mathematicians do real hard work all the time, but it's not physics.

I just meant that deducting a theorem, is indeed a hard result, but it's not a physical result ie. is not quite comparable to experimental data or the result of a physical process. The theorem is always and forever true in it's axiom system, but the question is the physical relevance of the choice of axiom system within the theorem lives.

So we still end up with a judgement, wether the "choice of axiomsystem" implicit in the string framework is the right one or not. Where right meaning, something that is "fit" as way of building models in nature.

About counting black hole states, I still consider that to be somewhat semi-classical and speculative as it's "results" arrived at my extrapolating things from different domains to some QG domain. ST has made some success there, to connect to semiclassical approximation results but I don't know how the entire notion and view of entropy, and states will be once we have a proper theory. Most treatments of that, make extrapolations of things into doubtful context - where we in fact lack experimental confirmation of methods.

/Fredrik

 

[Fra]

I just realized that maybe I made myself unclear:

Well there is more than armchair philosophy - there are plenty of very non-trivial computational results; hard facts, so to say, which _do_ mean something!

With "choice of reasoning, set of premises and abstractions that guiding string theory research" that you called armchar philosophy, I rather didn't mean that all ST do is sit an ponder! :) I know they don't.

On the contrary, with this I meant the choice of framework, axioms, and mathematical abstractions that characterize string research. Sure, once that choice is made, you do real work. You try to investigate connections between different results, prove theorems etc.

But the "signifiance" from the point of physics (not just mathematical truths) is still conditional upon wether the choice of framework is correct.

/Fredrik