String Field Theory and Background Independence?

[atyy]

Now the CDT theory says let the size of the triangles go to zero. So you see there is finally no discreteness! There is no minimal length..

Could you point me to a reference for how they do this?

I read Loll's "Emergence of Spacetime" (arXiv:0711.0273v2) where she says they look for scaling behavior indicating a continuum limit. But the scaling she describes seems to be for macroscopic volume or diffusion steps, keeping minimal length fixed.

Her 1998 Living Reviews article seems to be entirely about discrete spacetime. Niedermaier and Reuter's 2006 Living Reviews article also seems to say say CDT has no naive continuum limit. But they do say it's possible to define a microscopic action that reproduces the discrete correlations in the continuum, but it would probably not look like the Einstein-Hilbert action, which I gather is why CDT and asymptotic safety are related.

 

[Fra]

a particular background specifies the field configuration

As I understand the "problem of B/I from the string point of view" (ie from the point of view of a given choice of action; ie. the string action) is that while there is this sort of dual view of background vs fields, enforced by consistency reqs, this also comes with an ambigouity. There seems to be a whole set of possible descriptions of reality, that in certain abstractions are dual, but still this makes no sense because from the point of view of a real observer, the view is definite. Somehow the observer is the one breaking the duality. In one abstraction it's clear that any observer is as good as any, but when it comes down to real observations, the observer is not arbitrary, with him comes a preferred choice. Although the preferred choice in an imaginary sense is arbitrary.

I think the missing link here is the dynamical evolution of these choices, as described by an inside observer. To attach this, I think one must consider also the CHOICE of action. Which to me at least suggest the the concept of strings, is not fundamental. This fixing of the string action, is part of the conceptual problem to me.

My minimal personal understanding of M-theory, that one of the conceptual points would be to relax this "choice of action" by considering that strings are not fundamental - thus neither is the action - the additional duality can be interpreted as relating different picture, where the chioce of action is different. I am willing to give this some hope, but I suspect that if something emerges out of this, it shouldn't be called string theory. In either case I personally think an implementation of the evolutionary step is necessary. Othrewise I suspect that M-theory will just end up with an YET bigger landscape, making it even worse, rather than better.

But may it's true that "all roads lead to Rome". The question is just which roads are the fastest, through the string bush, or some other way. I remember once I was in a foreign city with a collegue, and we were taking the train from the airport to the city. The same train went in two directions. He spotted the train just about to leave in 20 seconds and said, that's the one. I said it was wrong, but he pulled me on the train. Eventually we came to the hotel, it's just that the trip took over an hour instead of 20 minutes because we circled the city in the wrong direction. The train was goin in a circle, but there were two directions.

/Fredrik

 

[atyy]

Now the CDT theory says let the size of the triangles go to zero. So you see there is finally no discreteness! There is no minimal length.

I guess this corresponds to Ambjorn et al (arXiv:hep-th/0604212) Eq. 27, 28? Then when they take the approximations Eq. 29-30, they get Eq. 31 which is the same as Eq. 33, a class of Einstein-Hilbert actions?

 

[atyy]

Do these mean that String Field Theory is "background independent" in the same sense that CDT is?

A String Field Theory based on Causal Dynamical Triangulations
J. Ambjorn, R. Loll, Y. Watabiki, W. Westra, S. Zohren
http://arxiv.org/abs/0810.2408

A new continuum limit of matrix models
J. Ambjorn, R. Loll, Y. Watabiki, W. Westra, S. Zohren
http://arxiv.org/abs/0802.0719

 

[atyy]

In Lubos Motl's view, string field theory is not background independent: http://motls.blogspot.com/2008/10/observables-in-quantum-gravity.html

Also has interesting comments about the emergence of space and time, btw.

 

[Fra]

In Lubos Motl's view, string field theory is not background independent: http://motls.blogspot.com/2008/10/observables-in-quantum-gravity.html

Also has interesting comments about the emergence of space and time, btw.

Perhaps it's interesting to connect to the discussion of "internal view" perspective from the other thread. After all, the core problem in these two threads are related, and more or less the same.

Lubos writes in the first two paragraph in an obvious way, what may not be so obvious in the context of consideration (the future understanding of foundations of physics):

"The goal of every quantum-mechanical theory is to predict the probabilities that particular physical quantities - "observables" - will take one value or another value after some evolution of the system, assuming certain initial conditions."

"Mathematics of quantum mechanics makes it inevitable that observables have to be identified with linear operators on the Hilbert space of allowed states."

This is rushing too fast. One of the key issues at least from my point of view, is that we should ask for a "physical inside basis". Then the concept of a continuum probability immediatly appears somewhat ambigous. The notion of a defined probability, implies the notion of a uniqued microstructure, or probability space.

Usually one considers the information needed to specify a distribution, in a distribution space. But one rarely considers the information needed to speficy the distribution space itself.

What is, from the inside point of view, the meaning of probability of a future event?
Does the repetitive, frequentist interpretation really make sense here? If not, it suggest that we do not understand the proper physical meaning of this "probability".

This is really basic stuff, and seemingly may have little to do with discussing spacetime, but the fact it's basic, and even part of our very reasoning, makes it even more remarkable and dangerous to not question it. This particular point, wasn't mentioned by Dreyer, but i think doing so, would take the vision of the ideas yet one step further. That is, the ultimate consequence of the "inside view" is a deep sort of "inside logic", and this is where I want to start.

One can not just talk about "the probability" unless the full process of acquisition, processing and computing the LIMIT, is made, as it's acknowledge tht this is not mathematical computations made in a parallell universe with infinitely fast computers and infinite memory; the "inside vision" constrains this to be physical processes!

(This is a further comment on the Dreyer's work, but put in this context. I think the more all questions can connect to a common issue for discussion, the more interesting new angles might emerge out of the discussion)

/Fredrik

 

[Fra]

One can not just talk about "the probability" unless the full process of acquisition, processing and computing the LIMIT, is made, as it's acknowledge tht this is not mathematical computations made in a parallell universe with infinitely fast computers and infinite memory; the "inside vision" constrains this to be physical processes!

I think ignoring this point (which while effectively valid in many cases, since the "interaction" make take in a small lab, or a small detector even, but the computations and acquisition is made in the massive context of the laboratory) is largely responsible for the fact that while we can DESCRIBE the laws, and FIT them to models, in the spirit of adaptive techniques, we do not understand the LOGIC of the interactions, and we do neither understand the values of the paramters beyond the level of fitting to experimental data. This is intself not a bad thing at all, but maybe there is much more to gain but seeing it from the inside. Then, the logic should be come more clear. The logic of the interactions, might be far more constrained than we currently can understand, because - also in line with Dreyer's reasoning - have so far imposed far more structure in the microscopic domain than what is physically possible.

/Fredrik

 

[Fra]

I admitt I didn't read Lubos blog in detail I just skimmed it, as there was some strange mentioning of other peoples low IQ in the same thread... but somewhere Ithink he made a noted about scattering amplitudes and theat the only predictable point of view was from the infinite horizin POV. And that a finite inside view can never be as accurate. This is possibly related to the point above. I think there is something to that, OTOH, I think that thte relevant perspective IS the inside view. Because we humans are tiny observers in a large world. In particula in the context of mixing theories of cosmology and theories of particle physics, do I think that choosing the most physical POV is imporatant.

So that raises the question if these infinite views, while suggested by certain mathematical consistency, is a valid physical view? And what is the cure?

/Fredrik

 

[Haelfix]

Atyy, yea that post by Motl has a similar argument to what I explained in the 2nd post of this blog. SFT from a certain point of view is not really background independant in the stringy sense, b/c it seems to miss various (buzzword incoming) superselection sectors of the full string/M theory.

Again it depends on how you define BI as there is no canonical definition in existence between different theories, its simply a statement of formalism rather than an accepted physical statement. Moshe has a nice paper that explains a lot of what's going on. Also there was a long discussion on BI on usenet that spilled over into the blogosphere like 'the string coffee table' circa 4-5 years ago.

 

[p-brane]

SFT from a certain point of view is not really background independant in the stringy sense, b/c it seems to miss various (buzzword incoming) superselection sectors of the full string/M theory.

But superselection sectors by definition are physically disjoint so that if your notion of what truly BI theories are is correct and if there is such a theory then ultimately there can be no such thing as a superselection sector.

 

[Haelfix]

Yea agreed. But for now, things like SFT are unable to see the same objects that for instance matrix theory can, so people divide it up into superselection sectors for lack of a good alternative. The dream is a single theory that encompasses it all, and that would be called BI.

Incidentally, to further confuse some people's preconceptions out there as emphasized on Moshe's blog. GR isn't really entirely BI either. There is a fixed topology, and further the asymptotics must be fixed. There is no continuous way to go from say an asymptotic ADS space to say a DS one (it takes an infinite amount of energy). There too you could presumably divide up the various GR theories into classes parametrized by the choice of boundary condition.

 

[marcus]

Incidentally, to further confuse some people's preconceptions out there as emphasized on Moshe's blog. GR isn't really entirely BI either. There is a fixed topology,..

We should note that, in Moshe Rozali's recent paper, his idea of BI is scarcely, if at all, connected with what non-string QG people have typically meant by it.

Also, as a separate comment, recall that the term BI was employed to refer to a rather simple straightforward feature of GR (its not needing a background metric) which the QG folks considered important and wished to carry over to quantum GR. Nothing said about topology--it doesn't enter the discussion. Indeed every theory has to start with some mathematical objects as basis and GR starts with a limp manifold, which like any manifold must have some topology. Non-reliance on a background metric geometry does not mean you can't have a manifold with a topology.
As Loop Gravity folks have used the term for well over a decade, BI refers to the absence of a metric, the absence of geometry, not to the absence of topology.

I looked at Rozali's paper on what he calls BI some weeks ago and was astonished at how little it relates to the Loop Gravity BI concept. Does anyone besides me think it would have been courteous of him to choose a different term, less apt to cause confusion?

 

[Haelfix]

The problem is that there are about 30 different quantum gravity proposals, and they all use the word a little differently. Some are really specific in their definition, others are at best ambiguous. There is overlap in some cases in the literature, but more often than naught it can be quite different concepts. Also, I really have no idea who and where the phrase starts with, but it was pretty obvious that a generalization was needed to incorporate more than just the metric tensor.

For instance, consider quantizing Brans Dicke theory. You could in principle vary the tensor component in the action, and keep the scalar fixed. But would it make sense to call the resultant quantum theory background independant, even if done nonperturbatively? Not really. And so a new definition is born, one which is primarily about dynamical degrees of freedom. But then that doesn't quite capture what some people wanted either, and so further tweaking to the def is made. Then people got back to basics and used GR as the prototype, and simply made it about diffeomorphism invariance, but well that doesn't capture many differences between theories either, b/c virtually every theory (other than lattice gravity) is manifestly diffeomorphism invariant.

Anyway, the point is the second comparisons started to be made for publicity purposes (starting with various books and online discussions) is when things really get silly and all trace of physics got lost in translation.

 

[Fra]

Ok here a last philosophical post from me on this thread :)

I understand Marcus argument that many use the word different than perhaps the original meaning of BI as originating from GR.

But if am not mistaken, I have even seen Smolin somewhere talk about the BI of GR as "weak form of BI" exactly because of what Halefix mentions, that the topology, dimension etc.

From my POV the interesting question is the origin of the phenomenon of holding the BI flag so high? Ie. what is the rational reasoning, that makes us think this is so important? ie how do we acquire enough confidence in this statement to hold it as a universal non-negotiable principle?

For myself, since I attack this whole issue in a different way. I see a deeper meaning of BI in terms of reasoning on incomplete information, which in my view is what observers do. Then BI can be thought of as "freedom to choose prior information", in the sense that regardless of the choice of prior information, the actions based on that information must be consistent with the actions of an arbitrary choice. IE. the actions relative thes "background priors" must be related by a symmetry transformation, becuase the symmetriy is to _restore consistency_, broken by the choice of prior. Without the symmetry transformations, the different choices lead to inconsistencies - it "the picture doesn't make sense" without it.

IMHO, this is a simple rational but abstracted argument around in favour of BI. And this applies to generic elements of reasoning. It means that everything on which the action is based is the "background".

I don't know how Einstein reasoned when his models was constructed, but this is a possible logic that can be understnad outside GR, thta might possibly lead to it. But when if we try once more, using the original reasoning of Einstein (rather than his results), but taken one step further - someone except my that seems to advocate this is Olaf Dreyer with his "internal relativity" - then perhaps we can make large progress.

One can imagine that the action taken by different observers, is rational, if you see if from the inside POV, they act upon the information at hand. Pretty much the logic of game theory and rational players, with the additional difference that without _konwledge_ of an established perfect symmetry, even the notion of "rationality" is prat of the background.

This is why, my only conlusion to this is thta if you take the BI idea deeper at the level of reasoning and actions, then it seems to be that symmetries can not exists beyond the emergence limit.

So in short, I see a clear logic why symmetries are required by consistency. But I think the simple answer IMHO is that the consistency is not an attainable fact by finite processes, it might be an "ambition" or limiting case.

IF this is so, then I think it should reflect our actions and strategies, because we should realize that the differential process is more important than the final state.

/Fredrik

 

[Fra]

So in short, I see a clear logic why symmetries are required by consistency. But I think the simple answer IMHO is that the consistency is not an attainable fact by finite processes, it might be an "ambition" or limiting case.

IF this is so, then I think it should reflect our actions and strategies, because we should realize that the differential process is more important than the final state.

If we are just recalling our own observations about our own actual knowledge of physical law though history, we regularly fact inconsistencies, but the trait of an intelligent observers is the ability to restore the consistency - this is critical to survival. It seems resolving inconsistenicies is a key process, to evolution of ourselves, and the emergence of our image of physical law. And in the context of evolving observers, inconsistencies tend to be transient. Only a persistent observed inconsistency would be deeply puzzling.

Either this is a sign of something deeper, or you can dismiss it as something to leave for brain research. But it there is going to be anything even worth the name of candidate to a unified description of reality, I think that's not acceptable. Popper did that mistake when he in his famous book on the scientific method, avoided this problem by dismissing the problem of hypothesis generation, and the connection between hypothesis generation and observation, to "psychology of theorists". With this dismissal, i think we also cripple our own ambitions. I am not willing to do that. I think there is a information processing perspective to this, which does not have to confuse this questions with humans at all. I don't know why popper insisted on that.

/Fredrik

 

[p-brane]

We should note that, in Moshe Rozali's recent paper, his idea of BI is scarcely, if at all, connected with what non-string QG people have typically meant by it.

Also, as a separate comment, recall that the term BI was employed to refer to a rather simple straightforward feature of GR (its not needing a background metric) which the QG folks considered important and wished to carry over to quantum GR. Nothing said about topology--it doesn't enter the discussion. Indeed every theory has to start with some mathematical objects as basis and GR starts with a limp manifold, which like any manifold must have some topology. Non-reliance on a background metric geometry does not mean you can't have a manifold with a topology.
As Loop Gravity folks have used the term for well over a decade, BI refers to the absence of a metric, the absence of geometry, not to the absence of topology.

I looked at Rozali's paper on what he calls BI some weeks ago and was astonished at how little it relates to the Loop Gravity BI concept. Does anyone besides me think it would have been courteous of him to choose a different term, less apt to cause confusion?

These remarks are nonsensical. You need to read rozali's paper more carefully and ask specific technical questions about it. There's little I could add of value that Haelfix hasn't already explained to you. Also look at lubos's discussion of it where he very accurately explains why string theory is more background-independent than general relativity.

 

[p-brane]

...string theory is more background-independent than general relativity.

The point behind this remark was that if your reason for quantizing GR directly is that it's BI, then since string theory is even more BI than GR is, shouldn't you be more interested in quantizing strings than you are in quantizing the metric of GR? The answer can only be yes.

 

[friend]

You hit the nail on the head! That is how LQG is constructed. It is based on a continuous manifold without any metric specified. So it is initially limp, shapeless, without geometry. Then, instead of metrics, there are defined quantum states of geometry, a hilbertspace of these. Observables are operators on that hilbertspace and some of the geometric observables turn out to have discrete spectrum.

===================

I wonder what meaning numbers could have when labeling spacetime points without a metric. I mean, can we even say that one number is larger or smaller without a metric? It would simply "appear" as if one number (spacetime point) is merely different than others, but how does that help us with calculations if we cannot even say that one is bigger than another? So I guess my question is how are we able to do math without a metric? Can addition and subtraction mean anything without a metric? Thanks.