String Field Theory and Background Independence?

[Fra]

So whatever the new model continuum looks like I expect the principle of DI (and BI) to persist. Because those principles are the most essential things that General Relativity tells us. But the principles will have to be reformulated in a somewhat different mathematical language, because differential manifolds and differential geometry as we know them today will not apply.

Thanks for your elaborations Marcus! This discussion partly replies to the question I raised on DI as a new thread.

I have often wondered, what Einstein would have come up with, if he was born after QM was matured so that he had gotten over his realist issues, so he would have in Bohrs measurement spirit, added general covariance. I always speculated that he would haved broadened the meaning of "that the laws of physics looks the same to all observers" to broaden the class of observers, and maybe also noted that the inside deduction of wether the laws of physics ARE in fact the same, is rather an induction, because there isn't enough information on hand for the inside observer to make a deduction. So one possible solution could be thta the spirit of GR is more to be seen as a deep "induction principle". This step from deduction to induction, might be requied to not clash with bohr spirit to stay away from realist visions. Realist visisions aren't wrong per see, I think they are rather speculative. So the choice is between a "speculative" deduction, or a confident "induction".

I too think a deeper formalism is necessary and as for the specific action of gravity, say E-H action. I think that will be emergent. The breaking of DI invariance that I picture in the emergent picture, doesn't necessarily mean that there is global breaking, I rather think of the breaking a result of indeterminsm, where you consider the symmetry itself as observable.

I think a basic conceptual problem, that relates also to the foundations of QM, is that whatever theory we come up with, this theory is constrained to a subsystem of the universe, to an observer. In this sense, I don't think there is enough information in a subsystem to deduce the certainty of a symmetry. I think this also applies generally to the physical basis of symmetries.

/Fredrik

 

[Fra]

Such a vision, of a hypothetical "Einsteinian reasoning" if he had some of bohr's spirit, might even provide unification of the GR "induction principle" and QM itself. The Heinseinberg uncerainty principle might emerge in the domain of small complexity, as a manifestation of induction based on incomplete information. The emergence of non-commuting observables might be a result of this SAME induction principle. A self-organizing observer, evolves to maintain answers to non-commuting questions, because it's a form of clever "data compression". I find this also very much sniffing Wilczek's reflections of "profound simplicity" and his comparasion with data compression. This is exactly what I associated when I read his book. But they way he talked about it in the rest of the book, I don't think Wilczek's himself fully spelled out the consquences of hte idea of the fact that the problem of optimum data compression is an intrinsically relative concept. It it context dependent.

/Fredrik

 

[marcus]

Thanks for your elaborations Marcus! This discussion partly replies to the question I raised on DI as a new thread.

I checked out your thread and added some response.
https://www.physicsforums.com/showthread.php?t=275482
It's encouraging to hear that some of what I'm saying makes sense to you!

 

[friend]

So it must arise from some more fundamental math. The appearance at large scale of a smooth continuum obeying GR dynamic geometry must be an illusion.

Something much more chaotic and fractally is probably going on with the geometry at very small scale.

Nowadays we sideliners are watching the development of a new idea of the continuum, that will not be smooth at small scale (like Riemann's 1850 smooth manifold everybody still uses) and which may have dimensionality declining gradually with scale (e.g. Loll spacetime 4d at large, 2d at small).

These kinds of statements confuse me. Afterall, when we look at Schrodinger's equation or Feynman path integrals, it would seem that all quantum observables are derived by using an underlying continuous spacetime in the equations. How then can spacetime itself be quantized? Have we developed a new quantization procedure that does not use underlying continuous parameters (a.k.a. spacetime)? Or is it the case that the underlying spacetime is continuous, but any observable that involves the metric is quantized?

 

[marcus]

...Or is it the case that the underlying spacetime is continuous, but any observable that involves the metric is quantized?

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.

===================
But keep in mind that it is not essential in quantization to divide something up into little bits.

The leading approaches to quantum gravity are LQG and CDT (Loll Triangulation approach) and neither of them divides space up into little bits. In LQG some discreteness comes in at the level of measurement, so you can say that there is a minimal nonzero length that you can get as read-out from a measurement--or at least a minimal nonzero area. This means that space as an observer measures it appears to have a certain graininess.

But in CDT, the other approach we hear most about, there is not even that kind of apparent graininess! The mathematical construction is based on a limp continuum, like for example topologically it could be the 3-sphere cross the real line: S³ x R. The continuum is without geometry, it is formless, because no metric distance function is defined on it. Then one specifies a quantum rule by which it can triangulate itself in millions of different ways.

Analogous to how a particle can get from point A to point B in millions of different ways in a Feynman path integral.

Each path will take the universe from an initial to a final state and it will have an amplitude. A path is a spacetime geometry. The amplitude-weighted average can be taken.
So they can produce millions of sample universes in the computer and study each one's properties (dimensionality, how radii and volumes are related, correlations over time etc) and they can also sum up analogous to a path integral.

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.
And the entire construction is still based on a topological continuum----like the three-sphere cross R that I mentioned earlier.

The triangulations are simply a regularization which allows the quantum path integral to be computed. The method is discrete only in the same sense as the Feynman path integral is discrete because it uses polygonal paths, piecewise linear paths, to approximate curved paths, at a certain stage in the calculation. No one pretends that Feynman's particle travels along a path made of straightline segments. And no one should pretend that the Loll quantum continuum is made of little triangles . The triangles could as well be squares or any other tile shape, their size is taken to zero and what shape they are doesn't matter.

Have a look at the Loll SciAm article. It's excellent. There is also a growing technical literature for CDT available on arxiv, but I recommend the SciAm article. It gives a good idea of what is likely to come out of the current multipronged research into quantum gravity. There are a number of approaches and signs that they may have begun to converge. Space doesn't necessarily get broken up into little chunks, but it may reveal a more chaotic, less smooth structure at very small scale. At the micro level it may have the geometric Heisenberg jitters.

Remember too, that whatever continuum we come to define and use will always be merely a mathematical model. Nobody should confuse it with reality. At present almost all physics is done on some sort of differential manifold---a thing invented around 1850 by Riemann. A thing which generalized classic Euclidean space by allowing internally measureable curvature, among other things. Just because that model of space works well and is typically what is used does not mean it corresponds to reality. Most likely it doesn't! Most likely Riemann gives a very bad picture of space at microscopic scale. (And this could be at the heart of physicists' unrenormalizable divergence pains---they use a continuum which is vintage 1850 and totally unrealistic at small scale.)

How then can spacetime itself be quantized? Have we developed a new quantization procedure that does not use underlying continuous parameters (a.k.a. spacetime)?

Well I've tried to suggest how geometry is quantized in the two leading approaches LQG and CDT. They don't actually quantize spacetime itself. They quantize the geometry. Gravity = geometry so quantizing geometry is the name of the game.

And there is an underlying continuum in both cases. Neither space nor spacetime is broken up into little chunks. So, in your sense, we continue to use continuous parameters. I think the answer to your second question "Have we developed...", if I understand it right, is no.
Because we don't need any revolutionary new proceedure---the geometry being defined on a continuum. (in those two cases)

I would urge you to read the Loll SciAm article on CDT. Here is the link:
http://www.signallake.com/innovation/SelfOrganizingQuantumJul08.pdf
The link is also in my sig.
CDT is easier to grasp than LQG, at intro level, and in certain respects it is currently more complete.

 

[atyy]

I would urge you to read the Loll SciAm article on CDT. Here is the link:
http://www.signallake.com/innovation/SelfOrganizingQuantumJul08.pdf
The link is also in my sig.
CDT is easier to grasp than LQG, at intro level, and in certain respects it is currently more complete.

Thanks for the link - that's a nice article!

 

[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.

So the only questions now are why and how to quantize gravity/geometry. It seems to me that this is something we should try simply because Einstein's Field Equations of GR can be derived from the Hilbert-Einstein Action. And Action integrals in general appear in Feynman Path Integrals to produce quantum theories. But if we could find a more fundamental reason for the existence of the Hilbert-Einstein action in the Feynman path integral, then that would prescribe the necessity of quantizing gravity.

 

[marcus]

... GR can be derived from the Hilbert-Einstein Action. And Action integrals in general appear in Feynman Path Integrals to produce quantum theories...

Indeed that is just how the Loll CDT approaches quantizes gravity/geometry!
They use the Einstein-Hilbert action, with a positive cosmological constant, to build the path integral.

It turns out that the E-H action has a nice combinatorial form based on counting identical triangles. Because in piecewise linear (identically triangulated) manifolds the curvature is expressed by how many triangles are gathered around a point, or more generally how many D-simplexes are joined to a D-2 simplex. After a big adding up and cancelation one sees that the E-H action is given simply by taking a census of the different simplex types---the different types of triangle. It is remarkably elegant.

Again, I urge you to have a look at the Loll CDT article in my sig. But you may also be wanting a more technical CDT article, if it interests you at all. So I'll see what would be a good arxiv link to suggest. Or you can just ask, if you want more technical detail.

Thanks for the link - that's a nice article!

atyy, I'm so glad you had a look at it! Loll is a good communicator. It makes a difference. I wish she'd write a book.

 

[friend]

Again, I urge you to have a look at the Loll CDT article in my sig. But you may also be wanting a more technical CDT article, if it interests you at all. So I'll see what would be a good arxiv link to suggest. Or you can just ask, if you want more technical detail.

Yes, I looked at the article. It is interesting. I wonder if the method they use to come up with the dimensionality at various scales has a general procedure in a continuous form. It would be nice if the 4D world could be made to pop out of any continuous, closed, non-perturbative form of Quantum Gravity.

 

[marcus]

...I wonder if the method they use to come up with the dimensionality at various scales has a general procedure in a continuous form. ...

It does! They used two methods to measure dimensionality, both of which work in the continuous case. I think in fact they were both invented to use in the continuous case and Loll has adapted them to her situation of a triangulated manifold.

The two methods which Loll's group has applied to investigate the small quantum universes they generate in the computer are:

A. Hausdorff dimension
B. Spectral dimension

Both can give fractional non-integer results, like 1.72 and 2.36.

A. Hausdorff dimension works in any space where you can define radius and volume. You just look at volume of balls of radius R and if the volume grows as R^d then d is the Hausdorff dimension.

B. Spectral dimension measuring works in any space where you can set up a diffusion process or Brownian motion. It doesn't have to be a space which is in any sense discrete.

Loll's group has a 2005 paper about measuring the spectral dimension. I'll get the link.
http://arxiv.org/abs/hep-th/0505113

 

[Fra]

But if we could find a more fundamental reason for the existence of the Hilbert-Einstein action in the Feynman path integral, then that would prescribe the necessity of quantizing gravity.

This is what I want to se as well. To just pull a particular action form, is not satisfactory. I agree that it's good that some try it, but I fail to see that such strategy addresses the full question. So even if there is partial success, I can't see how it can possibly be the full answer. I think the emergence of actions in general, unavoidably also deals with the foundational issues of QM. But of course to start with another fixed non-trivial action, like string action, doesn't solve the problem.

I expect in the similar spirit that GR wants BI, I think the actions are also part of this. The ACTION is part of the "larger background" consisting of all possible observers IMO. The action does IMO corresponds to a kind of logic that governs behaviour. If you CHOOSE a background action, you can have anything you want emerge - just like by the choice of ergodic hypothesis and microstructure, you can prove that anything is "probable".

This I see as the same dog buried under the physical basis of probability in measurement theory.

I think this is a profound problem, that goes down to our use of logic. It also relates to the processes of deduction and induction.

This is IMHO at least, the reason what the concept of "background independece" is really not trivial.

/Fredrik

 

[friend]

This is what I want to se as well. To just pull a particular action form, is not satisfactory. I agree that it's good that some try it, but I fail to see that such strategy addresses the full question. So even if there is partial success, I can't see how it can possibly be the full answer. I think the emergence of actions in general, unavoidably also deals with the foundational issues of QM. But of course to start with another fixed non-trivial action, like string action, doesn't solve the problem.

Another question is how matter fits into the picture of Quantum Gravity. I hear language like "coupling matter" into the equations. I take this to mean that they just add lagrangians for particles in the Hilbert-Einstein action with some coupling constant in front of the matter lagrangian. Is this the case? If so it seems some justification is need to do this. Why not instead reinterpret the particle lagrangian as a lagrangian for gravity/geometry? Particle physics may just be a local form of gravity.

 

[marcus]

Another question is how matter fits into the picture of Quantum Gravity.

In the case of canonical LQG, matter is added to the picture by adding extra labels to the links (edges) of the spin network.
It looks to me as if the idea is to make the matter fields ride on top of the quantum state of the universe's geometry. The matter fields are riding on the back of the gravitational field, which describes the state of geometry.

At this point in the development, there is nothing but fields. fields defined on top of fields. The lattice that the matter fields are defined on, that lattice is itself the gravitational field.

The most recent introductory-level overview of LQG that we have is the video and slides of Rovelli's talk at Strings 2008.
Here are the links again.
Video:
http://cdsweb.cern.ch/record/1121957?ln=en
Slides:
http://indico.cern.ch/getFile.py/access?contribId=30&resId=0&materialId=slides&confId=21917[/QUOTE]

To get more grasp of the notation and ideas, one should watch the video, and also listen to the questions which the string theorist audience asked at the end of the talk. For most of them the talk probably was about new stuff, so it is instructive to see what they asked about.

Look at slide #28 where it says

|S> = |gamma, i_n, j_l, k_l>

the i's are socalled intertwiner labels at the nodes, the j's are spin labels at the links, the k's are quantum number labels for matter, also at the links

I can't shed any special light on this. It looks to me like it is analogous to a lattice treatment of matter fields, but with a highly random and highly irregular lattice.

The spin network, by itself without matter, is
|S> = |gamma, i_n, j_l>

representing a quantum state of geometry. (The continuum has been washed out of the picture by this point, there is no more space apart from this bare-bones skeleton of geometric relationships)

Now I should say more about gamma:

LQG has borrowed an idea from a branch of topology called knot theory. A knot is an equivalence class of embeddings. Two embedded knots are equivalent if you can deform one into the other by a diffeomorphism (by a smooth mooshing around of the space.). That makes sense. The two are really the same knot if you can make one into the other just by moving the rope around a little. One starts with a knot in space, and then one throws away the space and has only the pure knot itself. Can you picture this? I hope this idea is OK.

So we can do the same thing with networks. Networks are just complicated knots. We can start with a continuum and have networks embedded in it. Then a spin network is an equivalence class of embedded networks. It is abstracted from the continuum we started with, and the continuum is thrown away. It is this network that bears the labels.

What I just said is shown with pictures on slide #13

BTW there is reference to matter at slide #4, where he states the main result:
==quote==
Main result
Definition of diffeomorphism-invariant quantum field theory (for gauge fields plus fermions),
in canonical and in covariant form.
==endquote==

 

[Fra]

It's encouraging to hear that some of what I'm saying makes sense to you!

Just for the record - this wasn't the first time this happened

/Fredrik

 

[Fra]

Another question is how matter fits into the picture of Quantum Gravity. I hear language like "coupling matter" into the equations. I take this to mean that they just add lagrangians for particles in the Hilbert-Einstein action with some coupling constant in front of the matter lagrangian. Is this the case? If so it seems some justification is need to do this. Why not instead reinterpret the particle lagrangian as a lagrangian for gravity/geometry? Particle physics may just be a local form of gravity.

In addition to Marcus reference to LQG, which I think he knows best on here; since you responded to my comment and vision on emergent actions, I though I might just add one *conceptual possibility* I see consistent with that particular reasoning is that matter is really just the physical manifestation of observers. Thus I envision that the "choice of action" and "choice of observer" is simply nothing but the specificaiton of matter. And the evolution of actions, are synonymous to emergence of matter in my abstraction.

The objection of fixing the actions forms, can thus also be interpreted as the objection of fixing the microstructure of matter. Thus there seems to be a duality between emergence of matter, and emergence of spacetime. This is I think even plausible, since if we think of spacetime as relations between "stuff", and "stuff" usually means matter, it really makes sense.

The difficulty is to see that this is not circular reasoning, it really prescribed an evolution. And of course, one would hope that this would turn out to be time.

/Fredrik

 

[marcus]

Just for the record - this wasn't the first time this happened

/Fredrik

Awwww. I didn't mean it that way.
What I meant was about my post #50, which was not guaranteed to make sense to you or anybody else.

My usual posts I think you certainly get the sense of, as much as you want, but in that case, ensabah had asked me to hazard a pure personal opinion speculation about the future course of research. I had to either ignore the question or gamble on my own intuitive hunches alone. Which I normally don't like to do. I'd rather report directions in current research, based on people's publications.

So in the case of #50 I was going out on a limb and not sure anyone would respond. So was very pleased by your understanding response.

 

[Fra]

Thanks for the clarification Marcus. I wasn't sure, and just didn't want to leave that possibility :)

The objection of fixing the actions forms, can thus also be interpreted as the objection of fixing the microstructure of matter. Thus there seems to be a duality between emergence of matter, and emergence of spacetime. This is I think even plausible, since if we think of spacetime as relations between "stuff", and "stuff" usually means matter, it really makes sense.

The difficulty is to see that this is not circular reasoning, it really prescribed an evolution. And of course, one would hope that this would turn out to be time.

As I've said before, I don't like string theory as it stands, but nevertheless there are elements of it that partly make sense to me. So while I don't advocate string theory at all, I think that similary with the outlined reasoning above, is the way string theory SHOULD emerge spacetime as well. As "relations between two interaction strings", and here the purpose of the string is a representation of the mictrostructure of matter.

This is not a bad idea IMO.

What string theory IMHO either misses, or has missed to convey to me at least, is

1) what the meaning of the background spacetime they use is. I think that this is not really a background space in the ordinary sense. It sure looks like that mathematically, but I think there might be another way.

2) the evolutionary character of the above reasoning is missing too as far as I can see.

I think this is related to string theories own quest for B/I. And it may also realte to the landscape, because if you really think that the background space relative to what the string action formulates is an ordinary space, then i am not surprised that you are lead to a landscape. Instead, it could be that the landscape really just represents different observers, and that the main problem is that since they have lost the evolutionary progression, they are LOST in the landscape.

This is what I would look into if I was a string theorist, but I am not. But I thought it might be worth noting the analogy, of a different reasoning.

/Fredrik

 

[friend]

In the case of canonical LQG, matter is added to the picture by adding extra labels to the links (edges) of the spin network.

The spin network, by itself without matter, is
|S> = |gamma, i_n, j_l>

representing a quantum state of geometry. (The continuum has been washed out of the picture by this point, there is no more space apart from this bare-bones skeleton of geometric relationships)

IIRC, LQG is derived using Hamiltonian in a Schrodinger type equation with commutation relations using cononically conjugate momentum, etc. What I'd like to know is if there is a Path Integral formulation and what these spin networks would look like in that formulation. Does such a thing exist? Thanks.

 

[marcus]

PF autolink for the word relation in case anyone wants it explained.
================

IIRC, LQG is derived using Hamiltonian in a Schrodinger type equation with commutation relations using cononically conjugate momentum, etc. What I'd like to know is if there is a Path Integral formulation and what these spin networks would look like in that formulation. Does such a thing exist? Thanks.

The development of the Path Integral formulation is an ongoing process, as is the knitting together of the two formulations. The latest paper on this was posted September 2008, and there was a June 2008 paper on it by the same authors

http://arxiv.org/abs/0806.4640
Path integral representation of spin foam models of 4d gravity
Florian Conrady, Laurent Freidel (Perimeter Inst. Theor. Phys.)
29 pages, 6 figures
(Submitted on 28 Jun 2008)

"We give a unified description of all recent spin foam models introduced by Engle, Livine, Pereira and Rovelli (ELPR) and by Freidel and Krasnov (FK). We show that the FK models are, for all values of the Immirzi parameter, equivalent to path integrals of a discrete theory and we provide an explicit formula for the associated actions. We discuss the relation between the FK and ELPR models and also study the corresponding boundary states. For general Immirzi parameter, these are given by Alexandrov's and Livine's SO(4) projected states. For 0 <= gamma < 1, the states can be restricted to SU(2) spin networks."

And here is the most recent work, continuing from the June paper:

http://arxiv.org/abs/0809.2280
On the semiclassical limit of 4d spin foam models
Florian Conrady, Laurent Freidel
32 pages, 5 figures
(Submitted on 15 Sep 2008)

The path integral version of LQG (more precisely "sum over histories" version) is called spinfoams. The earlier canonical version is called either canonical LQG, or simply LQG (although confusion can result from not specifying.)
A spinfoam is what you get if you make a spin network evolve in time.
Freidel and Conrady have established a connection between spinfoam sum over spacetime histories and the more usual kind of path integral with an action (as one gets e.g. in Loll CDT, the triangulations approach). A spinfoam is dual to a spacetime triangulation.

There are several competing versions of canonical LQG and several competing versions of spinfoam LQG. This paper by Conrady-Freidel is part of a shakedown and consolidation process where some of the alternatives on both sides are being eliminated. And one is seeing which path integral version best fits together with which canonical version. In the end I think there will be at most one combined version left standing.

Most of the recent results (like n-point functions, graviton propagator, classical limit in special cases...) have been achieved using the spinfoam, i.e. path integral, version.There's a spinfoam quantum amplitude formula is called the spinfoam vertex amplitude, or simply the spinfoam vertex. A spinfoam has a finite number of vertices and the dynamics depends critically on how the amplitudes for these are calculated. It's not clear which version of the vertex formula is going to win out. The closely related (dual in a sense?) path integral formulation does not need a vertex formula because it has an action and a more conventional setup. All this stuff is in the process of being hammered out.Sorry this is so fragmentary. I haven't taken the time to organize.

Anyway it is a very interesting and active area of current research, what you asked about.

 

[atyy]

Hmm, it seems string field theory may be background independent in the sense that a particular background specifies the field configuration (like in GR choosing the metric specifies the stress-energy tensor, in the geometric coordinate independent sense). So one is not free to choose the background, then put arbitrary fields on it as is done in SR or QFT in curved spacetime.

String Field Theory
Washington Taylor
http://arxiv.org/abs/hep-th/0605202

 

[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.