Is Background Independence Desirable?

[jgraber]

Of course, the majority opinion among knowledgeable physicists seems to be “Yes”.
However, there are at least two cogent arguments that Background Independence (hereafter BI) should be regarded as a bug, rather than a feature.

First, local conservation of energy. In particular, GR, the paramount BI theory, has a major problem even defining local energy, much less conserving it. This can be recovered in an asymptotically flat spacetime, which has in some sense a preferred background.

Second, linear superposition in quantum mechanics. The fact that no one has been able to make a nonlinear quantum mechanics work, or do superposition in general curved spacetimes is another argument that a preferred background in which linear superposition works is a necessary requirement for a viable physical theory.

So perhaps the background dependence of String Theory should be regarded as a feature, rather than a bug.

(This post is submitted at this time partly in response to the recent exchange between marcus and sol2 in the thread “Olaf Dreyer: the Cosmological Constant paradox”.)

I know this general topic has been much discussed, but I haven’t seen this particular angle considered. If there are good references, either in the literature or in the forums, please point me to them. Thanks.

Jim Graber

 

[marcus]

Of course, the majority opinion among knowledgeable physicists seems to be “Yes”.
However, there are at least two cogent arguments that Background Independence (hereafter BI) should be regarded as a bug, rather than a feature.

First, local conservation of energy. In particular, GR, the paramount BI theory, has a major problem even defining local energy, much less conserving it. This can be recovered in an asymptotically flat spacetime, which has in some sense a preferred background.

Second, linear superposition in quantum mechanics. The fact that no one has been able to make a nonlinear quantum mechanics work, or do superposition in general curved spacetimes is another argument that a preferred background in which linear superposition works is a necessary requirement for a viable physical theory.

So perhaps the background dependence of String Theory should be regarded as a feature, rather than a bug.
...

this is an interesting issue and hasn't been discussed at PF in a systematic way---not thoroughly IIRC. Haelfix gave an interesting argument, which he claimed not to subscribe to but one he hears used, for "Who needs background independence?"

I will try to recall or find that argument.

I have tried to imagine what the alternative to a B.I. theory of gravity would be and I think there are two possibilities: multi-shape and single-shape

in multi-shape approach you decide ahead of time what all the interesting pure geometries are and make a list (then you do field theory on each geometry and define or derive a graviton describing interaction)

the list would include flat Minkowski and various kinds of black holes, an expanding universe, perhaps some types of collapse or collision, perhaps an inflation. there would be a geometric typology which would cover the main cases and you would build a theory on top of each geometric setup

this multishape approach is pragmatic and allows for calculating, in principle, all the interesting cases on might encounter and want to predict.

IIRC this multishape argument was what Haelfix said he had heard string theorists using when they wanted to say "who needs background independence?"

the single-geometry approach is harder for me to imagine. I guess one would decide on Minkowski space and try to make everything fit in that.
I don't see how one could do cosmology with an expanding universe, but some way might be found. one would have a lot of gravitons whizzing around bending lightrays. it is hard for me to see how one would study black holes in Minkowski space, but again a way might be found (or perhaps has already been found and i just don't know about it!)

actually, instead of guessing how a fixed-geometry approach to quantum gravity might go, I should ask you to flesh the idea out some! How do you picture it, Jim? Has it perhaps even been done already----under the "effective field theory" rubric?

have to go for a moment, back soon

 

[marcus]

... I haven’t seen this particular angle considered. If there are good references, either in the literature or in the forums, please point me to them...

Edward Witten has a couple of short articles explaining reasons for wanting B.I. in string theory, as he saw it at the time, and some ideas of how string theory might be made B.I. don't know if these will help clarify the issue or not. Here are Witten's papers:

Quantum Background Independence in String Theory
http://arxiv.org/hep-th/9306122

On Background Independent Open String Theory
http://arxiv.org/hep-th/9208027

 

[marlon]

Besides, isn't background independence not the "thing" "we" are all looking for? The approach in LQG differs from that of Stringtheory in that aspect that in LQG we start from the principles of GTR and we try to "rewrite" QFT with background-independence. Now in stringtheory background-independence is still maintained from the start (against the "will" of Einstein) but in the end we need to recover somehow general covariance, right?

Just a thought, couldn't it be possible that LQG and Strings are somehow dual, describing the same thing in two different manners?

I personally would go for the approach of LQG since it seems more "natural" to me. I do think that starting from GTR is a solid basis since it already implements the most ingenious model of physics at large scale, known to man kind...
regards
marlon

 

[marcus]

Besides, isn't background independence not the "thing" "we" are all looking for? The approach in LQG differs from that of Stringtheory in that aspect that in LQG we start from the principles of GTR and we try to "rewrite" QFT with background-independence. Now in stringtheory background-independence is still maintained from the start (against the "will" of Einstein) but in the end we need to recover somehow general covariance, right?

Just a thought, couldn't it be possible that LQG and Strings are somehow dual, describing the same thing in two different manners?

I personally would go for the approach of LQG since it seems more "natural" to me. I do think that starting from GTR is a solid basis since it already implements the most ingenious model of physics at large scale, known to man kind...
regards
marlon

marlon, I agree with you strongly. BI seems like a natural thing to want, if one can get it. my reservations are
1. Jim Graber is experienced and has solid judgement. I want to hear all possible arguments from him because if he finds reasons they may contain good ideas. so I hope he pursues the idea that B. dependence is good.

2. Florian conrady (Potsdam MPI and Marseille) has constructed a LQG vacuum. Could this perhaps be used as a basis for perturbation theory calculations? Maybe LQG can be B.I. and nonperturbative at a fundamental level but have access to convenient perturbgation-theory calcuations?

have to go

3. was about Xiao-Gang Wen work on condensed matter approach that seems both string like and also LQG like
("...couldn't it be possible that LQG and Strings are...describing the same thing in two different manners?...")

near the end of Xiao-Gang Wen's paper
http://arxiv.org/cond-mat/0407140
A unification of light and electrons based on spin models
he mentions LQG. this is at the top of page 7, first paragraph.
I believe that X-G's "string-nets" are not real strings, they remind me more of the spin-networks of LQG. they seem to live in familiar 3+1 dimensional world---in 3D actually. X-G is innovative, how did they come to let him join the faculty at MIT? He is a mystery to me at present. But he seems to be successfully developing a theory that it is a bit like this and a bit like that. And he has a book contract with Oxford U. Press, so perhaps there is some chance that what he is doing will yield solid results

He likes to describe particles, not gravity, but he uses something strangely similar to LQG. (I can't recommend because only yesterday found out about it and don't understand it)
see also
http://arxiv.org/cond-mat/0406441

 

[sol2]

There seems to be a cultural shift in how BI is seen in regards to GR? I wanted to expand my understanding on how LQG and String are identifying themselves in relation to BI, and BD

If someone is going after some tangible proof, for the instantaneous feature of gravity, where are we suppose to look for this? I have these images in mind that are really confusing to me become they seem to cross reference each other. For instantance, the spacetime fabric has this mass impression and we know the photon is reactive to this.

Yet there is another point in which the photon is intersecting, as we all know, and is telling us something about the origins of things from our past.

So we apply energy considerations, as we would applied mass considerations, and the photon is applicable to both? The photon is telling us something.

Now for this string to emerge from this background, was there some geometical consistancy to point us in the direction of the evolution of this string? What fundamentals take us from the very emergence of the string from the Planck epoch to have it tell us about the nature of the energies that can move as bosons along its length(wraps in KKtower energy modes) that we could also consider the twisting that the energy demonstrates on this string to have it diverge into feynmens toy model scenarios.

Am I capturing the essence of the two perspectives?

Just realized today the M stands for a Matrix.

I also wanted to add Marcus's comments in quote.

String is not a quantization of the theory of general relativity, so there is no contradiction.

At the very start, to define a vibrating string, one is depending on a rigid background framework-----a fixed background geometry in which to define the string itself.

this has been recognized as a major problem and heroic efforts have been made to redefine String so as to give it a background independent formulation.

M-theory is one such effort. Tom Banks, one of the founders of M-theory, discusses the problem of achieving background independence----ultimately necessary but discouragingly difficult to attain---in his paper "A critique of pure string theory".

Popularizers of String rarely mention this problem, perhaps assuming that it is too technical to describe to a general audience and that it will quietly be solved in due course.

In contrast to popularizers, Ed Witten, Tom Banks, and Lubos Motl have discussed the need for background independence. They are also among those most strongly opposed to invoking the Anthropic Principle. Seeing them take these stands has contributed considerably to my sense of their integrity (although I remain free to disagree with or doubt other of their statements.)

https://www.physicsforums.com/archive/t-37835_Background_Independence_Question.html

Thanks Marcus. You have been really great here in ellucidating the questions about these principles.

One thing though first in regards to your links given to curious6. This would lead one to believe, that strings are background independant, when it should read, the desire is to become back ground independant and those links supportive of those attempts?

For a consistent geometrical apporach, which I believe is necessary, allows an overall perspective, even in regards to the thread of yours on Smolin and the cosmological principal. We recognize Omega, and the issues of critical density as a value worth speaking on. We have also recognized the Friedmann equations in helping us understand the curvature parameters.

As I read Smolin's article, it even becomes more apparent, that such a vision is necessary?

If you do not have this geometry (https://www.physicsforums.com/showthread.php?t=30419) capability, then the theory will suffer?

https://www.physicsforums.com/archive/t-37835_Background_Independence_Question.html

I am sorry if it seems babbling aside from Marcus quote, but the desire would be to see the references of BI and BD applicable in general concepts that we could have swallowed. Why I introduced photon and string emergence as a geometrical model, respective of LQG and M theory.

 

[jgraber]

Background Free or Background Independent?

I see over in S.P.S there is a thread entitled Background Independence in which a fairly technical discussion of what background independence actually means is proceeding. In a post today, Urs Schreiber states that background *independence* is desirable, as opposed to background *freedom* which may be problematic.

This made me wonder if I should have couched my post in terms of background freedom, instead of background independence. (I vaguely recall, but have not yet looked up several posts by John Baez on various levels of background freedom or background independence. If I get around to looking them up and find something interesting, I will post links later.) So I will simply raise the question (two questions actually) as to whether it is background freedom rather than background independence which interferes with defining local energy and retaining linear superposition. My first reaction is that perhaps the answer is yes in both cases.

Then I wonder if everyone means the same thing by background independent and background free. My impression is that at least some string theorists claim that string theory is background independent, but not background free (I sort of gather that from Urs’ post.) On the other hand GR is “truly background free” according to most, and hence I think most LQG folks also claim LQG is background free in the same sense. On the other hand, Ashtekar and Lewandowski, in their recent review gr-qc/0404018, use the term “background independent” in the title. I suspect that at least in part, there is some terminological confusion or ambiguity involved.

The main physics drift of my original post is the idea that these particular issues (local energy and linear superposition) support quantum mechanics rather than GR, and hence suggest that the ultimate unified quantum gravity may *not* have the extreme form of background independence or background freedom that GR does.

In my mind, this follows the spirit, if not the letter, of the quantum dominated approach to quantifying gravity taken by Feynman and Weinberg, among others. I guess this could be interpreted as supporting strings as against LQG, but that is not the issue I am trying to address.

Jim

 

[sol2]

Like you Jim, I have gathered a few perspectives from within the physics forum to support the questions you are asking. I had to see Marcus's responses that he has made, to try is see what exactly has been covered here in these discussions.

One thing I would like to say is, I have found a deeper explanation philospohically that is governing Smolins thoughts on this approach, that help me understand the divergence and method by which he maintains LQG. Why Marcus possibly maintains it as well. I have gather together my thoughts here, as the idea here, is to capture that true essence.

I have partly done this by pointing to the ideas of Chandra's attempts placed upon those heavily involved in the graviational issues comments. Smolin has a personal perspective, that I had not understood before, that really helped me in this direction, to understand these differences.

I must say to those he has pointed out the issue of theoretical values which should be more enshrined with those gifted, with the deep comprehension of GR. I have to defend myself when I say, that I am not limited, to the deep perspectives that can arise from those who speak on these issues. I do not like to be considered as one more who is trying to change the way in which we deal with the spacetime fabric, but to try and find the beauty of the thoughts that these theorecticst can have and how they interject them from their perspective fields.

My personal devotion to the hobby, has been a very relaxed one, and I enjoy it. That doesn't mean I should suffer from what can be aspired too, in sifting the reasons why Smolin stands to ground he does, and the labels that could drive a wedge in the relations of LQG and Strings respectively. I know I have to validate this point.

A case in point, is the understanding of Smolin's position.

I have followed his thinking as a example of the rigourous, and summations, although at a much generalized level. I do not think I should have been faulted on this as a crank( an overall generalization of those who have not developed fully from the roads GR has taught us, including those who wish to try and make a discription of the gravity waves fit some gravitonic expression)?

Smolin tells us that General Relativity is not about adding to those structures or even about substituting those structures for possible new structures. Of course we must understand what he is referring to here .

The basis of Smolins position rejects the idea, that space and time are fixed. He believes it evolves dynamically. He then subcribes, in my way of thinking, to the value of using this structure( it is contradictory to me as I stated up in previous post about photon intersections[Glast limitations] and the intersection of grvatonic considerations. In the methods explained in terms of Glast's experimental standing we see where this can be taken furthe? Smolin calls it a set of relationships between events that take place. To place such attempts at redscribing the nature of the spacetime fabric disturbs him?

All the best to you Jim as I'll be watching from the sidelines and posting from here.

 

[setAI]

a background is a conceptual carpet in which the big problems are swept under and forgotten

 

[marlon]

a background is a conceptual carpet in which the big problems are swept under and forgotten

Then you might as well say that General Relativity is a conceptual carpet in which the big problems are swept under and forgotten. This is a very, eeuuuhh, simplistic view that is worth nothing. Saying something is bad is easy, defending something good is difficult. Obviously you take the easy way out. I think we all know where that leads to. It sure as hell ain't background-independence...

regards
marlon

Dearest setAI, what do you mean by this statement...

 

[marcus]

...On the other hand GR is “truly background free” according to most, and hence I think most LQG folks also claim LQG is background free in the same sense. On the other hand, Ashtekar and Lewandowski, in their recent review gr-qc/0404018, use the term “background independent” in the title. I suspect that at least in part, there is some terminological confusion or ambiguity involved.

...

Loop Quantum Gravity people and String people use the term "background independent" to mean different things.
I have seen this noted in LQG writings, can't remember where.

In LQG articles they never say "background freedom", that I can remember. If someone did it would probably be just a synonym for "background independence".

I don't know exactly what String people mean by B.I.

LQG people use the term B.I. in the same sense as classical relativists when they describe the classical GR theory as B.I. You start with no pre-ordained metric on the manifold. You don't choose a metric or a geometry---it choses you.

It will cause a lot of confusion if String people start using the words "background independent" to mean something else.
there are a lot of them, so sheer weight of numbers will tend to drag the term away from the meaning it has customarily had among students of GR and QG.

Since relativists (quantum or classical) have AFAIK always used the term B.I. in just this way (no dependence on an initial assumption of a metric) they can fairly say "Unfair verbal practice!" but they are few in number compared with particle physicists.

If String theorists all take to saying B.I. and meaning something else by it, then it may be difficult for Relativists to retain control of this essential term

 

[marlon]

True story marcus,

Besides background-independence (as in you can choose any metric you want) is fundamental in the theoretical development. it gives the biggest "feeling" of freedom thus yielding the most universal theory...

regards
marlon

 

[jgraber]

A few references:

The abstract of Jan Ambjorn, Jerzy Jurkiewicz and Renate Loll, Emergence of a 4d world
from causal quantum gravity, available as hep-th/0404156, uses the term background independent,
as do John Baez and Lubos Motl in their recent disagreement
in SPS thread This Week's Finds in Mathematical Physics (Week 206).
On the other hand, John Baez’s FAQ
http://math.ucr.edu/home/baez/background.html uses primarily the term background free.
I don’t know how Urs uses these terms, so I posted a response on SPS to ask him.
Hopefully, he will respond. Jim

 

[setAI]

Dearest setAI, what do you mean by this statement...

https://www.physicsforums.com/showthread.php?p=275133#post275133

 

[sol2]

This is a link taken from the post Jim offer of John Baez interpretaion of Back ground Independence and some clarity around background freedom.

Higher-Dimensional Algebra and Planck-Scale Physics


John C. Baez

This is a nontechnical introduction to recent work on quantum gravity using ideas from higher-dimensional algebra. We argue that reconciling general relativity with the Standard Model requires a `background-free quantum theory with local degrees of freedom propagating causally'. We describe the insights provided by work on topological quantum field theories such as quantum gravity in 3-dimensional spacetime. These are background-free quantum theories lacking local degrees of freedom, so they only display some of the features we seek. However, they suggest a deep link between the concepts of `space' and `state', and similarly those of `spacetime' and `process', which we argue is to be expected in any background-free quantum theory. We sketch how higher-dimensional algebra provides the mathematical tools to make this link precise. Finally, we comment on attempts to formulate a theory of quantum gravity in 4-dimensional spacetime using `spin networks' and `spin foams'.

http://math.ucr.edu/home/baez/planck/planck.html

I wonder if John's feelings here have changed since 1999?

 

[sol2]

A New Toy Model?

[Moderator's note: I agree, of course, but my feeling was that the
discussion was focussed on weakly-coupled perturbative backgrounds
that still do not have to be geometric such as various
Gepner-like models. One can still ask whether they can be always
connected with geometric backgrounds. Various islands, orbifolds
by T-dualities and other CFTs with possibly frozen "size" modulus
suggest that the answer is "No", at least if we want them to connect
on-shell. LM]

https://www.physicsforums.com/showpost.php?p=309678&postcount=16

What strikes me as strange is how we could have perceived the language of branes, with somekind of toy model even though we can't see them. For me as a sideliner, who views the world of these theoreticists, I had to try and make sense of this language they are talking about.

So I look for some comparison and geometrodynamcis came into view, but I mean this couldn't have even been fathomable if we say it is hidden ,what the heck does this mean?

So in the spirit of Feynmen, how about we use these new features to help us orientate the views of the world that is hidden and help many understand the world contained in the vacuum, that many could never have comprehended.

It is part and parcel of the view I am developing, in relation to the geometrical undertanding that comes out of the view of how this universe came to be. I know this would quickly align some persepctives in that geometrical consideration.

Issues on Poincare conjecture seem relevant somehow, and the link to Peter Woits gives a interesting perspective on this.

So any way, here is the new toy model that one should work with, and correspond developing language in relation too GR's developing views along side of the small world we all are trying to capture.

LQG is successful here in the intersecting bubble technology, in regards to it's nodes, but how would strig theory survive. You ahd to know that underlying this language is some consistancy and I hope to show that.

http://science.nasa.gov/headlines/y2003/images/nosoap/spiralgalaxy.gif

http://science.nasa.gov/headlines/y2003/25feb_nosoap.htm

Would there be some diagreement in using this to encapsulate everything Lubos is saying? I do not believe this to be inconistent with Reinmann's view and Greene's view on the new geometry that must emerge?

Now remember this relation was made here first in this posting.

 

[sol2]

It is always interesting to see/vision of what abstractions arise in braneworlds. But rightly so, this should be put in "What are Branes thread," so In the spirit of what leads one to post a further response I thought I should appropriately post it to this thread and say thanks.

What happens with the worldsheet as you increase the coupling?

Well,
it transmutes into a M-volume, which is the worldvolume of M, which
is the non-perturbative generalization of a string. ;-) The worldsheet
becomes a bit fuzzy, non-local, its dimension may effectively grow
(strings become membranes, but don't imagine quite local membranes). I
think that its internal dynamics is itself target space dynamics of
some other string theory; I have the N=2 and string in mind.

https://www.physicsforums.com/showpost.php?p=313961&postcount=1

 

[sol2]

Incidentally, your flawed thinking, combined with Mach's principle,
was one of the reason why the relativists could not understand that
there exist gravitational waves for such a long time - they spent
literally years trying to prove that these solutions are pure gauge.

https://www.physicsforums.com/showpost.php?p=314758&postcount=30

One of the rules appear to be in recognizing the back ground is smooth, and without this supesymmetrical view no geometry can emerge form such a view.

Without the gravitonic emission(now we have to remember what this geometricalization is telling us in regards to those gravity waves)the spacetime is flat.

So LQG, cannot emerge with a overview of on quantum gravity, although it is describing, and is much closer to the interactive examples(path integrals) we might see from Glast perspectives. How would Topos theory arise out of such views, and abstractually consider itself, anymore a model, then strings?

How would such a view hurt the ideals of such a geometry arising from supersymmetrical realizations?