# Background Independence Question

## Main Question or Discussion Point

It is said that a flaw in string theory is that it is background dependent, whilst loop quantum gravity isn't background dependent. I don't see why this would actually be a flaw, because from what I understand is that background dependence means that the theory relies on a background of spacetime, so why should it necessiraly be 'bad' that it depends on this background? If string theory would be proven to be correct, being background dependent, would it be a sort of incomplete theory? Would it somehow be better if it was background independent? I would appreciate any answers.

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marcus
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Curious6 said:
It is said that a flaw in string theory is that it is background dependent, whilst loop quantum gravity isn't background dependent. I don't see why this would actually be a flaw, because from what I understand is that background dependence means that the theory relies on a background of spacetime, so why should it necessiraly be 'bad' that it depends on this background? If string theory would be proven to be correct, being background dependent, would it be a sort of incomplete theory? Would it somehow be better if it was background independent? I would appreciate any answers.
Haelfix put the string viewpoint on it rather well a couple of months ago in another thread----he said "it is argued that"....and then ended up with "so who needs background independence?"
Other string fellows will argue, somewhat abstrusely, that Loop Quantum Gravity does not really have background independence either!

the importance of background independence was outlined in a circa 1994 paper of Edward witten which said essentially "the big unsolved problem with string theory is we dont have background independence---do something about it!"

None of that matters. whether string does nor doesnt have BI, whether LQG does or doesnt have BI, is all low level squabbling.

this is what matters:
a background is a metric----a distance function that lets you calculate distances and angles and areas and volumes: all the geometry----on spacetime.

in Gen Rel the metric is the gravitational field
therefore the metric (the geometric background) is free to ripple and go everywhichway and make black holes and expand and contract.

the background is actually a dynamic player in the game. it is not a background. it is the gravitational field interacting with matter as matter flows around.

We say Einstein's 1915 Gen Rel is "background indep" but we could say it is a "dynamic background" theory or a "free active background" theory.

this means it is different from all other physics theories. All the other theories are set out on a predetermined fixed background----which then it may be possible to perturb a little bit----basically chosen in advance.

According to 1915 Gen Rel, nature does not work that way. nature has no precommitment to some static choice of background geometry.

so there is a tug of war going on. either one has to get rid of Gen Rel or one has to somehow coax the other theories to loosen up and become background independent versions of themselves.

It is really quite hard, a kind of crisis or impasse in physics. it has been going on for some decades now.

the kicker is that 1915 Gen Rel actually predicts things very accurately and no one sees how to get a more accurate theory, also it is the source of popular stuff like dark energy and black holes and corrections to the Global Positioning Satellite system, and the big bang and cosmology and stuff people like to explore. It is sort of coming into its own as a major force in theoretical physics these days so it doesnt seem like it is ready to be thrown out. this suggests to me that B.I. is here to stay.

Quantum Gravity models tend to be quantizations of Gen Rel, so they at least try to be background indep like Gen Rel is. How well the various approaches to QG succeed is a separate issue.

you asked what is it and why is it important---that's about it

If GR is background Independant, then how did strings make it dependant?

OK, thanks for the replies. Does anybody know if there are any papers published talking about background independence in string theory?

I don't think the argument from general relativity is very strong. What we should demand of our basic theories is not that they share the features of our best approximations of them, just that they explain why these approximations are good approximations.

Or is the argument that a background-independent theory could never be a good approximation to a deeper background-dependent theory?

(edit: I don't really understand any of this stuff, so maybe it would all become clearer then.)

Are there other arguments for or against background-independence?

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String theory is background dependant, and why I placed question about the joining of GR to QM from a string perspective.

If one thinks about back ground independance, could one just as easily think of the photon's travel? I might be confusing the nature of the question in regards to LQG persepctive? These deal mainly with path integrals approach of Feynman toys models

Strings, being background dependant needs the spacetime fabric to allow these gravitational waves, to be quantizied so it surpasses Lqg by moving past SR.

Any corrections, as I would not like to mislead here.

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marcus
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Curious6 said:
OK, thanks for the replies. Does anybody know if there are any papers published talking about background independence in string theory?
Edward Witten
http://arxiv.org/hep-th/9306122 [Broken]
"Quantum background independence in sring theory"

Edward Witten
http://arxiv.org/hep-th/9208027 [Broken]
"On background independent open-string field theory"

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Curious6 said:
It is said that a flaw in string theory is that it is background dependent, whilst loop quantum gravity isn't background dependent. I don't see why this would actually be a flaw, because from what I understand is that background dependence means that the theory relies on a background of spacetime, so why should it necessiraly be 'bad' that it depends on this background? If string theory would be proven to be correct, being background dependent, would it be a sort of incomplete theory? Would it somehow be better if it was background independent? I would appreciate any answers.
Why is it important to have back-ground independence? Without a theory that explains the creation of the background spacetime in which everything happens, then it is not an explanation at all. To presuppose what you are trying to explain is "begging the question" - or the logical error of petitio principii. Shall we simply start with a infinite, eternal spacetime that has physical properties that limit speeds and allow QM? Or is it required of a true theory of creation to explain where spacetime came from to begin with? We obviously need to explain where spacetime came from. Space time could not be eternally infinite and still have an explanation. So spacetime must have started as tiny curled up dimensions and expanded from there.

marcus
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sol2 said:
If GR is background Independant, then how did strings make it dependant?
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.)

marcus
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Mike2 said:
...Without a theory that explains the creation of the background spacetime in which everything happens, then it is not an explanation at all. To presuppose what you are trying to explain is "begging the question" - or the logical error of petitio principii. Shall we simply start with a infinite, eternal spacetime that has physical properties that limit speeds and allow QM? Or is it required of a true theory of creation to explain where spacetime came from to begin with? ...
this is a strongly persuasive argument that background independence is absolutely necessary, and encourages one to dismiss string theory until and if it is reformulated independently of a prior geometry

string theory, not to mention also 20th century quantum field theory, does start with an unexplained, typically Minkowski, geometry. This is the stage or frame you need to start defining strings in.

Minkowski space is, indeed, an "infinite eternal spacetime" with a built-in speed limit, just as you say Mike.

In a background independent theory one starts with no pre-ordained geometry and one lets the geometry (the metric, the gravitational field) emerge dynamically----this is closer to what you ask for: a theory that makes some effort to see how the geometry arose in the first place.

Background independence means working without a preconceived geometry and making the geometry happen however it is going to happen, depending on the distribution of matter and energy or quantum fluctuations or whatever. You can see intuitively why it is challenging and interesting to achieve in a theory of gravity.

I dont know whether I am just repeating and emphasizing what you said or whether I am extending your argument. I assume your initial question (why do we need B.I.) was rhetorical. Any fundamental theory of spacetime desperately needs background independence, from the ground up.

Historically though, people have dodged this requirement because it is really tough to achieve------standard QFT doesnt have it, for example.

I still don't get why background independence is necessary. Is it necessarily bad that a background spacetime would have no explanation, given that the most basic laws can't have an explanation anyway? If the background spacetime is replaced by something else, what explains that something else?

Are there physical reasons why background-dependent theories can't work?

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marcus said:
In a background independent theory one starts with no pre-ordained geometry and one lets the geometry (the metric, the gravitational field) emerge dynamically----this is closer to what you ask for: a theory that makes some effort to see how the geometry arose in the first place.
...
I'm wondering off the top of my head whether a spacetime which expands from the infinitesimal can actually be equivalent to a metric inside a pre-existing, eternal space where such a metric starts with zero distance and the distances expand with time, etc. Any thoughts?

marcus said:
Historically though, people have dodged this requirement because it is really tough to achieve------standard QFT doesnt have it, for example.
This is why I think that the emergence of the universe as a whole to begin with is not the result of quantum effects, because QFT requires a pre-existing spacetime as a background. Though, I'm not so sure about topological quantum field theories (TQFT). Perhpas topological quantities can remained fixed or have quantized values even though the topological space can emerge from the infinitesimal.

marcus
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Ontoplankton said:
Are there physical reasons why background-dependent theories can't work?
a background dependent theory starts with an absolute rigid spacetime.

if you want to study a black hole of a particular type then you pick by hand the absolute spacetime geometry corresponding to that type of black hole and you set up your fields in that frame

if you want to study a particular big bang scenario then you pick by hand the absolute spacetime shape corresponding to that idea of bang and you set up your fields in that frame

if you want to study particles whizing in a collider at earth surface where the spacetime is approximately flat Minkowski, then you pick by hand the absolute Minkowski spacetime that is customary in QFT and you set up your fields in that frame

You should read Haelfix post about this, which recounts the argument by which string theorists convince themselves that "Who needs background independence?" Haelfix seems to know what he is talking about.

So the answer to your question is, if you define "works" loosely enough then NO there is no reason why an Absolute Space theory can't "work".
Newton postulated an Absolute Spacetime in which all that stuff with gravity happened, and it gave pretty good predictions in an approximately flat situation.
You can get a Fixed Background theory to "work" in the sense of predicting numbers, as long as you keep changing the pre-selected background spacetime to fit the situation----you have a collection of flat and curved ones and you pick a flat one to roughly fit an approximately-most-of-the-time flat reality----and you pick a particular curved one to roughly match some ripply wiggly curved reality.

there is a deeper reason why String needs background independence and that was the reason given by Edward Witten in 1992 and 1993 when he urged people to work towards it and achieve it. what Witten said is: until we have a background independent theory we will not really know what a string is

To paraphrase Witten: rigid Absolute Space models use an artificial human arbitrary construct for space, like Newtons or Minkowski's, which is not real. So if you define a string in some Absolute Space it is not the real thing.

I will get the Witten quote for you (I gave the links earlier)

marcus said:
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.)
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 Freidmann 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 capability, then the theory will suffer?

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marcus
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-----Witten quotes----
“Finding the right framework for an intrinsic, background independent formulation of string theory is one of the main problems in string theory, and so far has remained out of reach.”

... “This problem is fundamental because it is here that one really has to address the question of what kind of geometrical object the string represents.”
----endquote---

I gave the links to the 1992 and 1993 papers earlier.

Nature does not have an Absolute Spacetime chosen from the menu of arbitrary static geometries which humans have invented for their convenience.

As long as objects in string theory are defined in some static construct spacetime, which one changes from time to time to cope with various contingencies, then one has not yet addressed the question of what kind of real object in real nature the artificially defined stringy objects correspond to.

(or if they correspond to something real, for that matter, but Witten
begs that question and merely asks what they correspond to)

marcus said:
-----Witten quotes----
“Finding the right framework for an intrinsic, background independent formulation of string theory is one of the main problems in string theory, and so far has remained out of reach.”

... “This problem is fundamental because it is here that one really has to address the question of what kind of geometrical object the string represents.”
----endquote---

I gave the links to the 1992 and 1993 papers earlier.

Nature does not have an Absolute Spacetime chosen from the menu of arbitrary static geometries which humans have invented for their convenience.

As long as objects in string theory are defined in some static construct spacetime, which one changes from time to time to cope with various contingencies, then one has not yet addressed the question of what kind of real object in real nature the artificially defined stringy objects correspond to.

(or if they correspond to something real, for that matter, but Witten
begs that question and merely asks what they correspond to)

Marcus I keep thinking back to Kip Thorne and the leading perspective with John Wheeler(his geons) directing the helm.

Should we dismiss the validity of theoretical research, that has gone on with ground and space based detecors of those gravitational fields?

If we do not develope the geometry for computerization, then we will not know the events(early universe) as they unfold. Smolin's perspective has indeed has gone this way for me, but is limited?

marcus
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marcus said:
Edward Witten
http://arxiv.org/hep-th/9306122 [Broken]
"Quantum background independence in sring theory"

Edward Witten
http://arxiv.org/hep-th/9208027 [Broken]
"On background independent open-string field theory"
the message of these papers is not that String theory is background independent but that it ought to be

hopes are offered but have remained unfulfilled

but the efforts urged by Witten continue! Vafa is rumored to
have made some progress toward B.I. in the past couple of years.
Other people doubtless have some links to Vafa work that would
give credible evidence of his progress, all I have is hearsay.

(I believe Vafa is one of the short list of tough ones who reject
the Anthropic Principle and refuse to give up the attempt to
solve the big core problems. Lubos has talked sometimes like he
is one of those too, at least he unequivocally rejects Anthropery
and has said something about the need to get background independence
before there is any more loose talk about Stringy cosmology and "colliding braneworlds" and whatnot. he posted about this on SPS and it increased
my respect for him considerably.)

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marcus: I think I see the problem now, thanks.

marcus
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Ontoplankton said:
marcus: I think I see the problem now, thanks.
hey great!

marcus
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Here's that Haelfix quote. It's quite appreciative of string theory but it also acknowledges the fact of its working on a set background geometry.

Haelfix said:
This is getting a little rehashed and boring, but its oft argued that 'who needs background independance if your theory outputs gravitons' (the thing that makes the geometry in the first place). So what if its perturbative?

Since physics is about predicting things, and we more or less know what geometries are interesting already, if String theory could output the full particle spectrum for each background, then you're really done. Thats the big 'if'!

I should add, String theory is a little bit more than background dependant.. It has consistency measures that force metric and even topology changes, and the fields themselves don't know anything about backgrounds. I should also add there are attempts (see what Vafa is doing) to make string theory somewhat more background independant in terms of rulers and lengths, but so far its still highly work in progress.

But yes, in principle BI is an unresolved problem motivated by mathematical elegance. But no one knows if thats the way the world works.

My personal opinion on the subject, is that String theorists seem to have stumbled on something very important (I very much like the group structure and the subtle connections to supersymmetric YM), but I think some of the ugliness in construction is man made.

If String theory turns out to be the theory of nature, 60 years down the line, I suspect things will have cleared up dramatically in notation and the physics will be far more workable, both in ease of calculation and intuitiveness.
I bolded a key phrase for emphasis. You have a menu of fixed geometries, which are artificial human mock-ups of spacetime giving a simplified approximation to various situations----a black hole, an expanding universe, a flat Minkowski non-expanding universe with no matter in it, etc.
We know what the interesting geometries are already so we
calculate a perturbation on each one of those set frameworks---we crank out a "graviton". then we can do predictions, and physics is about predictions.

At any rate curvature is a second-order effect and ought not to effect microscopic things too much---a curved space is almost flat and locally looks pretty flat.

these are, I think, very practical working-physicist perceptions and attitudes. I found the argument Haelfix offered personally very congenial although I differed with the conclusion.

marcus said:
We know what the interesting geometries are already so we calculate a perturbation on each one of those set frameworks---we crank out a "graviton". then we can do predictions, and physics is about predictions.
Do you think we can get to the true meaning of reality if we settle for curve-fitting, engineering approximations? You're still begging the question as to where the background spacetime came from. If the particles are physical, then the space they move in is physical. And we are obligated to explain where that space came from, unless of course you're just interested in engineering.

the basic problem with background dependence for me is a core conceptual error that forces you to look at the wrong problem- background dependant theories mistakenly divide Reality into a background of absolute space/time and some dynamics/physics which occur within the backgrond- then they focus on the wrong half of the problem and try to investigate the physics/dynamics that emerge in the background-

but cosmology is the pursuit of knowledge about the FUNDAMENTAL forces of Reality- so a person interested in cosmology- when given the duality of background and dynamics- should be more intersted in the BACKGROUND-

looking at a background dependent theory- my questions are NOT for instance- how do strings/branes interact and evolve to generate forces/matter/energy- my question is what is the background that allows strigs/branes to emerge made of? what is it's fundamental structure? why does the background exist? what is motion had how does the background allow motion to exist? what is distance/extension and how is the background structured to allow metrics to exist?

to me- the physics and dynamics of background dependent theories are like biology: descriptions of reality that don't deal with or expalin the fundamental structures of being- of course still very useful and explanatory of EMERGENT phenomena- but if your goal is to ask questions about the WHOLE of the universe and how it fundamentally exists/works- a background dependent theory by DEFINITION cannot help you-

after all- once you have an established background of space/time- ANYTHING can be made-up to expalin the rest- strings/ aether/ fairy magic/ whatever- as long as it works- after all- the hard questions about existence/distance/motion are simply ignored and assumed to be self-evident- but if a theory is background independent- it has to expalin everything from being/motion/distance through emergent phenomenology- which makes it stronger becasue nothing is assumed

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marcus
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Mike2 said:
Do you think we can get to the true meaning of reality if we settle for curve-fitting, engineering approximations? You're still begging the question as to where the background spacetime came from. If the particles are physical, then the space they move in is physical. And we are obligated to explain where that space came from, unless of course you're just interested in engineering.
All I can say is I hear you, I can see both sides of the issue. I did not mean to sound like I was leaning one way or the other-----I appreciate successful engineering very much and also good accurate curve-fitting and phenomenological physics that gets good numbers.

And on the other hand there is the appeal of something that is somehow
more fundamental and has more integrity (if one can find it) and
gives more an idea of where it came from.

Oddly enough Haelfix, whom I was trying to paraphrase, did not himself take a side on this. He repeated an argument given by string theorists----he said "it is argued that...."
Later in a subsequent post he clarified that it was just a string theorist argument that "Who needs background independence?" It wasnt something
that Haelfix subscribes to either.

(as a mere watcher I admit to sometimes, like you, lean more towards hoping for a fundamental
background independent theory however, esp. as the one using fixed backgrounds does not actually calculate all that much numbers anyway)

setAI said:
descriptions of reality that don't deal with or expalin the fundamental structures of being- of course still very useful and explanatory of EMERGENT phenomena- but if your goal is to ask questions about the WHOLE of the universe and how it fundamentally exists/works- a background dependent theory by DEFINITION cannot help you-
I think you are missing someything very fundamental here.

You talk about emergent realites and then dismiss, the question of background dependance.

From what I see now, every discussion that takes place, deals with high energy considerations that emmanate from the planck epoch.

I mean we have thrown around these two concepts here and I have greatly appreciate it, for it has made me aware of something that string theory wants and does not yet have.

But still, looking at the early universe, such features cannot be easily dismissed.

No one has directed the attention to the features of this early universe,whether there would be supermetric points of consideration(supergravity) and from this metrics points also derived?

If such supersymmetry exists in the very beginning, from those points on the branes, then what has this meant in terms of the "energy scale" such as that describe from the start of the Planck epoch. The plan is emergent(phase transitions), once you can see from the planck epoch where everything was supposedly joined, that the standard model can be derived from that early universe?

G -> H -> ... -> SU(3) x SU(2) x U(1) -> SU(3) x U(1).
Here, each arrow represents a symmetry breaking phase transition where matter changes form and the groups - G, H, SU(3), etc. - represent the different types of matter, specifically the symmetries that the matter exhibits and they are associated with the different fundamental forces of nature
So we definitely have our work cut out for us.