Does string provide a quantum gravity theory?

[marcus]

This seems like an important issue.
In his recent talk (reported on Woit's blog) David Gross said yes:

Gross:"String theory is a consistent, finite quantum theory of gravity"

However Woit says not:

"Simply not true. Peturbative string theory is a divergent expansion, non-perturbative definitions don't work for four large flat dimensions, rest small."

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some here may wish to discuss this

as a string-non-expert I had always assumed that string theory, as long as it was background dependent, could not include a background-independent quantum gravity
To me seems obvious and elementary. Gen Rel is our standard and successful classical theory of how gravity works and it continues to be checked out in intereresting regimes where spacetime curvature is significant. GR is background independent and it makes predictions and is checked more and more in regimes where that background independency matters a whole bunch.

So I have to say that on the face of it string seems irrelevant to quantizing the real theory of gravity---the one that works and is B.I.
I doesn't look like you need to be a rocket scientist to see that.

But I would be happy if some other people would present different points of view. I am always intrigued when someone argues that string gives a quantization of General Relativity (so often characterized as the Holy Grail of the physics of our time).

Does string provide a quantization of GR?

seems like Gross says yes
and Woit says no

 

[Haelfix]

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 that's 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.

 

[jeff]

Does string provide a quantum gravity theory?
Gross says yes
Woit says no

No marcus: Everyone says yes because the answer is yes. Also, it's ridiculous to compare the "opinions" of one of the world's premier theorists with a guy who by his own admission doesn't do much research, and is certainly not an expert on string theory, finding it too "complicated" and "intricate".

 

[marcus]

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'!

A graviton is a mathematical fiction that helps describe the behavior of the gravitational field in some idealized case of a fixed (usually flat) geometry.
So the idea seems to be to get a list of interesting cases and see if you can "output a graviton" in each case.

That still would not be a quantization of the gravitational field which is a dynamic changeable thing that doesn't conform to a set menu of geometries but it would be a pragmatic approach to predicting, if you could crank out a graviton in a whole lot of interesting different geometries. That itself is, as you say, a big if.

I'm curious about what people think the list of interesting geometries is. I can think of several (near-colliding black holes, two spinning neutron stars in tight orbit, an expanding universe ab initio, Schwarzschild black hole of course, and minkowski space, must be a lot more)
I'm very glad to hear from you that Vafa is working on getting something
in the direction of background independence.

I don't agree with the idea "who needs background independence" or that you are really done if you can predict gravitons in certain set cases. But I do understand the argument and appreciate your clarification!

 

[jeff]

A graviton is a mathematical fiction...[/B]

This is arguably in some sense true of physics theories period.

I don't agree with the idea "who needs background independence" or that you are really done if you can predict gravitons in certain set cases.

Few serious people do. But consider this...

QGT's to be correct must have appropriate low energy physics, the only known example of such a theory being string theory. On the other hand, as far as we know, the characteristic of background independence is not logically required to quantize gravity, and even if it is, we can't yet know whether spin-networks is the way to do it. This is why comparisons of strings with lqg to the effect that the problems of one are the achievements of the other are misleading. (Also, strings is making progress on the issue of background-independence, and in particular, it's teaching us that spin-networks probably isn't the only way of achieving it).

...interesting geometries...[/B]

Why do you find the equivalence in string theory between geometry and gauge theory uninteresting? That, for example, CFT in the bulk of spacetime can be equivalent to yang-mills on it's boundary? This is a striking illustration of the holographic principle which states that physics in the bulk is encoded in spaces of one dimension less and whose impetus comes from the area-entropy relation suggesting black hole states are encoded on their horizons. More generally, it's an illustration of why physicists find strings so compelling: It's just so damn hard to believe that such relations would arise in a theory that is fundamentally wrong. I just don't think there's anything in LQG that can compare to this.

 

[alexsok]

Jeff
I consent with most of what you've said, particularly, all regarding the holographic principle, which a great amount of people enthrone to be the guiding principle of string theory, or perhaps in the near future, M-theory.

But I don't believe that LQG is utterly useless in this fascinating research at all! AFAIW, LQG & String theory have proved over the years, that without a wee of a doubt, they're both plausible and feasible, and sometimes, it's enrapturing that some of the "blunders" in String theory, are literally remedied by the advanced & elegant machinery of LQG! I'm groping a loose end here, but i'd go on my limb to say that from a far-sighted perspective, they both could prove to be reconcilable and harmonizable and future probes, such as Neutrino & B-Meson factories, Gamma & Cosmic-ray bursts, LHC, Linear Collider, etc, which are in a perennial drift of complexification, would go a long way towards validating or falsifying some of the assumptions made within the respective territories of these theories and elucidating the true nature of our universe!

Just my 2 cents m8.

 

[marcus]

A graviton is a mathematical fiction that helps describe the behavior of the gravitational field in some idealized case of a fixed (usually flat) geometry.

This is not a feature of physics theories "period", or in general. It is simply false to suggest that all physical models exist only in some fixed (usually flat) geometry. It is not true, for example, that the gravitational field is restricted to a particular idealized case of (e.g. flat) geometry. A graviton, on the other hand, is a rather fragile construct in the sense that it doesn't travel very well from one geometric situation to another---from flat space to bigbang space to space-around-a-black-hole to dynamic-space-of-no-set-shape. A "graviton" is a mathematical entity that depends on the geometry it was set up in.

The gravitational field of GR has a more robust existence, not depending for its mathematical construction on some particular idealized geometric setup. In fact the graviational field is the geometry itself.

I don't agree with the idea "who needs background independence" or that you are really done if you can predict gravitons in certain set cases.

The characteristic of background independence is logically required by a theory which purports to quantize Relativity because Relativity is background independent.

There have been other attempts to construct a Background Independent Quantum Gravity----that is, a quantum theory of General Relativity---going back AFAIK to Wheeler and DeWitt in 1970s and maybe earlier. It should be well-known that other approaches besides spin networks have B.I.
IIRC Husain and Winkler just came out with a paper confirming Bojowald's result in cosmology using not spin network but the earlier form of quantum GR.

... if you could crank out a graviton in a whole lot of interesting different geometries. That itself is, as you say, a big if.

I was echoing Haelfix, who raised the issue of which geometries should be called interesting and which not interesting. If this needs clarfication maybe Haelfix can explain. He said:

"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'!"

The question is not about what special cases of fixed spacetime geometry happen to interest me personally. I actually don't find it a fundamental or satisfying approach to gravity to isolate a few fixed geometrical templates and crank out "gravitons" in those few situations.

Instead I would prefer to consider a dynamic geometry that can include unforeseen shapes and vary from one to another, and for this gravitational field to accommodate waves, which you may or may not wish to call "gravitons".

I personally find the case-by-case prediction of gravity, in set geometries, to be unsatisfying. But that is my individual taste and other people are welcome to indulge a predilection for perturbing fixed backgrounds.

In all events Haelfix is the one to take up the question of which fixed background geometries are deemed interesting.

 

[jeff]

The characteristic of background independence is logically required by a theory which purports to quantize Relativity because Relativity is background independent.[/B]

I'm sorry marcus, but really, just because an idea seems natural or reasonable doesn't mean it's logically required. There really is no proof that what you're claiming is true. If there were, such a proof would be too important and thus too famous to remain unknown for long. I'm sure the focus of research would be quite different. Certainly nowhere in the lqg literature is such a proof presented, just arguments about the significance of background-independence. As you know, there are many ideas that make sense classically which don't survive quantization.

It is simply false to suggest that all physical models exist only in some fixed (usually flat) geometry.[/B]

Who was suggesting this?

I was echoing Haelfix, who raised the issue of which geometries should be called interesting[/B]

So I gather.

In all events Haelfix is the one to take up the question of which fixed background geometries are deemed interesting.

Why's that exactly?

 

[Haelfix]

Note, I was saying what is often argued, not what I may or may not think of the situation.

The thing is, even in General relativity, all manifolds can be taken to have a locally smooth chart.. Its hard to think of curvature entering any perturbative theory of gravitons, unless its at least 2nd order effects or higher. Now, the principle contribution to quantum curvature is precisely what belongs to the manifold itself, degenerate geometries would intuitively be small perturbations of that.

Hence, its hard to see how a perturbative theory of gravitons (string theory) will be able to feel the effects of background independance until very high orders (or probably all orders of perturbation theory).