Alternatives to QFT

atyy

No, that wasn't a reply. Basically, gravity as spin 2 already works at low energies. Any new theory must reduce to a working old theory in the appropriate regime. Carlip has some references in here http://arxiv.org/abs/gr-qc/0108040, try searching for "Donoghue".

Hence, one way to see if LQG works is to see if it reproduces the graviton propagator http://arxiv.org/abs/0905.4082.

Haelfix

I am a little uneasy with the quote in 118 for a number of reasons. The local vs global thing is a bit of a red herring.

First of all, working with linearized gravity does not preclude cosmological or vacuum blackhole solutions in any way, nor does it require an R^4 topology. Those solutions are readily studied, and in fact entire textbooks have been written on those solutions (see eg Weinberg 'Gravitation')

However it is true that GR does not in general, uniquely constrain the topology of spacetime. That is additional structure is necessary to fix the exact physics (eg by appealing to experiment).

But not so fast! Working with the standard formulation has the exact same problem! That is why for instance in the case of cosmology, it is still an open question what the exact topology of the universe is like. There is no extra physical information that one formulation gives over the other, which is why they are isomorphic mathematically.

The real fundamental difference (between any of the tens of different formulations of GR) is that in some cases using one formulation allows you to solve problems in a more straightforward way.

You wouldn't want to appeal to the geometric theory to solve the classical black hole merger problem for instance. You want a heavy dose of linearized perturbation theory to tackle that (and a very good computer)!

However trying to prove singularity theorems alla Hawking-Penrose, is more or less completely opaque if all you could see were infinite series of curvature invariants.

So anyway, this whole story is pretty well understood classically. The real question is what happens when you introduce quantum mechanics? And indeed, theorists have tried quantizing pretty much every single formulation of gravity out there, so far unsuccessfully and indeed it is perhaps the case that they give unitarily inequivalent theories.

suprised

No, thats by far not enough. The propagator captures only the quadratic piece of the effective action. But the Einstein action involves quite a number of extra vertices, and all those need to be reproduced as well; in other words, not just the free part, but also all the interactions must come out right. Obviously no sensible person would try to prove this term by term, rather one should find an indirect argument as to why all terms must come out right.

In string theory it is worldsheet conformal invariance that guarantees that all terms come out right, in this sense GR emerges automatically. I dont know of any such principle in LQG that would guarantee the correct outcome.



I guess it is the other way around.

atyy

Yes, I agree.

Did I say it backwards? I meant strings introduces new degress of freedome, canonical LQG doesn't.

atyy

BTW, although massless spin 2 can be equivalent to Einstein gravity in spacetimes that can be covered by harmonic coordinates (or similar), I don't think the reverse is true that the existence of a spin 2 field is sufficient to produce Einstein gravity.

Zhang and Hu, A Four Dimensional Generalization of the Quantum Hall Effect
Elvang and Polchinski, The Quantum Hall Effect on R^4

Bekaert et al, How higher-spin gravity surpasses the spin two barrier

waterfall

So standard string theory assumes there is spacetime curvature and the gravitons are just quanta of the gravitational field much like in QFTs where the photons are quanta of the electromagnetic field or the electrons qunta of the electron field?

For 5 years. I actually thought all string theories use the mentioned concept of flat spacetime plus spin 2 = curved spacetime idea. So absolutely no active working string theorists like Witten ever use or entertain the concept?

But still Lee Smolin kept emphasizing strings occured in the backdrop of a fixed spacetime background. When he said fixed. It includes spactime curvature but the strings not part of spacetime versus the idea in LQG where the spin networks are spacetime itself (and not in it)?

How come string theorists continue with the strings in a fixed background idea.. maybe because they still hope that perhaps nature is like that? But the idea of General Relativity is already based on no prior geometry or background independence. Maybe string theories thought the strings in a fixed background is more fundamental and GR just unnatural? Hope someone can elaborate on all this. Thanks.

atyy

That's just the starting point of the theory. As Smolin wrote "it seems that any acceptable quantum theory of gravity, whatever its ultimate formulation, is likely to reduce to a perturbative string theory in the appropriate limit."

In fact, string theory's AdS/CFT duality is the first theory to have a pretty convincing proposal of a non-perturbative, almost fully background independent theory of quantum gravity for some universes. The only background in that theory is at the boundary of the space, the bulk is just as background independent as classical GR with a negative cosmological constant.

Also, string theorists are working on generalizations. One example is Heckman and Verlinde's twistor matrix proposal: "Part of the issue is that in situations where maximal theoretical control is available, space-time is treated as a classical background, rather than as an emergent concept. Related to this, the understanding of holography on space-times of positive curvature remains elusive. In this paper we propose and develop a new dual matrix formulation of 4D field theory, in which the space-time and field theory degrees of freedom simultaneously emerge from a large N double scaling limit."

waterfall

So next time Lee Smolin proclaimed to laymen that superstrings were not background independent. We would tell him "That's just the starting point of the theory. They have a dual in AdS/CFT which is background independent". Good.

Craig Hogan is building the Holo-meter as this month Sci-Am detailed. What's funny is that if it produces non-null. It confirms the discreteness of spacetime and supporting digital universe. But what does it support, the discreteness of spacetime due to LQG or the digital feature due to the Ads/CFT?

So String Theory can only be truly background independent if the universe supports the holographic principle? Yet I think the holographic principle is not widely supported and even on the speculative side. So it means there are some String Theorists who still think nature doesn't have to be background independent and GR is just some side effect of the theory?

atyy

I think that even though they already have AdS/CFT, most string theorists are still looking for other non-perturbative background independent formulations of string theory. This is because the cosmological constant in AdS/CFT is negative, whereas that of our universe is positive. They are studying AdS/CFT or gauge/gravity duality to try and see if it can be generalized. For example, Heemskerk, Marolf and Polchinski write "Gauge/gravity duality presently describes only spacetimes with special boundary conditions, and the duality dictionary describes in direct way only observations made at the boundary. It is important to understand its lessons for more general observations and more general spacetimes."

waterfall

What are these other non-perturbative background independent formulations of string theory that doesn't involve AdS/CFT? It's strange that billions of dollars have been invested in String theory and many graduates spent all 5 years of their post-graduate time in it when it is fundamentally not background independent (so don't even support GR at its core). Or maybe the funding and studies only occured after Ads/CFT was discovered and so giving them hopes or the motivation? This is the reason why I asked if background independent is a law of nature that must be followed. If it is. And string theory was not compatible with it 20 years ago. What gave the initial go ahead for billion dollars funding for something that doesn't have promise? Maybe they got impressed by Witten?

martinbn

What do you mean billions of dollar? And why shouldn't people spend their time on background dependent theories? Almost all of QFT is on a fixed Minkowski background, and many physicists spend their professional lives doing QFT, and it has been very successful.

waterfall

Smolin claimed those. Maybe he just wanted to start a fad. He looks like a guru and can command followers. But reflecting on all this. Isn't it the background independence in GR is only about mass/energy/momentum causing spacetime curvature. It doesn't say the mass, etc. made up spacetime. In LQG, spin networks make up spacetime. In String theories. Say there are a hundred different vacuo with different spacetimes. If you throw the strings from our universe into any one of those other universes with different backgrounds. It creates the spacetime analogous to our universe, so strings seem to be independent of background. We can give the following summary:

GR = mass/stress/energy causing spacetime curvature
LQG = spin networks/foam make up spacetime
Strings = Strings modes create spacetime irregardless of the backgrounds

Therefore background independence means differently in each case. And maybe we must not prefer one over the other. About QFT. Maybe it just ignores the mass/stress/energy effect on spacetime because it's negligible anyways.

waterfall

This is just to clarify. You agreed Atyy that "In string theory, part of spacetime emerges as the excitations of strings." How does this differs to the above idea of massless spin 2 producing the curvature? Do you include strings as massless spin 2 thing? You agreed spacetime could emerge as the excitating of strings but not the curvature? Why not?

Also you seem to be saying that perturbative string theory can do that. How does this differs to non-perturbative string theory (is this about AdS/CFT?)?

atyy

In perturbative string theory, massless spin 2 = spacetime curvature (deviation from flat spacetime) emerges as an excitation of the string. So this is the same idea as gravitons producing spacetime curvature. However, gravitons are not fundamental since they are just one excitation type of the string, and the string is more fundamental.

In AdS/CFT, even strings are not fundamental, and instead emerge holographically from the boundary theory.

waterfall

Earlier when I mentioned about the idea of flat spacetime + gravitons = curve spacetime. Marcus emphasized it was not standard in string theory. Now you are saying it's standard. Or maybe if we add strings in the context. Then it's standard in string theory. When no strings and just the idea of flat spacetime + gravitons = curve spacetime , then not standard. Is this it? Please elaborate as this got me confused for 5 years already. Thanks.

atyy

It's standard. All the different quantum gravity approaches have gravitons at low energy. The differences are in whether at high energy they still exist in a similar form or whether something completely different like strings are needed.

waterfall

Are you talking in terms of the gravitational field having gravitons at quanta at low energy that is standard? I'm talking about this flat spacetime thing with addition of gravitons that produced curved spacetime. Marcus mentioned in thread #115 this:

"I think some relevant comment is contained in the posts that follow #4. By starting with a flat background you rule out big bang and black hole stuff. Also rule out one of the more common spatially finite versions of standard cosmology. As I recall someone in the thread was pointing that out. Basically it is inconvenient, one could say crippling, to start out that way but you can recover a sector of the geometric theory, at least locally.

I'd say no QG approach has to explicitly deal with this special flat model because it empirically indistinguishable where it applies. (and since it doesn't cover all the cases it would be a bother---so people normally use the full theory.) but mathematically interesting certainly."

Marcus seems to disagree. If it's standard, why didn't he agree? Now I'm confused.