Are There Viable Alternatives to Quantum Field Theory and Second Quantization?

[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 black hole 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]

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

No, that's 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 don't know of any such principle in LQG that would guarantee the correct outcome.

.. The difference between strings and LQG is whether the gravitational field still exists at high energies. Strings says no, canonical LQG tries to say yes.

I guess it is the other way around.

 

[atyy]

No, that's by far not enough. The propagator captures only the quadratic piece of the effective action.

Yes, I agree.

I guess it is the other way around.

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

 

[atyy]

Atyy, was that a response to my question? I should probably explain. I've heard that any quantum field theory, which contains massless particle of spin 2 contains gravity. i would be interested to see that too, but to me it seems that it applies only to quantum field theries, at least as stated, and it doesn't say anything about other type of theories. For example string theory, it is not exactly quantum field theory, right? And often it is said that it is a theory of quantum gravity, but why? Does the statement apply here?

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 occurred 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]

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 occurred 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.

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]

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."

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]

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?

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]

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."

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 occurred 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 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).

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]

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.

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 anyone 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 regardless 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]

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

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]

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?)?

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]

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.

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]

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.

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]

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.

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.

 

[marcus]

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.

This sounds right to me. The basic idea of "perturbative" is to make an approximation by fixing a flat or other simple background and studying small "perturbations". It provides excellent means of calculation.

But it has recognized limitations as a way to think about reality. The "flat space+small curvature perturbations" picture is not taken as fundamental.

In non-string QG there was a bunch of papers about gravitons, doing calculations. In Loop the graviton papers started coming in around 2007, certain things had to be checked so people did that.

 

[atyy]

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.

I think you misunderstood him. He was just saying that in contrast to strings which built up perturbatively then got to AdS/CFT, loop quantum gravity started out from non-perturbative assumptions (ie. if it were string theory, it'd be like trying to find AdS/CFT without first knowing about strings, which is in principle possible, although it didn't happen that way). Both AdS/CFT and LQG are conjectured to produce gravitons at low energies.

 

[marcus]

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.

I agree. A perturbative approach is useful (even essential) for calculation at low energy. Loop, for instance "has gravitons" when one is explicitly studying low density, nearly flat, geometries. Low energy=low curvature, so that kind of approximation works.

I don't take issue with that. It's not a good way to picture reality when you are thinking about big bang cosmology. I take issue with someone calling the flat picture the real "territory" and the GR picture a mere "map".

 

[waterfall]

I think you misunderstood him. He was just saying that in contrast to strings which built up perturbatively then got to AdS/CFT, loop quantum gravity started out from non-perturbative assumptions (ie. if it were string theory, it'd be like trying to find AdS/CFT without first knowing about strings, which is in principle possible, although it didn't happen that way). Both AdS/CFT and LQG are conjectured to produce gravitons at low energies.

No. He was referring to the idea of flat space + spin 2 graviton = curved spacetime. He wrote this in message #106.

"Everything the whole universe, would be happening in some fixed eternal Euclidean space, and everything includes BH collapse. Your theory would then have to explain how a "graviton" gets from the heart of a black hole out past the horizon to exert a "pull" on somebody orbiting the BH. And all the stuff about how the clock on the mountain top runs faster than the one in the valley. I guess because the "gravitons" slow clocks down."

Marcus didn't agree with it. But you Atyy agreed that we could be living in a flat spacetime and gravitons giving us GR.

Marcus. I think Atyy is saying the flat picture is the real "territory" and the GR picture a mere "map".

 

[waterfall]

Wait. You mean in the Wheeler Gravitation book the writers were referring to low energies only? I thought it includes high energies which if true means the strings were moving in flat background and these graviton modes giving all the curvature. Hence. The flat picture is the real "territory" and the GR picture a mere "map". Maybe Hobba just misunderstood this from Carlip and the Wheeler Gravitation.

 

[atyy]

Wait. You mean in the Wheeler Gravitation book the writers were referring to low energies only? I thought it includes high energies which if true means the strings were moving in flat background and these graviton modes giving all the curvature. Hence. The flat picture is the real "territory" and the GR picture a mere "map". Maybe Hobba just misunderstood this from Carlip and the Wheeler Gravitation.

Wheeler was referring to classical gravity. In classical gravity there are two pictures. The first is gravity as spacetime curvature, the second is as spin-2 on flat spacetime. The second picture is equivalent to the first picture if spacetime can be covered by harmonic coordinates.

Now what about the quantum versions? The first classical picture has no known quantization. The second classical picture has a quantum version, but the quantum version only works below the Planck scale.

String theory tries to complete the quantum version of the second picture above the Planck scale by introducing new objects called strings. Loops tries to complete the quantum version of the second picture by quantizing the first classical picture.

 

[waterfall]

This sounds right to me. The basic idea of "perturbative" is to make an approximation by fixing a flat or other simple background and studying small "perturbations". It provides excellent means of calculation.

But it has recognized limitations as a way to think about reality. The "flat space+small curvature perturbations" picture is not taken as fundamental.

In non-string QG there was a bunch of papers about gravitons, doing calculations. In Loop the graviton papers started coming in around 2007, certain things had to be checked so people did that.

I think my mistake was thinking it was fundamental when I learned it 5 years ago from sci.physics from Hobba. This was because Brian Greene and other laymen book didn't talk about it. So when Hobba was referring to the following for example.. he was talking only of low energies (which I thought include high energies):

"Gravitons interact with all matter-energy. They interact in such a way as to make rulers and clocks behave as if space-time had curvature. It is a semantic issue of zero scientific value if space-time is thus curved or just appears curved. At this stage their is no way to experimentally distinguish between the two views."

Good to understood now it is only low energies. Thanks.
(Bhobba, who is a participant here, please comment if you don't agree).

 

[marcus]

Maybe Hobba just misunderstood this from Carlip and the Wheeler Gravitation.

Yes, I think that's a good guess. Wheeler's book is a huge thick tome about non-perturbative GR which has a section or two about the perturbative treatment. I've met Carlip when he was here giving a talk about several kinds of non-perturbative QG. He works mainly with that (not with "gravitons"). He has his PhD students working on things like CDT, Loop, Shape Dynamics. A Carlip grad student just finished his PhD on Loop last year, I forget the guy's name.

As far as I know CDT and Shape do not have any graviton papers as yet. It is not the main concern, at some point you want to see if you can handle the low energy nearly flat case and reproduce certain results. Loop has done this now to some extent, but those others not.

I don't know if Hobba misunderstood or whether he knew better but was just goofing off.
Attention-getting? I can't say, because I've only a cursory glimpse. The whole thing with Hobba struck me as having a kind of geriatric flavor. Harking back to papers from the 1970s. Weinberg's *Gravitation and Cosmology* book from 1972 etc. Or something Carlip said at some point in the past.
There was a temporary suspicion among particle theorists back then that you actually did not have to take GR seriously and maybe you could do everything with a fixed flat space.

But you might want to look at Weinberg's NEW book (2008). You can browse the ToC and Index on Amazon. It is called *Cosmology*. You will not find much if anything about the perturbative representation of GR. Very little if any mention of "gravitons".

https://www.amazon.com/dp/0198526822/?tag=pfamazon01-20
The Physics Today review said it would be a great help to "particle physicists tooling up for cosmology"
All based on dynamic changing curved geometry. HEP theorists taking GR more seriously now than, say, in 1972.

Think about a massive star collapsing to form a black hole. Are you going to model that whole process from beginning to end using a fixed unchanging flat space with ripples running around on it? Perturbative methods of calculation very good for some things. Not a full picture of reality. The full picture has to be able to handle extremes, highly dynamic changing geometry, extreme density, extreme moments of expansion. "Graviton" picture is inconvenient not to say unworkable. So (as Atyy indicates) the fashion among researchers has swung towards nonperturbative models. (which is where the relativists have been all along.)

 

[Haelfix]

Think about a massive star collapsing to form a black hole. Are you going to model that whole process from beginning to end using a fixed unchanging flat space with ripples running around on it?

Amusingly, you picked a really bad example. The state of the art in the physics of stellar collapse requires the heavy usage of weak field limits. The only analytic solution in the whole business is known as the Oppenheimer-Snyder solution, which is unphysical for a number of reasons.

 

[marcus]

Amusingly, you picked a really bad example. The state of the art in the physics of stellar collapse requires the heavy usage of weak field limits. The only analytic solution in the whole business is known as the Oppenheimer-Snyder solution, which is unphysical for a number of reasons.

That's interesting. I'm guessing you are talking about numerical modeling of stellar collapse using a computer and I would like to see more! Do you have an arxiv reference to share?

I know that lots of numerical work (black hole merger etc) USES weak field approximation. Almost by definition when you simulate something in a computer you are going to make judicious use of a fixed background geometry---but realizing its limitations and not asking it to do too much. Adjusting it by hand if and when it forms a singularity, and so on.

I don't have any illusion that what you are talking about represents reality, but I would like to see a write-up of a state of the art numerical calculation of stellar collapse.

 

[atyy]

Also, I think harmonic coordinates (the condition for a curved spacetime being exactly realizable as spin-2 on flat spacetime) can penetrate the event horizon. I think it's only close to the singularity that harmonic coordinates fail, where we don't trust GR anyway. I'm not sure, but that's what I think http://relativity.livingreviews.org/Articles/lrr-2000-5/ (discussion around Eq 103,104) says.

 

[marcus]

Let's wait and see what Haelfix comes up with. Atyy what you cite is a static solution in a paper from around 2001. It is not modeling the collapse of a star to form a bh, but a bh that is just sitting there not changing.

It doesn't really matter but I'm curious to see what "state of art" numerical model of bh collapse Haelfix is talking about.

Whatever attitudes and poses people strike, we all know that there is a huge drive in physics theory to get a nonperturbative quantum field theory if possible containing a quantum geometry of the universe.

The intense interest among string people in AdS/CFT for the past 10 years illustrates this trend. You have been pointing this out---AdS/CFT even though the real world does not appear to be AdS offers the hope of a nonperturbative version of string. M-theory though not yet formulated is another hope in the same nonperturbative direction.

Asym Safe gravity is another example---it is precisely a bid for nonperturbative renormalizability.

Triangulations (CDT) gravity is another---it explicitly advertises itself as a nonperturbative QG, like in the first paragraph of the main papers on the subject.

One can go down the list. Loop, of course, is basically nonperturbative (although developing approximation methods).

It's not something I have to talk about, or anyone needs to explain, you just open your eyes and look around. Perturbative computational techniques are techniques. As such they are marvelously well-developed and absolutely indispensable And their limitations are recognized.

 

[waterfall]

I agree. A perturbative approach is useful (even essential) for calculation at low energy. Loop, for instance "has gravitons" when one is explicitly studying low density, nearly flat, geometries. Low energy=low curvature, so that kind of approximation works.

I don't take issue with that. It's not a good way to picture reality when you are thinking about big bang cosmology. I take issue with someone calling the flat picture the real "territory" and the GR picture a mere "map".

There seems to be some vagueness in the use of the terms low and high energy and the source of my confusion as well as most laymen. I know it comes from the fact that the de Broglie relations show that the wavelength is inversely proportional to the momentum of a particle, so you need high energy to probe small spaces. So when you mention high energy, do you only mean small scale only or actually injecting energy? Also I saw the definition of High Energy Physics "It is called "high energy" because experimentally one needs very high energy probes to try to take these "elementary particles" apart.". But in quantum gravity, what are you taking apart? Maybe in quantum gravity. High energy just means small scale? Or do you actually have to inject energy in the Planck scale as in what happens in singularity in black hole or Big Bang? But here's the point. A string is always there in Planck scale. Even if you don't introduce Planck scale energy, a string still exist. So when you mentioned low energy to mean large scale. Note large scale is composed of many small scales. Large scale is still made up of strings in the small scales. Hence when you say these flat spacetime plus spin 2 gravitons giving curved spacetime is only a low energy large scale expression. but note the fact large scale is still composed of low scale so what are those gravitons doing in the small scale during the large scale approximation. Also I don't understand this perturbation thing as applied to quantum gravity. I know what it is in QFT. But in gravitons, I don't understand the connection. Anyway. When you mention low energy large scale, you mean you just pretend the gravitons don't exist and general relativity apply and just give this statement "flat spacetime plus gravitons equal to curve spacetime" without actually admitting the gravitons are really doing that? This is such a serious semantic mismatch issue. Can you give another example in physics where such statements are used because I'd like to understand the subtle semantic context. Thanks.
(atyy, pls. also comment on this message as this is the core of misunderstanding for many because of the many PUN and double entendre meanings used that even differs to standard high energy physics like QCD)

 

[atyy]

There seems to be some vagueness in the use of the terms low and high energy and the source of my confusion as well as most laymen. I know it comes from the fact that the de Broglie relations show that the wavelength is inversely proportional to the momentum of a particle, so you need high energy to probe small spaces. So when you mention high energy, do you only mean small scale only or actually injecting energy? Also I saw the definition of High Energy Physics "It is called "high energy" because experimentally one needs very high energy probes to try to take these "elementary particles" apart.". But in quantum gravity, what are you taking apart? Maybe in quantum gravity. High energy just means small scale? Or do you actually have to inject energy in the Planck scale as in what happens in singularity in black hole or Big Bang? But here's the point. A string is always there in Planck scale. Even if you don't introduce Planck scale energy, a string still exist. So when you mentioned low energy to mean large scale. Note large scale is composed of many small scales. Large scale is still made up of strings in the small scales. Hence when you say these flat spacetime plus spin 2 gravitons giving curved spacetime is only a low energy large scale expression. but note the fact large scale is still composed of low scale so what are those gravitons doing in the small scale during the large scale approximation. Also I don't understand this perturbation thing as applied to quantum gravity. I know what it is in QFT. But in gravitons, I don't understand the connection. Anyway. When you mention low energy large scale, you mean you just pretend the gravitons don't exist and general relativity apply and just give this statement "flat spacetime plus gravitons equal to curve spacetime" without actually admitting the gravitons are really doing that? This is such a serious semantic mismatch issue. Can you give another example in physics where such statements are used because I'd like to understand the subtle semantic context. Thanks.
(atyy, pls. also comment on this message as this is the core of misunderstanding for many because of the many PUN and double entendre meanings used that even differs to standard high energy physics like QCD)

Yes, in the string picture the strings are always there, but at low energy or large length scale it's a pretty good approximation to replace the string with a particle. Low energy or large length scale means we don't look so carefully, since we aren't looking at fine scales, so we could mistake a string for a particle such as a graviton or electron. In this sense particles "emerge" at low energies or large length scales as excellent approximation to strings.