Alternatives to QFT

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Aren't you mixing two concepts above, one below and above the planck scale? This spin two gravitons thing causing spacetime curvature is outside the planck scale. Or are you saying the gravitons exist inside the planck scale and somehow it can cause spacetime curvature outside? This is also a question to others. Do gravitons exist inside or outside the planck scale?
Whats going on there is that the properties of spin 2 particles in the background of flat space-time all by themselves leads to GR with its space-time curvature. It causes flat space-time to behave like it has an infinitesimal curvature. It was Steve Carlip that pointed out correctly there is no difference between a theory that causes objects to behave like space-time was curved and it actually being curved. This is the type of thing I mean by emerge. You will find a discussion on this sort of stuff if Feynmans Lectures On Gravitation where the often made claim about spin two particles that it leads to space-time curvature is detailed. I am saying we know so little about the Plank scale don't assume anything - but certainly our usual 4d space can and probably does emerge from whatever it is

Thanks
Bill
 
Whats going on there is that the properties of spin 2 particles in the background of flat space-time all by themselves leads to GR with its space-time curvature. It causes flat space-time to behave like it has an infinitesimal curvature. It was Steve Carlip that pointed out correctly there is no difference between a theory that causes objects to behave like space-time was curved and it actually being curved. This is the type of thing I mean by emerge. You will find a discussion on this sort of stuff if Feynmans Lectures On Gravitation where the often made claim about spin two particles that it leads to space-time curvature is detailed. I am saying we know so little about the Plank scale don't assume anything - but certainly our usual 4d space can and probably does emerge from whatever it is

Thanks
Bill
I see. So you are not referring actually to string theory which has Calabi-Yau manifold inside the planck scale while that in LQG, the spin network is the size of the planck so there is nothing inside. Since these two are not proven. What is inside planck scale is unknown. It may even be all solid. But our spacetime as a continuum may not be the primary. I guess it's like water molecules. The water is our spacetime, the molecules are the planck scale and there is no water inside the molecules. This may be what you mean GR emerge as a limit of this completely unknown planck scale physics. About the flat spacetime thing. I have questions about it.

1. Are you saying that spin 2 gravitons can produce GR even if the background is not flat? Because Carlip and even Feynman were simply referring to existing flat spacetime with spin 2 gravitons producing spacetime curvature. But you added the planck scale thing or issue.

2. Are you saying unknown physics inside planck scale first produce flat spacetime, then later it goes into spin 2 mode and produce curvature from that flat spacetime to produce gravity?

3. How did the flat spacetime arise from the planck scale? Is this a valid question?
 
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1. Are you saying that spin 2 gravitons can produce GR even if the background is not flat? Because Carlip and even Feynman were simply referring to existing flat spacetime with spin 2 gravitons producing spacetime curvature. But you added the planck scale thing or issue.

2. Are you saying unknown physics inside planck scale first produce flat spacetime, then later it goes into spin 2 mode and produce curvature from that flat spacetime to produce gravity?

3. How did the flat spacetime arise from the planck scale? Is this a valid question?
I am saying in a similar, but as yet unknown way, that curved space time emerges from flat via spin 2 particles then flat can emerge from something else eg LQG - but don't ask me because I haven't studied it - might get around to it one day - along with the tons of other stuff I want to study - right now studying Category Theory.

As I said before once you feel comfortable with single variable Calculus - get Boas. If you study a bit each day you will be surprised what you learn over time - an understanding those who just read popular accounts like Hawking can never appreciate.

Thanks
Bill
 
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Why don't you study an easier example, namely classical electromagnetic fields, before trying to understand gravity? Perhaps there it is easier to understand the difference between a classical field configuration, and small oscillations around them, which are called photons when quantized. Then you see that it is a misguided question to ask how a non-perturbative field configuration is made out of "spin 1 photons". At best, it can be viewed as coherent superposition of an infinite number of field quanta, but that viewpoint is not really helpful here. It is by definition not possible that by adding single photons one after the other you can build up a non-perturbative field configuration (with non-trivial, macroscopic curvature = field strength). A photon is a single particle, perturbative concept and this can capture only physics that is close to a given macroscopic background. Sometimes it is possible to resum infinitely many contributions, eg one can show how the classical potential between two charges can be obtained by summing virtual photons. But that won't work for non-perturbative configurations like instantons.

This applies analogously to gravity and gravitons.
 
I am saying in a similar, but as yet unknown way, that curved space time emerges from flat via spin 2 particles then flat can emerge from something else eg LQG - but don't ask me because I haven't studied it - might get around to it one day - along with the tons of other stuff I want to study - right now studying Category Theory.

As I said before once you feel comfortable with single variable Calculus - get Boas. If you study a bit each day you will be surprised what you learn over time - an understanding those who just read popular accounts like Hawking can never appreciate.

Thanks
Bill
Ok. Thanks. So our flat spacetime is another Effective Field Theory. Good to know.

Speaking of calculus. Reminds me of the virtual particles. You know what. Perturbation theory is not something permanent like the Diract Equation, it's only because we don't know the interacting theory. Therefore remembering that virtual particles corresponds to each term of the power series of the Perturbation Theory and PT is only a temporarity math rule. Then virtual particles don't exist. We don't even need Neumaier arguments that everything is field.
So what if there is effects in the casimir plates, etc. They can be explained by others because simply of the fact that virtual particles being a symptoms of perturbation theory being a symptoms of non-interacting theory is just a math artifact. I think you agree with this.
 
Why don't you study an easier example, namely classical electromagnetic fields, before trying to understand gravity? Perhaps there it is easier to understand the difference between a classical field configuration, and small oscillations around them, which are called photons when quantized. Then you see that it is a misguided question to ask how a non-perturbative field configuration is made out of "spin 1 photons". At best, it can be viewed as coherent superposition of an infinite number of field quanta, but that viewpoint is not really helpful here. It is by definition not possible that by adding single photons one after the other you can build up a non-perturbative field configuration (with non-trivial, macroscopic curvature = field strength). A photon is a single particle, perturbative concept and this can capture only physics that is close to a given macroscopic background. Sometimes it is possible to resum infinitely many contributions, eg one can show how the classical potential between two charges can be obtained by summing virtual photons. But that won't work for non-perturbative configurations like instantons.

This applies analogously to gravity and gravitons.
Try reading this which I am right now:

http://www.scribd.com/doc/54251898/The-Feynman-Lectures-on-Gravitation [Broken]

"The Feynman Lectures on Gravitation"

"The claim that the only sensible theory of an interacting massless spin-2 field is essentially general relativity (or is well approximated by general relativity in the limit of low energy) is still often invoked today. (For example, one argues that since superstring theory contains an interacting massless spin-2 particle, it must be a theory of gravity.) In fact, Feynman was not the very first to make such a claim.

The field equation for a free massless spin-2 field was written down by Fierz and Pauli in 1939[FiPa 39]. Thereafter, the idea of treating Einstein gravity as a theory of a spin-2 field in flat space surfaced occasionally in the literature."
 
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Try reading this which I am right now:

http://www.scribd.com/doc/54251898/The-Feynman-Lectures-on-Gravitation [Broken]

"The Feynman Lectures on Gravitation"

"The claim that the only sensible theory of an interacting massless spin-2 field is essentially general relativity (or is well approximated by general relativity in the limit of low energy) is still often invoked today. (For example, one argues that since superstring theory contains an interacting massless spin-2 particle, it must be a theory of gravity.) In fact, Feynman was not the very first to make such a claim.

The field equation for a free massless spin-2 field was written down by Fierz and Pauli in 1939[FiPa 39]. Thereafter, the idea of treating Einstein gravity as a theory of a spin-2 field in flat space surfaced occasionally in the literature."
The idea that GR is just a spin-2 field theory over flat spacetime is completely incorrect. Already Wald, in his General Relativity textbook, warn readers that the term "spin-2" is not well-defined beyond linearized GR. Wald also devotes a chapter of his book to explain different approaches to QG where remarks that the string theory approach (spin-2 approach) misses basic aspects of GR as causality.

Feynman textbook is misguided and usually avoided for serious GR courses. Carlip claims, cited before, do not stand up on close inspection.

The myth that GR is a spin-2 field is very common in the string theory literature, but has always been rejected by general relativists (who started their canonical approach to QG).

Some of typical textbooks mistakes are corrected in From Gravitons to Gravity: Myths and Reality

It is fair to remark that string theorists already abandoned string theory and are now seeking for a background-independent alternative. Since they have no idea of what this alternative has to be, they named it M-theory (M from Mistery). As they agree nobody really know that M-theory is or even if it exists (it is only conjectured that exists).
 
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atyy

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The idea that GR is just a spin-2 field theory over flat spacetime is completely incorrect. Already Wald, in his General Relativity textbook, warn readers that the term "spin-2" is not well-defined beyond linearized GR. Wald also devotes a chapter of his book to explain different approaches to QG where remarks that the string theory approach (spin-2 approach) misses basic aspects of GR as causality.

Feynman textbook is misguided and usually avoided for serious GR courses. Carlip claims, cited before, do not stand up on close inspection.

The myth that GR is a spin-2 field is very common in the string theory literature, but has always been rejected by general relativists (who started their canonical approach to QG).

Some of typical textbooks mistakes are corrected in From Gravitons to Gravity: Myths and Reality

It is fair to remark that string theorists already abandoned string theory and are now seeking for a background-independent alternative. Since they have no idea of what this alternative has to be, they named it M-theory (M from Mistery). As they agree nobody really know that M-theory is or even if it exists (it is only conjectured that exists).
Wald's writes about terminology, not that gravity is not massless spin 2.
 
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It is fair to remark that string theorists already abandoned string theory and are now seeking for a background-independent alternative.
This is plain nonsense. If, then they look for an extension of string theory, like an "unbroken topological phase". One interesting recent work in this direction is eg, http://www-spires.dur.ac.uk/cgi-bin/spiface/hep/www?eprint=arXiv:1112.5210

And no, GR ist not just the theory of a spin 2 graviton; string theorists know this probably better than anyone. How often needs it to be repeated that gravitons corresponds to "small ripples on a water surface" and not to the whole ocean including vortices etc.

The amount of misconceptions, desinformation and plain nonsense propagated here is really staggering!
 
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Wald's writes about terminology, not that gravity is not massless spin 2.
I have Wald, it is my favorite GR Textbook, and I can't recall anything in there about spin 2 particles. If anyone knows it give me that page and I would love to read it.

Regarding Feynman's book it may have problems - after all it pretty ancient now, but I have been through it and cant recall anything that looked dubious.

Thanks
Bill
 
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Wald's writes about terminology, not that gravity is not massless spin 2.
Nope. He emphasizes that the both mass and spin of a field require a flat background to be unambiguously defined. Outside linearized GR the background is lost and you cannot unambiguously define basic properties of the field doing that the common claim «full GR is a (massless) spin-2 field theory» is not different from «full GR is a xkgncmcfs», where «xkgncmcfs» is not defined :uhh:.
 
I have Wald, it is my favorite GR Textbook, and I can't recall anything in there about spin 2 particles. If anyone knows it give me that page and I would love to read it.

Regarding Feynman's book it may have problems - after all it pretty ancient now, but I have been through it and cant recall anything that looked dubious.

Thanks
Bill
Here are the relevant passages in Wald's (anyone can read this at scribd which I did):

page 74 in the subject "Linearized Gravity: The Newtonian Limit and Gravitational Radiation

"The aim of this section is to treat the approximation in which gravity is "weak." In the context of general relativity this means that the spacetime metric is nearly flat. In practice, this is an excellent approximation in nature except for phenomena dealing with gravitational collapse and black holes and phenomena dealing with the large scale structure of the universe.

page 76:

"In vacuum (Tab=0) equations (4.4.11) and (4.4.12) are precisely the equations written down by Fierz and Pauli (1939) to describe a massless spin-2 field propagating in flat spacetime (see chapter 13). Thus, in the linear approximation, general relativity reduces to the theory of a massless spin-2 field. The full theory of general relativity thus may be viewed as that of a massless spin-2 field which undergoes a nonlinear self-interaction. It should be noted, however, that the notion of the mass and spin of a field require the presence of a flat background metric n(ab) which one has in the linear approximation but not in the full theory, so the statement that, in general relativity, gravity is treated as a massless spin-2 field is not one that can be given precise meaning outside the context of the linear approximation."

------------

I think linearized approximation means it only works in weak gravity and not near singularity. This may be what atyy means by harmonic coordinates. So Bill. It seems we can't truly model curved space as spin-2 field in flat spacetime. This doesn't work fully therefore do you agree now that gravity is geometry only and can't be modeled by this spin-2 field over flat spacetime thing? If you don't, please elaborate. Thanks.
 

Haelfix

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he presence of a flat background metric n(ab) which one has in the linear approximation but not in the full theory, so the statement that, in general relativity, gravity is treated as a massless spin-2 field is not one that can be given precise meaning outside the context of the linear approximation."
That's exactly what it means. In fact, that's the case in quantum chromodynamics as well, when we speak about quarks and gluons.

It's always the case in physics that some particular object only has ontological meaning in some well defined framework, which typically is only an approximation to the real thing.

For instance, the notion of a unique particle strictly speaking really only makes sense in flat space in the infinite past and future, where there is some sort of perfectly massive detector registering them. That doesn't prevent us from modeling reality by pretending like that condition is relaxed (and to a very high degree of accuracy, it is).
 

Haelfix

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Some of typical textbooks mistakes are corrected in From Gravitons to Gravity: Myths and Reality
That paper was addressed by Deser himself:
http://arxiv.org/abs/0910.2975v3

Eg, the standard textbook treatment is in fact correct (see chapter 18 of MTW). It turns out for *classical* physics, that you can always resum the infinite linearized series. You do this, not by any sort of brute force approach, but by guessing the correct resummation, which is essentially unique and forced on you by consistency criteria.

Anyway, this is of course not the case for the quantum theory (not just gravity, but almost all field theories fail to be Borel resummable). Hence the judicious use of the philosophy and tools of effective field theory, and the higher derivative towers, etc
 
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I think linearized approximation means it only works in weak gravity and not near singularity. This may be what atyy means by harmonic coordinates. So Bill. It seems we can't truly model curved space as spin-2 field in flat spacetime. This doesn't work fully therefore do you agree now that gravity is geometry only and can't be modeled by this spin-2 field over flat spacetime thing? If you don't, please elaborate. Thanks.
Well I am not sure I want to go into this because my interests these days is on the foundations of QM, but no I do not agree linearised gravity does not imply GR. One of the first textbooks I ever got on GR many many moons ago was Ohanian - Gravitation and Space Time a copy now falling to pieces I still have. That book takes an entirely different view of GR, first deriving linear GR from field theory via analogy with with EM then showing how full GR can be derived from the linear equations - you will find the details in Chapter 7 of that book. However something does go into it - namely the following assumption from page 380 - the equation is of second differential order and is linear in second derivatives. That pretty much follows from the fact it should be derivable from a Lagrangian containing only first order derivatives - which GR can be -but usually isn't - the covariant form based on the very elegant Einstein-Hilbert action is usually used - but is of second order. However when the variation is done terms linear in second order - which the Einstein-Hilbert action is - make no contribution so can be removed - which leaves a non covariant action but only containing first order terms. Bottom line is this means the EFE's must be linear in second order. A full discussion of this can be found in Chapter 8 of Lovelock and Rund where the most general form is given on page 321 of that reference (its pretty ucky).

That's about all I really want to say about the issue because GR is the furthest thing from my mind or interests right now and refreshing my mind on this stuff took a good couple of hours.

Thanks
Bill
 
Well I am not sure I want to go into this because my interests these days is on the foundations of QM, but no I do not agree linearised gravity does not imply GR. One of the first textbooks I ever got on GR many many moons ago was Ohanian - Gravitation and Space Time a copy now falling to pieces I still have. That book takes an entirely different view of GR, first deriving linear GR from field theory via analogy with with EM then showing how full GR can be derived from the linear equations - you will find the details in Chapter 7 of that book. However something does go into it - namely the following assumption from page 380 - the equation is of second differential order and is linear in second derivatives. That pretty much follows from the fact it should be derivable from a Lagrangian containing only first order derivatives - which GR can be -but usually isn't - the covariant form based on the very elegant Einstein-Hilbert action is usually used - but is of second order. However when the variation is done terms linear in second order - which the Einstein-Hilbert action is - make no contribution so can be removed - which leaves a non covariant action but only containing first order terms. Bottom line is this means the EFE's must be linear in second order. A full discussion of this can be found in Chapter 8 of Lovelock and Rund where the most general form is given on page 321 of that reference (its pretty ucky).

That's about all I really want to say about the issue because GR is the furthest thing from my mind or interests right now and refreshing my mind on this stuff took a good couple of hours.

Thanks
Bill
Juanrga, Haelfix or other anti-spin twoners, can you please point out the mistakes in the analysis above without showing any other references but directly addressing the issues? Let's get to the bottom of this. Thanks.
 
waterfall, what Bill says sounds OK but it is just a statement about the classical theory.

People today don't say that all of quantum gravity can be reduced to perturbation theory of a spin-2 field; what they do say is that a massless spin-2 field implies gravity - that if your theory contains such a field, then the only consistent way for it to interact is as gravity.

But that in itself doesn't tell you what the fundamental theory looks like. We can all agree that the standard model plus a spin-2 graviton field resembles reality. But that in itself doesn't tell you whether asymptotic safety, loop quantum gravity, or string theory (or something else) is the ultimate framework.
 
waterfall, what Bill says sounds OK but it is just a statement about the classical theory.
But what Juanrga, Haelfix, friend are saying and with attached papers is that even those things or techniques Bill mentioned is not enough to approximate the classical GR theory. This is the bottom line.

This is very important to settle because it can give clue to what approach to take in quantum gravity whether to focus on fields as primary or spacetime curvature as primary (like in LQG).
Get my point?

People today don't say that all of quantum gravity can be reduced to perturbation theory of a spin-2 field; what they do say is that a massless spin-2 field implies gravity - that if your theory contains such a field, then the only consistent way for it to interact is as gravity.

But that in itself doesn't tell you what the fundamental theory looks like. We can all agree that the standard model plus a spin-2 graviton field resembles reality. But that in itself doesn't tell you whether asymptotic safety, loop quantum gravity, or string theory (or something else) is the ultimate framework.
 

Haelfix

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But what Juanrga, Haelfix, friend are saying and with attached papers is that even those things or techniques Bill mentioned is not enough to approximate the classical GR theory. This is the bottom line.
Sorry, that is decidedly not what i am saying and I don't understand how it can be read that way...

Further, the classic story about linearized gravity is completely irrelevant (one way or the other) to the quantum story.

I have absolutely no problem with physicists using semiclassical methods, so long as they are utilized in the proper settings and not extrapolated to regimes where they no longer make sense. I do also have issues with certain theoretical physicists who forget the insights that these techniques give, especially when phrased and understood in the regimes where they are admissible. For instance, the blackhole information paradox and the area law is almost entirely phrased and understood utillizing semiclassical gravity (gravitons et al).
 

atyy

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Wald, p383, we may view the full Einstein equation (γab not assumed to be "small") as the sum of this free piece, plus a nonlinear self-interacting term, ie. we may view Einstein's equation as an equation for a self-interacting spin-2 field ...
 
Sorry, that is decidedly not what i am saying and I don't understand how it can be read that way...

Further, the classic story about linearized gravity is completely irrelevant (one way or the other) to the quantum story.

Have you missed the message of juanrga in post #182 where he shared the paper :
http://www.worldscinet.com/ijmpd/17/1703n04/free-access/S0218271808012085.pdf

FROM GRAVITONS TO GRAVITY: MYTHS AND REALITY

Abstract:
There is a general belief, reinforced by statements in standard textbooks, that: (i) one can obtain the full nonlinear Einstein theory of gravity by coupling a massless, spin 2 field h(ab) self-consistently to the total energy–momentum tensor, including its own; (ii) this procedure is unique and leads to Einstein–Hilbert (EH) action; and (iii) it uses only standard concepts in Lorentz-invariant field theory and does not involve any geometrical assumptions. After providing several reasons why such beliefs are suspect — and critically re-examining several previous attempts — we provide a detailed analysis aimed at clarifying the situation. First, we prove that it is impossible to obtain the EH action, starting from the standard action for gravitons in linear theory and iterating repeatedly.
What the above may mean is that any quantum gravity theory that uses spin-2 field can't recreate General Relativity. So it's like a no-go theorem for any field approach to gravity and a yes-go theorem for GR being geometry forever. No?

If no. Do you think it's possible, as Bill Hobba believes, that superstings can produce graviton spin-2 field mode where they occur in the background of flat spacetime? That is.. the curveness is not a priori, but only appeared curved because of the strings gravitons spin-2 field on totally flat spacetime?

I have absolutely no problem with physicists using semiclassical methods, so long as they are utilized in the proper settings and not extrapolated to regimes where they no longer make sense. I do also have issues with certain theoretical physicists who forget the insights that these techniques give, especially when phrased and understood in the regimes where they are admissible. For instance, the blackhole information paradox and the area law is almost entirely phrased and understood utillizing semiclassical gravity (gravitons et al).
 
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Haelfix

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If no. Do you think it's possible, as Bill Hobba believes, that superstings can produce graviton spin-2 field mode where they occur in the background of flat spacetime? That is.. the curveness is not a priori, but only appeared curved because of the strings gravitons spin-2 field on totally flat spacetime?
You need to stop inserting your own assumptions and wording into what other people write... He was decidedly talking about classical physics, not string theory! My point earlier, is that you can't go around throwing terms around out of context without making a complete logical mess of the discussion.

What is clear, is that if a quantum theory contains gravitons in the usual way (which is quantum physics, not classical physics) with the correct couplings, you do end up with a classical limit that looks approximately GRish. But details matter here...

Further, just b/c you have gravitons, does not mean you have the correct theory of quantum gravity. You really do need a formalism or theory that describes the physics in all relevant physical regimes, not just those that are covered by weak coupling. SO what do I think?
I think string theory captures a part of the correct physics of quantum gravity, in particular in those regimes where the perturbative picture holds or where a duality is possible. I do not understand the rest and so I simply do not know more than that one way or the other.

As for the graviton myth or reality paper, I linked a direct response by Stanley Deser, one of the original creators of the spin2 linearized formalism.
 
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That's exactly what it means. In fact, that's the case in quantum chromodynamics as well, when we speak about quarks and gluons.
You have cutted off the part where Walds says «a field require the presence of a flat background metric n(ab)»

This is what makes GR completely different to QCD. In QCD causality is defined over the flat background whereas in GR it is not. That is part of Wald's criticism of the covariant perturbation method approach to quantum gravity
 
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That paper was addressed by Deser himself:
http://arxiv.org/abs/0910.2975v3

Eg, the standard textbook treatment is in fact correct (see chapter 18 of MTW). It turns out for *classical* physics, that you can always resum the infinite linearized series. You do this, not by any sort of brute force approach, but by guessing the correct resummation, which is essentially unique and forced on you by consistency criteria.

Anyway, this is of course not the case for the quantum theory (not just gravity, but almost all field theories fail to be Borel resummable). Hence the judicious use of the philosophy and tools of effective field theory, and the higher derivative towers, etc
Deser only partially answers the criticism and avoids the main points against his 'proof'. I am tempted to write a detailed proof on why his claim is not right.

You cite chapter 18 in MTW but that only deals with linearized GR. What linearized GR can be thought as the theory of a massless spin-2 field was acknowledged above in one of my posts.
 
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This is very important to settle because it can give clue to what approach to take in quantum gravity whether to focus on fields as primary or spacetime curvature as primary (like in LQG).
Neither one nor other.
 

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