Quantizing GR: Exact Quantum Loop Results in General Relativity

[selfAdjoint]

The following is either the most important paper so far in the 21st century, or a big mistake.

hep-ph/0607198

Exact Quantum Loop Results in the Theory of General Relativity
Authors: B.F.L. Ward (1) ((1) Dept. of Physics, Baylor University, Waco, TX, USA)
Comments: 26 pages, 3 figures; improved text
Report-no: BU-HEPP-05-07
We present a new approach to quantum general relativity based on the idea of Feynman to treat the graviton in Einstein's theory as a point particle field subject to quantum fluctuations just as any such field is in the well-known Standard Model of the electroweak and strong interactions. We show that by using resummation techniques based on the extension of the methods of Yennie, Frautschi and Suura to Feynman's formulation of Einstein's theory, we get calculable loop corrections that are even free of UV divergences. One further by-product of our analysis is that we can apply it to a large class of interacting field theories, both renormalizable and non-renormalizable, to render their UV divergences finite as well. We illustrate our results with applications of some phenomenological interest.

They use vanilla QFT, and the resumming techniques they apply go back to 1961:

18] D. R. Yennie, S. C. Frautschi, and H. Suura, Ann. Phys. 13 (1961) 379; see also
K. T. Mahanthappa, Phys. Rev. 126 (1962) 329, for a related analysis.


Although the present author and colleagues have had good results using them in phenomological contexts at CERN:

[19] S. Jadach and B.F.L. Ward, Phys. Rev D38 (1988) 2897; ibid. D39 (1989) 1471; ibid.
D40 (1989) 3582; Comput. Phys. Commun.56(1990) 351; Phys.Lett.B274 (1992)
470; S. Jadach et al., Comput. Phys. Commun. 102 (1997) 229; S. Jadach, W.
Placzek and B.F.L Ward, Phys.Lett. B390 (1997) 298; S. Jadach, M. Skrzypek and
B.F.L. Ward,Phys.Rev. D55 (1997) 1206; S. Jadach, W. Placzek and B.F.L. Ward,
Phys. Rev. D56 (1997) 6939; S. Jadach, B.F.L. Ward and Z. Was,Phys. Rev. D63
(2001) 113009; Comp. Phys. Commun. 130 (2000) 260; S. Jadach et al., ibid.140
(2001) 432, 475; S. Jadach, M. Skrzypek and B.F.L. Ward, Phys. Rev. D47 (1993)
3733; Phys. Lett. B257 (1991) 173; in ”Zo Physics”, Proc. XXVth Rencontre de
Moriond, Les Arcs, France, 1990, ed. J. Tran Thanh Van (Editions Frontieres, Gif-
Sur-Yvette, 1990); S. Jadach et al., Phys. Rev. D44 (1991) 2669; S. Jadach and
B.F.L. Ward, preprint TPJU 19/89; in Proc. Brighton Workshop, eds. N. Dombey
and F. Boudjema (Plenum, London, 1990), p. 325.


So people, what do you think? Have they quantized GR in one swell foop, or not?

 

[Careful]

So people, what do you think? Have they quantized GR in one swell foop, or not?

That would be cool no . I will study it tomorrow, but the surprising thing for me is that he claims his renormalization procedure washes out black holes.

Careful

 

[Farsight]

Hmmmn, interesting.

http://lanl.arxiv.org/abs/hep-ph/0607198

"In this paper we have introduced a new paradigm in the history of point particle field theory: a UV finite theory of the quantum general relativity. It appears to be a solution to most of the outstanding problems in the union of the ideas of Bohr and Einstein. More importantly, it shows that quantum mechanics, while not necessarily the ultimate theory, is not an incomplete theory. Our paradigm does not contradict any known experimental or theoretical fact; rather, it allows us to better understand the known physics and, hopefully, to make new testable predictions. Our paradigm does not contradict string theory or loop quantum gravity, to the best of our knowledge..."

 

[selfAdjoint]

That would be cool no . I will study it tomorrow, but the surprising thing for me is that he claims his renormalization procedure washes out black holes.

Careful

The way I read it is that black holes for a sufficiently small mass do not have horizons; this gets him around the problem that massive point particles should be black holes, and he also applies this result to the final states of evaporated black holes.

Note that he uses Reuter's "asymptotic safety" calculations to achieve this result. I do not have to remind you that Reuter has been severely criticized by Jacques Distler.

 

[MathematicalPhysicist]

sorry to interrupt the conversation, but wha is vanilla qft?
i know what qft is, but i didnt know it comes in flavours.

 

[selfAdjoint]

sorry to interrupt the conversation, but wha is vanilla qft?
i know what qft is, but i didnt know it comes in flavours.

I just meant not any fancy modern stuff like we frequently discuss here. His methods are all taken from QED techniques as far as I could see. For non-USers, "vanilla" is slang for "the plain version".

 

[Sauron]

He refers that it is standar QFT. The basic one which is studied in undergraduate courses.

In comparation string theory or LQG use much more mathemathical sofistication and made some very nonstandard asumptions: Extended objects instead of puntual ones, aditional dimensions in he case of strings. About LQG i don´t say anithing taking account of your nick xD.

One of the things which surprise me is the argument that the fomr of the propagator implies that in the hard U.V. region implies that in this regime gravity is repulsive instead of atractive.

I mena, in the works of bojowald, Astekhar and others about singularities of black holes (or evenincosmology) they get similar result.But in a lot more sofisticated way.

I will keep reading it with more care anyway.

 

[Careful]

The way I read it is that black holes for a sufficiently small mass do not have horizons; this gets him around the problem that massive point particles should be black holes, and he also applies this result to the final states of evaporated black holes.

Note that he uses Reuter's "asymptotic safety" calculations to achieve this result. I do not have to remind you that Reuter has been severely criticized by Jacques Distler.

Black holes are defined by means of an horizon
And no, I have not studied Reuters results (in any detail) - neither did I look at this paper yet : I met a physics buddy today and told him about the claim in this paper. I basically do not believe (on physical grounds) that perturbation theory around de Sitter is going to solve the UV problem in perturbative QG. It is virtually impossible to follow everything in detail and if Reuter's results were rigorously proven to be valid, then for sure it would be quickly accepted by everyone (in which case I would study it).

Careful

 

[selfAdjoint]

Black holes are defined by means of an horizon

Sorry that was a trope: "container for the thing contained". I meant "mass confined inside its Schwartzschild radius". If the mass is sufficientrly small, the author, using Reuter, says that a horizon will not form, or in the case of a depleted black hole, apparently we are to conclude the horizon will dissipate. Wonder what that does to the information problem.

 

[Careful]

Sorry that was a trope: "container for the thing contained". I meant "mass confined inside its Schwartzschild radius". If the mass is sufficientrly small, the author, using Reuter, says that a horizon will not form, or in the case of a depleted black hole, apparently we are to conclude the horizon will dissipate. Wonder what that does to the information problem.

But anyhow, could you remind us of Distler's comments on Reuter's work ? That might be useful.

 

[Hans de Vries]

But anyhow, could you remind us of Distler's comments on Reuter's work ? That might be useful.

I do not have the impression that he relies on Reuters work. The
"asymptotically safe" UV behavior seems to arise from the resummation
of a perturbative series. Where the latter originates from original Feynman
work on Gravitation (ref[11-12]) (See page 6)

He arrives at an improved "Newtonian" potential of:

$$\Phi_N(r)\ =\ -\frac{G_N M}{r}\left( 1-e^{-ar}\right)$$

form.(28) where,

$$a\ \approx\ 0.210 M_{Pl}$$

This guarantees that masses below Planck's mass can not become black holes.
(All point particles would be black holes otherwise.)Regards, Hans.

 

[Careful]

$$\Phi_N(r)\ =\ -\frac{G_N M}{r}\left( 1-e^{-ar}\right)$$

Hi Hans,

Yeh, that is the guy I quickly noticed while scanning the paper. Could you tell a bit more about the magic he claims to happen ?

Careful

 

[Hans de Vries]

$$\Phi_N(r)\ =\ -\frac{G_N M}{r}\left( 1-e^{-ar}\right)$$

Hi Hans,

Yeh, that is the guy I quickly noticed while scanning the paper. Could you tell a bit more about the magic he claims to happen ?

Careful

He seems to get S. Perlmutter's value for the (non-zero) mass of the
graviton (3.1 10^-33 eV) from the masses of the other particles of the
SM up to a factor of [itex]\sqrt{2}[/tex]. <br /> <br /> [39] S. Perlmutter et al., Astrophys. J. 517 (1999) 565;This mass also plays a role in the determination of 'a' in the previous post.<br /> I would say that Permutter's mass would change the 1/r potential in a <br /> Yukawa type one e^-sr/r where s is in the order of 6 billion light years.<br /> <br /> I don't know how valid his method is but he has many peer-reviewed<br /> publications in QFT. Personally I feel I could agree with SelfAdjoint's<br /> opening comments.Regards, HansP.S. I recently played with the same type of cut-off potential <br /> $$V \ =\ -\frac{q}{4\pi\epsilon}\ <br /> \left(\frac{1}{r}-\frac{e^{-r/r_o}}{r}\right)$$<br /> here: <a href="https://www.physicsforums.com/showpost.php?p=997155&postcount=251" class="link link--internal">https://www.physicsforums.com/showpost.php?p=997155&postcount=251</a>[/itex]

 

[selfAdjoint]

Hans, in his discussion of that equation he references [25] as authority. Reference 25 is:

[25] A. Bonnanno and M. Reuter, Phys. Rev. D62 (2000) 043008.


careful: Here is a link to Distler's post on Reuter:

http://golem.ph.utexas.edu/~distler/blog/archives/000648.html

and a quotation from it for the flavor:

This really is a coupled set of differential equations in an infinite number of variables. Except for the Gaussian fixed point, g 2 (p,−p)≠0 ,g n=0 ∀n>0 the fixed-point sets (though they are finite dimensional) do not line up nicely, so that only a finite number of coupling in L *(ϕ) are nonzero.
Despite the adjective “Exact”, (2) is very much a perturbative equation. The formal manipulations, by which we arrived at it, were justified to the extent that introducing the cutoff function, K(p 2 /Λ 2 ) really does provide a UV regulator. This is true in perturbation theory, where it provides a cutoff on the loop-momentum integrals for all Feynman diagrams
1. It is, most certainly, not true nonperturbatively

2.What’s “exact” about (2) is not that we have somehow magically learned something about the nonperturbative behaviour of the theory by summing some tree and 1-loop Feynman diagrams. What’s exact is that, whereas in the usual formulations of the perturbative RGE the β-function receives contributions at all loop-orders, here the perturbative β-function is given exactly by 1-loop. The cost of this “simplification” is that we must consider, simultaneously, the β-functions for the full infinite set of couplings in the effective Lagrangian.

 

[Farsight]

As a layman I got as far as page 4 before I got lost. But I think he said a point particle isn't a black hole because the uncertainty of its position exceeds the Schwarzschild radius. Aw, there's a lot I don't know. I look forward to listening in on what you guys talk about.

 

[selfAdjoint]

As a layman I got as far as page 4 before I got lost. But I think he said a point particle isn't a black hole because the uncertainty of its position exceeds the Schwarzschild radius. Aw, there's a lot I don't know. I look forward to listening in on what you guys talk about.

No, for he says

Note that we distinguish here the uncertainty in the position of the particle, which is connected to its Compton wavelength when the particle is at rest, from the accessibility of the mass of that particle, which is connected to its black hole character.

He actually gets the result from classical theory. First, referring to the particles of the Standard Model, and citing a paper of his own, he asserts that for the line element-with-lapse-function
$$ds^2 = f(r)dt^2 - f(r)^{-1}dr^2 - r^2d\Omega^2$$
the lapse function f assumes the form
$$f(r) = 1 - \frac{2G(r)m}{r}$$
with
$$G(r) = G_N(1 - e^{-ar})$$
- G_N being Newton's constant.

So with these formulas f remains finite as r approaches 0, and no horizon forms. Then he cites a paper by Reuter, apparently part of Reuter's project to show GR is asymptotically safe in Weinberg's sense (though I have not seen the paper, so I shouldn't characterize it too quickly), to the effect that the same formulas work for the case of a dissipated black hole.

You see that nowhere in this argument did he appeal to QM.

 

[selfAdjoint]

A question

Can anyone tell me exactly what Ward means by "Large Euclidean momenta" and the "Deep Euclidean regime"? Does he mean spacelike?

Thanks.

 

[Hans de Vries]

Can anyone tell me exactly what Ward means by "Large Euclidean momenta" and the "Deep Euclidean regime"? Does he mean spacelike?

Thanks.

May be, it doesn't seem widely used terminology. Googling for it leads to
earlier work of Ward where he arrives at the same UV safe potential:

http://arxiv.org/abs/hep-ph/0204102
http://arxiv.org/abs/hep-ph/0502104

$$\Phi_N(r)\ =\ -\frac{G_N M}{r}\left( 1-e^{-ar}\right)$$

It's the value of 'a' which is different in the various paper.
the propagator which leads to this potential, which I find interesting by its
own right, has a quartic term in the denominator:

$$q^2 - Cq^4 +i\epsilon$$Regards, Hans

 

[Mike2]

By "resumming" does he mean that he has been able to find a symmetry that allows him to interchange the terms in the sum so that some of them cancel out so that there is no need to renormalize for UV divergences?

 

[selfAdjoint]

By "resumming" does he mean that he has been able to find a symmetry that allows him to interchange the terms in the sum so that some of them cancel out so that there is no need to renormalize for UV divergences?

He does use the boson symmetry to do some combining, but the real reason his summations converge is that, as he asserts, the graviton self-energy goes repulsive in the "deep Euclidean regime". There's a little apparent, but I think not real, circularity in his argument in this paper because he assumes that in doing his summations and then when he finally gets down to his finite answer he says "see, it does go negative". The reason I think this is just a mirage is the prior papers that Hans found(THANKS HANS!). He really developed this technique before, and in fact he gives cites to earlier published papers that are not on the arxiv for details of the summation calculations.

 

[Mike2]

It seems he is also assuming a flat background for his calculations - I thought I read that remark in his paper. However, Wald suggests that particles may only be possible in resonably stable (not necessarily flat) spacetime backgrounds. So it would seem that this paper, which assumes the possibility of graviton of interest (in highly curved and/or changing spacetime curvature) may contradict the work of Wald. Or have I misinterpreted these works? Thanks.

 

[selfAdjoint]

It seems he is also assuming a flat background for his calculations - I thought I read that remark in his paper. However, Wald suggests that particles may only be possible in resonably stable (not necessarily flat) spacetime backgrounds. So it would seem that this paper, which assumes the possibility of graviton of interest (in highly curved and/or changing spacetime curvature) may contradict the work of Wald. Or have I misinterpreted these works? Thanks.

Dunno the Wald reference. How does he mean particles? Quantized particles in GR? Gravitons? Or what? Our universe is substantially flat, but SM particles seem to make it OK between the gravity wells; see cosmic rays, supernova neutrino flux, et al.

Ward sets his cosmological constant to zero when developing his simplified pedagogical model, but I don't think he retains that in the full bore calculation, I'll have to check.

 

[Mike2]

Dunno the Wald reference. How does he mean particles? Quantized particles in GR? Gravitons? Or what? Our universe is substantially flat, but SM particles seem to make it OK between the gravity wells; see cosmic rays, supernova neutrino flux, et al.

Ward sets his cosmological constant to zero when developing his simplified pedagogical model, but I don't think he retains that in the full bore calculation, I'll have to check.

In Quantum Field Theory in Curved Spacetime and Black Hole Thermodynamics, by Robert M. Wald, 1994, page59, he writes, " ... Indeed , although a considerable amount of effort has been expended by researchers to obtain a perferred definition of 'particles', these efforts have not been successful, except in some restricted clases of spacetimes (most notably, the class of stationary spacetimes discussed in the next section) where symmetries or other structure can be used to naturally select a u. To put this statement in perspective, we should point out that there is no difficulty defining an approximate notion of 'particles' when the spacetime is nearly flat (or more generally, nearly stationary); more precisely, the notion of 'particles' becomes highly ambiguous only for modes whose frequency is smaller than typical inverse timescales for the change of the metric. Thus, in our universe, serious difficulties would arise if we attemp to define a meaningful notion of 'particles' whose wavelength is larger than the Hubble radius, but, as a paractical matter, there is little difficulty employing a particle concept in most other circumstances. Nevertheless, as a matter of principle, it should be stressed that, in general, the notion of 'particles' in curved spacetime is, at best, only an approximate one. While some readers familiar with standard presentations of quantum field theory in flat spacetime might be disturbed by the lack of a notion of 'particles' in curved spacetime, we have taken great care to emphasize here that this should not be a cause of alarm, since the notion of 'particles' plays no essential role in the formation of quantum field theory. Indeed I view the lack of an algorithm for defining a preferred notion of 'particles' in quantum field theory in curves spacetime to be closely analogous to the lack of an algorithm for defining a preferred system of coordinates in classical general relativity. ..."

So this seems to suggest that the particle of gravitons can only be an approximation at best.

Is the paper under discusion in this thread treating gravity as another force whose particle nature in flat spacetime can be achieved with the use of QFT? If so, then gravity here seems to have lost its connection with geometry. How can qunatum gravity (thus quantum geometry) be calculated on flat spacetime. In that case where did the flat spacetime come from to begin with (on which we are calculating curved spacetime?)

 

[Hans de Vries]

Is the paper under discusion in this thread treating gravity as another force whose particle nature in flat spacetime can be achieved with the use of QFT? If so, then gravity here seems to have lost its connection with geometry. How can qunatum gravity (thus quantum geometry) be calculated on flat spacetime. In that case where did the flat spacetime come from to begin with (on which we are calculating curved spacetime?)

He starts with Feynman's work on Gravity.

[6] R. P. Feynman, Acta Phys. Pol. 24 (1963) 697.
[7] R. P. Feynman, Feynman Lectures on Gravitation, eds. F.B. Moringo and W.G. Wagner (Caltech, Pasadena, 1971).


https://www.amazon.com/gp/product/0201627345/?tag=pfamazon01-20

From the link above referring to the Lectures on Gravity:

Characteristically, Feynman took and untraditional non-geometric approach to gravitation and general relativity based on the underlying quantum aspects of gravity. Hence, these lectures contain a unique pedagogical account of the development of Einsteins general relativity as the inevitable result of the demand for a self-consistent theory of a massless spin-2 field (the graviton) coupled to the energy-momentum tensor of matter. This approach also demonstrates the intimate and fundamental connection between gauge invariance and the Principle of Equivalence.

hmmm, just ordered the book (as if I don't have enough books )


Regards, Hans

 

[Mike2]

He starts with Feynman's work on Gravity.

[6] R. P. Feynman, Acta Phys. Pol. 24 (1963) 697.
[7] R. P. Feynman, Feynman Lectures on Gravitation, eds. F.B. Moringo and W.G. Wagner (Caltech, Pasadena, 1971).


https://www.amazon.com/gp/product/020...lance&n=283155&tag=pfamazon01-20

From the link above referring to the Lectures on Gravity:


Quote:
Originally Posted by Feynman Lectures on Gravitation
Characteristically, Feynman took and untraditional non-geometric approach to gravitation and general relativity based on the underlying quantum aspects of gravity. Hence, these lectures contain a unique pedagogical account of the development of Einsteins general relativity as the inevitable result of the demand for a self-consistent theory of a massless spin-2 field (the graviton) coupled to the energy-momentum tensor of matter. This approach also demonstrates the intimate and fundamental connection between gauge invariance and the Principle of Equivalence.

Regards, Hans

using QFT to derive GR...? On what background to they do the QFT, flat spacetime to derive curved spacetime?

 

[Sauron]

Hans, i advise you.

I have readed that Feyman book (it is in the library of my faculty).

It is a great book. But a book about classical gravity. The diferenece is that Feyman dedicates some chapters to a "what if" in the ansatz that gravity is a theory mediated by a graviton and he goves a few interesting ideas.

What he never does is to formulate a quantum field theory of gravity.

Feyman also has an article in which he tries to do that.But he fails.That is because he lacks the right technical tools. Later de Witt took the Feyman ideas and he presented the background field methodwich implements what Feyman wanted. He also, in a diferent paper, presented the canconical quantum gravity in his first incarnation.

Later, afther the t´hoof proof of renormalization of gauge theories the mechanismo of the background method was sustantially simplified. and perturbative quantum gravity was presented in very simple ways.Ways which allowed first the classical paper of t´hoof and Veltman probing that pure gravity is renormalizable at one loop and later the paper of Sagnoti which probed that similar thing didnn´t happen in two and more loops.

I have all these papers (and some more) so i am almost confident that what Ward calls "Feyman gravity" is the conventional perturbative quantum gravity presented in the papers of t´hoof, Veltman and Goroff-Sagnotti.

I need to read carefully these article and compare before beeing sure, butr now i am studying spin foams and its "applications" (the wilson loops as particles papers and all that).

P.S. Feyman does perturbation about flat backgrounds.The method of de Witt wichimplements his idea perturbates about arbitrary backgrounds (in the usuall way which is presented in, for example, the introductory chapters of string theory books).

 

[Hans de Vries]

Later, afther the t´hoof proof of renormalization of gauge theories the mechanismo of the background method was sustantially simplified. and perturbative quantum gravity was presented in very simple ways.Ways which allowed first the classical paper of t´hoof and Veltman probing that pure gravity is renormalizable at one loop and later the paper of Sagnoti which probed that similar thing didnn´t happen in two and more loops.

That would be this paper then:

One-loop divergencies in the theory of gravitation
G. 't HOOFT (*) and M. VELTMAN (*)
http://igitur-archive.library.uu.nl/phys/2005-0622-153852/14054.pdf

— All one-loop divergencies of pure gravity and all those
of gravitation interacting with a scalar particle are calculated. In the case
of pure gravity, no physically relevant divergencies remain; they can all
be absorbed in a field renormalization. In case of gravitation interacting
with scalar particles, divergencies in physical quantities remain, even
when employing the socalled improved energy-momentum tensor.

Thanks, Hans.

 

[selfAdjoint]

From the current paper by Ward (page 13):

Turning now to Figs. 2, the pure gravity loops, we use a contact between our work and that of refs[42]. In Refs. [42], the entire set of one loop divergences have been computed for the theory in {2} (expression 2 is his Lagrangean, from Feynmann). The basic observation is the following. As we work only to the leading logarithmic accuracy in $ln \lambda_C$, it is sufficient to identify the correspondence between the divergences as calculated in the n-dimensional regularization scheme in Ref [42] and as they would occur when $\lambda_C \rightarrow 0$. This we do by comparing our result for {21} when $q^2 \rightarrow 0$ with the corresponding result in Ref [42] for the same theory. In this way we see that we have the correspondence
$$-ln \lambda_C \leftrightarrow \frac{1}{2 - n/2}$$
This allows us to read-off the leading log result for the pure gravity loops directly from the results in Ref [42].

Reference 42 is
G. 't Hooft and M. Veltman, Ann. Inst. Henri Poincare XX, 69 (1974)

Which is precisely the paper cited by Sauron and found online by Hans.

So he not only builds on 't Hooft and Veltman, he uses it critically in getting his results.

Added: I just noticed this paragraph further down the page which addresses the concerns of the last few posts:

We note that, for $\lambda_C \rightarrow 0$, the constant c₂ is infinite and, as we have already imposed both the mass and field renormalization counter-terms, there would be no physical parameter into which that infinity could be absorbed; this is just another manifestation that QGR, without our resummation, is a non-renormalizable theory.

 

[Sauron]

What has happened with these paper?

Anyone found a falliure on it? Has gained any credibility?

Anyway, i would like to add two more related hints. On one side there has been a recent paper which using string theory arguments seems to prove that N=8 supergravity (for point particles) is afther all not only renormalizable but finite.It is here http://www.arxiv.org/abs/hep-th/0610299

Previously it had been argued, using these time twistor methods, the same result. I know most of you read "not even wrong" (http://www.math.columbia.edu/~woit/wordpress/?p=268) or the motl blog so I guess that you were already aware of these. But I thinnk it could be interesting to discues it here, and relate it with the ward paper.

Maybe that it could be interesting to desrve mayor atention to "naive" quantum gravity, at least as a complement to The "modern" more refined ones.

 

[Chronos]

GR might be the answer. GR has accumulated a great deal of credibility via observational evidence. I do not object to string theory - only to theories that make no testable predictions.