# Can This Be Real?

1. Jul 19, 2006

Staff Emeritus
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?

2. Jul 20, 2006

### Careful

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

3. Jul 20, 2006

### 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..."

Last edited: Jul 20, 2006
4. Jul 20, 2006

Staff Emeritus
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.

5. Jul 20, 2006

### MathematicalPhysicist

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

6. Jul 20, 2006

Staff Emeritus

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".

7. Jul 20, 2006

### Sauron

He refers that it is standar QFT. The basic one wich 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 wich 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.

8. Jul 20, 2006

### Careful

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

Last edited: Jul 20, 2006
9. Jul 20, 2006

Staff Emeritus
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.

10. Jul 20, 2006

### Careful

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

11. Jul 20, 2006

### Hans de Vries

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.

Last edited: Jul 20, 2006
12. Jul 20, 2006

### 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

13. Jul 20, 2006

### Hans de Vries

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].

[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.
I would say that Permutter's mass would change the 1/r potential in a
Yukawa type one e-sr/r where s is in the order of 6 billion light years.

I don't know how valid his method is but he has many peer-reviewed
publications in QFT. Personally I feel I could agree with SelfAdjoint's

Regards, Hans

P.S. I recently played with the same type of cut-off potential
$$V \ =\ -\frac{q}{4\pi\epsilon}\ \left(\frac{1}{r}-\frac{e^{-r/r_o}}{r}\right)$$
here: https://www.physicsforums.com/showpost.php?p=997155&postcount=251

Last edited: Jul 20, 2006
14. Jul 20, 2006

Staff Emeritus
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:

Last edited: Jul 20, 2006
15. Jul 21, 2006

### 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.

Last edited: Jul 21, 2006
16. Jul 21, 2006

Staff Emeritus
No, for he says
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.

17. Jul 21, 2006

Staff Emeritus
A question

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

Thanks.

18. Jul 22, 2006

### Hans de Vries

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

19. Jul 22, 2006

### 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?

20. Jul 22, 2006