Does String Theory Truly Encompass Gravity?

[marcus]

Another voice has spoken up (this time the Madrid string theorist Enrique Alvarez) in the interesting controversy over the claim that string theory encompasses gravity.

Alvarez paper is http://arxiv.org/hep-th/0501146
a revised copy was posted this month, March 2005. Here is a quote from Alvarez section 5, Conclusions, page 14:

"...Given the fact that the equations of motion are identical, and, as we have shown, this property remains true when higher order (in the curvature) corrections are considered, it is clear that the identification of the low energy limit of string theories as general relativity is premature;..."

On page 2, Alvarez cites a paper by Padmanabhan as previous work:
From Gravitons to Gravity, Myth or Reality?
http://www.arxiv.org/abs/gr-qc/0409089

We had a discussion of the Padmanabhan paper here at PF back in November. selfAdjoint noticed the paper and started a thread called
String Gravitons Yield GR. NOT.
https://www.physicsforums.com/showthread.php?t=44414

The thread about Padmanabhan's paper attracted lively interest and discussion. It was expected that it would be answered by string theorists who would attempt to vindicate the claim that string theory includes some recognizable form of Gen Rel.

However several months have gone by since November and the Padmanabhan paper has not been challenged. Now Alvarez (a string theorist at least until the last few years) has posted a paper that in a general way agrees with Padmanabhan's conclusions.

I hope and expect that we have not heard the end of this, and that someone will attempt to raise the string banner saying "We Do Gravity Too!" and
openly demonstrate some error in Padmanabhan or Alvarez work. So far the indication is that string theorists just discuss the paper privately and do not make their objections public.

Well it is potentially an interesting controversy so I am going to gather the essentials here in this "update" thread. Including Padmanabhan's abstract, which we never got around to entering in the November discussion in
String Gravitons Yield GR. NOT.

 

[marcus]

here's a quote from the abstract of the Padmanabhan paper:
http://www.arxiv.org/abs/gr-qc/0409089

From Gravitons to Gravity: Myths and Reality
T. Padmanabhan

"There is a general belief, reinforced by statements in standard textbooks, that:

(i) one can obtain the full non-linear Einstein’s 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 action and

(iii) it only uses 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 Einstein-Hilbert (EH) action, starting from the standard action for gravitons in linear theory and iterating repeatedly.

This result follows from the fact that EH action has a part (viz. the surface term arising from second derivatives of the metric tensor) which is non-analytic in the coupling constant, when expanded in terms of the graviton field. Thus, at best, one can only hope to obtain the remaining, quadratic, part of the EH Lagrangian (viz. the Gamma² Lagrangian) if no additional assumptions are made. Second, we use the Taylor series expansion of the action for Einstein’s theory, to identify the tensor S^ab, to which the graviton field h_ab couples to the lowest order (through a term of the form S^ab h_ab in the lagrangian). We show that the second rank tensor S^ab is not the conventional energy momentum tensor T^ab of the graviton and provide an explanation for this feature.

Third, we construct the full nonlinear Einstein’s theory with the source being spin-0 field, spin-1 field or relativistic particles by explicitly coupling the spin-2 field to this second rank tensor S^ab order by order and summing up the infinite series. Finally, we construct the theory obtained by self consistently coupling h_ab to the conventional energy momentum tensor T^ab order by order and show that this does not lead to Einstein’s theory. The implications are discussed."

 

[ohwilleke]

Interesting. The Alvarez paper, however, is all over the place. It is almost more like a brain storming session than an attempt to reach a conclusion. It seems to say, "here is every way we could think of that you might go about linking QM to GR". Now, it isn't clear than any of those are EH answers. But, Padmanadham's paper also doesn't get an unequivocal endorsement.

 

[Chronos]

Oddly enough, I just read both papers [Padmanabhan and Alvarez] yesterday and was thinking about starting a thread. Padmanabhan's paper is pretty strong stuff. I expect a rebuttal, but it looks like a tough nut to crack so I'm not surprised it's taking some time. I tried to follow the Alvarez paper, but it was a real struggle and I came away mostly shell shocked.