Stability of Minkowski space in semiclassical gravity?

1. Jan 28, 2016

bcrowell

Staff Emeritus
Wald, General Relativity, p. 411, says that Minkowski space is unstable in semiclassical gravity. He gives a reference to this paper:

Horowitz, "Semiclassical relativity: The weak-field limit," Phys. Rev. D 21, 1445, http://journals.aps.org/prd/abstract/10.1103/PhysRevD.21.1445

The Horowitz paper is paywalled and is not on arxiv. If true, this would seem to be a pretty serious indictment of semiclassical gravity. Is it true according to the current state of the art?

A search for citations of the Horowitz paper turned up the following:

Anderson, http://arxiv.org/abs/gr-qc/0209075

Hu, http://arxiv.org/abs/gr-qc/0402029

Hu, http://arxiv.org/abs/gr-qc/0508010

2. Jan 29, 2016

FieldTheorist

The Mattola paper (the first one) seems to indicate that there's no problem, and that Minkowski is a stable solution. It's possible that these Horowitz solutions are gauge artifacts (I suspect this is the case). I'd have to pull out my copy of Wald to see what's going on there, but my copy appears to be at work.

In any case, if this were a problem, a lot fewer people (including Wald) would trust GR as an effective field theory. It's worth linking to Donoghue's effective field theory description of GR review right now, and as the one-loop corrections to the graviton self-interactions are what you'd be worried about giving rise to instabilities, this again does not appear to be a problem.

3. Jan 29, 2016

Haelfix

There are at least two different things called semiclassical Gravity. One has gravitons and is a consistent loop expansion, the other does not. Just glancing at some of those papers seems to indicate they are talking about different things. I'll try to look into this when I have more time.

4. Jan 30, 2016

haushofer

You mean an iteration of Fierz-Pauli theory? Afaik, such a theory is a perturbation around the Minkowski vacuum. If this vacuum would be unstable, wouldn't this come back in the theory itself in some way, just like e.g. tachyons appear in string theory due to an instable vacuum?

Interesting question; I'm often wondering how much sense these semi-classical analyses really make, like e.g. the quantum-cosmology papers by Hawking.

5. Jan 30, 2016

bcrowell

Staff Emeritus
Yeah, that was really the motivation for the question. It seems to me that the whole business of semiclassical gravity is shaky, both logically and empirically.

6. Feb 1, 2016

julian

Is this relevant: pages 5 and 6 of Thiemann's book "Modern Canonical Quantum gravity", subsection "backreaction".

"...the back reaction of matter on m, geometry couples to matter through Einstein's equations

$$R_{\mu \nu} - {1 \over 2} R g_{\mu \nu} = \kappa T_{\mu \nu}$$ and since matter underlines the rules of quantum mechanics, the right hand side of this equation, the stress-energy tensor $T_{\mu \nu} [g]$, becomes an operator. One has tried to keep geometry classical while matter is quantum mechanical by replacing $T_{\mu \nu} [g]$ by the Minkowski vacuum $\Omega_\eta$ expectation value $< \Omega_\eta , \hat{T}_{\mu \nu} [ \eta ] \Omega_\eta>$, but the solution of this equation will be give $g \not= \eta$ which one then has to feed back into the definition of the vacuum expectation value, and so on. Notice that the notion of vacuum itself depends on the background metric, so that it is a highly non-trivial iteration process. the resulting iteration does not converge in general [at this point he refers to the paper I've given below]. Thus, such a procedure is also inconsistent, whence we must quantise the gravitational field as well."

Reference: The Wald paper: E. E. Flanagan and R. M. Wald. Does backreaction enforce the averaged null energy condition in semiclassical gravity? Phys. Rev. D54 (1996)6233-83. [gr-qc/9602052].

Last edited: Feb 1, 2016
7. Feb 1, 2016

bcrowell

Staff Emeritus
I had come across the Flanagan-Wald paper before and read the abstract, but from the abstract I didn't get the impression that they were advocating the interpretation Thiemann seems to give in this quote.

It seems like there could be two different issues, although they may be related. (1) If spacetime is initially Minkowski, can arbitrarily small perturbations cause it to differ from flatness at later times by an amount that increases exponentially with time? (2) Do we need to renormalize to get rid of divergences in the stress-energy tensor when we do the iteration process described by Flanagan and Wald?

I don't have the Thiemann book, but it's not clear to me whether Thiemann is arguing that semiclassical gravity is simply wrong, or that it's an approximation that's valid under certain conditions...?

8. Feb 1, 2016

julian

Not sure. But he obviously tries to give at as motivation to quantize gravity.

He has done work to address the question of how one might obtain the semiclassical limit of ordinary matter quantum fields (QFT) propagating on curved spacetimes (CST) from full fledged Quantum General Relativity. I dont know, but perhaps he thinks that this is the only way it could work.

Maybe there are others who disagree.

Last edited: Feb 1, 2016