Propagation of the Faith

Carlo Rovelli and some coauthors have a couple of new papers out, including this one on constructing the Graviton propagator in loop quantum gravity and another on Relational EPR.

Luboš Motl has weighed in on the first of these, and predictably enough, is not impressed. I took a look, expecting the usual rant, long on bombast and short on analysis, but that's not quite what I found. Instead, he provides a short description the semiclassical approach to GR and then a paradigm for writing down a propagator.

We needed several completely necessary assumptions and steps to be able to talk about a propagator at all, namely

the choice of a completely serious and fixed background (classical solution) around which we expand the existence of a unique quantum state corresponding to this background (even if we do thermal physics, there exists a unique state but it is a mixed state)

the existence of continuous (or at least effectively continuous) degrees of freedom in which the action can be Taylor expanded

in theories with local symmetries - which certainly includes general relativity - one needs to gauge-fix the gauge symmetry to obtain a non-singular propagator

in the path integral formalism, we need to sum over all configurations - in fact, the generic configurations that contribute to the path integral are non-differentiable almost everywhere and they look like a mess to a classical physicist

Before trying to address this, let me remind myself what the heck we need a propagator for anyway. The propagator (essentially a Green's function) is a basic building block of perturbation theory, and not coincidentally, the basis for computing scattering amplitudes. Rovelli and co-authors start as follows:

An open problem in quantum gravity is to compute particle scattering amplitudes from the full background–independent theory, and recover low–energy physics [1]. The difficulty is that general covariance makes conventional n-point functions ill–defined in the absence of a background.

Rovelli and co-authors have a proposal for getting around this, but Luboš won't hear of it. It doesn't fit his prescription, so it just can't be so.

Professor Motl has some more technical objections which can be found at the previous link, but I want to focus on the fundamental quarrel and what he has to say about it. LQG types think the most important thing in GR is background independence, and are happy to sacrifice conventional QFT in the quest to quantize GR. Stringers give pride of place to the perturbation expansion ala QFT, and regard background independence as an annoying side issue. Lumo says:

A physics theory per se cannot be background-independent. Background independence is a property of a particular way how a theory is formulated and how its predictions are computed: for example, the calculation of a propagator is always background-dependent.

String field theory is "background-independent" while the light-cone gauge matrix theory is not. But they describe the same physics. They describe the same physics in two different but equivalent formalisms. One cannot make an experiment to determine whether the world is "background-independent" or not...

I didn't know anything about string field theory, so I peeked at Wikipedia on the subject, some of which was written by Lumo. The article mentions that SFT hasen't proven too useful, since apparently they don't know how to incorporate D-Branes. I mainly wanted to know why Lumo was so sure SFT was background independent. I don't know, of course, but there is this paper by Sen and Zwiebach hep-th/9311009 I will cite just one sentence from their abstract:

Our result puts on firm ground the widely believed statement that string theories built from nearby conformal theories are different states of the same theory.

I won't pretend to understand any details of the paper, but I'm far from convinced that constitutes full background independence. That "nearby conformal theories" qualification hardly looks innocent to me.

I'm sure that if Lumo reads this he will find ample reason to call me stupid, but any explanatory details would be appreciated.