Alright, time to discuss some physics again. A while back I outlined the basic dichotomy of quantum gravity. In brief: we have classical general relativity as an excellent description of all observed gravitational phenomena, but when we go to extremely short distances we need to have a good description of quantum gravity. There are two possibilities: either the description of gravitational phenomena by the machinery of general relativity (metric, the principle of equivalence, etc.) holds all the way down to those extremely short distances, or it doesn’t. If it doesn’t, which is my own prejudice, classical general relativity and its variables are never to be quantized, there is no range of energies (or distance scales) which is described by quantum metrics obeying a quantum version of Einstein’s equations.
This situation is similar to the hydrodynamical description of fluid motion: it is a classical effective field theory, which breaks down long before quantum mechanics is needed. We can observe granularity in the fluid on distance scales much larger than those relevant to quantum mechanics. From that perspective, quantizing Einstein’s equations makes as much sense as quantizing the Navier-Stokes equations, which is to say not too much sense.
But, since lots of smart people do not share my prejudice, and continue to look for just the right trick to quantize the metric field (be it dynamical triangulations, loop quantization, or anything else), let us just agree that there is this basic dichotomy, and one has to choose their own path. The path I find plausible is that where the gravitational field is a manifestation of some deeper structure at short distances, distances shorter than the ones currently probed by experiment, but not as short as the Planck length. This path is sometime dubbed emergent gravity, a name which I find somewhat misleading, for reasons I’ll describe below.
It is important to keep in mind that many of the problems of what is labeled “quantum gravity” are just problems of one of the approaches to the problem, that of quantizing the metric field. When dropping this assumption, life seems to simplify quite a bit, so let’s do that – imagine we are quantizing some dynamical system, and in a certain classical limit that system starts to look like a gravitational system. By that I mean very simply that it has objects moving in some large spacetime, and attract each other with universal Newtonian potential. Or in other words, it has apples and they fall from trees.
But which dynamical system? fundamentally, it doesn’t have to look at all like Einstein’s gravity, it could be pretty much anything. This looks like hopeless guesswork, but we have a few things working for us. First, it is not that easy to obtain a theory that look like classical general relativity at low energies: Lorentz invariance and the principle of equivalence are very restrictive. We understand the structure well enough to rule out many attempts a priori, without further examination. This is very valuable for busy people who can attend only so many conferences…
Secondly, we do have some examples of the idea working perfectly, within string theory, so we know of possible loopholes. There is much more to say, but for now let me borrow the slogan from the beautiful paper of Elvang and Polchinski: The emergence of general relativity requires the emergence of spacetime itself.
What does that mean? Recall the idea of duality: some notions are not a property of the physics, just of a certain description thereof. Surprising as it sounds, this includes the question of how many dimensions spacetime has. The attempt to derive general relativity from something else, living in the same spacetime, is likely to fail. The examples we have working all have the property of holography: the microscopic system from which general relativity emerges lives in a different spacetime, usually a lower dimensional one. In that sense the subject is different from what is usually titled as emergence, for example in quantum condensed matter physics, so we probably need to use a different word. Besides, emergence was all the rage in the 1970s, maybe it’s time for it to join old ABBA albums and John Travolta posters and all those things…
And that is it for today, hope everyone has enough to chew on for Turkey day. If everyone excuse me now, I have an exam to give.
Update: for a thoughtful summary and elaboration on the discussion here, you can turn to Lubos.