The Quantum Structure of Space and Time (293 pages)

206 The Quantum Structure of Space and Time

distances outside our horizon-so even if we had a precise description, sort of

reductionist description in the far future where the universe is infinitely large

and so on, it might involve regions outside our horizon, and then when we ask a

question about our universe, we need to sum over everything that’s going on in

the outside, so we have to sum over theories and so on. That would be probably

an important part.

T. Damour I am confused about in what sense really dynamical gravity emerges

in AdS/CFT, and the apparent contradiction with the theorem of Weinberg and
Witten. So, in what we saw from Sasha and Juan, the h,, on the boundary does
not satisfy any constraint, so it’s not really dynamical; how will the Wheeler-de
Witt equation come out? Or let me ask a more practical question, are there
correlators, multi-correlators in super Yang-Mills, where I see the massless spin
two pole of a dynamical graviton emerging, in super Yang-Mills?
J. Maldacena The answer is no, because the graviton is not a massless particle
in four dimensions. So it is a massless particle in five dimensions. So we don’t
have a local stress tensor in five dimensions, we have a local stress tensor in
four. And so the gravity that emerges is the five dimensional gravity, and this
is an important point.

G. Gibbons I have a question really for Tom Banks, which is that the formalism

he outlined seems to take causal structures primary and given once and for all.

So do you envisage that the causal structure varies and fluctuates, or that we

have always a fixed causal structure? And if the latter, one normally says that

nine tenths of the metric, in dimension four, are given by the causal structure,

so you also seem not to be allowing the gravitational field to fluctuate, if you

took the view that the causal structure was fixed.

T. Banks In this formalism, the causal structure is put in, but the variables that

are going to describe the geometry are quantum fluctuating, so it’s a quantum

mechanical causal structure. You get a geometry that comes out of it in the

large area limit which is unique, and indeed that causal structure will be fixed,

but it will only be fixed in the large area limit where things are approximately

semiclassical.

G. Gibbons So for you locality is really not a problem, it is fixed. We always have

a local theory if I understand you... and it makes sense to say things commute

at space-like separations...

T. Banks There are certainly no operators here that you can define at local points

that commute in space-like separations in this formalism. Perhaps we should,

I should talk to you privately about this.

J. Harvey David, did you have something you wanted to say?

D. Gross Yes. I think Gerard correctly pointed out some of the things one would

like space and time to satisfy in an emergent scenario. The problem is that it

might not be obvious how to do that when one looks for the principle that will

lead to an ordering and one time. Perhaps some kind of reductionism, although