Emergent Spacetime^181
W. Fischler It was a question, I just do not know the answer.
G. Horowitz I wanted to mention a couple of other examples of emergent time. I
think one is 2 + 1 gravity, which as you know can be written as a Chern-Simons
theory, there is a state of zero metric, no space, no time, anything, and that’s
perfectly, you know, allowed and understood, and yet we see how we can get
classical space-times out of that theory. And in string theory there is sort of at
least a formal generalization of all of that in the purely cubic action in string
field theory.
N. Seiberg Well, Chern-Simons theory has time, right? You write the integral
Jd2zdt of something. So t appears there. I think we would like something
which is a little bit more dramatic than this.
J. Harvey Yes, I would have thought space-time was there, it was just rewriting
the action in a different form.
G. Horowitz There is a state of zero metric, so I am not sure what time or space
would mean if the metric is zero.
A. Ashtekar In terms of this emergent time, there is a lot of literature, in the
relativity circles, quantum gravity circles, about emergent time. Basically there
is a relation to dynamics, and how one of the variables, under circumstances
when there is actually a semiclassical space-time, can be taken to be time. But
in general there would be no such variable, and then we would not have a good
notion of time. In a particular example that I sketched, which had to do with
scalar fields coupled with gravity in cosmology, in that example a scalar field
is a good notion of time, in quantum theory I am talking about. But near the
Big-Bang singularity, it becomes very very fuzzy, we do not have the standard
notion, and again, it reemerges as the standard notion on the other side. So it
seems to me that there are definite examples, certainly not a completely general
theorem or anything like that, but lots and lots of such examples, that exist in
the literature.
J. Harvey I think that this might be a good point to stop, have a coffee break,
and I would like to continue this discussion, so if you have things to say, please
make a note of that and we will continue in half an hour and have time for
discussion after the next four talks.
