The Quantum Structure of Space and Time (293 pages)

Singularities^69

3.4 Discussion

Prepared comment by S. Shenker.

D. Gross In the context of resolving the information paradox, it has been sug-

gested by J. Maldacena and S. Hawking that puzzles disappear when we take

into account different semi-classical space-times. When resolving singularities,

might it not be the case that taking seriously superpositions of geometries would

similarly resolve puzzles?

S. Shenker We have defined in pedestrian fashion an observable with a pole (on

the second sheet) and we can ask what happens to that pole. What happens
to the observable might be related to many geometries contributing. A first
signal of that would be large gs K 1/N corrections of the sort gs(&)z for some
power x. The closer the geodesic gets to the singularity at t = t, the larger the
quantum effects are. That could be interpretable as many geometries becoming
important. Or as branes becoming light. Imagine further that we have a power
series gy(&)"" that we resum, and then taking a double scaling limit. That
might lead to an understanding of non-perturbative physics at the singularity.
A. Ashtekar In how far do your conclusions depend on analyticity?
S. Shenker They heavily do. Analyticity is a crucial property of quantum field

G. Gibbons You have these two disjoint components to the boundary and a field

S. Shenker As J. Maldacena observed, the state in which you evaluate the corre-

G. Gibbons So, you are not thinking of the quantum field theories as disjoint?

S. Shenker Well, you cannot build these states from non-singular data (if that is

your question).

G. Gibbons I am more concerned with the quantum mechanics on the boundary.

I thought the idea was to reduce the problem to standard quantum mechanics?

S. Shenker There is a corollary to that which is that if you have two Hilbert spaces

in this case, one for each boundary.

G. Gibbons Is this a true generalization of quantum mechanics?

S. Shenker I am not going to agree with that. Perhaps somebody else would like

theory and it would be bad to lose it.

theory on each. How, within field theory, do they talk to one another?

lation functions is a correlated state, the Hartle-Hawking state.

to.