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Zenith Grant Awardee

Samir Mathur

The Ohio State University

Project Title

What is an event?

Project Summary

We are used to thinking of space as being made of points in three dimensions. Einstein taught us a century ago that we should instead think in terms of events, which are points in four dimensional spacetime. But once we include effects of quantum mechanics, we find that it is not so easy to define the notion of an event, since spacetime has quantum fluctuations. What then should replace the notion of an event? It turns out that the idea of events must be completely altered; what happens at an event in classical relativity must be described in very indirect ways in quantum gravity. In particular, in string theory, the effects at one event have to be encoded in large nonlocal matrices in a `dual\' theory which has no gravity. More interestingly, the spacetime inside a black hole emerges as an approximate dual description of an even larger physical system: the space of all states of the black hole. This picture of the black hole interior arises from the fuzzball paradigm, which resolves Hawking\'s well known `information paradox\' in string theory by showing that black holes swell up into `fuzzballs\' that have, strictly speaking, no horizon or singularity.

Technical Abstract

The notion of an event is fundamental to the way we understand spacetime in special and general relativity. But in quantum gravity the notion of an event must almost certainly be replaced by something more basic. We argue that there are two separate effects that make the notion of an event imprecise. One is the quantum fluctuations of spacetime, and the other is the thermal effects that are built into quantum gravity through black hole thermodynamics. We explore the first of these effects through the AdS/CFT correspondence, where the spacetime manifold must arise an as approximate description of a dual gauge theory. The second effect is both more interesting and more involved, and we address it through the conjecture of fuzzball complementarity. In this conjecture, the microstates of black holes have no region interior to a horizon, but an effective interior arises as an approximate dual spacetime for infalling objects with energy E much larger than the temperature T of the hole. Thus the notion of what is actually happening at a point in spacetime becomes much more abstract, and can have descriptions that look nothing like the local operators that we are normally used to.

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