Samir Mathur

The Ohio State University
What is an observer?

The notion of an observer has been a puzzling one since the advent of quantum mechanics. This issue becomes more vexing when we come to gravity. An observer who falls into a black hole cannot make measurements on things outside, and an observer who stays outside cannot see things inside the hole. Do we now have two different wavefunctions, one for the inside and one for the outside? Or does the Hilbert space contain events that can never be seen by a given observer?
With string theory we now have a paradigm where we can address this question. One finds that black holes are ‘fuzzballs’, with no horizon. Thus we do not have a region inside the horizon which can disconnect the different classes of observers.
Now the question is: do cosmological horizons behave the same way as the black hole horizon? In that case, quantum gravity would give a completely new notion of an observer: the entire wavefunction will get automatically limited to the domain which can be see by the observer. But if cosmological horizons are different, then we would not be able to implement this philosophy. This proposal seeks to resolve this issue.

The notion of an observer brings up a deep issue in gravity. We can have causal horizons, which prevent observers in one region from communicating with observers in another region. In this situation, should there be a common Hilbert space for both observers, or different Hilbert spaces? The postulate of complementarity suggested that we have different Hilbert spaces, but we now know that this postulate has internal contradictions. We can ask the question for black holes, where string theory has gives a clear answer: the classical picture of the hole breaks down, and we get fuzzballs, which have no horizon or region interior to the horizon. More precisely, when a horizon is about to form and causally trap a region of spacetime, an ‘entropy enhanced tunneling’ prevents the formation of this horizon and produces a spacetime with a new topological structure – the fuzzball. The question now is: are cosmological horizons like the black hole horizon? If they are, then large quantum gravity effects should modify semiclassical physics to produce effective local regions with a self-contained description. Thus we hope to answer the question: does a region of spacetime have any meaning for an observer if he cannot see it?

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