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Zenith Grant Awardee

Steve Giddings

University of California, Santa Barbara

Project Title

Observables in quantum spacetime

Project Summary

Our current description of nature faces a conflict among its basic principles: those of quantum mechanics and relativity, and the principle of locality. This conflict is particularly seen in describing black holes, whose evaporation leads to an apparent paradox discovered by Hawking. Evidently part of our current foundation requires modification. Quantum mechanics is well-tested, but locality is ultimately difficult to even formulate, partly since quantum mechanics indicates that space and time themselves have a certain quantum fuzziness. A key part of the structure of quantum mechanics is specification of certain mathematical objects called “q-observables.” These play a central role in describing the division of a system like the universe into smaller systems, such as observers and the systems that they measure, and in describing interactions. In current physics, they also tell us how to formulate the principle of locality. This work will investigate properties of q-observables, and how they might help guide us to a more basic quantum space-time. In short, familiar space and time may be an illusion, emerging from a more basic quantum reality; the q-observables can help us make contact between this more basic reality and what we describe as “happening.”

Technical Abstract

In facing the profound conflict between the principles of quantum mechanics, the principle of locality, and the principles of relativity, reasonable working assumptions are that quantum mechanics is a cornerstone of physics, and likewise elements of relativity (e.g. Poincare invariance) are foundational. For quantum mechanical systems, the observables play a fundamental role in describing the structure of the theory and the notion of \"happening,\" or a quantum version of events. In local quantum field theory, observables also encode locality. However, even in the weak-field limit of gravity, such gauge-invariant observables do not generally have local commutators. This work will study aspects of the observables that are expected to be essential in a quantum-mechanical formulation of gravity. One aspect is their role in describing the emergence of locality, and spacetime, in the zero-gravity limit; here their algebra is a key characteristic. Another is the formulation of such observables in closed universes. Another is their potential role in \"decoding the hologram\" of AdS/CFT. Finally, a key aspect is relating such quantum observables to a description of observations which are made by observers who are part of the system — here, the Universe.

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