The Hilbert Space of Quantum Gravity Is Locally Finite-Dimensional

Abstract

We argue in a model-independent way that the Hilbert space of quantum gravity is locally finite-dimensional. In other words, the density operator describing the state corresponding to a small region of space, when such a notion makes sense, is defined on a finite-dimensional factor of a larger Hilbert space. Because quantum gravity potentially describes superpo- sitions of different geometries, it is crucial that we associate Hilbert-space factors with spatial regions only on individual decohered branches of the universal wave function. We discuss some implications of this claim, including the fact that quantum field theory cannot be a fundamental description of Nature.

Essay written for the Gravity Research Foundation 2017 Awards for Essays on Gravitation. 6 pages

References in corpus (2)

• Observables, gravitational dressing, and obstructions to locality and subsystems
• Emergent Gravity requires (kinematic) non-locality

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