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.

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

References in corpus (17)

• Building up spacetime with quantum entanglement
• The Stretched Horizon and Black Hole Complementarity
• Modern tests of Lorentz invariance
• A Covariant Entropy Conjecture
• Quantum Gravity In De Sitter Space
• Remarks on entanglement entropy for gauge fields
• Disturbing Implications of a Cosmological Constant
• Positive vacuum energy and the N-bound
• Wormholes, Emergent Gauge Fields, and the Weak Gravity Conjecture
• Cosmological Breaking of Supersymmetry?
• Space from Hilbert Space: Recovering Geometry from Bulk Entanglement
• Diffeomorphism-invariant observables and their nonlocal algebra
• Observables, gravitational dressing, and obstructions to locality and subsystems
• De Sitter Holography with a Finite Number of States
• Cosmic Equilibration: A Holographic No-Hair Theorem from the Generalized Second Law
• Emergent Gravity requires (kinematic) non-locality
• From physical symmetries to emergent gauge symmetries

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