Asymptotic Charges Cannot Be Measured in Finite Time

Abstract

To study quantum gravity in asymptotically flat spacetimes, one would like to understand the algebra of observables at null infinity. Here we show that the Bondi mass cannot be observed in finite retarded time, and so is not contained in the algebra on any finite portion of ${\mathcal{I}}^{+}$. This follows immediately from recently discovered asymptotic entropy bounds. We verify this explicitly, and we find that attempts to measure a conserved charge at arbitrarily large radius in fixed retarded time are thwarted by quantum fluctuations. We comment on the implications of our results to flat space holography and the BMS charges at ${\mathcal{I}}^{+}$.

9 pages, 3 figures. v2 typos fixed and minor additions

References in corpus (6)

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• 4D Scattering Amplitudes and Asymptotic Symmetries from 2D CFT
• Proof of a Quantum Bousso Bound
• Entropy on a null surface for interacting quantum field theories and the Bousso bound
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Cited by in corpus (9)

• The Holographic Nature of Null Infinity
• Failure of the split property in gravity and the information paradox
• Quantum Null Geometry and Gravity
• Holography of Information in AdS/CFT
• BMS symmetry, soft particles and memory
• Gapless Topological Order, Gravity, and Black Holes
• Asymptotic Limit of Null Hypersurfaces
• Modest holography and bulk reconstruction in asymptotically flat spacetimes
• Infrared Finite Scattering Theory in Quantum Field Theory and Quantum Gravity