Asymptotic Charges Cannot Be Measured in Finite Time

TL;DR

This paper demonstrates that asymptotic charges like the Bondi mass cannot be measured within finite retarded time due to quantum fluctuations, impacting the understanding of observables in quantum gravity at null infinity.

Contribution

It shows that asymptotic charges are unmeasurable in finite time, revealing fundamental limitations on observable quantities in quantum gravity at null infinity.

Findings

Bondi mass cannot be observed in finite retarded time

Attempts to measure charges at large radius are hindered by quantum fluctuations

Implications for flat space holography and BMS charges

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 ${\mathscr{I}}^+$. 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 ${\mathscr{I}}^+$.