Asymptotic charges cannot be measured in finite time

Raphael Bousso,Illan F Halpern,Venkatesa Chandrasekaran,Aron C Wall

doi:10.1103/physrevd.97.046014

Raphael Bousso, Illan F Halpern + Show 2 more

Open Access

https://doi.org/10.1103/physrevd.97.046014

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

Highlights

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 Iþ
We find that attempts to measure a conserved charge at arbitrarily large radius in fixed retarded time are thwarted by quantum fluctuations
When Bob wakes up, he measures the new Bondi mass M of Alice’s planet. This can be done at arbitrary distance, by measuring the surface integral that defines the Bondi mass [see Eqs. (1) and (2) below]

Summary

COMMUNICATION WITHOUT ENERGY?

Alice would like to send Bob a message. Alice lives on a small, massive planet. Before Bob traveled to the Dyson sphere, Alice told Bob the mass M0 of her planet She promised not to radiate any of it away until the agreed time when the message is to be sent. When Bob wakes up, he measures the new Bondi mass M of Alice’s planet. Bob to perform measurements after he wakes up, no matter how big the Dyson sphere is That is, it should succeed in the limit as rB → ∞ at fixed retarded time u ≡ t − r and fixed δu (see Fig. 1). T vanishes: Bob receives no energy at all He missed the radiation Alice sent earlier, and by the time he measures the mass or charge, there is no radiative flux at all.

BONDI ELECTRIC CHARGE

BONDI MASS

DISCUSSION