New paper to end the year with Kristan and Antony. Last year, with Jonathan, Antony and Kristan studied quantum information measures for subregions in gravitational theories. Some of their results might appear puzzling if you have been following recent progress on the holography of information. In quantum gravity, information in a bounded subregion is available in its complement. This might suggest that it shouldn’t make sense to measure the information content of a bounded region in gravitational theories.
In today’s paper we reconcile these observations. One should think about the holographic properties of gravity like unitarity. Unitarity is important for precise nonperturbative questions about any system, and can be verified in perturbation theory about simple states, as we do in elementary QFT courses. But, in the presence of a macroscopic background, if we coarse grain our observables — as we do in everyday life — physics appears dissipative. Similarly, holography is important if we ask precise questions about information loss. And, for simple states, one can check perturbatively that gravity localizes information differently from quantum field theories. But, in the presence of a macroscopic observer with coarse-grained abilities, holography can be obscured and this allows one to define “algebras” for bounded regions and their complements and quantify their information content.
The observer needs to be heavier than the cosmological scale but lighter than the Planck scale. In our world, a virus on top of the vacuum would do: the mass of a virus is 10^(-15)g (see the biophysics paper in our refs ) — well above the cosmological scale (410^(-66) g) and well below the Planck scale (210^(-5)g).
Quasilocal observables about macroscopic backgrounds have been studied many times before. But it doesn’t seem to have been noted that, with some jiggling of notation, the formulas used to define these observables go over exactly into the formulas used to define the so-called “crossed product” in the literature on von Neumann algebras. This is not only true for the formulas in today’s paper. We went back and looked at a paper with Kyriakos from 2015, exploring the interior of an eternal black hole, and the crossed product had appeared secretly there as well!
P.S: Just to be clear and to anticipate possibe confusion: these techniques can’t be used to define a meaningful Page curve for black-hole evaporation. The unitarity of black-hole evaporation relies on nonperturbative effects and in this regime, these quasilocal constructions break down. It is an invitation to paradox to conflate everyday intuition about locality with intuition from unitarity, as both Hawking and Page did.
Of course, if one demands that the Page curve should be the answer then one can find the right question by adding nongravitational baths to AdS, or by dividing the boundary into two regions etc. but these curves don’t represent information “emerging” from the black hole; holography of information tells us the information never goes “in”, and so it doesn’t have to emerge.
See http://www.arxiv.org/pdf/2412.21185 for this discussion and more!
