## Friday, May 19, 2017 ... /////

### Spacetimes as thick (objects and) amplifiers of information

There are a whopping 23 new hep-th papers today, not counting the cross-listed ones, and some of them are very interesting. For example, Kachru and Tripathy find some cute number theory inside the engine of $K3\times T^2$ compactifications of type II string theory. Max Guillen shows the equivalence of the 11-dimensional pure spinor formalism to an older one.

Dvali studies the chiral symmetry breaking, a physicist named Wu presents a theory of everything based on "gauge theory in a hyperspacetime". Some paper answers whether patience is a virtue by references to cosmic censorship LOL. But mainly the following two papers look like they belong to the black hole (or spacetime's) quantum information industry:

Spacetime has a `thickness' (Samir Mathur)

Classical Spacetimes as Amplified Information in Holographic Quantum Theories (Nomura, Rath, Salzetta)
Mathur wrote a (silver medal) essay for a "gravity foundation" and the point is right. However, the suggestion that these are new ideas is not really valid. He says that the spacetime (or its state) isn't just given by a shape. One must also specify the "thickness" of the wave functional defined on the configuration space (the space of 3-geometries).

[The 4th prize in the same contest went to Shahar Hod, also cross-listed today, who claims to have proven our weak gravity conjecture as a consequence of "generalized Bekenstein's" [I wouldn't use these words] second law of thermodynamics within quantum gravity. The second law implies that the relaxation time is $\tau\gt 1/(\pi T)$. When the imaginary parts of quasinormal models of a charged black hole are used to extract the relaxation time, one proves the weak gravity inequality. If it were a correct paper, he would have repaid my proof and our proof of his log-3 numerical observation. Well, I would still view it as "another" proof among many – similar to the proofs we already had in the original paper. It's surely personally intriguing that he has combined two things I've studied, the quasinormal modes and the weak gravity conjecture.]

If you think just a little bit, you will realize that it's an equivalent statement to my 2013 observation that coherent states form an overcomplete basis which implies that that field operators in QG cannot be localized in a background-independent way. Derivations with similar or stronger consequences have appeared in papers by Raju and Papadodimas, Berenstein and Miller, and a few others.

Even if the content of papers like Mathur were totally right, it's an unfortunate development – trend towards Smolinization of physics – for researchers not to follow their colleagues' work.

Nomura et al. do follow the literature. To say the least, when they derive that semiclassical operators must be defined in a state-dependent way, they do refer to two papers by Raju and Papadodimas who have crisply formulated this conceptual insight – I was fortunate to watch them when they were localizing the true "new lesson" of their perfectionist analyses of the possible operator algebras describing the black hole interior.

At the same moment, Nomura et al. study an idea that is new within papers on quantum gravity that include some justification:
Classical spacetimes represent amplified information.
I have – and, I am sure, many of you have – articulated the idea that the local operators in theories of quantum gravity (but even other theories with classical limits) are those that amplify some information, that make it more classical. You may therefore imagine quantum gravity as some process of "organizing a pre-existing spacetime-less quantum information" and the classification of possible spacetimes in quantum gravity should therefore be equivalent to some task of finding out all the ways that allow the information to be amplified.

As far as my thinking about these matters go, the amplification should include the requirement the condition of a classical limit that the commutators between the relevant observables are much smaller than the generic ones – while this subalgebra of operators (field operators in a spacetime) evolves in a way that only depends on the operators in this subalgebra. (I am not acturally sure whether there is any tangible difference between the two conditions, amplification and the classical limit.) It's left as a homework exercise for you to show how e.g. T-duality (including mirror symmetry) and the ER-EPR correspondence may be derived as the existence of numerous inequivalent ways in which the information may be amplified.

But Nomura et al. talk about a stronger, exponential selection of the important semiclassical spacetime-like operators. These operators may be dynamically selected by time evolution.

What makes the task of finding the amplified information nontrivial in quantum gravity is that you don't have the answer from the beginning. In non-gravitational quantum field theories, we know what the Hamiltonian is and it is simply constructed as a functional of the fields that are capable of amplifying the information. However, in holographic descriptions of quantum gravity, the boundary or similar description uses different degrees of freedom and it doesn't have the bulk fields from the beginning. You really have to reconstruct them and the task is nontrivial.

If you demand the hypothetical subalgebra of these bulk operators to have small commutators with each other and the Hamiltonian, you should pretty much derive that the subalgebra includes the bulk field operators and their simple enough functionals. To be more precise, in the absence of a black hole in the bulk, only the field operators in the black hole exterior should be produced in this way. The exterior is picked because we have included the Hamiltonian into the definition of the problem (see the bold face word in this paragraph) and the CFT Hamiltonian is only simply related to the evolution outside the black hole. Note that the infalling observer's Hamiltonian has no relationship to the Killing field. Because the space and time are interchanged inside the black holes, the infalling observer's Hamiltonian is mathematically closer to some momentum operators outside the black hole.