I want to briefly mention three recent papers on the fate of the information in quantum gravity.

First, a week ago, Raphael Bousso argued that there is a simple

Universal Limit on Communication.When you are sending the information by photons, one photon of frequency \(\omega\) must occupy the time at least \(\Delta t \sim 1/ \omega\) and transmits \(\O(1)\) nats (or bits) of information, e.g. a bit from the polarization of the photon. The energy of the photon is \(E=\hbar\omega\).

You might think that the number of bits per photon may be increased arbitrarily because the information may be carried e.g. in the precisely determined angular direction of the photon's motion. But Raphael argues that due to the unavoidable appearance of some quantum effects that are there despite the seemingly classical setup, the recipient of the information (whose name is Bob and who surrounds the source, Alice, by a big sphere) will actually not be able to extract much more information, and the total transmitted information can't be above \(E \cdot \Delta t / \hbar\), after all.

There have been various limits involving the information and entropy etc. Some of them seem to be universal in quantum mechanics, not just results in quantum gravity. This bound doesn't explicitly depend on Newton's constant \(G_N\) and even though the "cultural context" of the derivation seems like quantum gravity (just like some Bekenstein-related bounds), I think it's right to say that this is a non-gravitational result (if it is true).

Today, Sudip Ghosh and Suvrat Raju wrote about

The Breakdown of String Perturbation Theory for Many External ParticlesIn the short paper, Sudip and Suvrat analyze the general behavior of the scattering amplitudes with very many, \(n\), external photons. They look at the high number of loops at the same moment, estimate the volumes of the Riemann moduli spaces, and if I simplify just a little bit, they conclude that the string perturbation theory breaks down exactly once the number of external strings reaches the entropy of the object inside (a black hole), \(n\sim S\).

This way of talking about the breakdown may have consequences for the information loss paradox. After all, the total number of Hawking particles that a black hole emits is also comparable to \(n\sim S\), the entropy, and that's exactly why the calculations of the amplitudes may break down. It means that these amplitudes may actually receive important corrections from some completely different configurations – that look like a non-local action involving all the Hawking particles etc. It may follow that locality works very well for a reasonably low number of external particles but it simply breaks down whenever you try to talk about very many of them – especially about all the Hawking particles that came from an evaporating black hole – and this may be a simple explanation why there seems to be a "Hawking paradox". Locality may be OK almost at all times and it may break down exactly when Hawking needed it to derive the paradox!

I have known about another nice Indian paper,

Towards a dS/MERA correspondence,for some weeks and the authors, Raj Sinai Kunkolienkar and Kinjal Banerjee, kindly overstated the usefulness of my not quite coherent comments about their work.

Last year, we discussed AdS/MERA stuff and tensor networks. These folks try to combine this machinery with a different spacetime than the anti de Sitter (AdS) space, namely with the de Sitter (dS) space. So their paper is proposed as a toy model for a hybrid of (e.g. Strominger's) dS/CFT and the MERA Ansätze.

Somewhat naturally, they study the two (past and future) boundaries of the de Sitter space and treat them as two a priori independent collections of degrees of freedom. That leads to the idea that the time connecting these two boundaries is emergent. In dS/CFT-style setups, time is as holographically emergent as the radial direction in AdS/CFT.

These are very interesting proposals but I am still not persuaded that it's possible to think in this way and what the details should be. An emergent time simply

*is*harder than the emergent spatial dimensions. In particular, relativistic theories allow guaranteed vanishing commutators – and therefore the independent existence of subsystems – exactly when the subsystems are spacelike-separated. Whether the two CFTs etc. may be considered independent is equivalent to their spacelike-vs-timelike separation and this information about the separation should better be known at the kinematic level. It decides about the size of the Hilbert space so it's even more systemic than dynamics. Although space and time seem to be continuations of each other, they also differ "qualitatively" by the zero-or-nonzero commutators. Maybe this qualitative difference may be deduced as a relative technicality from some normalizability of modes or something like that – but it shouldn't be denied altogether. In particular, due to their time-like separation, I am not sure it's possible to treat the two past-and-future boundaries of the dS space as independent ones.

There are some potential problems I feel uneasy about but there may exist crisp solutions to these problems, too. At any rate, the authors hope to revive the research of holography in de Sitter spaces. They may hope that many physicists will try to check whether the dS quantum gravity subsubfield really has to be stagnating, like it was in recent years – or whether some recently found tools in quantum gravity allow us to derive some cool results that were impossible just a decade ago.

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