## Friday, August 30, 2019 ... //

### Juan et al.: the BH interior is accessible from the final radiation through a new dimension

A new clever way to clarify the resolution of the information loss puzzle

Years ago, we had lots of top physics authors whose every new paper was a holiday we were looking forward to. I think it's harder to say the same these days... but I am still mostly looking forward to new papers by Juan Maldacena and perhaps a few others. OK, there is a new paper today

The Page curve of Hawking radiation from semiclassical geometry (by Almheiri+Mahajan+Maldacena+Zhao)
I initially read the abstract too quickly, thinking that it says "we do another somewhat boring combination of ER=EPR with RT/HRT and other things". However, that's a totally wrong way of reading it, perhaps influenced by Juan's and co-authors excessive shyness.

Instead, as @mmanuF at Twitter generously forced me to understand by his crispier summaries of the paper, they are really saying something like
Listen to us, puddies, pussies, and puppies: we really have a crisp new solution to the information loss puzzle, i.e. an answer to the question how the Hawking radiation may possibly carry away the information from the causally disconnected black hole (BH) interior. We add an extra antiholographic dimension for the evaporating matter and find out that the interior is connected to and accessible from the asymptotic region – so in some sense, the BH interior still lives in the Hawking radiation after the BH evaporates away. In other words, we visualize the ER-EPR wormholes connected to the Hawking radiation in a new, antiholographic way.
And that's something worth reading. The PDF file only has 21 pages.

The authors (AMMZ) study a two-dimensional theory of gravity with a BH in it. Two is the lowest spacetime dimension in which "something like quantum gravity" has been studied (they generally conjecture that their constructions may hopefully be extended to higher dimensions – but they only studied the $D=2$ black holes).

By holography, their $D=2$ gravitational spacetime is equivalent to a non-gravitational theory in a lower spacetime dimension, in $D=1$. But they go into the other direction, $D=3$, which is why I call it "antiholography". But it's not some crackpot new principle. Instead, it's supposed to be a normal holography applied in an unusual way:

They localize the "matter part" of the $D=2$ theory in which gravity couples to matter. And the matter part is a "non-gravitational" theory, a theory similar to CFTs, so it could be equivalent to a gravitational dual in a higher dimension, i.e. $D=3$. Great. So to study the gravitational theory with a BH in $D=2$, they consider a $D=3$ theory, locally an $AdS_3$ geometry.

They added one new antiholographic dimension on top of the $D=2$ of the gravitational theory – which means that they are two dimensions above the conceivable $D=1$ "CFT" that you could find for the $D=2$ theory if it were an AdS-like gravitational theory. Clearly, they want to use the new higher-dimensional, $D=3$ spacetime mainly to look at the "location of the Hawking radiation" in a new way. The Hawking radiation is composed of the "matter" so why wouldn't you try to look for a higher-dimensional AdS spacetime dual to this matter?

I must say in advance that this antiholographic treatment seems non-rigorously established to me, especially because the matter and the gravity aren't cleanly decoupled. Not only that: the Hawking radiation in a higher dimensional theories isn't just "matter", is it? In $D=4$ and higher, there are also gravitons in the Hawking radiation, aren't there? This could complicate the generalization of their paper to the more interesting, higher dimensions such as the $D=4$ that many somewhat naive people think that we inhabit. But there are no physical gravitons in $D=2$ and even $D=3$ so it's not a real issue in the toy model that they study which is still interesting.

Fine, so they try to calculate "quantum extremal surfaces" (QES) in the $D=2$ gravitational theory. To do so, they use the new antiholographic $D=3$ theory in which the search for the QES is equivalent to RT/HRT surfaces (Ryu-Tadaši/Hubený-Rangamani-Tadaši where I helpfully used Takayanagi's first name and made sure that not just Veronika's but a majority of the names is spelled in the Czech way).

With a new dimension, however risky this description it may be, the "location" of all the information is seen through totally new eyes. So while the black hole interior was an "island" causally disconnected from the infinity in the $D=2$ theory, it just becomes connected through an "entanglement wedge". Almheiri – a co-author who has also been on the deceptively clever and notorious firewall AMPS paper (which has 888 citations now) – summarizes their paper as follows:

In order to understand the clicky-hacky symbols, I learned Arabic and I think that they only say, like the English nickname, that Almheiri is from the Emirates (Abu Dhabi, UAE). So you don't need to learn Arabic so far. Raghu Mahajan is from India but has been in the U.K. and U.S. (Cambridge, Microsoft...) for years. Juan is a Princetonian from Argentina. Ying Zhao is a Stanfordian from China.

When you include the new antiholographic dimension to promote the matter part of your $D=2$ theory into higher dimensions, a new locally $AdS_3$ space emerges and through this new space, the black hole interior simply becomes connected with the location of the Hawking radiation at infinity – even long after the BH has evaporated.

Their solution to the puzzle "how may the information escape from the interior" is therefore
"it may escape because when a previously overlooked (antiholographic) dimension is added to the spacetime, the interior isn't really disconnected from infinity anymore".
That sounds simple and persuasive enough. Needless to say, a new Ersatz problem emerges instead of the old one:
This new $D=3$ theory including the antiholographic dimension seems nonlocal – it seems that it has little trouble to directly access the interior which would be nonlocal in the $D=2$ theory. How can these two very different theories, a local and non-local one, be reconciled?
I think that they realize this "new problem" that they have created by their new original solution to the old one – and they don't have a solution yet. A theory in which certain "interior to infinity" influences are prohibited, the $D=2$, is claimed to be equivalent to a theory in which these influences are easy. Isn't it a contradiction? A proof that the antiholographic duality cannot really work? And if it is not a contradiction, can one prove that the $D=3$ theory only allows "very subtle influences" that are basically interpreted as "no influences at all" or "exponentially tiny influences" in the $D=2$ theory?

There are surely many surprising consequences of the paper and many new questions that are opened. But they are also giving us new tools in which all these questions could potentially be answered in a controllable way.

At any rate, I want you to notice that these big shots in the information-loss research basically agree about the basic qualitative answers to the Yes/No questions concerning the information loss:
1. black holes exist,
2. firewalls don't exist,
3. remnants don't exist,
4. the information isn't lost,
5. the information doesn't come out extremely early,
6. the information doesn't come out extremely late.
7. Instead, it comes out at the expected times, during the generic lifetime of the black hole, and the ways how the locality condition is violated – or apparently violated – are rather subtle. We want to understand "where the information is" by various new constructions using the "entanglement is glue" paradigm and it's possible that a future understanding of the Hawking radiation – which carries away the microscopic information about the initial state – will be very transparent.
You can't take seriously any writer who, even in 2019, still pretends that the possibilities (negations of) 1-6 above are comparably likely to the correct general solution 7. Such a person is completely decoupled from all serious quantum gravity research in the recent 20-40 years and he or she is just deceiving gullible laymen. Note that Almheiri is one of the co-authors of the firewall AMPS paper which surely contradicts the statements of the new paper. I believe that Almheiri would agree that AMPS was just an example of a "clever argumentation in favor of the firewall" that is ultimately a wrong conclusion in Nature because the assumptions of AMPS – including some extremely precise locality and separability of the degrees of freedom to the interior and exterior – doesn't hold in quantum gravity.

The separation of the degrees of freedom to the mutually commuting "interior" and "exterior" degrees of freedom must be partly wrong – in other words, the black hole complementarity is at least morally right – and the new AMMZ paper is giving us a rather explicit tool to clarify "why" the complementarity really holds. Perhaps to figure out what the right degrees of freedom are and how independent they are, you should quantize the whole slices in the $D=3$ theory and this antiholographic theory will prevent you from treating the island (interior) separately from the exterior.

The AMMZ paper is dedicated to Steve Gubser who tragically died in the Alps.