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We report a surprising result today with Hao Geng, Andreas Karch, Carlos Pérez, Lisa Randall, Marcos Riojas and Sanjit Shashi. We show that the island rule leads to inconsistent results in standard theories of long range gravity, and is only consistent in theories with massive gravitons.

This is the story in some more detail.

𝐓𝐡𝐞 𝐂𝐨𝐧𝐟𝐥𝐢𝐜𝐭 We have recently described a principle of holography of information for theories of gravity: this states that information that is present in the bulk of a Cauchy slice is also available near its boundary. (More on this in a few days)

On a different track, significant progress has been made in understanding AdS black holes coupled to non-gravitational baths. Here a part of the bath describes a part of the region inside the gravitational region, called the “Island”.

The two ideas above sound vaguely similar: in each case degrees of freedom in one part of space describe degrees of freedom that appear to be localized in another part of space. But a little more examination reveals that they are conflict with each other. The fact that information about the island is hidden from the asymptotic boundary of the gravitating region but instead available somewhere else contradicts the principle of holography of information.

In today’s paper, we turned this into a sharp puzzle. In standard theories of gravity, the energy of an excitation inside the island can be measured from outside the island using just the humble Gauss law. (The same Gauss law that we use to determine the mass of the sun without ever visiting it). This leads to the conclusion that not only is the paradigm of islands in contradiction with the principle of holography of information, it is inconsistent even with the Gauss law. And this inconsistency is already visible in perturbation theory.

𝐓𝐡𝐞 𝐃𝐞𝐧𝐨𝐮𝐞𝐦𝐞𝐧𝐭 This doesn’t mean that the papers about islands are wrong. (Well, given the number of papers that continue to be written on islands, some of them are wrong, but I’m talking about the right ones.)

We found the resolution to our puzzle hiding in plain sight. The models that have been used to study islands couple a theory of gravity in AdS to a bath. When a theory in AdS is coupled to a bath, the graviton in AdS necessarily picks up a mass. This follows almost from conformal representation theory. The stress-tensor on the AdS boundary ceases to be conserved because energy is leaking into the bath. So it picks up an anomalous dimension. Voila, in the bulk, the graviton picks up a mass.

But theories of massive gravity do not have a Gauss law (or a principle of holography of information). What this means is that in theories of massive gravity, one cannot determine the energy inside a bounded region by integrating some component of the metric outside that region. So there is no puzzle if such theories contain islands.

The mass of the graviton was noted earlier by Andreas and Hao. But it was sometimes believed that this was an unwanted feature of specific models, and one should be able to wish away the mass in some way. What our paper today shows is that the mass of the graviton is not a technicality that can be wished away but is crucial in ensuring the consistency of the island story.

𝐄𝐩𝐢𝐥𝐨𝐠𝐮𝐞 In standard theories of long-range gravity, the principle of holography of information appears to hold. There are no islands. Applied to black holes, information about even the interior of a black hole is always available outside for sufficiently complicated measurements.

Islands are consistent in theories of massive gravity. Applied to black holes, information about the black hole emerges gradually according to a Page curve, as an island grows in the interior. But the paradigm of islands (at least in its current form) should not be applied to black holes in standard theories of massless gravity.

Read more at: https://arxiv.org/pdf/2107.03390.pdf

We have archived our recent ICTS course on the black hole information paradox. This was a research-level topical course covering several recent developments.

The lecture archive is here: https://www.youtube.com/channel/UCJ-YA8uOwUlACfn49iD7TvA

and some more resources including handwritten lecture-specific notes and assignments are available at: http://www.suvratraju.net/classes/black-hole-information-paradox

The course followed the lecture notes available at: https://arxiv.org/pdf/2012.05770.pdf

Thanks to Chandramouli, for being such a great teaching fellow!

Some reflections:

I felt this was an interesting experiment in teaching. Usually for a very specialized course of this kind, we would have a small group of participants across Bangalore institutions — ICTS, IISc and RRI. But this time since it was virtual, we opened it up more widely.

So not only were there participants from other institutes in India, we had a large international group including participants from at least 10 other countries across 4 continents.

Zoom teaching can end up being a lecturer’s monologue but these lectures were pleasantly interactive because of the diversity of students.

The course did involve a lot of work. My estimate for the first time I teach a graduate course is that preparation hours:lecture hours is about 5:1 (reducing by a factor of 2 for every time the course is repeated.) For this course, I think it was more like 10:1. I’m not sure why. Perhaps one reason was that I knew everything was being recorded. In the classroom, if one messes up the algebra one can say “and if you work in units where 2=1, the answer will come out right as you can check at home.” :-) But I was uncomfortable doing this while being recorded, which obviously meant more work. Also, since there is no visual feedback, teaching virtually just requires work in organizing the subject matter better.

On the other hand, we generated a lot of archived teaching material, and hopefully this will be useful for students in the future as well.

Some institutional ideas:

Online teaching has been rightly criticized. I can see how much of a disaster it has been at school level. The most serious problem is that it exacerbates inequities among students. But even for those privileged school students who have access to stable internet, a place to study and parental support I think the last year was largely a washout. The same problems persist at an undergraduate level. Also the state uses virtual education as an excuse to reduce investment in education. So to be clear: I hold no brief for the virtual classroom, in general.

Nevertheless, I have been wondering whether, within the niche area of graduate education, such virtual courses might have an important role even when the pandemic ends.

Just within theoretical physics, most institutions have neither the faculty strength not enough student demand to run regular courses on a subject like advanced QFT. It is even rarer to have topical research courses of the kind above. So cross-institutional courses could help to bridge this gap. At this level, participants are both mature and highly motivated and so may be able to benefit from virtual courses.

In India, there has been an indefensible policy of separating research institutions and teaching institutions. These kinds of courses are a small reform that might help in the short run. (In the longer run, obviously, the policy must change.)

There are some immediate administrative issues. In this course, except for a small set of ICTS students, everyone was “sitting in”, and we couldn’t give anyone else “credit” for the course. This is because most institutions have administrative issues in accepting credit for courses from other institutions. These barriers need to be dismantled. We also need a system of sharing teaching fellows so that if X students from an institution take a course, the institution also offers grading support to avoid an undue burden on the home institution. But these don’t seem to be insuperable.

I’m skeptical of my own ideas since I’m skeptical of virtual teaching for the reasons above. Am I missing some obvious reason that this is a bad idea?

I was part of a “podcast with video” series on the “Black Hole Wars” that the students at DAMTP organized as part of the 2021 Cambridge Festival. This was the concluding episode in a series exploring the information paradox.

I tried to explain how theories of gravity store quantum information differently from other quantum field theories; how this is an effect that was missed in Hawking’s argument for information loss; and how replacing Hawking’s “principle of ignorance” (about the interior) with a “principle of holography of information” provides a neat resolution to the paradox.

The festival is a public outreach program at the University, and so I was told not to target Cambridge undergraduates and to keep things at a high school level i.e. not even assume the Gauss law or the uncertainty principle! I’m not sure I succeeded at that but hopefully some of it is accessible to undergraduate students.

I’ve also never tried to explain a complex scientific topic in a “podcast style” conversation. This has its own challenges. In a popular talk, one can start at a basic level and then organize topics in some clever way to communicate an advanced idea or at least build up a sequence of analogies. But here the idea was to bring out the physics as part of a conversation.

Anyway, it was a new experience, so I had fun.

Thanks to Ayngaran Thavanesan for organizing this and to Rifath Khan and Goncalo Regado for anchoring the conversation.

This is pretty far afield from the topics that I usually write about but after reading Rudrangshu Mukherjee’s article on “Dharma and Caste in the Mahabharata” in the India Forum I felt that perhaps a brief response was warranted. So I wrote a letter on “Caste and Skin Colour” in the Mahabharata, which appears here.

https://www.theindiaforum.in/letters/dharma-and-caste-mahabharata

One simple point that appears not to be widely appreciated (at least in some circles) about the Mahabharata is this. In the original text, many of the main heroes, and the most beautiful men and women are described as being dark or having black-colored skin. There is a lot of explicit discussion about the complexion of characters, and there is no ambiguity about this issue. I give several examples in the letter but even a cursory reading of the text will reveal this aspect.

So it is incorrect to try and link skin color and caste while analyzing the text. The relation doesn’t exist as far as I can see.

(Of course, it is absurd that in modern picturizations of the Mahabharata — whether in the Amar Chitra Katha or the Doordarshan serial — the main characters (especially the women) are all depicted as having fair skin.)

On the other hand, there are other important issues and discussions of caste in the Mahabharata. It is clear that the text is presented from a dominant-caste narrative but there are several nuggets of dissent. I tried to give some examples of those as well. I think this reflects the fact that the text is accretive and I view these episodes as a sign of dialectical currents in the society of the time and as an acknowledgments of old revolts against a hierarchical order.

My study of the Mahabharata has been superficial, at best, so I would appreciate comments and corrections.

An opinion piece I wrote for the Scientific American describing our response, as members of the Indian scientific community, to the Citizenship Amendment Act. Members of the scientific community have also spoken out on other issues over the past year. I tried to place this in the context of broader questions of academic freedom in public research institutes in India.

https://www.scientificamerican.com/article/scientists-weigh-in-on-indias-citizenship-debate/

A popular-level talk on Black Holes and the Reversibility of Time that I gave today to start off the new ICTS outreach series called the Vigyan Adda. I even talked about the principle of holography of information at the end of the talk, although I’m not sure how successful I was in communicating the idea. Thanks to the amazing ICTS outreach team!

https://www.youtube.com/watch?v=zyaf5GfkfV4

Here is another article that appeared today, reviewing some of the lessons that I think the information paradox teaches us about broader aspects of quantum gravity. https://arxiv.org/pdf/2012.05770.pdf

I started this article with the plan of writing up some of the discussions we had at the summer conferences. But then I realized that there were many ideas that people were talking about that were not explained clearly in any one place. So I kept writing … and kept writing … and when I finished, I found that I was at 156 pages :D As they say, in runner’s parlance, that’s a PB.

But I tried my best to write a coherent story about an old subject; to emphasize the main physical ideas with as few technicalities as possible and provide the background material necessary to understand these ideas. In fact the only parts that are somewhat technical are about issues that are conceptually well understood.

So although the article is long, I hope that it will still be fun to read, and useful.

And send me comments if you have any.

We have (in my unbiased opinion :-) ) an interesting paper out today: https://arxiv.org/pdf/2012.04671 with Hao Geng, Andreas Karch, Carlos Perez-Pardavila, Lisa Randall, Marcos Riojas, and Sanjit Shashi. One of the significant problems we managed to solve was to “how to set up multiple Zoom meetings across four time zones on opposite sides of the world.”

More seriously, there has been a lot of recent activity on computing the entropy of “Hawking radiation” using entanglement islands. However, the precise computations actually deal with black holes that are rather different from black holes in our world. More specifically, they generally consider an entire holographic system that has an asymptotic AdS region of its own, which is then coupled to a nongravitational bath. As several of us have pointed out, it is not clear if the lessons learned from such setups hold when gravity is everywhere dynamical, as it is in our world.

So the idea of today’s paper was to turn on gravity in the bath itself. This can be done elegantly in the braneworld scenarios that have been used for higher-dimensional computations (and that were studied by Andreas and Lisa long ago) by just introducing a second brane into the geometry. And, lo and behold, when we do this, the Page curve disappears!

So we find that the nongravitational bath is not just a calculational device, but it modifies the physics in a significant way. This is also precisely what one would expect from our previous work on black holes in asymptotically flat space: we pointed out that when gravity is dynamical, information about the black-hole interior is always available outside, and so there should be no Page curve for the fine-grained entropy of radiation. On the other hand, there might be other questions one could ask that might yield a Page curve.

And indeed, even in the setup of today’s paper, there is still a codimension 2 boundary that is nongravitational. On this nongravitational boundary, we can divide the Hilbert space into two parts. If we ask about the entanglement between these two parts, we recover a Page curve. This Page curve has many interesting properties, and islands play a role provided the branes obey some interesting geometric constraints.

This Page curve is answering a nongravitational question, that can nevertheless be studied by analyzing minimal surfaces in a dual geometry. It is not a Page curve that describes how information “emerges” from a black hole.

I think this is also how previous Page-curve computations should be interpreted. One takes a nongravitational theory, maybe N=4 SYM, and divides it into two parts. Or maybe one takes a SYK model and couples it to a CFT. There is no gravity in sight. But when the theories have a bulk dual, it is still possible to compute the entanglement between these two subsystems using bulk extremal surfaces.

So the Page curves that have been computed should not be interpreted as telling us the rate at which information is transferred from the black hole into the radiation; rather they are telling us about how information is transferred from one nongravitational region to another.