Blog

Not a new paper but, in this version, I’ve added some comments on the difference between gauge theories and gravity and the relevance to the AMPS paradox, about which I got a number a questions.

It seems to have been clear for a while that the resolution to the Mathur/AMPS paradox is that operators in the black-hole interior can be expressed as complicated combinations of operators outside. This was also a feature of the construction of the interior that Kyriakos Papadodimas and I set up. However, I’ve long felt that it would be nice to have a toy model where this could be demonstrated as cleanly as possible with no conjectures or hand waving. This paper sets out such a model.

The technical tool is to use Bell correlators to express the monogamy of entanglement. (Bell correlators are far better controlled than the von Neumann entropy). Then one can show that that, even in empty AdS, if one is allowed to use arbitrarily complicated operators from distinct regions, it is possible to violate the monogamy inequalities precisely like the Mathur/AMPS paradox. Moreover, everything can be calculated cleanly, with explicit numbers. In this model, I violate the monogamy inequalities by 42.5%!

What this shows is that, in quantum gravity, operators which appear to be in different regions may secretly be acting on the same degrees of freedom and so can access the same quantum information.

It is important that this phenomenon appears only in gravity, and not in gauge theories. In gauge theories, because there exist exactly local gauge-invariant operators, one cannot read off information about interior excitations from a far-away region; someone could act with a little localized Wilson loop in the interior, while leaving every observable for the far-away observer invariant. So, while in gauge theories, operators from different regions may not commute because their Wilson lines intersect, “complementarity” (in the sense described above) seems to be a feature unique to quantum gravity.

Comments (especially critical ones!) are welcome. https://arxiv.org/abs/1809.10154

I had a sad and startling conversation with a taxi driver the day before yesterday. I had gone to Ashoka University to give a talk, and the ride to Delhi airport is almost a couple of hours. I hadn’t seen the news in the morning, and when I saw the news on my phone, I expressed my disgust at the escalating tensions to the taxi driver: “अरे देखो कितना ख़राब हो रहा है.” At which point, he looked at me and said: “तो हम क्या करें? उन्होंने हमारे लोगों को मारा, तो क्या चुप बैठें ? अब चाहे हमारे लाख मर जाएँ, उनके ज़्यादा मारेंगे.” So I tried to explain the futility of war etc. and the problem in Kashmir at which point he says: “वो लोग तो पत्थर फेंकते हैं. मैं अगर फ़ौज में वहां होता तो बंदूक से सब को उड़ा देता.” So we went on talking for a while, and I kept trying to tell him about how matters were not so simple. He was surprisingly receptive. By the end of the journey, he started saying, “हाँ ,शायद इमरान खान भी ठीक बोल रहा है. उसको मौका देना चाहिए” and about Kashmir, " हाँ, भारत सरकार ने भी कुछ गलत किया होगा इसलिए कश्मीर के लोग नाराज़ होंगे. So, I was happy with my persuasive skills and while getting off, I told him “और लोगों से भी बातचीत करना और यह सब समझाना” at which point he replied “मैं यह सब बात नहीं कर सकता. मुझे पाकिस्तानी कहेंगे. मैं तो वैसे भी मुसलमान हूँ. अगर हिन्दू होता तो शायद कह पाता” I was absolutely dumbstruck. It turns out he had agreed with me all along, but because of his identity, he was terrified to express himself honestly. Even though I was obviously anti-war, he nevertheless felt compelled to pretend to be a bloodthirsty war-mongerer. Someone else said something similar to me yesterday. There must be something really wrong …

We considered relativistic correlation functions at finite temperature in the limit where the momenta of the operators become spacelike and large. Surprisingly, these correlators are bounded by a beautiful geometric quantity: they must die off at least as fast as exp[-R/T] where R is the radius of the smallest sphere that encloses the nonplanar polygon formed by the momenta and T is the temperature. https://arxiv.org/abs/1902.07203

some thoughts on the situation in Venezuela. https://thewire.in/world/indias-stake-in-the-crisis-in-venezuela