I heard today a sad news that Jacob Bekenstein passed away at age 68. I know him mostly from reading his papers on gravity and information theory, but I also remember him through some personal communications. Below I will write it but before this, let me comment on his pioneering works out of the box a bit.

He was a brilliant scientist who will be missed in the community of quantum gravity. He had great contribution to the thermodynamics of black holes and its entropy, known as the Bekenstein entropy.

The original thought he had relies on an assumption that the information may be organized into binary digits on the black hole horizon where information exchange with black hole interior region (in his view) stops. This idea although is very heuristic, but motivated further investigates, without which it would take long time before thermodynamics of black holes is found.

Since then there have been many attempts to calculate the black hole entropy. For example, in one of the most recent attempts Ashtekar, et.al showed that from writing the action of spacetime dynamic in terms of gauge fields, the associated action to a black hole horizon becomes the Chern-Simons action. Quantization will end up in some punctures on the horizon, which carry degenerate states. Other arguments for similar derivation has been made much earlier in string theory by Vafa et. al.

Now, let me go back to the story between me and Jacobe Bekenstein. In 2007 I was a third year PhD student at the Perimeter Institute in Canada working on black holes. I have just published two solo-author long papers in Nuclear Physics B (

this and

this) where in I discussed the full spectrum of area operator in loop quantum gravity carries an internal degeneracy. The longer paper was first discussing an explicit mathematical proof to show the full spectrum of area no matter in what gauge representation is made of infinite number of equidistant subsets. Moreover, Jacobe Bekenstein and Viatcheslav Mukhanov (BM) have earlier argued based on the heuristic area quantization that black holes must radiate an evenly spaced spectrum of photons on top of Hawking radiation. The explicit quantization of area modified this result. Although it supports that a black hole radiates photons of discrete energies, however it predicts that, despite what BM predicts, the energy spectrum is not evenly spaced and that if one can detect at least three of the frequency lines it determines the internal gauge symmetry of the universe.

For these works I received the John Brodie prize and was nominated for a fellowship at Harvard which was almost hopeless to get in the presence of a nasty war in the blog sphere flaming between string theorists and those who take different approach, similar to that of Bekenstein's. Students were the first victims of this unnecessary hurlyburly.

Anyways, let me go back to the story. On a cold Suday morning of Canada in Nov 2007 when I woke up into the warm radiation of sun spreading in front of my little window in Waterloo, I checked my emails and to my absolute surprise I saw an email from "Jacobe Bekenstein" among my messages, which first I thought it must be fake. When I opened it up I saw it is from himself cc-ed to Viatcheslav Mukhanov. I read it and was shocked in the honour. Jacobe has already read my papers and prepared some comments on it. He started his rather long letter with:

"Dear Dr. Ansari,

Your paper on loop quantum gravity's predictions for the black hole area spectrum is interesting...

Although you find another series of levels that are not equidistant, you correctly argue that the

transitions between equidistant ones will prevail in the radiated spectrum. From an "observational" point of view, the equidistant levels are all that matters.

..."

He continued his letter with 4 important comments that helped to improve my papers and the history of proper references. I was a bit in shock to see that one of my heros in quantum information and gravity initiated writing such a descriptive letter to a random PhD student with such an exquisite accuracy of equation numbers and pages.

In a few days I responded to him, cc-ed to Mukhanov:

"Dear Professor Bekenstein,

It is a pleasure that I read your valuable comments. Thank

you for your message. I was not aware of the history of this line of

research to this depth. Previously, I enjoyed a discussion with Prof. Mukhanov

on this topic in a talk I gave a while ago at the Perimeter

Institute. I will read and study the references you mentiond and also

in the next version of the paper I will give the information to

readers and put enough stress on the origins of the methods.

..."

Then I explained some technical details about the work and explaining how different is the spectrum of loop quantum gravity from that of his. At the end, I asked him the following question:

"I am very interested to see the possibility of observing these lines (evenly-spaced, or unevenly-spaced ones). Do you have any estimate about the possibility of their detections. Some recent work suggest that they should potentially been detectable in INTEGRAL observations etc."

In response he wrote:

"... Regarding the observability of the lines (in whatever scheme, yours, or ours) the problem will

always be astrophysical radiation background. Usually lines of interest can be picked up if one knows a priori their frequencies. Here one does not because the mass of the hole could be anything."

Although I did not see Jacobe and do not know him in person, but these short communication helped me to see that one can be a great mind and at the same time not reluctant to learn from a nobody junior scientist.

Mohammad H. Ansari