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Jacob Bekenstein (1947-2015)

Sadly, Jacob Bekenstein, the forefather of black hole thermodynamics affiliated with the Hebrew University in Jerusalem, died in Helsinki on Sunday night. I've known him well enough, especially from his Spring 2004 visit to Harvard when I talked to him many times (although less frequently than with the most important communication counterparts).

I took this picture in his office in the Jefferson Labs. He was born in Mexico City, moved to a polytechnic in New York, and studied as John Wheeler's student at Princeton University (PhD in 1972).

You must have heard that aside from the world, there also exists the anti-world where everything is anti-. For example, antiphysics is being studied by anti-Semites over there. This joke is rather accurate but when we talk about Jewish physicists, we almost exclusively mean staunch atheists.

Well, Jacob Bekenstein was a staunch believer who had a jarmulka on his head at almost all times. Just to be sure, he treated God mainly as the creator and insisted that his faith hasn't influenced his research. He also told me some stories about some of their troubles with the Arabs – he wouldn't ever actively use the word Palestinians.

My research that has been most interesting for him was the research on the quasinormal modes which primarily made the "loop quantum gravity" folks excited (I mean both the paper I wrote and our paper with Andy Neitzke a month later that was more flexible). He shared some of the LQG ideas but disliked most others. But he was convinced about some rather naive ideas that the black hole masses or areas of event horizons are quantized with rather big gaps.

This has always seemed ironic especially because of his insights that were so crucial for our understanding of the black hole thermodynamics. For the black hole radiation to be thermal, for example, the spacing between the microstates' energy must be tiny. And indeed, I do believe that it's exponentially tiny, comparable to \(\Delta E \sim \exp(-S/k)\), even though it's almost certainly not equally spaced in any sense (my guess is that the precise microstates are spaced like eigenvalues in the Random Matrix Theory: the roots of the zeta-function are non-Poisson and asymptotically repel each other in the same qualitative way). His musings – he would often describe with Viacheslav Mukhanov – were envisioning a generic black hole's spectrum with huge gaps \(\Delta E \sim T_{\rm Hawking}\). There are so many and so clear reasons why I wouldn't believe such a thing for a microsecond that I won't annoy you with that.

Also, Jacob Bekenstein has been a top researcher of MOND, the Modified Newtonian Dynamics. He wrote some original papers and co-authored papers with Milgrom, the main founder of MOND, too. MOND seems unlikely to me but it is not insanely unlikely or too obviously wrong. It is somewhat interesting. Bekenstein fathered and promoted the version of MOND that is most directly compatible with relativity, the TeVeS theory (tensor-vector-scalar).

Even though I believe that those later "ambitious" ideas haven't been on the right track, I surely do think that Jacob Bekenstein was a classic visionary, a genius who has always been likely enough to make important advances outside the box and he did them especially in the early 1970s.

In 1972, years before Hawking calculated the thermal radiation from a black hole, Jacob Bekenstein published a paper that included the correct black hole entropy, up to an unknown numerical factor:\[

S = \frac{Akc^3}{4G\hbar}

\] The factor of \(1/4\) was originally stated to be a "number of order one" – based on aesthetic considerations. This weaker claim was correct and the correct value was derived later, once Hawking deduced the black hole radiation in detail. When announcing his big picture, Bekenstein mostly built on the fact that both \(S\) (the entropy) and \(A\) (the total area of event horizons of black holes) never decrease. For the black holes, this "second law" was derived as a theorem by Hawking – so yes, Hawking's work was important even before Bekenstein announced his vision.

In the following years, he wrote lots of papers about the thermodynamics, quantum gravitational dynamics, charges, and even practical usability of black holes. The "Bekenstein bounds" (the entropy is smaller than something – and the something has been expressed in various ways) are arguably the most important spinoffs after the formula for the entropy. They may be viewed as predecessors of the holographic principle.

Bekenstein has received numerous prizes named after Einstein, Wolf, Weizmann, Israel, World Jewish Academy membership, Israeli Academy of Sciences and Humanities, Rothschild, Landau, and Bergmann. Every single one of these prizes is named after some Jewish people. His 1981 first prize of the Gravity Research Foundation is the only award I am aware of that is not "manifestly" Jewish. I view this asymmetry as a sign of anti-Semitic or anti-Israel bias of similar scientific institutions.

RIP, Dr Bekenstein.

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