## Saturday, August 22, 2015

### NYT on Bekenstein and his argument with Hawking

Jacob Bekenstein died of heart attack. It is the first new piece of information in the New York Times obituary
Jacob Bekenstein, Physicist Who Revolutionized Theory of Black Holes, Dies at 68
written by (not only) their top science writer Dennis Overbye. A heart attack is a terrible thing and unlike many people who die when they're 103 or something like that, I feel it is totally right to say that Bekenstein's death was a premature one.

Overbye discusses Bekenstein's family – Polish Jewish immigrants to Mexico etc. But what is cute is the description of a feud with Stephen Hawking. It shows how surprising, convoluted, and comical the paths throughout physicists' hearts picked by the truth may be.

Recall that Bekenstein noticed that both the "total area of event horizons" and the "total entropy" never decrease. These laws are similar and using some other hints as well, Bekenstein was able to guess that the black hole entropy is proportional to the area of its event horizon.

In 1972 when he published it, Stephen Hawking was irritated:
Dr. Hawking denounced the idea. According to classical physics, anything with entropy had to have a temperature, and anything with a temperature — from a fevered brow to a star — must radiate heat and light with a characteristic spectrum. But a black hole could not radiate, and thus it could have no temperature and therefore no entropy.
You must realize the many levels at which Hawking's opposition is so surprising – and unique to physics. If it were a political question, you could mostly guess how the question polarizes the opponents and which side they will pick.

But in physics, if you deal with physicists who honestly evaluate the evidence they see, it's much more subtle and unpredictable. First, Bekenstein used an insight proven mostly by Stephen Hawking – the result in general relativity that the total horizon area never goes down. So far so good: Bekenstein has built on insights of another man. Even some politicians could do it.

However, the funny thing is that Stephen Hawking didn't like it. Ordinary people without the scientific integrity could automatically like a result that makes their own previous paper important or that sort of vindicates this older paper of theirs! But even though Bekenstein was building on Hawking's previous work, he just didn't like it. Needless to say, Hawking's argument against Bekenstein's formula was initially totally sensible. A black hole can't emit anything – because it's black, more precisely because the interior is causally and perfectly isolated from the exterior. And that's why it can't emit the black body radiation, either. It can't have a nonzero temperature as measured from the color of this radiation – but this temperature would follow from a nonzero entropy.

In other words, Hawking quickly conceived an argument – his new brainchild – that was designed to kill one of his braingrandchildren (?), namely Bekenstein's idea inspired by Hawking's previous paper. Hawking had no problem to give life to a nephew-killer among ideas, if I haven't confused the family relationships. (You're invited to fix them.)

To make things worse, the new Hawking's brainchild has nearly become a double murderer. It has killed not only its nephew but it planned to kill its younger brother, Hawking's soon-to-be-published calculation of the Hawking black hole thermal radiation. Fortunately, children among ideas have teeth so if the knives used to kill them have loopholes, these children just jump through these loopholes, survive, and they're doing fine.

So Hawking has finally proven that his criticism against Bekenstein's formula was incorrect – and the formula may actually be proven by a combination of quantum field theory on curved spaces; and some basic universal macroscopic formulae in thermodynamics. I am pretty sure that the risk that Hawking has unjustly criticized Bekenstein has contributed to Hawking's desire to play with this question and check and recheck the claim the the radiation just couldn't exist. A statistical mechanical embedding of all these claims into a well-defined Hilbert space had to wait for 20 more years, for Strominger's and Vafa's string-theoretical insights.

It often happens in physics that certain persuasive arguments actually have some loopholes. The claim that "nothing can escape from the black hole" is a claim that may be strictly believed only if you insist on the exact validity of the classical spacetime geometry (and if you also ban things like the quantum tunneling – because the Hawking radiation may be interpreted as a quantum tunneling of a sort). However, in the full quantum theory of gravity, the radiation becomes possible, after all.

This is an example of a guess based on an approximation – that is actually rejected by the exact theory. Sometimes, the exact theory may modify the results of the approximate one not only by "small quantitative corrections" but it may change the answers "qualitatively", too. But Hawking has proposed another superficially sensible guess which turned out to be wrong, too. After he has derived the radiation and falsified his previous objection, he used the causality in the black hole spacetime again and argued that the thermal radiation itself cannot possibly depend on the initial state of matter from which the black hole was created. The information must be lost!

This claim doesn't assume "completely classical physics". The radiation is composed of electromagnetic quanta and other things – which clearly need a quantum theory. But the background geometry is still treated "sort of" classically and this fact is still sufficient for the no-go theorem to actually be incorrect. When the spacetime geometry is treated in the quantum way as well, and it has to be, the radiation may not only exist but it is capable of remembering all the information about the initial collapsing matter – the information is encoded in subtle correlations of the Hawking quanta even though this would be impossible in quantum field theory on a curved (classical) background.

The history of physics is full of stories in which physicists were sometimes excessively critical of their own ideas (e.g. Planck incorrectly thought that his light quanta in his derivation of the black body spectrum were just some bizarre auxiliary dirty trick he should be ashamed of that would be explained by something totally different later) – or they embraced an attitude that a straightforward, naive, somewhat egotist mortal would almost certainly not take. But good physicists – and I would hope that one may say good scientists in general (and perhaps many non-scientists, too) – often love to shoot down their own ideas and fall in love with their former foes' ideas and do all sorts of similarly "surprising" things if they suddenly see the evidence. And sometimes they do it even without sufficient evidence because it's a cool credible sign of one's own integrity if he can attack his own ideas. ;-)

I added a smiley face because at the end, I am convinced that such a reversed bias is a bias, too. Physicists can't afford to be biased in favor of their own ideas just because they're theirs; but they shouldn't be incredible hostile or skeptical towards their own ideas because they're theirs, either!