## Wednesday, January 04, 2012 ... /////

### Stephen Hawking: 70th birthday

Congratulations!

On January 8th, 2012, the most famous living scientist Stephen Hawking celebrates his 70th birthday. That's despite the fact that various doctors were predicting his imminent demise as early as 35 years ago.

I love Hawking's ability to show that the doomsayers' predictions may be ludicrous even in such situations and that life has many more ways to thrive than what various doctors may imagine in their narrow-minded skulls. I am sure that Hawking has the same sentiments. ;-)

Your humble correspondent has never co-authored a paper with Stephen Hawking but our collaboration distance is 2 because we share a co-author, Andy Strominger.

I have only met Stephen Hawking (I mean encounters when the distance is below 2 meters) in Santa Barbara 10 years ago – he gave a talk instructing the audience to get friendly with the ghosts (in quantum gravity) – but I didn't know how to talk to him.

My exposure to Stephen Hawking began when I was a high school kid. My mother told me that some of her (female) friends were reading a book by Stephen Hawking that I could be interested in. Of course, it was A Brief History of Time. I concluded that the book had to be really stupid if my mother's friends were reading it and I avoided it for almost a year. ;-)

While my sociological heuristic criterion to pick quality reading was pretty good and I still keep on using similar rules today, they're not flawless. And in that case, it was very far from a flawless rule, indeed! I understood that my initial conclusion – namely that Stephen Hawking was a media bubble created for the likes of my mother's friends – was very wrong about two years later when I started to understand the content of the scientific breakthroughs connected with Stephen Hawking's name.

Moreover, I understood that my negative conclusion was based on an incorrect assumption that my mother's friends have actually read the book. It seems very likely that much like most consumers who bought the product, they only used it to increase their IQs by putting the book into their bookshelves. ;-) This comment, namely that most consumers haven't read the book, comes from Hawking himself. His first bestseller has sold about 9 million copies. Be sure that when you succeed in a similar way, you won't die of hunger.

Path integral master

About 40-50 years ago, Stephen Hawking was working hard to become the world's top theoretical physicist. Slightly inspired by Richard Feynman, he became an amazing "Feynman path integral calculator". He could calculate lots of expressions linked to path integrals in his head. There were three elementary operations he could do instinctively: addition, subtraction, and the path integral.

What made Hawking somewhat special was that he was very good not only in quantum field theory as understood by particle physicists: he was doing lots of important research in general relativity, too. This pretty unusual combination has predestined him to become the first person who usefully merges these two mostly incompatible pillars of fundamental physics, namely QFT and GR.

Black hole thermodynamics

In the 1970s, Hawking would find various results in GR, like the conclusion that the area of black hole event horizons never decreases, an observation that helped Jacob Bekenstein propose that black holes did carry a huge entropy proportional to the area of the event horizon. Hawking also co-authored singularity theorems with Roger Penrose when they mathematically proved that under rather generic circumstances, a sufficiently dense configuration of matter inevitably leads to the birth of a black hole (including an event horizon and a singularity at the center).

Hawking finally did a calculation that was much more technologically sophisticated than other conceptual advances, including Bekenstein's vision: he calculated the fate of a quantum field in a black hole background. This led him to conclude that black holes aren't completely black: they are radiating thermal radiation whose temperature is proportional to the "acceleration" at the event horizon in some natural Planckian units.

(It was an example of a calculation done with excessive brain capacity. For example, it preceded the calculation of Bill Unruh (2,000+ citations) who repeated the same derivation of radiation in the Rindler space, i.e. in the flat spacetime as observed by a uniformly accelerating observer. Hawking could have done it directly in the nontrivial curved black hole background!)

One reason I didn't talk to Hawking in Santa Barbara 10 years ago was that there were other people, such as Gross and Witten, who may have wanted to talk to him. ;-) But this picture is actually from TIFR, India, 2001.

The typical wavelength of such thermal radiation is comparable to the black hole size so the corresponding radiation is extremely feeble for large black holes. But small enough black holes may radiate truly intensely and quickly (the temperature may be hot) which guarantees that all black holes ultimately evaporate away (if there's no more food around that they may eat).

See Hawking's most famous paper as a PDF file (5,000+ citations).

Indirectly, one may translate the known temperature to an even more fundamental thermodynamic quantity describing the black hole, namely the entropy. Even though Bekenstein and Hawking couldn't have found out what the entropy is by directly counting the microscopic states of some "atoms" that make up the given black hole, they could compute that the entropy is
$S = \frac{Ac^3k}{4G\hbar}$which would be written as $S=A/4G$ or $S=A/4$ by mature physicists. The number of "bits" that a black hole carries is close to the area of the event horizon $A$ expressed in Planck areas, about $10^{-70}\,\,{\rm m}^2$. This formula actually applies to charged and rotating black holes (much larger than the Planck scale) in any spacetime dimension.

Various formal methods have been proposed to find the result above as the logarithm of a number of microstates of some sort, or the logarithm of some volume of a phase space. But the first controllable calculation only occurred in early 1996 when Strominger and Vafa computed the entropy of a five-dimensional black hole in string theory. That result was generalized to many large multi-parameter families of black holes in string theory, including rotating, near-extremal, and non-extremal black holes. There's no doubt today that string theory produces the right value of the black hole entropy in all cases; after all, this is guaranteed by string theory's internal consistency.

Despite widespread lies claiming something else, string theory is also the only known quantum gravity framework that manages to pass this test. (Well, one may find working computations of black hole entropy in various AdS/CFT schemes that are not "really" superstring theory. I would still say that they are exotic vacua of string theory as long as they are consistent.)

One conclusion coming from Hawking's calculation – a conclusion that is pretty much incorporated to the basic strategy that Hawking used – is that the information about the matter that originally collapsed to create the black hole should be lost. It simply gets destroyed in the singularity and because the information cannot propagate faster than light, it can never influence the detailed properties of the majority of the Hawking radiation.

At the level of accuracy that Hawking applied, this conclusion ("information is lost") is inevitable. That's because the Penrose causal diagram above shows the basic causal structure of the spacetime, including the teeth of the singularity where the life of the information ends, and everything that occurs (including the process of Hawking evaporation itself) is just a small perturbation of the basic spacetime background above.

And Hawking has believed for decades that the qualitative outcome should remain unchanged even if we did a precise calculation. However, the developments in string theory started in the late 1990s have shown that every consistent theory of quantum gravity – i.e. every element of the set {string theory} – is much more clever.

In string theory, Hawking's approximate calculations actually hold and the conclusion "information is lost" generalizes to all orders. However, non-perturbatively, the theory simultaneously guarantees that the natural conclusion of quantum mechanics and its unitarity, "information cannot be lost", is finally upheld. Some weak, nonlocal features of the Hawking radiation – which is a form of quantum tunneling – guarantee that the Hawking radiation ultimately stores all the information about the initial object that collapsed into the black hole even though the "code" by which the information is stored is safely unreadable in practice.

Especially because of some papers by Juan Maldacena, Stephen Hawking officially admitted a few years ago that he was wrong. He formally surrendered in his bets in which he had claimed that "the information was lost" and published a not-quite-comprehensible (but still inspiring) paper that helped him to psychologically reconcile himself with the conclusion that the "information is preserved"; and that even allowed him to present himself as a co-discoverer of the fact. The second point left many fellow quantum gravitists puzzled. ;-)

At any rate, Hawking surely deserves a Nobel prize (and one of the exceptional ones!) for his discovery of the Hawking radiation, the first demonstration that the mysterious combination of general relativity and quantum field theory does imply some reliable results, nevertheless. Unfortunately, there are not too many light enough black holes around us and the Scandinavian tradition tells us that the results rewarded by the physics Nobel prize have to pass some very transparent experimental tests (unlike the results rewarded by the peace Nobel prize). So even though no sane physicist doubts that the Hawking radiation does exist, Hawking will probably never receive the prize he deserves.

No-boundary wave function of the Universe

There are of course many important papers that Hawking has written (or co-authored) and I don't even have to talk about the popular books. But let me mention one of them which may still be waiting for its most glorious days: the no-boundary wave function of the Universe that Hawking proposed together with Jim Hartle.

In this setup, one creates the Universe out of nothing and the wave function of the Universe whose topology is $S^3$ may be deduced from the Euclideanized path integral over the ball $B^4$ which is the interior of the three-sphere. As you may see, the birth of the Universe is a completely "smooth" and "non-singular" event in its history. When properly applied to all of string theory, a similar prescription should actually allow us to calculate not just the transition probabilities; but also the probabilities of various states of the Universe without any detailed knowledge about the beginning.

This Hartle-Hawking proposal also automatically incorporates a trivial point, namely that the earliest entropy of the Universe was zero.

Except for some bold stringy papers that remain enigmatic to most string theorists, people only know how to apply the Hartle-Hawking machinery in various crude approximate schemes, in various "minisuperspace approximations". That's a pity because many signs remain uncertain, these calculations seem relatively impotent, and there's not enough data to become certain about the right way to calculate the initial state of the Universe.

However, I believe that there should exist a machinery by which the Hartle-Hawking idea is applied to string theory and the resulting calculation could tell us everything about the "preferred compactifications". In other words, the Hartle-Hawking program should ultimately solve the "vacuum selection problem" (claimed by many to be the arena where the anthropic principle shows its muscles). It's hard to get solid results and I don't know how many physicists are spending a substantial percentage of their research time by similar considerations. But I still feel that the number of bold physicists doing this task is way too low. More precisely, it would be great if I learned that I am not alone. ;-)

Weightless astronaut Stephen Hawking. A collaborator of the two of us whose name won't be mentioned here was able to use his detailed knowledge to calculate the trajectories that the saliva had to choose during the event pictured above. ;-)

Festivities: summary

See The Guardian where a few physicists who know him really closely offer their stories and intimate details or 213 articles on TRF that contain the word "Hawking" (not a bad score), including a future article on Gibbons-Hawking and Euclidean gravity.

You may want to be hired for a \$38,500-per-year job of Hawking's technical assistant. Without a manual, you have to be able to maintain Hawking's voice system that he uses to speak, control a TV set, and command the Universe.

At any rate, I wish Stephen Hawking – a physicist, author, father, and astronaut – a few more decades or centuries that are ahead of him.

Bonus: Kaley Cuoco's decision

As a bonus, there's some good news for physics and a bad news for TV. Kaley Cuoco – known as Penny in The Big Bang Theory – will leave TV and become a physicist. She plans to study psychics in order to prove that blondes are not that stupid. Click the picture above for the story.