Stephen Hawking got a flat tire

...but sang the Big Bang Theory theme song...

Just like your humble correspondent yesterday, Stephen Hawking got a flat tire which is why he couldn't be at the Comic Con. At least, he prerecorded this monologue:



He also sings the theme song of TBBT, a very successful sitcom of CBS that is nominated for Emmy 2013 much like Sheldon Cooper and Amy Farrah Fowler.




Much like Sheldon Cooper, I am the last drafted man when teams are being divided in collective games – unless there is someone on the wheelchair. But it seems likely that Stephen Hawking would be drafted ahead of me, too. ;-)




If you listen to the monologue carefully, you will also notice that Hawking announced a new book and a new movie, both of them primarily about himself. You may already buy the movie today for $3,900.

Via Daily Mail (where you may learn the theater by which the TBBT actors sold the message from Hawking)

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Michio Kaku's confusing Higgs remarks

I partly but not quite agree with Sean Carroll's and Matt Strassler's criticisms of this CBS interview (HTML) with Michio Kaku, a co-father of string field theory and a sometimes excessively lively popularizer of physics, not to mention more general aspects of science fiction marketed as science:



Sorry if CBS inserts half a minute of ads.

It seems that Michio Kaku who watches The Big Bang Theory on the same TV station – together with 20 million Americans in average – couldn't resist to incorporate the Big Bang to his new story about the Higgs boson. And the result of his creative artistic work sounded strange to physics ears.

However, see also Phil Gibbs' take on this which is closer to mine.




The fuse behind the interview was the CERN announcement a few days ago that the 126 GeV Higgs-like particle really behaves like the Standard Model Higgs boson. The agreement is striking but I think that this "event" has been heavily overhyped.

We've been learning that the new particle is extremely similar to the Standard Model Higgs boson for more than a year and we have had very strong prior reasons to think it's the case, anyway. Moreover, the evidence that the particle behaves in the Standard-Model-prescribed ways was growing gradually and there wasn't any real eruption a few days ago.




Michio Kaku says that the event was huge and champagne was flowing in physics departments throughout the world. I am not sure. What I am sure about is that this was the legitimate description of the excitement on July 4th, 2012. Champagne was surely flowing across the halls of the Institute for Advanced Studies in Princeton, New Jersey. If you care about the microscopic details, Nima Arkani-Hamed paid for the beverage and Robbert Dijkgraaf, the director, was the waiter. Yes, it seems like Ed Witten, Juan Maldacena, and others had to be satisfied with the role of rank-and-file drunkards.

So aside from the confusing timing, Kaku's colorful description of the excitement sort of conveys a true story. And yes, Michio Kaku may be expected to make similar stories sound a little bit more spicy.

Also, CBS used the term "God particle" and Michio Kaku actually mentioned that the phrase usually makes physicists cringe. Well, as you know, I have no real problem with this phrase and I even think that it's arguably more polite and fair when it comes to the credit that should be given to several fathers of the "Higgs" mechanism.

Bizarre claims about cosmological links

But the most controversial point of the interview is the claim that the Higgs discovery helps us to understand how the Universe began. Michio Kaku even says that the Higgs boson is what gave the bang to the Big Bang and that it is the missing piece of the Big Bang theory, and so on. These highly unusual comments are combined with the usual remarks that the Higgs field gives masses to all other particle species.

Well, a physicist will have a trouble to understand why exactly the Higgs boson should be responsible for the ignition of the Big Bang. The Higgs condensate was born and it was immediately important a trillionth of a second after the Big Bang when the electroweak phase transition took place. But all other fields were very important when the Universe was dense and hot, too. There have probably been many other phase transitions right after the Big Bang, too. So why is the Higgs field getting these exclusive rights to boast the authorship of the Big Bang?

As several later sentences by Kaku reveal, Kaku justifies his idiosyncratic hype by the Higgs boson's being a relative of the inflaton. And yes, the inflaton is what probably gave the bang to the Big Bang. In fact, five years ago, I discussed some problematic yet intriguing models in which the Higgs boson actually is the inflaton (a paper with 250+ cits). For these models to work, there has to be an uncommon interaction term in the Lagrangian, the squared Higgs multiplied by the Ricci scalar:\[

\LL_{\rm tot} = \LL_{\rm SM} -\frac{M^2}{2} R - \xi H^\dagger H R

\] The usual minimal theory has \(\xi=0\) but for \(\xi\) of order tens of thousands, you start to get a behavior in which the Higgs field may behave as the inflaton, too. Well, these models are problematic (the Lagrangian above mixes a nicely renormalizable Standard Model with the non-renormalizable gravity treated as a field theory and various extra problems result from that) and they have surely not been demonstrated at the LHC. On the other hand, I don't think that the LHC has brought us the relevant data that would exclude these couplings to the spacetime curvature, either. Am I wrong? I realize that the LHC has surely excluded many other, more conventional yet non-standard non-gravitational couplings of the Higgs field.

But even if we ignore these unpopular models, I must sympathize with Michio Kaku's general point that the Higgs boson is the first fundamental scalar we have discovered in Nature and it belongs to the same family as the (still hypothetical) inflaton. And the scalar fields are those that may get vevs so they're naturally more important than the spinning particles for various phase transitions and other changes that have been shaping the character of the Cosmos around us.

In particular, fundamental scalar fields are mundane in string theory and because assorted non-string theorists have proposed various memes and would-be reasons why fundamental scalar fields shouldn't exist in Nature at all (think about the philosophy beyond preon theories of numerous kinds), the discovery of the Higgs boson is a positive point for string theory even though, of course, string theory is not needed to explain the existence and the behavior of the Higgs boson. However, in a non-stringy setup, one is offered various reasons why such fields could be forbidden in general while string theory has always unequivocally stated that scalar fields should exist.

So I don't think that there exists a justification to say that the Higgs boson (or field) found at the LHC is the key particle (or field) that launched the Big Bang.

On the other hand, I do think that the Higgs field (and its quanta) did play a somewhat elevated role right after the Big Bang, especially during the electroweak phase transition. The cosmological spin of the Higgs boson discovery is certainly an unusual rhetorical exercise but I would personally not trash Michio Kaku just for saying something that is unusual – because within the error margins that are unavoidable in similar shows and proclamations addressed to the laymen, his story isn't qualitatively less true than the other things that are often being said about the Higgs boson (and other things) in the popular media.

In fact, I can even turn Kaku's claim that "the Higgs boson is the last missing piece of the Big Bang theory" to a valid claim by making just one modest modification. Replace the "Big Bang theory" by "the standard model of cosmology" which is pretty much a refined synonym. The standard model of cosmology contains the usual solutions to Einstein's equations of general relativity but, in a less central way, it also incorporates the Standard Model of particle physics. The latter is needed to understand many events right after the Big Bang. Because the Higgs boson was the last missing particle of the Standard Model of particle physics, you may perhaps also say that it was the last missing piece of the standard model of cosmology – and therefore the Big Bang theory, too.

Well, I needed a long explanation to partially justify Kaku's words but the same is true for many other popular "licenses" that are constantly repeated by the popularizers of science. The only difference is that everyone knows the "partial justification" of the usual stories but because Kaku was the first major pundit who have spun the Higgs boson discovery in this cosmological way, almost no one understands the justification for his oversimplified story. I tried to give you one. Be sure that Kaku's cosmological interpretation of the Higgs is much more justifiable by physics than Carroll's cosmological interpretation of the origin of the arrow of time!

So I would give Michio Kaku C– for accuracy but A– for originality. ;-)

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Lost City Raiders, a B movie

My newly favorite Czech TV channel, Prima Cool (which airs not only The Big Bang Theory), was broadcasting a silly 2008 U.S.-German-Austrian science-fiction catastrophic global warming film, Lost City Raiders, tonight.

If you have 98 minutes, the whole movie is right here on this blog.



I kind of enjoy watching catastrophic movies – and view it as 1% of my job, too. In this case, I feel satisfied and you should also feel satisfied because this cheap $6 million movie scored the worst grades you may think of, see e.g. 39% at IMDb.

The rest of the blog entry is full of spoilers.




It's year 2048, a power of two, and the sea level has increased by something like 15 meters (the reality will be less than 0.1 meters) which, the authors believe, puts about 1/2 of North America (mostly the Eastern 50%) under water (in reality, even 15 meters would only submerge a tiny percentage of the land).

So they realize that the IPCC was right – in fact, the catastrophic global warming was worse than previously thought, even when they said that it was worse than previously thought – and a clever cardinal from the New Vatican (which is the ordinary Vatican with some buildings replaced by floating islands above the former city) figures out how to save the Earth. They must find the staff of Moses in the flooded streets of the New York City that became a part of the ocean. A man, a scuba diver who later dies – but has two (adopted) sons – accepts the challenge and the sons ultimately complete the task (despite explosives and puzzles in the churches) and meet with their tough babes in a restaurant in order to emit a few "wise" words about the future.

You may think that the effects are cheap and unspectacular but it's probably nothing compared to the predictable and stupid plot. The movie was addressed to the most undemanding audiences and once again, we must feel some kind of a satisfaction when we see that a politically correct theme and attitudes aren't enough for success. Thank God – even though in some cases, it does look like these conditions are sufficient for success.

When I said all these critical words, I must say that I have enjoyed the movie as entertainment. My rating is 60%.

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P.S.: Some details. Moses' scepter is originally supposed to be in a Vatican library. It's not there: a member of the Order of the Temple stole it 800 years ago. So it could be in his grave in Dresden, DDR. They go there but find out that they have a competition: the former girlfriend of one of the sons, Giovanna. She's a scuba diver and self-taught geologist who tries to lower the global sea level by whole millimeters by detonating small holes in the ponds. ;-)

She's hired by an even more hopeless crackpot, the greatest owner of the land in the world, who wants to slow down the sea level rise, too. He has two methods: to hire Giovanna as a researcher who creates holes in the Mediterranean Sea so that the ocean pours into these holes (it sounds similar to some policies proposed by the IPCC); and to hire her to find the scepter, too. Well, a competition for the father and two sons. The rich guy who hired Giovanna has a spy in the Vatican, another cardinal. In Dresden, the graves have double floors etc. The father dies there after an explosion when a rock falls upon him.

After his death, the sons bring some historical object from the grave to the "good cardinal": the father asked them to do so. However, they want to abandon the risky job of looking for the scepter. That changes when the good cardinal tells them that the good cardinal, their adoptive dad, as well as their (late) biological fathers (archaeologists) were members of a special cult looking for the scepter.

Meanwhile, it also turns out that the rich guy, Niklas, has sold his land. He actually wants to raise the sea levels and then turn it back when he cheaply buys the land beneath the sea level, and so on. He wants to destroy almost everything and control the world. His cardinal-spy is caught at some time and his motivation was even worse: he wanted to complete the end of the world, a job that God began 2 millenniums earlier. ;-)

The sons who have decided to continue in their three fathers' mission hire a busty waitress-mechanic, Carol, who gets a new coil for their boat, avoids a fat innkeeper who wants sex with her because an old placard for his pub only covers 1/2 of the value of the old stolen coil (she abruptly becomes a sweetheart of the other brother who didn't have sex with Giovanna), and they go to see the grave of Richard the Lionheart – it may be at 3 places. Giovanna and the rich guy are there before them and find the scepter. Giovanna becomes sure that the rich guy is a villain a minute before he closes her body to the grave together with Richard the Lionheart so that some archaeologists may find the bones of Richard and Giovanna in the year 3048.

When the grave with Giovanna and Richard is thrown to the ocean, it just happens that her former boyfriend is swimming around. He opens the box, saves the babe, and they easily overtake the boat of the richest guy in the world. ;-) Once they're in charge of the scepter, they notice that it works as a perfect projector. It shows a movie about Pangaea and some "electromagnetic intersections" around the Earth. By a complete coincidence, Giovanna who watches is is the only person in the world who understands these electromagnetic intersections. So their skepticism goes away. (Giovanna starts to tell everyone that science is constantly failing because they used to be 9 planets and now there are just 8 planets – surely a hot topic in the year 2048; her anti-science interpretation of the redefinition of a "planet" remains unchallenged).

They sail to one of the intersections and find out a cave. The scepter is also a key to a lock which opens a sophisticated lab. Inside the lab, there is a convenient 13,000-kilometer-deep (about 3 meters in diameter) hole through the Earth, too. :-) The plans on the walls prove that the mechanism is nothing else than what Giovanna has been working on (but a greater realization of it) – a plan to lower the sea level. The door closes, confines them, and for some time, they're afraid they would die while they could save the land. But 3 of the 4 young people escape when the door temporarily opens.

The last guy has to return to the lab in the cave when he finds out that the evil cardinal – who escaped from the New Vatican after he was outed by the good cardinal as a spy (he instantly jumped to the New Vatican waters) – tries to stop the process of the saving of the Earth. They fight for a while. Finally, the son manages to throw the cardinal to the 13,000-kilometer-deep hole and save the scepter. He restores the process and thinks that he will die. But fortunately, he saves his life, too.

The process is activated after a while. A huge hole is created in the Earth and a big fraction of the world ocean pours there – some kind of giant waterfalls. Well, as the two couples are drinking champagne in the restaurant, they're told by the good cardinal on the screen of a 2008-style cell phone that the sea level dropped by 10 meters in the Mediterranean Sea. They don't want to be annoyed by such details when they are having fun. The cardinal tells them that the sea level in other parts of the world ocean isn't dropping but it seems that they will have some extra job, to go to a few dozens of other similar spots where they have to produce a similar huge hole into the Earth to stop the flood.

All the previous activities done for the cardinal and the scepter cult were unfunded. So I suppose that the rest of the activity needed to save the Earth didn't receive a eurocent of the EU taxpayers' or New Vatican money, either. Obviously, they saved the world in a cheaper way than the UNFCCC and the Kyoto protocol.

As I have said, I developed the pleasure of watching and enjoying movies even if every second of them is completely illogical nonsense, so I liked the film despite – and perhaps partly because – of its immense stupidity and lack of realism. Realistic if not mundane yet fictitious movies and novels is something I can't stand; it's the socialist realism that I am immensely bored by (independently of the politics).

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Movie: 2012

One day later, on Sunday, I watched another catastrophic movie called 2012 and shot in 2009. Its budget was $200 million, about 30 times more expensive than the Lost City Raiders, but it was more chaotic and even more silly from a scientific viewpoint.



Full movie

The Mayan prophecy about December 21st, 2012 gets realized in a bizarre way. The Earth's core gets quickly hot and the surface is cracking, and so on. The reason behind all these phenomena? The neutrinos from the Sun "mutated" and became equivalent to microwaves. Holy crap. Didn't they also wanted to say that neutrinos started to have sex with bunnies? ;-)

Alternatively, couldn't they have just asked a physics grad student to invent something slightly less dumb if they already pay $200 million for the movie so that all the movie staff wouldn't be identified as a gang of uneducated naive imbeciles on physics blogs?

With this being said, it was clear that the effects were much more professional and expensive than in the Lost City Raiders – and I was crying like a small baby.

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Leonard Susskind on Higgs boson

If you have 75 minutes, you may want to listen to the July 30th, 2012 post-discovery talk about the Higgs boson by Leonard Susskind that was addressed to the curious pensioners in Palo Alto, California.



At the beginning, he reminds you that you have already heard that the Higgs boson – called the Weinberg toilet by Sheldon Glashow – is the best thing since the invention of the flush toilet.

Instead, he discusses the quantization of spin and he shows you his hat and semitechnical properties of the Higgs potential, the relationship between fields and particles, the impact of the vacuum condensate (compared to dipoles) on other particles, the role of the uncertainty principle for the finite i.e. short range of the weak force.




So as you can check, Susskind focused on different issues than toilets.

Incidentally, because the Higgs boson seems to behave in the single a priori most likely way – the plain vanilla, Standard Model way (its deviations from the SM behavior have apparently faded away and shrank to an undetectably modest level) – journalists are saying that maybe, it was just a summer romance.



Clearly, we will have to wait for quite some time before some hypothetical exotic qualities of the Higgs boson become visible. Some other discoveries may be done earlier than that, independently of the Higgs sector. I find the English term "plain vanilla" for "boring common things" somewhat bizarre because vanilla is a flavor extracted from orchids in the exotic country of Mexico. :-) Moreover, the extract of vanilla costs about $30 per kilogram – buy via amazon.com – which is as expensive as the best type of South Indian coconut oil that I consider the "fanciest part of my food" now.

Nima on the Higgs

Concerning the Higgs boson talks, you should also watch this IAS talk by the Milner Prize winner Nima Arkani-Hamed:¨

The Inevitability of Physical Laws: Why the Higgs Has to Exist (live or download)

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Anthony Watts' television channel

Al Gore has a new TV competitor

Last year, Al Gore's Climate Parody Day spent millions of dollars and attracted a few thousand viewers in the whole world who watched the boring show for a few minutes in average.




Because the man behind the world's most viewed climate website, Watts Up With That (150 million views or so), apparently thinks that it was a success (sorry for this comment, Anthony, but I just couldn't resist), he wants to attract a few percent of Gore's audience and that's why he has established a new television channel to compete with Current TV, Climate Parody Day, and Fox News. Here is the video:



Free live streaming by Ustream

Before the main program begins, you may look at a monoscope with an assertive monotonic sound.

Both Gore's Climate Reality Day II and Watts' competing program begin tonight, U.S. time. Already now, you may compare a funny dirty reality weather forecast by Al Gore with the temperatures in the real reality – most of the U.S. is under the freezing point. ;-)

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The holographic principle

The newest episode of The Big Bang Theory that was aired last night was called "The Holographic Excitation" (S06E05).

It's pretty cool that a TV sitcom manages not only to show a hologram but Leonard Hofstadter was even allowed to present a rather accurate definition of the holographic principle in quantum gravity i.e. string theory (you won't find it in any popular science TV program that claims to explain modern physics!). And as a result, he was able to have an intercourse with Penny right after she wore some glasses and was shown a moving holographic pencil and a moving holographic globe. (Later, he repeated the same achievement using Maglev.)

(And I even think that Prof Nina Byers whom I know rather well walks behind the main actors around 9:15. This theory seems to make sense because she's at UCLA, much like the TBBT science adviser David Saltzberg.)



The holographic principle of quantum gravity is an incredible example of the ability of the quantum gravity and string theory research to teach us things we really didn't and perhaps couldn't anticipate, force us to modify or abandon some prejudices, and adopt ideas about the unification of ideas and concepts that philosophers couldn't have invented after thousands of years of disciplined reasoning but physicists may be forced to realize them if they carefully follow the mathematical arguments sprinkling from a theory that they randomly discovered in a cave.

But let's return half a century into the past. Holography started in "everyday life physics" in the late 1940s.




So let us begin with this exercise in wave optics that has nothing to do with quantum gravity or string theory so far – but you will see that it exhibits a similar mechanism that is apparently "recycled" by the laws of quantum gravity.

Dennis Gabor's 3D images

Hungarian-British physicist Dennis Gabor was playing with X-ray microscopy and invented a new technology that is rather cute. One may create two-dimensional patterns on a piece of film which, when illuminated by a laser, create the illusion of a three-dimensional object floating in the space around it. I saw my first hologram sometime in 1985 – it was a Soviet one, the mascot of the 1980 Olympics in Moscow – in the National Technological Museum in Prague where we went to a school excursion. I couldn't believe my eyes. :-)

The basic setup involves a monochromatic laser beam, some interference, and a photographic plate. First, we must create the hologram – a film with strip-like patterns that don't resemble the bear at all but which allow the bear to jump out once you use another laser. Fine. Let's create a hologram.



You see that a monochromatic (one sharp frequency) laser beam is coming from the upper left corner. Each photon's wave function gets divided into two portions by a beam splitter – note that the wave function has a probabilistic interpretation for one particle but if many photons are in the same state, it may be interpreted as a classical field.

Two parts of the wave are moving from the beamsplitter. One gets reflected from a simple mirror. More interestingly, the other one gets reflected from the object we want to see on the hologram. They interfere – these waves are recombined – in the right lower corner and they create a system of interference strips on the photographic plate.

We have created a hologram and now we may sell it. What will the buyers do with it?



This interference pattern may be shined upon by a "reconstruction beam" of the same frequency and what we see is a virtual image behind the plate. You may actually move your head and eyes and the position of all points on the image are moving just like if the virtual image were a real object. So it's not just a stereographic image offering two different pictures for the two eyes: the hologram is ready to provide the right electromagnetic field regardless of the direction from which you observe it! If you want to see the right face of the object, you move your head to the right side, and so on.

Why does it work? It's very useful to think about the hologram for a simple object, e.g. a point at a given distance. The total wave function on the photographic plate parameterized by coordinates \(x,y\) is given by \(U_O + U_R\) where \(U_O\) is the complicated wave reflected from the object and \(U_R\) is the simple reference beam reflected from the plain mirror.

You may imagine that for an object being a point, \(U_R=1\) and \(U_O(x,y)=\exp(iks(x,y))\) where \(s\) is the distance between the point (the real object we want to holographically photograph) and the given point \((x,y)\) on the photographic plate. The wave number is of course the inverse wavelength, \(k=2\pi/\lambda\). The sum \(U_R+U_O\) gives you some simple concentric circles (with decreasing distances between neighbors) around the point on the plate that is closest to the photographed point. Fine. The total intensity – how much the point on the film changes the color – is given by \[

T \sim \abs{U_O}^2 + \abs{U_R}^2 + U_R^* U_O + U_O^* U_R.

\] I omitted an unimportant overall normalization and used the symbol \(T\) for this quantity because the darkness of the point of the film will be interpreted as the transmittance, the ability of the place of the hologram to transmit the other, reconstruction beam when we actually want to reconstruct the image.

For a simple explanation why you will see the reconstructed virtual image, assume that the reference beam \(U_R\) is much stronger than the object-induced wave \(U_O\) i.e. \(U_R\gg U_O\). So the total wave function may be written as \[

U = 1 + \varepsilon \exp(iks)

\] where \(\varepsilon\) is small, \(\varepsilon\ll 1\). You see that the squared absolute value is\[

T \sim |U|^2 = 1 + \varepsilon \exp(iks) + \varepsilon \exp(-iks) + {\mathcal O}(\varepsilon^2).

\] Imagine that this transmittance is just multiplying another simple reference beam \(U_R\to T \cdot U_R\) and produces some electromagnetic field in the vicinity of the hologram. For the sake of simplicity, assume \(U_R=1\) again. It's only \(U_O\) that carries the "complicated information about the photographed object" but we still need some nonzero \(U_R\).

You may see that \(T\) is almost the same thing as \(U\) except that it has an extra, complex conjugate term. So the electromagnetic field in front of the hologram (on the side with the air) will be the same field as the electromagnetic field we used to have when there was a real object in front of the hologram plus some complex conjugate term. One of these terms creates a nice virtual image behind the plate because it has a similar mathematical structure and when the fields have the same values, we see the same thing.

The other term induces the feeling of another copy of the object – a real image. It's because all the waves should also be multiplied by the universal time-dependent factor \(\exp(-i\omega t)\) (before you interpret the real and imaginary value of the overall sum as the electric and magnetic fields, respectively, kind of) and the complex conjugation is equivalent to \(t\to -t\) which means that the wave is kind of moving backwards in time which is effectively equivalent to moving from the other side of the mirror.

So when you look at the hologram, you actually see one virtual image behind the plate and one real image in front of the plate (which may overlap with your head). I don't want to figure out which term is which because odds would be close to 50% that my answer would be wrong. To be sure about the answer to this not-so-critical question, I would have to decompose the electromagnetic wave to the electric and magnetic components, consider \(x\) and \(y\) polarizations, be careful about the spatial dependence and all the signs, etc. But things clearly work up to this "which is which" question that I am not too interested in.

In this brute calculation, I have neglected the \({\mathcal O}(\varepsilon^2)\) terms which indicates that the hologram will be badly perturbed if \(\varepsilon\sim {\mathcal O}(1)\) but a more accurate analysis shows that the result won't be too bad even if you include these second-order terms. At any rate, I have created a virtual image of a point! By the superposition principle, you are allowed to envision any object to be composed of many points (perhaps as an "integral of them") and add the terms \(\exp(iks_P)\) from each point \(P\) and you get the idea how it work for a general object.

There exist generalizations – colorful holograms, perhaps moving holograms and holographic TV, and so on, but I don't want to go into these topics on the boundary of physics and engineering. Everyone knows that holograms are cool. What's important for us is that they store much more than some two-dimensional projections of a 3D object as seen from one direction or two directions; they store the information about the 3D object as seen from any direction (in an interval). They're the whole thing.

Instead of discussing advanced topics of holography in wave optics, we want to switch to the real topic, the holographic principle in quantum gravity.

The holographic principle

In the research of quantum gravity, the notion of holography was introduced by somewhat speculative but highly playful papers by Gerard 't Hooft in 1993 and Lenny Susskind in 1994. Charles Thorn is mentioned as having suspected similar ideas for years.

It may sound unusual ;-) but Lenny Susskind's paper was the technically more detailed one, getting well beyond the hot philosophical buzzwords. Susskind also suppressed some unjustified and unjustifiable "digital" comments by 't Hooft who had written that the information had to be encoded in binary digits (bits). Of course, there's no reason whatsoever why it couldn't be trinary digits, other digits, or – much more likely – (for humans and computers) some much less readable but more natural codes.

What's the basic logic behind holography in quantum gravity?

In classical general relativity, a black hole is the final stage of the collapse of a star or another massive object. Because the entropy never decreases, as the second law of thermodynamics demands, the "final stage" must also be the stage with the maximum entropy. So the black hole has the highest entropy among all bound or localized objects of the same mass (and the same values of charges and the angular momentum). I emphasize the adjectives "bound or localized" because delocalized arrangements of particles with a given total energy – e.g. the Hawking radiation resulting from a black hole that has already evaporated – may carry a higher entropy (that's inevitably the case because the process of Hawking radiation must be increasing the total entropy, too).

But we've known from the insights by Jacob Bekenstein and Stephen Hawking in the 1970s that the black hole entropy is\[

S_{BH} = \frac{A}{4G}

\] in the relativistic \(c=\hbar=1\) units. It's one-quarter of the area of the event horizon \(A\) in the units of the Planck area. In normal units, you must replace\[

G \to l_{\rm Planck}^2 \equiv \frac{G\hbar}{c^3}.

\] So the maximum entropy of a bound localized object of a given mass is actually given by the area of the black hole of the same mass. Because you can't really squeeze the matter into higher densities than the black hole, the black hole is also the "smallest object" that may contain the given mass.

To summarize, we see that the black hole is the "highest entropy" object as well as the "geometrically smallest" object among localized or bound objects of the given mass. It follows that it also maximizes the "entropy density" (entropy per unit volume) among the localized arrangement of matter of the same total mass. But the entropy carried by a black hole is only proportional to the surface area in the Planck units, \({\mathcal O}(R^2)\), so the entropy density per unit volume – the latter scales as \({\mathcal O}(R^3)\) – is therefore going to zero for large black holes i.e. for large masses or large regions.

The maximum density of entropy or information you may achieve with a given mass is actually going to zero if the mass is sent to infinity. If you try to squeeze too many memory chips into your warehouse, they will start to be heavy at some point and will gravitationally collapse and create a black hole which will have a certain radius – either smaller than or larger than your warehouse. At any rate, this black hole will only be able to carry \(1/4\) of a nat (a bit is \(\ln(2)\) nats) of information per unit surface area (by the surface, I mean the event horizon).

We see that the maximum information is carried by a constant density per unit area rather than the unit volume. You should appreciate how shocking it is. In some sense, it was completely unexpected by virtually all experts in the field. Quantum field theories predict some new phenomena at a characteristic distance scale. For example, Quantum Chromodynamics (QCD) says that quarks like to bind themselves into bound states where their distance is comparable to the QCD length scale, about one fermi or \(10^{-15}\) meters. So by the dimensional analysis, the only sensible "density of information" we may get in QCD is "approximately one bit per cubic fermi" or per "volume of the proton".

People would expect a similar thing in any QFT – which was mostly right – but they thought it would also hold in quantum gravity. So quantum gravity may achieve "one bit per Planck volume". But that was wrong. You see that the previous paragraph assumed a bit more than the dimensional analysis: it also implicitly and uncritically postulated that the information is proportional to the volume. This assumption followed from locality. But this assumption breaks down in quantum gravity where the information only scales as the surface area.

Because the "proportionality to the volume" is linked to "locality" – each unit volume is independent from others – the violation of the "proportionality of the information to the volume" that the holographic principle forces upon us also means that locality is violated, at least to some extent. And indeed, this violation of the locality is a fact responsible for the resolution of other puzzling questions in quantum gravity, too. In particular, some tiny and hard to observe but nevertheless real non-locality occurs during the evaporation of the black hole which is why the information may get from the black hole interior to infinity, after all – even though classical general relativity strictly prohibits such an acausal export of the information (locally, it's equivalent to the superluminal transport of information which was already banned in special relativity). In quantum gravity, this "ban" is softened because the information may temporarily violate the rule in analogy with the quantum tunneling. In fact, the black hole evaporation is a version of quantum tunneling.

Whether the holographic principle was real and what it exactly it meant and what it didn't mean remained a somewhat open question for 3 more years or so. However, at the end of 1997, Juan Maldacena presented his AdS/CFT correspondence which is a set of totally controllable mathematical frameworks in which holography holds. The information about a region – namely the whole anti de Sitter space – is stored at the boundary of the region – which is the asymptotic region at infinity which nevertheless looks like a "finite surface of a cylindrical Penrose diagram" if you use the language of Penrose causal diagrams.

The holographic principle surely captures the right "spirit" of quantum gravity but it is a bit vague. The AdS/CFT correspondence is a totally well-defined "refinement" of the holographic principle but it is arguably too special. Nevertheless, one must be careful about deriving potentially invalid corollaries of the holographic principle in other contexts.

For example, if you replace the anti de Sitter space by a finite-volume region of ordinary space, it seems clear to me that the holographic principle will only be true in some rather modest sense: it will be true that the entropy bounds hold. You can't squeeze too much entropy into a given region. However, if you will try to find the "theory on the boundary" that is equivalent to the evolution inside the region, you will find out that such a theory on the boundary "exists" – but the existence of such a theory is just an awkward translation of the ordinary evolution to some artificial degrees of freedom that you placed on the boundary.

What is special about the AdS/CFT correspondence is that the theory on the boundary is a theory of a completely normal type – namely a perfectly local, conformal quantum field theory. In fact, the boundary theory is more local than the gravitational theory in the bulk – because we just said that the gravitating theory in the bulk must be somewhat non-local. I am confident this fact depends on the infinite warp factor of the AdS space at infinity and won't hold for finite regions. In other words, I think that the "holographic theory living on a boundary" of a generic finite region won't be local in any sense – the boundary still has a preferred length scale, the Planck length, and other things so it is surely not conformal etc. And because it won't be local, it won't be simple or useful, either.

So one shouldn't generalize the holographic principle as seen in the AdS/CFT correspondence too far and too naively.

Lessons

In the 1970s, people got used to Ken Wilson's "Renormalization Group" inspired thinking about all effective field theories. Each theory predicted some phenomena at a characteristic length scale. The third power of the length scale gave us a characteristic volume. And one could expect roughly one nat (or bit) per one characteristic volume. It was nice, it made sense, it has lots of applications.

But Nature sometimes has surprises in store and quantum gravity had one, too. You may still use almost the same logic – one nat per unit region – but the region must actually be measured by its surface area, not its volume. So quantum gravity tells us that one of the spatial dimensions may be thought of as an "artificial" or "emergent" one and other mechanisms supporting this general paradigm have appeared as well.

A brutally arrogant yet extremely limited physicist who really sucks – think of Lee Smolin, for example – may think that he has all the right ideas how the final theory should look like from the beginning. Except that none of them works (except as tools to impress some stupid laymen). But other physicists who are much smarter but much more modest may see that all Smolin's prejudices are just wrong and Nature's inner organization is much more clever, creative, surprising, and forcing us to learn new concepts and new way of thinking more often than Smolin and many others would expect. One must still be ingenious or semi-ingenious to discover some important wisdom about Nature – e.g. holography and the AdS/CFT correspondence – but Nature just doesn't appreciate men who try to paint themselves as wiser than herself. Science is the process of convergence towards Her great wisdom; it is not a pissing contest in which idiots such as Lee Smolin try to pretend that they're smarter than Nature.

The story of the holographic principle also shows us that Nature recycles many ideas. The fields defined on the boundary CFT in the AdS/CFT correspondence literally emulate the waves \(U\) and \(T\) that I mentioned in the discussion of the "ordinary" holography by Dennis Gabor.

And the story of the holographic principle is another anecdotal piece of evidence in favor of the assertion that string/M-theory contains all the good ideas in physics. 't Hooft and Susskind, building on the work by Bekenstein, Hawking, and others, had some "feelings" about the right theory of quantum gravity and there had to be something right about them. And indeed, string theory showed us that they were mostly right. Because string theory is a much more mathematically well-defined a structure than "quantum gravity without adjectives", it also allowed us to convert the philosophical speculations into sharp and rigorous mathematical structures and equations and decide which of the philosophical speculations may be proven as meaningful ones and which can't.

The holographic principle is also another step in the evolution of physics that makes our theories "increasingly more quantum mechanical". While the spacetime remains continuous, we see that the information in a region may be bounded in unexpected ways and a whole dimension of space may be emergent. Needless to say, the equivalence between theories that disagree about the number of spacetime dimensions is only possible if you take the effects of quantum mechanics into account.

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The Higgs boson observation: Sheldon hires a hottie

American readers shouldn't forget to watch the TV's #1 comedy, the 3rd episode of 6th season of The Big Bang Theory at 8 pm tonight. The Biden-Ryan vice-presidential debate begins at 9 pm ET (update: video).



It's called "The Higgs Boson Observation". I guess that the fathers of the sitcom were speculating about the Nobel prize so they chose a Higgs-related name of the episode for the Nobel prize (and Nobel-related content of the episode: Sheldon wants to determine whether he found the Higgs boson before Higgs etc., probably not). If so, they were not the only ones whose guess was wrong.




In the episode, Sheldon Cooper hires a young female assistant, Alex Jensen. Imagine what it may do to Amy Farrah Fowler. Howard Wolowitz at the International Space Station feels homesick, especially when it comes to the terrestrial gravity.

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BBC: Who's afraid of a big black hole?

Another episode about fundamental physics of the BBC 2 "Horizon" program, featuring people such as Andy Strominger (in a dark classroom of the Jefferson Lab and in his office), was aired in November 2009.




Here's the 59-minute video:



At the beginning, they edit a few interviews so that all the physicists say that no one understands black holes. A little bit over the edge but funny.

After 5:00, they switch to an astronomer who explains what stars and black holes are. He believes that a bright star went supernova and then it became a black hole because we see nothing there. ;-)

They switch to theorists at 8:40, Kaku, Strominger, Tegmark... History of black holes from Einstein. Kaku under skyscrapers about GR and gravity. Funny ancient TV "popularizations" of GR. Comments about black hole – hydrodynamics link. Tegmark tortured by waterfalls; nothing as dramatic as my talk about black hole event horizons while skydiving. ;-)

At 16:05, Tegmark says that we know that you may perfectly survive the crossing of the event horizon; no firewalls here. Inner horizon of a rotating black hole. At 19:20, the singularity is presented as a bug or monster of GR, Kaku.

21:45, Strominger, singularity means we don't know what to do. Less concisely, Tegmark says the same thing. Einstein wrote a paper that black holes couldn't arise, Krauss. 23:50, X-ray observations of black holes. Reinhard Genzel, a guy from the Max Planck Institute who was looking for certain BHs. Well, the galactic center BH. Using motion of stars around it. Won a $1 million astronomy prize. He gave it away and bought a new car.

30:55, Ramesh Narayan of Harvard-Smithsonian is comparing the BH with others. I actually covered his paper in an astronomy course at Rutgers – my talk was exactly about the evidence that there was a giant BH at the center of the Milky Way (two-temperature plasma etc.).

Lots of stellar black holes.

35:30 GR bad for the small world. Need quantum mechanics. Why Krauss? ;-) 36:50, Andy says that to understand the final fate of BHs, QM will be needed. Krauss misinterprets QM: "a particle can be at many points at the same time". It's just ain't the case. A particle may have nonzero probabilities to be at many points but we may still prove that there're just one point where the particle is although it's unknowable in principle before the measurement.

At 38:30, Andy says that QM describes everything, one can't escape it. All objects are quantum and the world is a quantum world. Most of the time, QM and GR are in peace. But there's an arena where they are in conflict, high-density, small size – inside BHs. "Quantum gravity" is said for the first time around 40:00. Kaku and Lagrangians. He sketches some toy UV divergence and adds big words to it. 42:30, Andy also talks about the breakdown of GR.

42:00 BHs – problems become opportunities, a next key, Andy. Linked to the Big Bang mysteries (singularity). Narayan, Andy, Krauss add a few words. We have no clues what QG is. And no one has seen a BH. The cameraman plays with the physicists' eyes, deforms their words (like near a black hole) etc.

50:20, a new telescope guy, Shep Doeleman of MIT. Computer-combines lots of telescope to get an image at a supercomputer. Huge increase of sharpness. Nerdy discussions with another empirical guy. Trying to see a horizon via shadows.

Sorry for these chaotic catchwords. It wasn't supposed to be a fully formatted text.

Verdict

It was a so so program. I find it very paradoxical that they haven't even tried to cover any new actual theory from the last 40 years. I mean, there was no black hole thermodynamics or string theory or information loss in the program. That's very paradoxical given the fact that Stephen Hawking is arguably the most recognized living scientist. What he's famous for among physicists has never been really covered by a popular program, or at least the number of such programs is infinitesimal.

And yes, I was annoyed by the highly repetitive occultist comments that everything about the black holes is completely mysterious and misunderstood. It's not really the case. Such programs help to reinforce the widespread laymen's misconception that physicists don't have a clue what they're doing and everyone could be employed as a physicist, too.

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