P vs NP & NP-completeness

Michael Sipser of MIT gave a very clear - and perhaps too elementary - colloquium about P vs NP and NP-completeness. Let me make a short introduction to these questions.

P and NP problems

Use a computer to multiply two numbers, 7x13 = 91, or some longer numbers. It will be done "quickly". For large enough input with "N" bytes, the required number of operations (time) will go like a power law, "N^a", where "a" is an exponent. These are the P (polynomial) problems: they are quickly solvable.

Then there are possibly harder problems that may be more time-consuming but if you have a solution, you can quickly prove that it satisfies the conditions. This class of problems is called NP (non-deterministically polynomial) and includes these seemingly difficult problems:

• find the best schedule for students
• find the factors whose product gives you a large number with "N" digits
  
• find the clique of size "M" (a number comparable to "N"); a clique is a subgraph where all vertices are connected with each other
• compute the permanent of a "N x N" matrix (determinant without the minus signs)
• protein folding - minimize the energy by folding a protein
  
• find a proof of a true theorem, a proof that has "M" characters
• find a vacuum with the smallest positive cosmological constant in some toy models of the landscape with "exp(N)" vacua
  

and many others. (About two entries were added by me.) Once you find a solution, you can check that it is a solution in polynomial time, "N^a". But apparently, the only way to find such a solution is to search through a significant part of possibilities which takes time longer than any power law, namely time such as "exp(N)" or even "N! ~ (N/e)^N".




NP problems are "quickly verifiable". You can easily see that P problems are a subset of NP problems: if a problem is quickly solvable, it must also be quickly verifiable. But is it a proper subset? Can't they be identical sets?

History

When was this science invented? It was around the mid 1960s, independently by Russian and American authors. When you have a Russian and an American who invent the same thing at the same time, you're usually not getting the whole story. If I tell you that it was all invented 10 years earlier, what was the citizenship of the inventor? Yes, you're right. It had to be a Czech. In fact, he was not just Czech: he was a German Czech at the IAS. ;-)

I claim that the description "German Czech" matches the U.S. standards - it is constructed just like e.g. "African American" - but no sane Czech person with a possible exception of your humble correspondent would ever seriously call Kurt Gödel a "Czech". ;-)

Recent analyses of John von Neumann's archive showed that in 1956, Kurt Gödel sent a letter to (ailing) von Neumann (both IAS Princeton) asking how much time "phi(N)" one needs to find a mathematical proof of a valid assertion, a proof that is known to contain "N" characters. It could be a power law, he speculated. This fact if true would have profound consequences for mathematics. He has also sketched other problems where similar questions can be asked. Gödel was clearly interested in the issue of finding proofs but his comments were more general and the other guys just repeated it 10 years later.

NP-completeness

The most important later development was NP-completeness. There exists a large and important subclass of NP problems that are exactly as difficult as each other. This NP-complete class contains many granddaddies - but the clique problem is one of them. This really means that a difficult, NP-complete problem can be converted to a clique problem (or one of many other granddaddies that are dual to each other).

The set of NP problems also contains problems that are not proven to be NP-complete such as the factorization problem. A factorization homework can be transformed into a clique problem which means that factorization problems can't be more difficult than the clique problem: but they can be easier although there exists no proof whether they're easier in either way.

Clique problem

Imagine that you have a group of scientists (vertices of a graph) with the information which pairs have shared a paper (links in this graph). Your task is to find the largest subgraph (subgroup of scientists) in which everyone wrote a paper with everyone else.

In paleoclimatology, it is clearly a P problem. The fast solution to identify the largest clique is to find Michael Mann in the graph, list all of his co-authors, sort them by a number of papers co-authored with Mann, and take the upper "M" of this list that still form a clique, if you want to get the largest clique in the graph.

This algorithm was discovered by Dr. Edward Wegman, a statistician who was asked by by the U.S. lawmakers to investigate similar problems connected with that particular bizarre clique generating a remarkable large number of flawed papers, especially about broken hockey sticks.

P=NP or not P=NP

However, the real question is whether this problem is quickly solvable for random large graphs outside paleoclimatology. If there is a solution that avoids the brute force search, then P=NP. Because such an identity would allow one to crack all possible codes, solve scheduling problems, identify cliques, calculate permanents, and even find proofs of true mathematical statements automatically and quickly, it is generally expected that P=NP is not true.

However, there are examples where similar intuition is wrong, such as the primarily test. One can quickly test whether a number with "N" digits is a prime by using Fermat's little theorem. It takes much less time than testing all possible factors up to those with "N/2" digits. The Lucas-Lehmer primality test is a similar example of this dramatic speed-up although it only works for Mersenne numbers.

NP-completeness means that if you find a universal fast (power law time) solution of one of those hard but easily testable problems, you can prove that you have solved all of them. Not all NP problems are NP-complete, but many of them - such as the clique problem - are.

Sipser continued with some additional questions whether we can check that someone knows a solution to a problem such as the isomorphism of two graphs. These are toy models of some concepts that are important in contemporary cryptography - such as the methods for someone to prove that she knows a password without revealing what it is.

Finally, he also mentioned how different levels of complexity that require memory or time scaling as various, generally different functions of "N" can be related to each other, suggesting that these relations could have something to do with the relations of space and time in physics. Well, I would guess that probably not but everyone is free to try to find this relation with physics, of course. ;-)

And that's the memo.

John Pendry: invisibility cloak

See also: Invisible tanks

What ambitious tasks the physicists who don't work on the theory of everything want to solve? One of the greatest dreams outside string theory is to create the invisibility cloak. ;-)



Figure 1: Japanese Harry Potter is testing a new invisible coat by Prof Susumu Tachi of Tokyo University.

One of the experimental leaders in this field is Prof Harry Potter and his sometimes underestimated female collaborator, Prof J.K. Rowling: we have learned that at least the Gentleman must be cited during all talks about this topic. However, the main person who should become invisible is the statue of Peter Pan. Prof John Pendry of the Imperial College in London has just given a captivating colloquium about the question of invisibility.

Methods

How do you become invisible? Prof G.G. of Harvard has proposed mirrors. He has seen many magicians who become invisible by putting mirrors around them. However, this trick only works if these magicians are observed from a particular direction.



Another method is to drink a lot of beer. It must be beer with a lower refractive index than your body. You may hope that if you drink a lot of beer, your refractive index will approach "n=1" and you will become transparent and invisible. However, FDA won't allow you to drink too much of this toxic stuff.

Finally, you may try to design various cloaks. Prof Pendry's cloak is the optical counterpart of barriers in the river: water flows around them, pretending that they don't exist. How do you construct such a cloak?




First, imagine that you want to become invisible. Place yourself into a ball of radius "r" and make this whole ball invisible. How do you do that? You embed this ball of radius "r" into a larger ball of radius "R". For simplicity, consider the two-dimensional case where the balls are replaced by disks. They correspond to a cylindrical geometry in three dimensions.

The annulus in between the radii "r" and "R" contains a particular kind of devices or metamaterials - a concept explained below - that makes the whole object of radius "R" invisible. The light simply goes through the large disk in such a way that it avoids the core altogether. How does it work?

First, as we have indicated, you need all optical rays to avoid the small ball, just like when water flows around a disk. If you remember the linear regime of hydrodynamics, you know that there is a conformal (angle-preserving) coordinate transformation that maps the full two-dimensional space to the full two-dimensional space with a disk removed. This conformal transformation is relevant for determining the trajectories of water flowing around the disk in the non-turbulent regime.

How do you force the photons to go along the path you want? That's a more general mathematical problem: the invisibility cloak is a special example of this problem. Let's try to find a configuration of epsilon(x,y,z) and mu(x,y,z), the permittivity and the permeability, such that the electromagnetic rays will propagate along paths that are curved but look completely straight in some different set of coordinates - for example the coordinates in which the full space corresponds to the full space without the ball of radius "r" in the normal coordinates.

That's a pretty well-defined task and it turns out that there is a solution. You can derive that "epsilon(x,y,z)" and "mu(x,y,z)" must actually be equal to one another. Moreover, you can solve the differential equations that realize a given coordinate transformation - for example the coordinate transformation needed for the invisibility cloak. The last steps you need to make is to construct the configuration of materials with the right "epsilon(x,y,z)" and "mu(x,y,z)" that bend the light rays exactly in the required way so that you become invisible.

If you think for a little while, the general method may work not only for screening against the "radiation field" but even against static fields of electric charges and magnets.

Metamaterials

If you look into your catalog of materials, you won't find any that have "epsilon" = "mu", especially not with the unusual values that the solution to the differential equation above requires. Will you give up? No way. You will create your own material. In fact, you need something more general than a material: you need a metamaterial.

An ordinary material is composed out of atoms or molecules. Their properties averaged over the volume whose size is comparable to the wavelength of light determine the behavior of light in such a material. If you think about it, one wavelength is rather long in comparison with the molecule. That's especially the case if you only want to become invisible by radio waves. At any rate, you have a lot of room to engineer your own metamolecules that react in a particular way to the electromagnetic field. These metamolecules must be smaller than the wavelength but you are still allowed to give them much more general properties than known simple elements or compounds can have.

To construct the cloak, you actually need "epsilon" and "mu" smaller than one. You can see that their refractive index is also equal to "epsilon" and equal to "mu" if the two Greek letters are set equal to one another as explained above. Therefore, the required refractive index can be smaller than one. That would mean that the velocity of light exceeds the speed of light in vacuum. Normally, you would say that this can't happen because of special relativity.

However, remember that it is only the group velocity that should never exceed the speed of light in vacuum: the group velocity is the derivative of the frequency with respect to the wave vector while the phase velocity is their simple ratio. The phase velocity determined by "epsilon" and "mu" can exceed the speed of light in the vacuum as long as it is frequency-dependent in such a way that the group velocity satisfies the causality bound.

The frequency dependence will inevitably cause some dispersion, making the invisibility cloak imperfect, especially if you deviate from the frequencies for which the cloak was designed. But Prof Pendry argued that this effect may be kept small for a pretty broad band of frequencies. This statement sounds somewhat surprising but because he didn't define too quantitatively how broad band can be realized, I can locate no sharp contradiction here.

So how do you build the metamaterials? He is a theorist but has shown a couple of technologies that have been actually constructed by experimenters: various magnetic moments are created by the external field and their characteristics may differ from conventional materials. These metamaterial exist. It is possible to make the permittivity negative, among other things. If you combine these technologies, you may produce the materials needed for the invisibility cloak and the cloak itself. Once again, it can't be perfect at all frequencies but you can make it look good in a wide range of frequencies, he says.

Other applications

There are many applications of this general technique - commanding the electric and magnetic lines and electromagnetic rays where to go, for example:

• Invisibility cloak: that we have discussed most of the time
  
• Super milk bottle: normal glass milk bottles seem to be filled with milk from one end to the other end - you don't see any "layer of glass" on the sides from the milk column. The super milk bottle is even better because the apparent size of the milk actually exceeds the size of the bottle! ;-)
• Dwarf tricks: you can make objects look smaller, larger, shifted, or deformed in rather general ways by designing a good configuration of "epsilon" and "mu": these methods allow you to circumvent certain inequalities that follow from conventional optics
• Correcting errors of telescopes: some types of systematic errors of your optics can be adjusted by additional layers of the generalized invisibility cloak

Most of the colloquium was about theory but at the very end, the speaker has simply disappeared! ;-)

Relativistic condensed matter physics: chiral QFT inside a pencil

Relativistic condensed matter physics sounds as a contradiction, doesn't it? If it's condensed, it must be low-energy, and whatever is low-energy, must be non-relativistic, if not low-brow, many people would say. ;-)

Andre Geim gave a colloquium at Harvard University in which he convinced us that the converse is true. One can study relativistic quantum field theory in condensed matter systems.

Andre Geim is an Ig Nobel prize winner for his discovery of a levitating frog; yes, it is now the featured Ig Nobel discovery on Wikipedia. He has also made it to the fifth annual "Scientific American 50" even though he is only scientific but not American, as Charles Marcus has emphasized with a strong nationalist - but still decisively leftist - accent. ;-) Geim was born in Russia although he works in Holland right now.

OK. What material do you need in order to study chiral quantum field theories within condensed matter physics systems?

Graphene

The material is called graphene and it was thought not to exist until 2004 or so when Geim et al. have made their breakthrough. It is a two-dimensional crystal of carbon filled with hexagons. This idealized material couldn't be observed in its two-dimensional incarnation for a long time but if had been observed in all other compactified editions (except for those with 4-10 large dimensions). We classify them according to the number of large dimensions:

• 3D: graphite - the material inside your pencil - is a lot of layers of graphene
• 2D: graphene - one layer - observed in 2004
  
• 1D: carbon nanotubes may be viewed as graphene with one dimension compactified on a circle
• 0D: carbon balls may be viewed as graphene compactified on a sphere
  

Fine. Geim et al. have simply used a better technology based on optics that allowed them to go to one layer of graphite: the graphene itself. Whenever you make a discovery, you should check literature and you will see that some Russian theorists or Japanese experimenters have done it 39 years ago. This was the case of nanotubes that were not discovered in 1991 but in 1952, we were told. Nevertheless, Geim et al. were lucky because they were indeed the first ones to isolate one layer of graphene.




Stability

The existence of purely two-dimensional crystals could have been surprising for many condensed matter physicists. It turns out that the substrate (sillicon) is important for stabilization of the two-dimensional shape of graphene. Without this background, graphene undergoes spontaneous compactification.

Relativistic dispersion relations

When you study electrons moving in this two-dimensional crystal, you will see that they have a different effective mass - the cyclotrone mass - and the effective speed of light is different, too. In their case, the speed is 1,000 km/s which is only 0.3% of the normal speed of light. Nevertheless, you find that the energy of the electrons grows linearly with the momentum:

• E = PC = MC^2

where PC doesn't stand for political correctness and M,C in the equation above have unusual values. So electrons effectively follow the laws of 2+1-dimensional relativistic quantum field theory.

An entertaining intermezzo: Relativity with a different speed of light is analogous to "relativity of sound" discovered by Jan Fikáček, a philosopher who was a former chairman of Mensa Czechoslovakia and who was always a fun company to talk to. He argued that we only substitute the speed of light into Einstein's equations because we rely on vision. People who prefer hearing and music - for example the blind people - would end up with another type of special relativity that is based on the speed of sound. One of the striking predictions of Fikáček's theory that make it so attractive and so falsifiable - as well as quadruply special if not quintuply special - is that the blind people can't fly with supersonic airplanes. ;-)

They have a new type of isospin with two possible values. It's because the hexagon grid has two carbons in each fundamental cell. The electron can sit on either of them. It is helpful to write the wavefunctions of the electrons on the two types of carbons separately, as two components that depend on the continuous positions x,y. The most elementary transition is in between the two types of the cells which means that the Hamiltonian is an off-diagonal 2x2 matrix proportional to

• p_x sigma_x + p_y sigma_y

Note that this differs from the non-relativistic Pauli equation where the Hamiltonian doesn't depend on the spin at all. The equation relevant for the electrons in graphene is more analogous to the Dirac equation for a Weyl spinor although the spin degree of freedom is "emergent". See their preprint. Once you identify this degree of freedom with the normal spin, you will find out that the precession of this spin agrees with the frequency of the rotation in a generic magnetic field.

Somewhat surprisingly, if you study a two-layer "graphene" instead of the single layer, the relativistic dispersion relation becomes non-relativistic again: the energy will scale like the momentum squared again. In this case, the emergent spin rotates with a frequency higher by a factor of two in comparison with the orbital angular momentum.

Resistivity

Geim has talked about various quantization rules for the resistivity. He also told us that it was already Mott, a Nobel prize winner who should be confused neither with your humble correspondent nor with the juice, who argued that the resistivity is always bounded from above and this law can be derived from a more fundamental fact that

• the mean path is never shorter than the de Broglie wavelength.

In the recent article about the AdS/QCD correspondence, we mentioned that this fact can be reinterpreted in the dual gravitational variables as the Bekenstein bound. I guess that Geim doesn't realize this interpretation. He considers the inequality to be falsified in all systems where localization and interference play an important role, and I am somewhat confused by this remark.

He listed the authors of roughly 20 theories to explain these facts using condensed matter methods. Most of these theories end up with a missing factor of pi. Geim showed the conventional picture of a "missing pie", a very sweet one. ;-)

IQHE

If you discover or explain QHE for the first time, you may get a Nobel prize. If you discover a new kind of IQHE, you get an Ig Nobel prize. ;-)

While the usual fractional quantum Hall effect gives you charges that are fractional multiples of the elementary charge with an odd denominator, Geim et al. have discovered different kinds of quantum Hall effects with graphene. One of them gives you half-integer multiples of the elementary charge which follows from the "relativistic" Dirac equation. Others give you something else, and so forth.

Applications

He believes that their work could turn out to be useful for a new generation of laptop batteries. Today, some laptop batteries are made of carbon nanotubes. In 2010, there could be laptop batteries made out of graphene that could hypothetically lead to a superior technology.

Also, carbon belongs to the same group as sillicon (remember the Czech verse: "Co Si Gertrudo Snědla? Olovo (Pb)" which means "What did you eat, Gertruda? Lead") and you could in principle imagine better semiconducting circuits than the sillicon circuits we use today. Carbon could in principle be more pure than sillicon. Purity is measured by the contrast between the minimum and maximum resistivity and they can get very high.

Stay tuned.

Andre Geim says that people should try to play with different materials than the graphene because there is too much competition there and you could see the condensed matter physicists' fists. ;-) Not all possibilities have been tried because the man-power was not sufficient so far. Nancy Hopkins didn't attend the colloquium so no one in the room could throw up because the offending term "man-power" was not replaced by the correct term "person-power".

Blayne Heckel: torsion balance tests of gravity

• Update - van der Waals and Casimir: Nima told me an obviously true statement whose validity I did not appreciate although I had to know it because it is apparently explained in the Landau-Lifshitz books. I thought that there were too problematic forces competing with gravity: the Casimir force and the van der Waals forces. In fact, they're the same one-loop effect. The Casimir force is a macroscopic description of the overall effect of van der Waals forces between the atoms of the metallic plates.

Blayne Heckel from University of Washington gave a colloquium about the submillimeter tests of gravity. He started with motivation for these experiments - with a review of Newton's theory, general relativity, old large dimensions, and warped dimensions, among other possibilities inspired by string theory.

What do you need in their experiment? You need a one-meter-long fiber and a hanging gadget whose size is seven centimeters. There are mirrors on the gadget: because they reflect a laser beam, you can measure the orientation of the gadget.

On that gadget, you find a horizontal disk with many holes that respect a Z_{21} symmetry. This disk can rotate relatively to another disk beneath it. In the experiments, it rotates very slowly, with a period comparable to several hours. The existence of holes exerts a gravitational torque on the gadget whose magnitude is periodically oscillating. This effect caused by gravity is still pretty large. Because you want to study deviations from the "1/r^2" force law, you add another disk with holes whose torques exactly cancel the previously discussed torques assuming that Newton's law is exact.

That's a method to measure the hypothetical deviations only. You must be careful about many details - for example, you must insert a thin conducting foil in between the different layers to screen the electromagnetic effects including the Casimir forces. This foil is really thin because eventually you are able to measure the forces at distances slightly below 100 microns.

The deviations are conveniently parameterized as a Yukawa force that is, relatively to Newton's force, suppressed by the factor "alpha.exp(-r/r0)". You measure the angular orientation of your gadget and finally you evaluate the data: you allow the coefficient "alpha", the distance scale of the new force "r0", as well as various parameters of your gadget's mass distribution to vary, and you calculate the best fit.

After having made several versions of their experiment with slightly modified details, they end up with

• alpha = (-0.7 +- 0.9) x 10^{-4}

which means that "alpha" is really zero and you can't therefore determine "r0" at all. What the value of alpha above shows that what we see is less than a one-sigma effect because 0.7 is less than the standard deviation of 0.9: while that would be enough in climate science to prove a new kind of looming catastrophe, it means "no discovery" in physics.

The intermediate results indicated some effects - equivalent to an additional repulsive force - but these were just 3 sigma effects that disappeared when they tried to do things slightly differently.

They also measure a possible existence of the preferred reference frame and other unusual terms and they can show that the coefficients of the terms responsible for these effects are at least 100,000 times weaker than what you would normally expect if you assumed that CPT and the Lorentz invariance are broken at the Planck scale. While Lee Smolin waits for GLAST to prove his unusual theories that the normal Lorentz invariance is broken, I think that these terrestrial experiments have already falsified these bizarre theories, proving that they were indeed (easily) falsifiable.

Bruce Rosen: brain imaging

Bruce Rosen started the colloquium by saying that it is useful to have two degrees - PhD and MD - because every time he gives a talk for the physicians, he may impress them by physics, and every time he speaks in front of the physicists, he may impress them by medicine. And he did.

Although there are many methods to study the anatomy and physiology of the brain - such as EEG and/or flattening the brain by a hammer which is what some of Rosen's students routinely do - Rosen considers NMR to be the epicenter of all these methods. (This is a conservative physics blog, so we still refer to these procedures as NMR and not MRI.) This bias should not be unexpected because Rosen's advisor was Ed Purcell.

Some of the results he shown were obtained by George Bush who is an extremely smart scientist as well as psychiatrist, besides being a good expert in B-physics.

Rosen has shown a lot of pictures and videosequences revealing how the activity of the brains depends on time in various situations, on the presence of various diseases, on the age, and on the precise way how the brains are being monitored. Many of these pictures were very detailed and methods already exist to extract useful data from the pictures and videos that can't be seen by a naked eye.

Human brains are being observed at 10 Tesla or so, and magnetic field of 15 Tesla is the state-of-the-art environment to scan the brains of smaller animals. The frequency used in these experiments is about half a gigahertz. Many tricks how to drastically reduce the required amount of drugs that the subject must take before the relevant structures are transparent have been found.

Most of the data comes from observations of water that is a dominant compound in the human body and not only the human body. It turns out that the blood that carries oxygen and the blood that carries carbon dioxide is diamagnetic and paramagnetic, respectively. That simplifies the NMR analysis considerably.

There's a lot of data in the field and fewer ways to draw the right conclusions and interpretations out of the data.

Elizabeth Lada: stars born in clusters

Elizabeth Lada from University of Florida is an astronomer who is most famous for defending the statement that most stars are born in clusters. This statement has brought two communities that studied star formation - those who only wanted the overall rate and those who investigated individual cases microscopically - closer together.

It was interesting to see a nice colloquium from an adjacent field - a field whose conclusions are slightly less theoretical, quantitative, universal, and principled than ours but one that can offer nicer pictures. Some of the main messages of the talk are the following:

• most stars are born in clusters
• most stars are born in embedded clusters
• the radius of the clusters is a few parsecs and their mass is a few dozens of the solar masses
  
• the mass distribution of the stars that are born is rather universal, peaked around "M = 0.3 solar mass": star creation is robust; the very light stars are exceptional
• star formation is an ongoing process that still occurs these days
  
• star formation is terribly inefficient: only roughly one percent of the matter ends up in stars
  
• infrared astronomy allows you to see things that are hidden from the visible spectrum astronomy: as you increase the wavelength, dark regions in the skies become increasingly transparent
• the observations have become much easier due to the technological progress - by Richard Wilson and others; some of her first major discoveries were deduced from pictures that were 60 x 60 pixels while today she works with a 4-megapixel arrays
  
• Orion is her (her son's) most favorite constellation

Back to my theme. Elizabeth Lada gave a nice and organized talk. Nevertheless, there is a cultural gap between physics - which includes condensed matter physics and experimental cosmology - on one side and astronomy on the other side. In physics, we are looking for patterns and laws that explain a whole class of phenomena and their details; something that allows us to predict the answers to new questions that were not used in creating our theories. Astronomy is a nice subject but from the viewpoint of the previous sentence, it is not a part of physics. In fact, I would say that the defining difference between astrophysics and astronomy is that astrophysics, as a part of physics, is predictive.

Incidentally, Josef Lada was a famous Czech artist whose pictures of a romantic Czech winter (and the good soldier Švejk) became one of the secondary national symbols of the Czechs. Recently, the musician Jaromír Nohavica recorded a song about the romantic "Ladian winter" (Ladovská zima) - combined with angry complaints about the upgef***ed snow that Nohavica has to remove every day at -30 degrees Celsius, and so forth.

Savas Dimopoulos wins the Sakurai prize

Congratulations, Savas! More details about Savas can be found

• on this blog, about a colloquium he gave at Harvard
• in a new press release of Stanford
  

Lawrence Krauss: Science under attack

The colloquium speaker was Lawrence Krauss. The room was almost full and the speaker was very entertaining. He discussed the relations between science and education, especially in the context of Intelligent Design, and I agreed with approximately 85 percent of his points. The figure is high especially because he carefully avoided any discussions about modern theoretical physics.

Krauss said that he has just given a talk for the American Enterprise Institute - and this comment was obviously meant to be a joke for the audience. Well, let me say that AEI is no joke but a leading think tank and indeed, Prof. Krauss has good reasons to be genuinely proud that he was offered to give a talk at the AEI.

Krauss has shown some statistics how many people in America believe various strange things. For example, 50% of the people answer that the Earth orbits the Sun and it takes 1 year, while 50% of the people think that the statement is wrong. Even more discouraging numbers describe the opinions about evolution.

He argued that the very advantage of science is that it can falsify statements so that we no longer have to talk about all of them; that different hypotheses are not equally valuable, and so forth. The advantage of science is that it can confirm or reject hypotheses regardless of our preconceptions and regardless of the possible consequences of such insights. Krauss also said that every person in science should see how an idea she completely loves is ruled out because it is a great lesson. I completely agree with him.

He offered several quantitative insights based on comparative literature that Intelligent Design directly replaces creationism without any development of the scientific content, without any new intellectual idea behind it. He has also shown that Intelligent Design is dead in scientific literature (where only a few engineering articles talk about intelligent design - indeed, in their case, the design should be intelligent). In fact, ID seems nearly dead in any literature. There are as many books about Intelligent Design as about the alien abduction. Should we create a controversy at schools just because there are some books about the alien abduction?




I agreed with all these points but his best joke occured when he was explaining that science is what works and all people want to use things that work whenever they are in a crisis situation. His funny example involved the bird flu: the U.S. president suddenly talks about the possible mutation of the virus that could be dangerous for the humankind. When a real potential crisis occurs, suddenly the president does not say Well, the virus was intelligently designed to kill us. ;-)

Krauss has also debunked several flawed arguments used by the creationists - using the same arguments that I also use, so I could not complain. The creationists often say that there is a clear boundary between "humans" and "non-humans" but if you draw all the skulls that different creationists consider to be the skull of the oldest human being, you get the full evolving chain. Clearly, there is no gap separating humans from non-humans.

Also, some creationists say that evolution is different from the rest of science because it is not a "real" science but a "historical" science. Krauss correctly argued that every science is strictly speaking historical because it is based on observations of past events. But it is science because it can also predict the future observations. Well, of course, some sciences - such as cosmology and the origin of currently existing species - that are "more" historical than others. But again, there is no sharp boundary.

Points where I disagreed

There were of course also many points where I disagreed. Let me mention a couple of examples.

The first one is just an amusing observation: Krauss has stated, apparently by mistake, that the hearing of whales was predicted by inflationary cosmology. ;-)

More seriously, there were some points that I found rather painful. After he explained that science should never advocate things that cannot be defended scientifically, because it is not right and moreover it diminishes the power of science, he listed approximately five principles of the scientific ethos (or even the scientific method), and one of them was "egalitarianism".

Now, this is a real shocker. I can't imagine how someone can make such a blunder after a rather carefully designed discussion of the scientific method. Egalitarianism has nothing whatsoever to do with the scientific method, much like any assumptions about races don't. It's pretty bad if someone tries to include a left-wing political principle as a part of the scientific package. Did Prof. Krauss also want to include the working class in the sentence, and the equal role of the sexes?

I am afraid that I am the very first person who found the inclusion of "egalitarianism" among the principles of science to be a shocker. There are many subtypes of egalitarianism, and I personally endorse the legal and moral egalitarianism only (certainly not the material one and others) - but not even these two have any relation with science. These are completely different issues. And indeed, science was developing long before these egalitarianisms were codified.

Europe vs. America

Another strange comment he made was that Europe was "ahead of America" in science education and maybe even in science and technology as such. That was a surprising comment - apparently not just for me. Isaac Silvera asked the speaker how is it possible that America has been quite demonstrably the leader in science and technology during the last 50 years, despite the fact that the percentages of those who know about evolution and heliocentrism has always been quite low.

Krauss' answer was that the separation of state and church was bad (!) for America because it has made the Church and its public relations more efficient. I just can't swallow such an appraisal. The separation of state and church has made many other things more efficient, too - and an increase in efficiency is a positive thing even if you don't like some of the new efficient institutions.

Why is America ahead?

America is simply efficient in giving the people the right roles which is why it is largely irrelevant that most people believe in creationism or geocentrism. These people live their often happy lives and do a lot of other important things: but astrophysics and biology is done by someone else. The percentages of people advocating creationism can be lower in Europe but it does not guarantee that all things are fine - especially because many people "believe" evolution just because they have been brainwashed, without being able to argue scientifically - as Jerry Gabrielse has also argued.

If someone actively believes creationism, it may irritate you more easily - indeed, eight years ago I was spending hundreds of hours with debates about evolution - but on the other hand, I feel that if someone blindly believes evolution without understanding the science behind it, it is equally unproductive as the belief in creationism.

Eight years ago, I had many creationists around. Today, creationism just does not seem to be one of the biggest threats for science. It is much more likely that someone includes "egalitarianism" or any other left-wing buzzword as a part of the scientific package than "God". Some people think that God (and the Heaven) must be a part of any solid science; other people believe that egalitarianism (and catastrophic climate change) must be a part of any solid science. I don't see any qualitative difference between these two un-scientific misconceptions except that the second one seems much more dangerous these days.

Lawrence Summers' resignation is an example of the fact that the political pressure on the actual science and Academia from the left is a more realistic threat than the pressure from the right. Unless, of course, you define science to be the combination of science - as understood by The Reference Frame - and left-wing political values. In this redefined framework, of course, the Left can never threaten science, by definition.

Let me keep my own definition of science.

Just like some Christians may have problems to understand our common ancestors with the chimpanzees, left-wing concerned scientists may find it difficult to understand that the male brain and the female brain can work very differently, when observed carefully. See this new article. If you ask me whether the evolution of apes millions of years ago is more important for the contemporary scientific reality than understanding of our actual brains today, I am afraid that my answer is No. The left-wing ignorance is likely to be more serious. Of course, Lawrence Krauss has not said a single word about left-wing un-scientific misconceptions.

Humiliating groups by choosing irrelevant examples

One of the speaker's main points was that the Bush administration is against science. I found these comments excessive and Krauss' selection of the quotes unfair. He would show you a quote by Bush father that was very positive about science, and a quote of a not-too-relevant person from the current administration to highlight the difference. (The newer quote was a stupid quote saying that good science is the science that is good for the American people but it seems that the joke during Krauss' talk was the most important application of the quote.)

Krauss has also shown some childish pictures of castles of (bad) evolution and (good) creation that fight against each other - and he claimed that the institute that has created the cartoon is important, at least in Ohio.

Much like in the previous case, he did not convince me it was important.

This is not what I call an entirely fair treatment of a controversy. If one is presenting a controversy, he should sketch the best arguments that both sides of a certain dispute - either scientific or political dispute - may offer instead of the worst ones. This was clearly not the case in many portions of this talk although many other portions of the talk did a better job. The choice of the cartoons could have been entertaining, but it reminds me of the quotations of irrelevant personal e-mails with other crackpots that you can find in Jack Sarfatti's books; unfortunately, Peter Woit's book is somewhat analogous.

Criticism of Richard Dawkins

Lawrence Krauss as well as a professor of Harvard argued that the evolutionary "camp" is losing the P.R. battle, and Richard Dawkins was the first person to be blamed. Why? Because Dawkins has said many things about the tension between religion and science - and these statements have culminated in his thesis that "Religion is bad science".

Well, I certainly find this statement of Dawkins too general - but if we assume a certain particular definition of religion, it may be true. Some people may imagine God in very abstract ways and it is somewhat hard to analyze what they really think or find sharp errors in their beliefs. But most people imagine God and His role in a very specific, mechanistic fashion that justifies people like Feynman, Weinberg, or Dawkins to say what they have said. (Feynman said that whenever we understand something, God diminishes: God is only hiding at places which we have not yet understood.)

Incidentally, the thing that Lawrence Krauss hates about Einstein is that Einstein often used the word "God" in his quotes. I certainly don't share Krauss' emotions. Einstein clearly meant something else by "God" than those who are criticized by Feynman, Weinberg, or Dawkins. I personally believe in Einstein's God (once you remove determinism from Him and replace it by the postulates of quantum mechanics).

Maybe I misunderstand something but I find Krauss' comments about the inclusion of religious attitudes to science a bit hypocritical. My understanding is that the very main point of his latest book, Hiding in the mirror, is to present the idea of extra dimensions as an essentially religious idea in order to diminish the credibility of the research of modern high-energy physics - because he knows that most of the readers are anti-religious.

Everyone who has ever worked in phenomenology or string theory knows very well that this research has nothing to do with religion. The link is an invention of Krauss' - one that is intended to politicize things and to encourage his readers to think about completely irrational relations between different ideas.

Which attitudes are anti-scientific according to Krauss

The theory of evolution - that Krauss finds more important than any discovery in physics including quantum theory and relativity (I am not sure about the order but I find Darwin's insights amazing, too) - was the main example of a "threatened" scientific field in his lecture but it was also the only one that I found un-controversial.

In one of his lists, he was showing the issues that were meant to demonstrate that the Bush administration is un-scientific, and the list started with

• global warming
• stem cell research
• missile defense

As you know very well, I think that some of the most principled republicans are more scientific on the issue #1 than Lawrence Krauss and many others. Krauss also mentioned that James Hansen, the father of global warming, feels that his ideas about the looming disaster are being suppressed. Given the fact that news.google.com finds over 8,000 articles about global warming in the MSM media from the last month, some of which are completely insane, I find Hansen's and Krauss' conspiratory theories about the suppression of their findings somewhat unconvincing, to put it extremely mildly. A healthy number of articles about the global climate would be smaller by 2-3 orders of magnitude.

Concerning the topic #2, I think that it is not the best idea to promote the maximized stem cell research hype after the Korean fiasco. The recent events have shown that it is not such a bad idea to be a bit cautious. Also, stem cell research is a scientific activity but one that is politically sensitive and one should not be surprised that the moral values will play a role in policy-making. Sometimes I feel that many concerned scientists including Lawrence Krauss don't want to understand that science cannot tell us what is "good" and what is "bad".

Concerning the point #3, I would say that even though Prof. Krauss likes to be described as an internationally known theoretical physicist, people like Edward Teller, the father of the H-bomb - who was the primary initial driver of the project of Star Wars - and John Wheeler - who has been a great supporter of the program - are more internationally known physicists. By the way, the H-bomb has worked after all.

More importantly, there is obviously no physical law that says that the missile defense is impossible. In fact, if the goal is to make the system 90% reliable, it is more or less guaranteed that it can be done. Anything that can be designed and tested with a 60% efficiency can also be boosted to a 90% efficiency.

Also, I did not like some of the descriptions of the reasons why the tests of the missile defense system were interrupted.

Punch line

The punch line of Krauss' talk is that the physicists should be evangelizing everyone else. The attack on evolution is really an attack on science, Krauss argues.

Well, this also seems as too strong a generalization to me. We could also argue that Krauss' latest book is not just an attack against modern high-energy theoretical physics but an attack against science as such. We could also present arguments similar to Krauss' arguments to support such a statement and argue that Krauss wants to blur the boundaries between physics and religion in order to diminish the power of physics arguments that he can't diminish otherwise. But such a generalization could be too strong, too.

Frank Wilczek and weak gravity

I plan to write a few words about the insightful and entertaining colloquium by Frank Wilczek - once I have some time.



The talk included a lot of classic material about QCD, the spectrum of hadrons, pictures of jets from the LEP, pictures of workers from the LHC - our civilization's answer to the age of pyramids (which is moreover driven by curiosity instead of autocratic rule and vanity), bubbling animations involving the averave topological density "Tr (F/\F)" as a function of space and time computed from lattice QCD, and justifications of the statement that 95% of the observed mass is due to QCD effects. We have also heard various jokes - for example, Frank Wilczek mentioned that the eye was only designed to see distances much longer than 1 fermi. Later he corrected himself that he should have said that the eye had evolved rather than having been designed. ;-)

In the second part of the talk, the weakness of gravity was explained by the fact that you must walk before you run. In the case that you don't know what it means, it means that near the Planck scale, the strength of the QCD coupling constant changes very slowly, and it only starts to run quickly when the coupling constant is of order one, which is near the QCD scale, which is where the proton mass has to be found.

This cute mechanism (that I have appreciated for a couple of years, much like Frank Wilczek himself) based on logarithmic running only explains the gap between the QCD scale and the Planck scale. Of course, the gap between the electroweak scale and the Planck seems to be a very different problem - it is the hierarchy problem that is harder to solve but some mechanisms of SUSY breaking effectively propose an analogous solution.

Too little time.




Dinner

I just returned from the dinner in the Society of Fellows which was fun, after a long time of having no such dinners. Andy Strominger confirmed my hypothesis that he is the center of the Universe if the metric is defined by the collaboration distance that we recently discussed on this blog. Several years ago, he was actually the #2 but it is more or less guaranteed that he became the #1.

Most of the debates were dedicated to various questions that were asked to David Elmer - who studies ancient Greek literature. Frank Wilczek asked many things about the existence of Homer and David, together with Frank, Bert Halperin, and perhaps me, did the best to evaluate the probability that Homer existed as a function of the chronological diversity of the contemporary texts in his epoch. If you didn't follow the details of the previous sentence, it does not matter because most of us did not follow them either.

At any rate, David did a very good job - although he finally admitted that he had to sweat a lot because of all these questions. David also asked a question to Frank Wilczek: What are you working on now because we're not interested in all this past nonsense that you did to be awarded by the Nobel prize. OK, the wording was a bit different. ;-) Would you expect such a focus on the most up-to-date issues from a classicist? Miracles occur in this world.

We also discussed the scenarios in which our civilization would be completely destroyed, much like the civization of the dinosaurs. The main question was whether any traces would be left for the future civilizations composed of robots or new kinds of birds. :-)

After Andy Strominger explained his profound consternation by the fact that we had not been able to analyze the civilization of native Americans who lived in Northern America as recently as 800 years ago, Frank Wilczek hypothesized that no future historian would be able to learn that on Monday, March 13th, 2005 AD, Frank Wilczek was sitting at the end of the table in Eliot House, Harvard University, next to Bert Halperin on his left side (followed by your humble correspondent) and David Elmer on his right side, and they were discussing ancient Greek music and history.

Of course, Bert Halperin knew better. He conjectured that the future historians were going to learn about this dinner anyway because there would be a distorted report about this event at The Reference Frame. The historians wouldn't have a better source so they would have to rely on this blog and analyze what can be trusted and what cannot be trusted. However, Bert Halperin has conjectured that there are so many blogs that the historians could not find the information anyway. Has he tried to find information about Wilczek and poems, for example? ;-)

Alison Farmer explained that we had made no interview because I apparently asked some completely crazy questions about the quark gluon plasma while her research is mostly about Saturn's rings (I really had to confuse her with someone else during my internet search) while Franziska Michor is in Japan and did not attend.

Topological quantum computation

The third, last Loeb lecture by John Preskill was about topological quantum computation. It is an elegant, alternative approach to error correction which is more natural than the brute force error correction explained in the second talk. In the case of quantum computation, the method is inherently robust because the basic operations are local in space.



I still have not said what operations are involved in topological quantum computation. You must have a system in which you are able to pair-create and destroy particles living in a plane with generalized statistics - namely anyons. An anyon is a generalization of the concept of bosons and fermions in which you pick a general phase if two particles rotate around each other. This is only possible in 2+1 dimensions because a loop around a point does not exist in less than 2+1 dimensions, and it is contractible in more than 2+1 dimensions.

Because of this property, the mathematical concept of braiding is relevant. One has to learn things like the Moore-Seiberg constraints, the hexagon identity and the Rumsfeld identity. The latter two completely determine to what extent the elementary R,F moves are not independent from each other. The polynomial conditions written in terms of R,F visually resemble the anomaly polynomials, especially because the same letters R,F are used in both cases. ;-)

The ultimate purpose of having systems with anyons, especially non-Abelian anyons where the holonomy is represented by an element of U(N) rather than a simple phase, is to construct a robust quantum computer. One can show that a topological, anyon-based quantum computer can be well emulated by a qubit quantum computer. The converse statement also holds as long as you pick a sufficiently non-trivial set of anyons.

Because I missed the beginning of the talk, I can't tell you what the Fibonacci model really is, except that the golden ratio is important here, much like in Fibonacci trading. But what I can tell you is that you can try to construct a system of anyons based on the fusion rules of the SU(2) Chern-Simons theory at level "k". The fusion rules reproduce the rules for the tensor products of an SU(2) group truncated down to spins "j" smaller or equal to "k/2". It turns out that the level "k=2" gives you too simple moves that are not enough to emulate a qubit computer. However, the level "k=3" Chern-Simons theory is good enough.

Eventually one wants to realize this alternative architecture for quantum computing. One needs to find a physical system (a generalized "material") whose ground state looks like a condensate of string networks so that the elementary excitations look like the required anyons. Steps towards this goal have been done by Kitaev, Demler, and others.

If you're interested in topological quantum computation, I recommend you this PDF file.

Quantum error correction

I only have one minute. The second talk of John Preskill was about quantum error correction and it was also very interesting. I hope to write a few more words after the dinner with the speaker...

The dinner was fun except that the discussion was focusing on the governance of Harvard (after some initial intriguing debates before the dinner about the relation between dualities in string theory and computer science). At the beginning of the dinner, I evaluated the situation and told myself: Luboši, shut up, drink wine, and enjoy the comments about the "conservative idiocy" and listen to larry-bashing, wisse-bashing, mansfield-bashing, and other bashings. :-)

This far left-wing silliness around is nothing else than the price for the dinner that is otherwise for free - what a great deal. You may not be at a politically reasonable, diverse, or free university, but you are still in a free country and you would be free to express your feelings after the dinner. If you could live in the environment of political diversity of the Pyongyang parliament for one half of your life, using the words of the Wall Street Journal, three more hours can't kill you.

I can effectively transform and rationalize the character of a political discussion if my minority viewpoint represents at least 25% of the environment, but this time, the actual number was very far from (below) this figure, so I had to enjoy the anti-conservative atmosphere just like I did so many times in the communist Czechoslovakia: we're back before 1989. But we had fun. And I learned many things, including news from the today's FAS faculty meeting that I did not attend. After Summers has announced his resignation, the situation at Harvard resembles anarchy a bit.

Back to the Loeb lecture. Preskill was speaking about the error corrections. First, one must understand the classical error correction algorithms. You need some redundant bits for each cluster of bits and they can guarantee that you can reconstruct the full information if at most one error occurs within the group. For qubits, the situation is more complex because there are different kinds of errors. Discretely, they can be classified as a flip of the eigenvalue of sigmaX, sigmaY, or sigmaZ Pauli matrices. You can make several simultaneous commuting measurements on a group of bits, determine what error occured, and perform the appropriate action that corrects the error.

For example, you can choose a group of five qubits to "emulate" a single qubit. One may choose four commuting operators M1,M2,M3,M4, each of them being a tensor product of the identity or Pauli matrix operators acting on each of the five qubits. By measuring the eigenvalues +-1 of these four operators, you get one of 16 possibilities. 16 is more than 15, and there are 15 different kinds of errors that can occur: a kind of error is described by choosing one of the 5 qubits where the error took place, and choosing one of three Pauli matrices whose eigenvalue was reverted. From the 4 bits of classical information you obtain from the measurements, you can determine exactly what error has occured.

In the case of 5 qubits, I was of course imagining how these operators M1,M2,M3,M4 may be represented as products of gamma matrices of SO(10) in the spinorial basis. ;-) But the number 5 is not so special since there are other error correcting codes with a different number of qubits such as 7 (where the 3+3 M-operators containing only 1,sigmaX and/or only 1,sigmaZ are decoupled).

If you want to make really long calculations, you need to reduce the error rate to a very small number. That's achieved by representing each qubit in your quantum computer by - for example - a group of five qubits, and each of these five qubits is emulated by another, embedded group of five qubits, and so forth. You need just a couple of levels in this hierarchy to make reasonably long calculations reliable enough: the error rate goes down as a power of some "elementary error rate" where the exponent grows exponentially with the number of levels in the hierarchy: the dependence is "doubly exponential".

These algorithms are able to fix a single error that can occur but they of course fail if you encounter more than one qubit error in the group. After the error corrections become a part of your calculation, all the overall probabilities of failure become proportional to "epsilon^2" where "epsilon" determines the rate of a single error. You can show that by making the computations increasingly hierarchical, you can arbitrarily improve the reliability of your quantum calculation if the probability of error per gate is reduced below a certain critical value.

For the Preskill et al. particular realization of the error codes, the probability of error per gate must be below 27.3 parts per million. Someone else has rigorously proved that a slightly more efficient algorithm of error correction allows you to use computers with the probability of error per gate being as high as 75 parts per million or so which is almost 10^{-4}. If your technology - and Preskill considers linear optics and ion traps to be the most developed and tested technologies - decreases under this threshold, a couple of levels of your hierarchy will allow you to build a usable and reliable quantum computer.

Actually the requirements on the reliability of the individual gates quantified above are pretty pessimistic - they follow from the worst case scenario. In reality, a computer might work even if the microscopic error rate were slightly higher than the figures above. A quantum computer and its algorithms should be fault tolerant which means that the problems with the errors are solvable. There are various mathematical theorems showing that goodness of a particular error correcting framework implies (apolitical) correctness. Such a proof can be done at the leading level, and there are tricks emulating the step of the mathematical induction that tell you that if "goodness implies correctness" at one level, the same statement holds at a slightly finer level.

There were various questions after the talk. Someone has effectively proposed to trash the whole talk - to trash the error correction algorithms - and consider a computer without any error correction mechanism in it, and just try to repeat the calculation many times to find the correct result. Of course, Preskill has explained that you would need exponentially large numbers of repetitions to find the result with such a flawed quantum computer and such an approach would not be too different from random guessing. In other words, an error correcting mechanism is a necessary part of any realistic quantum computer we can think of. The level corrections slow down the calculations by a small amount: the exponential speed-up is unaffected. It is only corrected by a power law "overhead".

There are various subtle details about the efficiency of the error correcting algorithms. The operations that only act on a single gate are the easiest ones to be fixed. To build a set of operations necessary for the "universal" calculations, you need several more operations that act on several bits simultaneously and transform them according to some unitary operator. One of the rules is that these operations must be local in space and time to make the error correcting algorithms usable.

Quantum computation is in some sense analogous to string theory because it is based on mathematically formulated physical laws that we believe to be almost certainly correct, but whose validity in this realm has not been verified experimentally and there exists a justifiable skepticism that a direct experimental realization or test of these ideas may be impossible in the foreseeable future.

I have drunk some wine so I apologize if the text above makes no sense whatsoever. ;-)

John Preskill: weirdness at work

John Preskill - yes, that's a new picture of him on the Wikipedia page that our fellow blogger just took - has given the first of his three prestigious Loeb lectures here at Harvard. It was an introduction to quantum computation. This fact makes it clear that the content of the lecture largely overlapped with the lectures number 23 and especially 24 of my quantum mechanical course in the fall; see the course website where the PDF files are available.

However, Preskill's presentation was completely smooth, comprehensible, and filled with very entertaining animations in his PowerPoint presentation. And in many respects, it went well beyond my lecture.

He explained things like

• entanglement (this word comes from Schrödinger, by the way)
  
• decoherence
• history of these EPR things, including Schrödinger's reply to the EPR 1935 paper (described as the last Einstein's paper whose relevance survived to the present days): did you know that the "spooky action at a distance" is even spookier in German? It is "spukhafte Fernwirkungen" :-)
  
• difference between bits and qubits, and the difference between (red) boxes and (red) soxes :-)
  
• explanations why the quantum computers can be faster, with the factoring algorithms as examples
  
• quantum cryptography and a safe transmission of the key to encode information - in a detailed way that makes all the necessary steps transparent; Alice and Bob were exchanging secret data while Eve (...) was eavesdropping ;-)
  
• history of quantum computation
• the nature of basic operations of quantum computers
  
• methods of error corrections - with a beaver trying to undo the errors introduced by a dragon
  
• basics of technical realizations of the quantum computers with ion traps (if I remember well) as the main example
  

Preskill started in our field - with various monopole solutions in GUT theories and other discoveries that were helpful to create the right atmosphere for cosmic inflation to be born - and gradually evolved into one of the leaders of the field of quantum information and quantum computation.

He has also become famous for having won the bet against Stephen Hawking; a well-deserved victory. Hawking used to argue that the information must be lost after a black hole evaporates. This followed from Hawking's semiclassical calculations but the rules of quantum mechanics - namely unitarity - dictated otherwise and John Preskill correctly decided that the postulates of quantum mechanics are primary.

Preskill is also a poet. Howard Georgi who introduced the speaker mentioned that Preskill's poem could also be thrown into a black hole. Fortunately, the information is preserved anyway, as argued below, which is why Georgi's efforts won't lead anywhere. You can compare Preskill's poem with a poem by a Nobel prize winner who will speak in the same room at the same time next week.

Mostly because of the convincing developments in string theory where black holes are found as objects within a completely unitary, quantum mechanical framework (and the case of the AdS/CFT correspondence may be even more convincing than Matrix theory and other approaches), Hawking decided that the main argument for the information loss, namely that it should be impossible to construct a consistent unitary theory which agrees with black hole physics in the semiclassical approximation, has been shown incorrect, and his bet is effectively lost. Hawking has bought Preskill an encyclopedia of Preskill's choice, namely an encyclopedia of baseball.

Note that this bet could only be ended because Hawking turned out to be very reasonable. If Preskill had made a bet against Peter Woit or someone like that, he would be told that no arguments for unitarity exist and the arguments based on string theory do not exist either because the existence and insights of string theory can simply be denied and pictured as an uncertain source of knowledge about quantum gravity. And Peter Woit would undoubtedly use even stronger and sillier words. ;-) In reality, string theory has shown its ability to authoritatively answer deep questions about quantum gravity such as the information loss paradox, and only complete outsiders misunderstand that these general insights are established despite our ignorance about the detailed choice of the vacuum. Yes, they are established by pure thought, if you need to hear it.

Finally, I want to say that without any exaggeration, John Preskill belongs to the top five best physics communicators in this world. Be sure that I haven't written this sentence more than five times in the last 10 years. He is a fast thinker who knows how to analyze things in details, present them in a completely comprehensible fashion, and answer the questions that appear along the way.

Keith Baker: TRT at ATLAS

I just returned from a colloquium about the LHC. Keith Baker from Hampton seems to be a very good speaker and he gave a convincing and inspiring talk. A bigger one half of the talk was about experimental high-energy physics - with some elementary introduction about the energy scales of the Universe - and a smaller one half was about the black physicists and related policy issues. The speaker was an African American himself.

The LHC will be completed in 2007. There are two major detectors: the CMS on the French side and ATLAS on the Swiss side. Baker and his collaborators work for ATLAS, much like some people from Harvard and many other places.

While Harvard is focusing on the muons, among other things, Hampton University's main interest is TRT which stands for transition radiation tracking. (In fact, TRT seems to be the "most American" segment of the LHC.) When charged particles move from one environment to another, they emit transition radiation and its detection is a useful tool to identify the particles and figure out other things, too. Baker described how well can they distinguish electrons from pions or how they attack the question of the angular distribution and others.

He also showed some maps and graphs of the grid. Hampton has 5 computers in it which is less than the BU+Harvard group but these five computers are run primarily by students and they are important for other reasons discussed below.

His main motivation was to confirm or falsify the Randall-Sundrum models of a warped extra dimension - and they can essentially complete this job within a year or so after the LHC starts, assuming a certain upper bound for the "amount of fine-tuning" in the RS theories. If you draw the parameter space of these models, a part of it is already excluded by experiments that have been done. Then there is a "fuzzy" boundary on the right side of the diagram imposed by the assumption of the absence of fine-tuning, and the precise nature and justification of this boundary was the topic of some debates.

What you actually want to detect in these models are the narrow resonances describing the excited warped KK modes of the graviton. A quark-antiquark pair annihilates into the excited graviton which subsequently decays into a lepton-antilepton pair. The main background is, of course, the same process with gluon as the intermediate state, and some extra work is needed to distinguish them from each other.

One question was about the coupling constant of the SM particles to this excited graviton mode, and I am not sure whether the answer was quite correct. I don't think that the rest mass influences the coupling of very high-energy leptons to the excited gravitons. Our phenomenology students quite certainly know the right answer but they did not intervene in this discussion.

Black colleges

Another important part of the colloquium was devoted to the role of the historically black colleges and universities (HBCUs) in particle physics. There are roughly 100 colleges, mostly in the Southeast of the U.S., that were created to educate the former slaves after slavery was abolished. (The oldest HBCU was founded in 1837, however.) Hampton University is the only one that has a PhD program and Baker's talk has shown that they are doing quite a serious and meaningful stuff. At Hampton, an unusually large portion of the work is done by students.

There were some funny moments - for example, when he was showing how good different teams working for ATLAS are, Hampton University was almost the best one in one aspect except that some Russians turned out to be ahead. Still good.

Despite being open-minded about the best arrangement, Baker has made a pretty good case for the HBCUs - someone may call it a case for "segregation". Unlike most of the far left-wing whackos, he seems to appreciate many aspects of reality. He discussed what thoughts the black students actually have when they decide where to go. They want a place with many potential partners (I mean girls and boys), and as far as physics is concerned, those who can make it often prefer the "majority" universities.

Baker says that the average students work on whatever they are asked to work on as long as they are paid. The best students want to work on cutting-edge problems, and if Hampton University is not able to show them that they will have a better environment than their colleagues at Harvard or elsewhere, then Hampton will rightfully lose these students, he said.

Also, and this counts as an advantage for HBCUs, the good students want to feel that they are as special and excellent as the good majority students do, and this goal may be easier to achieve with this "segregation". Some of Baker's arguments about educating the black elite were similar to those of La Griffe du Lion who praised the basic principles of the Meyerhoff scholarships which were very successful at least back in 2000.

Another simple reason why HBCUs are important is that a rather large majority of degrees awarded to the blacks comes from these schools.

Loeb lecture: John Preskill

John Preskill is a very interesting physicist, and he will become the next Loeb lecturer at Harvard next month.

At the faculty lunch seminar, Xi Yin was deriving OSV from M-theory, using the "AdS3 x S2 x CY3" near-horizon geometry (work with Andy Strominger and Davide Gaiotto) of M5-branes wrapped on some four-cycles of the three-fold. If I will time, I will describe it in some more detail.

Computation after 90th birthday

We just had a dinner to celebrate the Loeb lecturer, John Hopfield from Princeton, who bravely applies physical reasoning to neural networks and other models of the human brain.

There have been many interesting discussions during the dinner but I will only mention a couple of them. Howard Georgi allowed me to understand a bit better the pretty high score of our F-group in the last homework problem set assigned in my class. Thanks, Howard, for the help. ;-) Yes, F stands for "female". Two different homework assignments have been made for the two groups, and no one has yet called the New York Times, not even Howard himself. ;-)

Incidentally, my feeling after the class in the morning was that 160 minutes is simply too little to properly teach scattering, partial wave analysis including all of its limiting cases, Born approximation, including all the kinematical relations between amplitudes, cross sections, transition rates, time-dependent perturbation theory, and examples including the Yukawa and Coulomb potentials, spherical well, and 38 other issues. Moreover, these calculations in the old-fashioned quantum mechanics are sometimes even messier than in quantum field theory. I would probably reduce the amount of material related to these questions in the syllabus.

Tai Wu, a member of our band, joined my opinions about the Summers controversy and Noam Chomsky and other things. We chatted about the LHC, too. And no, C.S. Wu did not belong to his family.

Ursula Holliger (harp) described many things including the music critics. Of course, they're often annoying and they became critics because they could not become the musicians. Not surprisingly, the very same thing probably holds for the literary critics and the physics critics, too. ;-)

Chris Stubbs has finished reading Barton Zwiebach's book on string theory. Because he learned many things and was pleasantly surprised that the whole modern high energy theoretical physics is fully accessible to him, he actually thinks that every experimental physicist should learn string theory from this book. I am happy to report this experimental conclusion. :-)

Incidentally, Chu Xing who works in a factory in Hong Kong also studies Barton's book. Sometimes, he would find it helpful to know the answers to Barton's problems in the book; he informed me in the e-mail. When I had the pleasure to talk to Dr. Simon Capelin who may be credited for having published so many great physics books in the Cambridge University Press today in the afternoon, he agreed that Chu Xing should get the password to access the web page of Barton's book at the CUP's server. We will see this week whether Barton will agree. ;-) Good luck, Chu.

One of the crimes against the copyright (not humankind) I did in 1993 was to ask a librarian in Prague to xerox the superstring textbook by Green, Schwarz, and Witten for me. She did so! For 12 years, I could not sleep because I worried that the Cambridge University Press would eventually sue me. It turned out today that Dr. Capelin who published the book will probably forgive me this particular sin!

Norman Ramsey has told me many stories about the history of physics, his lectures on 9/11/2001 (the day of my PhD defense), the development of atomic clocks, negative temperatures of lasers, the most precise current experiments testing both special and general relativity, and his recent studies of string theory. He believes that the vacuum energy is gonna be an important question in physics for the years to come. Another very illuminating comment from him was about the changes of your approach to research when you're older than 90 years. Of course, when you're above 90, almost everything works easier than before. Just the short-term memory is slightly worse. When you need to finish some integral - that you otherwise do on the top of your head - with your calculator, it is sometimes a bit more difficult to remember what you want to type on your calculator. It is slightly more difficult than when you are young, e.g. about 85 years or so.

Well, what an impressive person. ;-)

In the afternoon, James Wells (Michigan) was explaining his children GUT constructions extending NMSSM but I will only mention the talk if I have really too much time tomorrow which is unlikely.

Optical signal processing

I decided to see a real physics talk - a colloquium about optics and experiments.

Kelvin Wagner from University of Colorado at Boulder was speaking about optical signal processing. While Eli Yablonovitch complained about the end of the semiconductor roadmap and the disaster that it will bring to the society, Kelvin Wagner was celebrating it.

In fact, the digital processing and electronics is a competitor of optical signal processing. The people in electronics are getting much more money, and it is only because they are cheating, Wagner was explaining: for example, they always use a fuzzy picture of the Los Angeles area obtained by optical signal processing if they want to show that their digital methods are superior.

What is optical signal processing all about? Wagner chose some old-fashioned optical computers as his first example. They were able to factorize the Mersenne number 2^{79}-1 decades ago, by a sophisticated combination of gears, holes, and light rays - this was about 1 million times faster than any other method available at that time. Well, today we have to look (digitally) for larger Mersenne numbers in order to find greater primes.

Wagner also showed the Fourier transform of various letters and argued that the methods of optical signal processing are useful for pattern recognition - and for some tasks, they are superior over the digital techniques.

This field of physics uses various two-level atomic systems. If the splitting is fine (e.g. hyperfine structure), the system is suited for long-term memory purposes. For example, Wagner argued that a system may be used to store 10^{14} bits in a piece of crystal (the memory decays after one day or so). On the other hand, other atomic systems with bigger energy splittings are appropriate for computing, fast response, and the application to wideband optical processing is the natural one. One is expected to use these methods in the religion, for example, to localize the signals from the ET aliens ("SETI").

One of the key methods he discussed was the so-called spectral holography. This concept is analogous to the usual, spatial holography (which itself is analogous to holography in quantum gravity). Instead of the interference pattern as a function of the position on the screen, which occurs in spatial holography, spectral holography creates "interference patterns" in the space of frequencies - in other words, it is about modulation. Such modulation may be obtained by superposing two signals that are shifted in time.

They are working to increase the bandwidth, the resolution - in order to solve massively parallel processing tasks - and he expects that unless electronics will cost 100% of the GDP, the optical signal processing over may take over around 2020, at least in some applications. I have not understood most technical details of the talk well enough to illuminate them.

Savas' colloquium

Savas Dimopoulos of Stanford University is not only an entertaining and pleasant (modern, not ancient) Greek physicist, but arguably one the most important persons behind the theories of phenomenology beyond the Standard Model. Nima summarized his achievements. The most striking - and perhaps a bit exaggerated - description was that "the joke is, whatever happens at the LHC after April 2007, Savas will be in good shape. The only question is which set of his collaborators will get to join in the fun - [Nima] hopes its [him]!" There are several choices

• a pure Standard Model with a single Higgs - it's a nightmare scenario for particle physics because Savas did not discover this one
• the Minimal Supersymmetric Standard Model, co-authored by Savas (well, yes, there has been a pre-history)
• the old large dimensions by Savas, Nima, Gia
• the warped large dimensions by Randall and Sundrum
• the (extended) technicolor by Savas and Lenny
• the Little Higgs model etc.
• the landscape, as proved by split supersymmetry of Savas and Nima
• a question mark - a new possibility which may or may not have been written down by Savas

Recently, the Landscape has unfortunately became Savas' most favorite scenario. I've discussed split supersymmetry in a text about Gia's paper here, and the related works about the friendly landscape here and here. The previous article about the anthropic reasoning described Vilenkin's seminar. Savas compared the conjectured huge multiplicity of the vacua to the statements of Giordano Bruno:

• There are many stars and many planets like the Earth, and our civilization is not a center of the Universe.

These statements were somewhat controversial, Savas said and supported this statement by a picture of burning Bruno. However, the good news is that Bruno's ideas, applied to the Universes themselves - the idea of the landscape - is now supported by physicists all of whom are tenured professors. Therefore, the young people should be careful if they don't want to get fired like Bruno. Incidentally, that would really be an excellent joke if it were a joke. ;-) Savas explained the anthropic principle and the "entropic principle". Unfortunately, he did not use the term "entropic principle" along the lines of the "entropic principle" of Ooguri, Vafa, and Verlinde, but rather as Michael Douglas' demographic approach to the statistics of vacua.

Savas holds a more reasonable opinion about these matters - and he said explicitly that the "equal weight" probability distribution among the vacua is not the full answer. One can't count just the "entropy" but the cosmological counterpart of "free energy".

In the second part of his talk, Savas focused on split supersymmetry and its virtues. One of the "virtues" is that it shows that naturalness is wrong. Another virtue is that it can preserve the gauge coupling unification of the Standard Model - by construction. We take the smallest set of light superpartners that can do the job (therefore, supersplit supersymmetry is not enough & it's also not enough to obtain a dark matter candidate). Not surprisingly, if we make particular guesses about the family of superpartner fields that remain light, we can predict many relations between the observed parameters that could become strong indications that the scenario of split SUSY is correct. Savas also likes the long-lived gluino that could decay during vacations at CERN.

Savas argued that such a hypothetical confirmation of the split SUSY spectrum will almost be a proof of the landscape and the anthropic thinking. Chris Stubbs did not understand why - neither did I - so he asked how the reasoning leading to the proof of the landscape worked. Nima helped Savas to answer this question a bit. He argued completely rationally that once we see that some numbers - such as the Higgs mass - are indeed lighter than the naturalness based on effective field theories would lead us to believe, and there is no other new physics related to the hierarchy problem seen at the TeV scale, there will be two possibilities to explain it:

• God
• Nima and Savas

God - or another divine intervention - is not a rational explanation, as most of the audience happily agreed, and therefore we will end up, completely logically, with the Landscape, which is the only rational alternative to God. That's a really cute argument. (In discussions later, Savas and Nima agreed that the Landscape does not imply split supersymmetry, and split supersymmetry does not imply the Landscape.)

Imagine that someone asked 100 years ago where did the large ratio between the unstable nuclei's lifetimes came from. It was completely unnatural and no one understood its explanation. At that time, a physicist could say that either the explanation was God, or the anthropic explanation proposed by that physicist 100 years ago that could give a large number of different Universes - in some of them, the lifetimes were large enough to allow for life.

Shockingly enough, today we understand the exponential hierarchy of the alpha decay rates of the nuclei using a simple effective model of quantum mechanics where the alpha particle tunnels through a barrier to get out of the nucleus, and the lifetime depends exponentially on the thickness and height of the barrier, which leads to very diverse scales for the decay rates. Large and small numbers can be explained and many of them have already been explained.

The bizarre statement that "the anthropic principle will be the only rational alternative to religion" may be formulated more accurately. It is an alternative to religion for those who want to answer any question that has not yet been understood by science. It's exactly this universal "applicability" of the anthropic reasoning and its hidden recommendation that we should not actually be looking for answers that depend on the question - the "anthropic reasoning" may be the universal answer for everything - which makes the anthropic reasoning effectively equivalent to religion - and the difference is just about the choice of the words.

However, Savas encouraged others to look for a truly scientific explanation of the hierarchy problem and perhaps also the cosmological constant problem. Bert Halperin noted that he had a solution to the cosmological constant problem, but based on obvious reasons, he could not have said what it was in front of Savas. ;-) Incidentally, I just solved the problem, too, but I can't tell you the whole story either.

Savas also admitted, completely fairly, that the landscape in string theory remains a controversial idea that can completely go away within a couple of years. Someone asked whether string theory was science and testable - because a certain gentleman named Laughlin gave a talk at the B.U. arguing otherwise - and Savas said that it was and many aspects of it may become testable very soon.

Michael Dine

Michael Dine of University of California at Santa Cruz visited us today. We had the opportunity for a brief discussion about the supersymmetry breaking scale, the validity of effective field theory, and the existence of landscape. Many of Michael's comments were very interesting. He also mentioned some interesting communication that followed their paper with Banks and Gorbatov.

Before he became a sort of landscape advocate, Michael has also been trying to prove that KKLT was incorrect. One of the conclusions that seems to have survived is that the complex structure moduli in the KKLT-like vacua were never guaranteed to be much/sufficiently lighter than the Kaluza-Klein modes. I've never noticed this thing. This should not happen if the effective field theory description is to be trusted, I/we think. If the background is to be viewed as a Calabi-Yau in the first approximation, then its moduli should be lighter than whatever lives on the Calabi-Yau space - especially the Kaluza-Klein modes. It's simply because it should be possible to integrate out local dynamics on the Calabi-Yau space - above the Kaluza-Klein scale - leaving just the overall parameters of the Calabi-Yau which includes the shape. Note that in flux-free vacua, the moduli are completely massless which is O.K. for the applicability of the effective theory.

On the other hand, such a thing - KK modes lighter than the complex structure moduli - generically occurs if the fluxes are large, which is what one needs to argue that there are many metastable vacua. We agreed that there is never a parameteric suppression that would justify the application of effective field theory (incidentally, such an ability to control things parameterically would imply that the number of vacua must be infinite), and Michael even argued that virtually all of the models that are abused to generate hypothetical large ensembles of vacua always need field strength that makes the description strongly coupled. I argued that this "fuzzy region" in the middle of string/M-theory should have a small volume, in a certain counting, i.e. a small number of vacua and possibilities. The large number of vacua that are supposed to be in the middle reflects a large number of different unjustifiable effective field theories that people write down, not true physics of string theory.