The light bulb wars are back.
In 2005, Fidel Castro easily switched his Freedom Island from incandescent light bulbs to the postmodern fluorescent ones. Castro was 4 years ahead of the camp of peace. In 2009, his European comrades followed the example of their great role model. Well, they're not quite the second ones in the world: the second pioneer after Fidel Castro was Hugo Chávez in Venezuela. ;-)
Starting from Tuesday, September 1st, 2009, the EU companies won't be allowed to produce and the shops won't be allowed to sell any conventional light bulbs with a milky or otherwise obscured surface as well as the transparent classic 100-Watt incandescent light bulbs - or any light bulbs above 80 Watts: see e.g. UPI. In one or two years, the cutoff will be lowered and new light bulbs will be banned, and so on. In 2012, only "efficient" light bulbs will be allowed and by 2016, they want to ban even the halogen lamps.
While Fidel Castro had some rational economic justifications for his decision (well, he simply wanted to reduce recurring blackouts), the reason behind the same policy in Europe is that the Eurocratic wise men think that American imperialist Thomas Alva Edison is causing a catastrophic global warming. ;-) Well, there are cases in which Fidel Castro looks relatively sensible, moderate, friendly to America, and pragmatic.
It's pretty clear that the total "warming" that classic light bulbs may have contributed since the birth of Edison was less than 0.01 °C, i.e. also less than a one-day fluctuation. Only a relatively small portion of the "man-made" CO2 comes from electricity production; only a very small portion of electricity is used for light (most are electric motors): this reduces the figure by more than an order of magnitude; only a part of light came from these light bulbs; only a part of the electricity is produced in coal-burning plants.
The light bulb wars are back.
Some early history
It's been 206 years since Lazare Carnot published the first paper sketching the law of an increasing entropy (Carnot, 1803), an insight that was later elaborated upon by his son Sadi Carnot (Carnot, 1824).
At the macroscopic, i.e. thermodynamic level, the notion was discussed by Rudolph Clausius and others in the 1850s and 1860s.
Finally, 113 years ago, the entropy was derived from the statistical properties of the atoms and it was proved that it can never macroscopically decrease (Ludwig Boltzmann, 1896).
First, congratulations to the 400th birthday of Galileo Galilei's astronomical telescope!
In July 2009, Buchmueller et al., a team of 10 theorists and experimenters including John Ellis, published an interesting frequentist analysis of the likely masses of new particles in supersymmetric models of particle physics:
Likelihood functions for supersymmetric observables in frequentist analyses of the CMSSM and NUHM1 (click)They focus on two models, constrained MSSM (CMSSM) and a non-universal Higgs mass model (NUHM1). Roughly speaking, they're two lower-dimensional slices in the MSSM parameter space, assuming that the spin-0 and lightest spin-1/2 superpartners have masses easily calculated from two parameters. Such artificially more specific submodels are useful to get an idea what's predicted by the MSSM.
The authors have used a frequentist analysis to estimate the probability distribution. It means that they calculate a "score" as a function of the parameter spaces. The lower score, the better (more likely) for a point in the parameter space. The "score" is schematically
chi-square = sum [(experiment-theory)/error]^2Note that in general, "theory" is a complicated function of the parameters predicted for the quantity by the theory. The quantity is measured in an "experiment", with an "error" margin. Additional terms from other considerations may be added to this "score".
The probabilistic distribution may be obtained as a chi-square distribution from the calculated function chi-square, as a function of the parameters, taking the right number of parameters into account (it affects the power law which multiples exp(-chi^2/2), the basic factor generalizing the normal distribution).
Click to zoom in.
When this process is completed for many high-precision quantities, they may offer some predictions for the masses of the new particles. For example, the universal (by assumption) masses of spin-0 and spin-1/2 are visualized on the graph above. The left chart refers to CMSSM while the right chart depicts NUHM1. You see that the masses are likely to be below 600 GeV or so, and the spin-0 masses in CMSSM are likely to be below 150 GeV.
Both the Higgs boson and a neutralino is favored near 120 GeV (and one of the models prefers such values even if you ignore the LEP constraints). The best stau mass estimates are close to 130 GeV. Tan(beta) is preferred around 10. The branching ratio of B_s to a muon pair is strongly favored near 4 parts per billion. However, gluinos are between 500 and 1,500 GeV, about 0-150 GeV heavier than the five light squark flavors.
Many other figures - and correlations between various pairs of unknown masses - are discussed in the paper, too. The announced numbers generally imply that if low-energy SUSY is there, it is more likely than not that the LHC will discover it pretty soon - literally within weeks after the collider is re-activated in November 2009.
Hat tip: Tommaso Dorigo, a supersymmetry foe who is gradually turning his coat, too ;-)
The United States Chamber of Commerce, the world's largest not-for-profit business federation (or "lobby") representing 3 million businesses, is afraid of the intent of some politicians to hurt the business by carbon limits and they want to put the science of global warming on trial:
Los Angeles Times (click)What they imagine is a Scopes Monkey Trial of the 21st century. Well, in my humble opinion, it is not the most flattering analogy. The Scopes Trial (Tennessee, 1926) led to the temporary verdict that it was illegal to teach Darwin's evolution at state-funded schools. ;-)
I don't know whether most of the officials of the U.S. Chamber of Commerce believe in creationism. But if the analogy is supposed to go too far, it surely hurts their case. After all, the analogy is upside down. The key mechanisms of climate change are natural, not man-made, much like the key mechanisms behind the origin of species.
Every competent high-energy physicist who knows Lee Smolin may confirm that Smolin is the ultimate symbol of the complete absence of the scientific integrity and, indeed, the very basic human ethical values.
David Gross discusses some experience with a double-faced Lee Smolin - concerning AdS/CFT and background independence - in their discussion with journalist George Johnson. It was the very first public video from which the laymen could learn that the top physicists consider Lee Smolin to be a crackpot - a fact that would be completely hidden if the information only depended on the journalists.
More worrisome and persistent stories are often told by A.S., A.V., R.B., and many other big shots.
But what he's doing and saying after the Fermi collaborations have proved that all the "theories" he has ever invented about quantum gravity were rubbish simply exceeds all the limits that could be tolerable for a person who should be allowed to freely walk on the street.
After many years when he was boasting about his "falsifiable predictions" of loop quantum gravity (Lee has even become a template for Leslie Winkle in an award-winning sitcom) that were moreover completely "generic", and when he was using these "predictions" to sling mud on the top research in high-energy physics, namely string theory, he has turned his coat.
The president of Hungary was just banned from Slovakia and I understand the extraordinary decision.
Ms Jana Kirschner, "Pokoj v duši" (Peace in the Soul).
Fourty-one years ago, the armies of five Warsaw Pact countries - Soviet, Hungarian, East German, Polish, and Bulgarian troops - invaded Czechoslovakia in order to suppress the Prague Spring, a short period of relative democracy and freedom led by Slovak reform communist politician Alexander Dubček [Doob-Czech]. Romania rejected to participate and so did Albania that left the pact because of the invasion.
In this act of "brotherly assistance", our comrades sent us 500,000 troops or so. We may guess that about 400,000 were Soviet troops, less than 0.2% of the Soviet population. Hungary sent approximately 30,000 troops, or 0.3% of the Hungarian population.
I think that the opinion that only Russia was responsible for the invasion is completely dishonest. Relatively speaking, the other four countries were equally responsible. The Soviet Army was bigger, but the guilt is also divided among many more citizens. In the case of Hungary, the invasion had a special dimension because Hungary used to control Slovakia in the past.
On this blog, we've had a lot of fun with Arnesen+Bancroft, Lewis Pugh, as well as Pen Hadow and company. All these teams were trapped in the brutal conditions of the Arctic while they were trying to prove that the Arctic has become balmy because of global warming.
Ladies and Gentlemen, they have a new friend. Yacht Fiona is participating in the Green Ocean Race, teaching a generation or two how to live without fossil fuels.
They report that they got "hopelessly trapped by the ice" two days ago. Despite a "favorable" ice report, they encountered 8/10ths of ice, with many old i.e. large bergs. They are not in immediate danger because the Canadian Coast Guard is sending them an icebreaker. Well, they're surely not the first carbon-neutral yacht gratefully saved at least by an oil tanker. ;-) Here is the small appendix of the energy-efficient yacht - a true chickabiddy:
Why don't they ask the U.S. government to break the ice by exploding an H-bomb? That would surely be a small price for the chance to save a few liters of gasoline! ;-)
This is how our apartment building looked from the 1970s through May 2009 (picture taken in 2002):
And this is how it looks today, after a three-month renovation and heat insulation (it is packed in a 10-cm polystyrene layer, too):
I think it is prettier, more friendly, more human, happier, and the neighborhoods are more diverse now. The other inhabitants - including many pensioners - were more conservative concerning the colors: I would prefer much wilder colors and pictures but it's OK with me. The modest advertisement made the contract cheaper by USD 10,000+ and it's pretty cool, too.
Concrete blocks were the main contribution of socialism to the field of architecture. Literally hundreds of millions of people were placed in these panelák's or "rabbit hutches", as ex-president Václav Havel called these boxes composed out of a few gigantic "bricks" ("panels" in Czech). ;-)
It used to be speculated that they would collapse within a decade or two. But you can see that with some creative and transformative forces of capitalism, things are not that bad and the fear may be forgotten.
Much of the three-month work was done by the Ukrainian construction workers. The most active one told me that he had to pay some money to his Ukrainian "mafia boss" - who is responsible for some paperwork - but the things are probably not that bad because he earns CZK 32,000 (USD 1,700) per month after this subtraction - 50% above the average Czech salary. He surely deserves it.
EurActiv.COM published a sensible yet pessimistic interview with David Zaruk, an environmental health risk consultant in Brussels.
He explains that Europe is not really becoming a knowledge-based society as people used to say but an influence-based society. And the influence is moving towards the eco-religious fundamentalists, cowards who are gradually replacing the presumption of innocence by the precautionary principle, i.e. the principle that researchers are held "guilty until proven innocent".
The scientific method as used in the EU policymaking.
The beauty of the precautionary principle is that "you can never be wrong" which is attractive for many people. But it's only true as long as you define "being wrong" as something else than "not being right". ;-) Indeed, the precautionary principle distinguishes these two situations while science (and logic) does not.
NGOs' lobbyists are becoming the most powerful force that shapes EU policies related to science and innovation is getting impossible. At the same moment, it is getting hard to hire good scientific experts for the EU's risk assessment process because they are increasingly fed up with the EU's being driven by ever strengthening non-scientific elements. Risk assessment is sadly being separated from risk management.
Future article: Nature and NYT report the demise of Lorentz-breaking theoriesString theory is the only beyond-QFT survivor of a today's earth-shaking astro-ph paper (see also Nature)
The following clip comes from the first episode of The Big Bang Theory that your humble correspondent has ever seen:
As of today, I've watched all the episodes that have been released in English and Czech, usually several times. ;-)
It's virtually certain that this exchange was inspired by your humble correspondent's debates with various advocates of loop quantum gravity whose irrational attacks on string theory and the very Lorentz invariance of the laws of physics, as established in 1905, have been persistent and bloody, and so had to be my rational responses.
See, for example, discussions about a subset of Sabine Hossenfelder's dumb papers (Jesus Christ, she's been always so incredibly unable to understand basic things in these discussions - her hiring as a postdoc shows that the system is completely broken) or
Objections to loop quantum gravityand dozens of other blog posts debunking loop quantum gravity, Hořava-Lifshitz gravity, doubly special relativity, and several other Lorentz-breaking theories.
Lorentz violation and deformed special relativity
MAGIC: dispersion of gamma rays?
MAGIC: rational arguments vs propaganda
Testing E=mc2 for centuries
Lorentz violation makes perpetuum mobile possible
Despite the chatter about a very great depression - an event that some people dream about in their quest to deconstruct capitalism - the numbers speak a very different language.
The quarter-on-quarter GDP growth has been just reported to be positive in Q2 of 2009 by three Central and Western Europe countries. Czechia, France, and Germany saw a 0.3% growth each. Unfortunately, the same figure in Italy, the U.K., and Spain were negative: -0.5%, -0.8%, and -1.0%, respectively.
The current year-on-year figures remain negative but it's likely that the "very great depression" is actually turning out to be the shortest possible recession that deserves this modest name, namely two quarters. I am sorry but these events don't look like a justification for any further distortion of the markets.
Hans Christian Ørsted was born in Rudkøbing, Denmark on August 14th, 1777. He died in Copenhagen in 1851.
Just like his brother, he received most of his education at home by self-study. And he was an achieved poet and writer. But we primarily remember him as a physicist. Ørsted believed in the unity of Nature which is why he instantly accepted Johann Wilhelm Ritter's speculations about the links between electricity and magnetism, despite the lack of evidence.
The most important story of his life occurred on April 21st, 1820 when he was preparing a lecture. An electrical circuit managed to move the needle in a nearby compass. Ørsted became the first famous person who produced a magnetic field by a time-dependent electric field: the first guy who actually managed to observe this effect was Gian Domenico Romagnosi who saw it 2 decades earlier but Romagnosi remained virtually unknown.
Ørsted's qualitative discovery was later upgraded into a mathematical, quantitative law by Andre-Marie Ampere. This effect shouldn't be confused with the electromagnetic induction which is the creation of an electric field (or voltage) by a time-dependent magnetic field and which was found much later. Note that the influence goes in the opposite direction.
Ørsted's beliefs about the unity of Nature surely turned out to be correct in the case of electromagnetism: the unity of electromagnetism with nuclear forces or even gravity turned out to be much more difficult.
There's one more cute meme that Ørsted should be credited with: he was the first physicist who began to produce gedanken (thought) experiments en masse and who gave them the name. Theoretical physics would advance at a much slower pace, if the progress were not completely impossible, without this technique.
This Danish physicist was also the first man who isolated aluminium as an element.
I just watched the second part of Impact, a German-American catastrophic TV miniseries (in the Czech dubbing) about our Moon that became 12 heavier by swallowing a "brown dwarf" and was otherwise determined to collide with the Earth before a team of unusually attractive astronauts and astrophysicists removed the 12-lunar-mass seed from the lunar core.
Like many other catastrophic movies, it was very emotional. And be sure that I am very sensitive about such matters that paint the sentiments of the people who see their beloved ones dying, deciding about the lives of others, or going to dangerous expeditions: yes, my reaction often includes tears. However, the underlying physics was just way too bad.
Their basic scientific story was that a bizarre heavy astrophysical object was absorbed by the Moon, our favorite natural satellite. People had some fun with cool meteor showers before they began to witness irregular anomalies - such as new kinds of thunderstorms, collapsing telecommunication networks, as well as trains and people floating above the ground. The elliptic orbit of the Moon was heavily distorted and only a few weeks of life were predicted before the eccentricity would have increased sufficiently dramatically for the Moon to hit the Earth. The mankind was getting ready for a judgement day.
What a nice opportunity for a glass of beer.
Today, Australia's Senate rejected Kevin Rudd's plans to copy the European fraudulent carbon indulgences industry to his continent.
Antarctica and Australia, two driest continents (in this order), are unlikely to revive this dead horse in any foreseeable future. It is probable that Asia, Africa, and South America will adopt a similar position. We're working hard for Europe and North America to behave sensibly, too.
The Labor Party has been so serious about this crap that they have even created a minister of climate change. In order to show their arrogance of power - and their ability to place an arbitrarily incompetent bureaucrat to control the citizens - they have made the new ministry really dumb and politicized, according to their best standards.
Reuters reported that the global carbon dioxide output in 2008 was 1.94 percent higher than in 2007. You can see that in 2008, the CO2 growth probably exceeded the GDP growth. Under normal circumstances, the CO2 growth may be equal to the GDP growth minus 1 percentage point or so (because of the gradually increasing "carbon efficiency" of the economy).
At any rate, such numbers make it very clear that the ideas about 20% or 80% reductions within a decade are completely unrealistic (and both 20% and 80% are qualitatively equally silly) unless a new revolutionary technology takes over the world: but the events of this unusual kind cannot be ordered by bureaucrats.
I find it likely that sometime in 30-100 years, such a breakthrough will indeed take place. But no one knows when and where this development will occur. It makes no sense to speculate about such events or include them in the short-term and medium-term planning.
Paul Adrien Maurice Dirac was born in Bristol, England, on August 8th, 1902, i.e. 107 years ago. He died in 1984 in Tallahassee, Florida.
His mother was English while his father was an immigrant from Switzerland and an obnoxious family Hitler who taught French and who forced his family to speak French at their English home. Paul's elder brother committed suicide in 1925. In Bristol, Paul gratefully avoided the classics which was the dominant subject taught to his contemporaries, and studied electrical engineering instead.
By the way, at his elementary school, he was asked to solve a famous problem with the three fishermen which may have helped him with the antiparticles 15 years later. I will discuss the episode later in my essay.
After some time spent with electrical engineering, he managed to move to Cambridge to meet his true love, mathematical physics. His PhD in 1926 was based on the work that described the analogy between the commutators on the quantum side (more precisely, in Heisenberg's matrix mechanics) and the Poisson brackets on the classical side. Note that Dirac was 24.
Later, he would study this map in detail. So he was also predestined to figure out how to quantize systems with second-class constraints (using Dirac brackets). Also, Dirac was convinced that the action from classical physics should be relevant for a formulation of quantum mechanics, and he sketched some very rough arguments that Richard Feynman was able to streamline when he invented the path integrals.
Dirac equation and Fermi-Dirac statistics
After some time, I spent several hours studying what's happening in the U.S. politics. And the controversy surrounding the healthcare program looks pretty scary.
In their efforts to defend an indefensible proposal for a communist healthcare system, the Left has introduced two basic and historically not-quite-new tools:
- HCAN (Health Care for America Now), the new Sturmabteilung
- Flag@whitehouse.gov, an internet-based system to organize informers and create a list of enemies of the currently governing party in the U.S.
Organized screaming is just one thing that HCAN is supposed to plan.
A CERN press release has revealed that the LHC will be restarted in November with 3.5 TeV per beam. A few weeks later, two beams should begin to collide. The people will learn how to deal with the machine at the reduced energy.
Sometime in 2010, the energy should be upgraded to 5 TeV per beam. Lead ions will replace the protons at the end of 2010. A break should prepare the machine for its prescribed 7 TeV per beam - 14 TeV of center-of-mass energy - sometime in 2011 or so.
The restart was recently delayed due to a problem with a faulty hose in the helium transport circuit and with loud sex in the tunnel. ;-) In Dennis Overbye's piece in The New York Times, Lisa Randall says that it may take time before the LHC picks the data she wants. Indeed, unless we're (and she's) extremely lucky, it may take millenia if not millions of years to detect the warped extra dimensions. :-)
Twenty-five years ago, John Schwarz and Michael Green were spending their summer in Aspen, Colorado and they were working hard. The physicists were realizing that superstring theory was so intellectually sexy that it simply couldn't have suffered from anomalies.
Type I string theory whose low-energy limit is the d=10 type I supergravity coupled to d=10 supersymmetric Yang-Mills theory was widely believed to have anomalies. It is a chiral, left-right asymmetric theory with a lot of charged chiral fermions and similar stuff. Vague arguments indicate that the anomalies have to be there and they have no good chance to cancel.
Clarion Congress Hotel where the event took place and other things related to the event (press the right arrow button to browse). For Vysočany, a colorless industrial neighborhood of Prague, the building looked impressive to me.
Yesterday, I spent a day in Prague, on a congress of mathematical physics, thanks to the hospitality of Miloš Zahradník, my (former) diploma advisor from Prague who was a co-organizer and who showed me a new concise version of a Taylor series problem we used to solve in different ways (why exp and ln are inverse to each other: permutation edition) and invited me for a lunch.
I've seen about seven talks, starting from Steven Weinberg's talk on asymptotic safety (and the history of QFT) that we have already discussed (Lenny Susskind asked most of the questions), continuing with various talks related to statistical physics, and ending with three talks about "science and society".
They were delivered by Joel Lebowitz, an ex-teacher of mine from Rutgers (who survived holocaust but that couldn't prevent him from doing a lot of great stuff for the human rights of scientists intellectuals across the world).
Šimon Pánek, a top student leader of the Velvet Revolution, gave a meaningful talk about the activities of their "People in Need" NGO, as well as memories about the fall of communism. It didn't hurt that he thought that physics was studied by physicians :-) and that the November 17th, 1989 demonstration he led was remembering a 1942 rally (rather than the correct answer: 1939).
And an African scientist whose name is somewhat difficult for me to reproduce told us everything about mathematical physics in Africa: it didn't exist before 1980 and since that time, the number of people on the black continent who are interested in such things and who attend various summer schools etc. increased from 30 to 50 or so. There were many names of the institutions from the (white) "North" who help them - but otherwise the talk wasn't bad. ;-)
I may add a lot of details later but I am busy right now. The picture of Lenny Susskind and Steven Weinberg on the left side (click to zoom in) appears because they haven't managed to disagree with its emergence yet, and I hope they won't. ;-) In fact, here you can see
This map looks like the New York Subway but it is actually a map of the tropical storms.
What do Arlene, Bret, Cindy, Dennis, Emily, Franklin, Gert, Harvey, and Irene have in common? Well, they're named tropical storms that occurred by August 4th. Nine of them.
Except that it wasn't in 2009. It was back in 2005. The map above is from 2005, too. The journalists would tell you that the hurricanes would always be like in 2005 - maybe because of global warming.
Except that we have moved on. It's 2009 and we don't hear that the current hurricane score symbolizes the future trends. The reason is simple. The number 9 in 2005 dropped to 0 (in words: zero) in 2009. See the 2009 Atlantic hurricane season. The total damage, fatalities, and ACE have been uniformly zero as of today.
It's obvious that a big hurricane is able to create a higher number of newspaper articles than the absence of hurricanes. Nevertheless, if a journalist only reports the events of the first kind and expects the readers to generalize them, he is being either stupid or dishonest.
Some pure astronautic entertainment. What would you expect from the 3000th posting on this blog? ;-)
Andrew Feustel, the last man who touched the Hubble Space Telescope during the recent service mission in May 2009, brought Jan Neruda's astro-emotional (Czech) poems, Cosmic Songs (1878), to outer space and back to Czechia.
He wants to fly to the Moon and Mars or beyond. Aden, his 13-year-old son, prefers to stay on the Earth unless a flight to the "scary outer space" becomes necessary. And let me tell him: it probably won't. ;-) The 15-year-old Ari is less hostile towards our broader cosmic environment.
Andrew Feustel revealed his goals today, during his fifth trip to my hometown of Pilsen where the uncle of his wife, Indira, surprisingly lives.
"Pilsen is a beautiful place, we like to stop here whenever we go to Germany. During our recent mission, we didn't have good enough position to see the Czech Republic, so at least I have tried to spot the Pilsner brewery."OK, I improved the answer a bit.
While Feustel could say "chata" [khuh-tuh] (cottage), a place they visit here, his wife (who has Czech roots after her mother and Indian after her father) remembers Ferda the Ant as well as Spejbl and Hurvínek, two famous series of Czech books and/or theater comedies for the kids. Because she also spoke to her friend by phone, she can create Czech sentences and listen to us.
Two days after I was defending The New York Times in a discussion with Noel Shepperd, the paper decided to prove me wrong. The article
Dan Bilefsky and Stephen Castle make it very clear that they have no clue what democracy or fair journalism mean. They expect all their readers to think that Václav Klaus is a villain while the typical Eurocrats are great guys. For NYT readers, it is apparently politically incorrect to realize that the truth is the opposite one.
OpenScience (Dan Gezelter), BackReaction (S.H.), and CommunistSocialistSwine (?) have discussed the question whether science should be "open" and whether partial results should be shared. They have many right ideas but I find most of their attitudes one-sided and misidentifying the real problems and tradeoffs.
When we advocate "open science", our goals are:
- Transparency in experimental methodology, observation, and collection of data.
- Public availability and reusability of scientific data.
- Public accessibility and transparency of scientific communication.
- Using web-based tools to facilitate scientific collaboration.
- Credit is more likely to go to the actual authors which motivates people to work harder and find some new results.
- Good new ideas are not being attacked just because they disagree with the average opinions (the "consensus") of the contemporary people: people don't get discouraged by premature criticism.
- Complete, final results of a "hidden" scientific process are likely to be of a higher quality than "shared" partial results.
The list of reasons why science should be transparent looks pretty much obvious. Especially when it comes to some "routine" scientific work, the advantages look indisputable. For example, if the taxpayers pay some teams for their measurements of the temperatures, it seems crystal clear to me that the measurements - and all the calculations - should be as transparent as possible.
Let me start with a sentence that occurs quite often on this blog, and it is no coincidence: The most interesting hep-th paper today is arguably the first one. Nima Arkani-Hamed, Freddy Cachazo, Clifford Cheung, and Jared Kaplan wrote about
a duality for the S-matrix (click).They present a concise formula for scattering amplitudes in N=4 supersymmetric Yang-Mills up to all orders in perturbation theory and they market it as a new "weak-weak dual description" for this S-matrix. The most informative formulae are equations (9) and (10), analyzed in the rest of the paper:
This is a formula for the scattering amplitude of "n" gluons with "k" of them having the opposite chirality than others. The amplitude is written as an integral over a "kn"-dimensional space of rectangular matrices "C" (with no twistorial indices!). These matrices may be interpreted as parameters of "k"-dimensional planes embedded in an "n"-dimensional space: the space of matrices is therefore an "(n choose k)-1"-dimensional projective space (plus an irrelevant scaling variable).
Breaking news: Jim Parsons wins the Television Critics Association's 2009 award in the category of highest individual achievements in comedy. Congratulations to my imitator!What is the method
Perturbation theory is an approximate method that describes a physical system in terms of a similar, simple enough, solvable, and often non-interacting physical system, "H_0", and a small perturbation of this system, "lambda V".
If you assume the letters to represent the Hamiltonians, or the formulae for the total energy (and evolution) of the systems, the total Hamiltonian is
H = H0 + lambda V.Here, the perturbation, "V", is normalized in such a way that it is comparable to "H_0". On the other hand, "lambda" must be smaller than one. Ideally, it should be much smaller than one.
While "H_0" may be solved exactly, the full "H_0 + V" cannot. But there exist sophisticated mathematical techniques that allow us to quantitatively answer any question about "H" by calculating appropriate Taylor expansion in "lambda". We are continuously moving from "lambda=0", which corresponds to "H_0", to the actual value of "lambda", which corresponds to "H".