336. Wehrner von Braun: video of the day
Save This Post as PDFAnother very nice song by Tom Lehrer, the guy who worked on random walks apart from being a great song writer. He is alive, 80 years old, and still performs sometimes…
By the way, as it turns out, he is quite popular on Amazon.
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335. What is twistor
Good Saturday evening, True Geeks!
Since everybody currently seems to be a bit crazy about twistors – see for example, the Witten’s paper “Perturbative gauge theory as a string theory in twistor space” and the buzz it started – I decided that the time has come for me to learn what it is and write minireview post about it.
So, what is twistor? Twistor is a straight line in the complex projective space 
, which is use to realize 4-dimensional Minkowski space, correspondingly, twistor space is a linear space of all such lines. Twistors were first introduced by Roger Penrose (on the left) in the late 1960s.
The set of all twistors – lines in the complex projective space – depends on 4 complex parameters. Minkowski space is realized if we choose a subset in the twistor space that depends on 4 real parameters. The idea to use complex geometry in order to work with real spacetime is highly non-trivial and powerful as we will see. The (twistor) space of all lines in can be interpreted as a complexified and conformally compactified Minkowski spacetime. If you consider two causally connected events (for example, connected by a ray of light) in Minkowski space, they correspond to lines in the twistor space which are crossing each other. Euclidean 4-dimensional space can also be naturally realized as a subset of twistor space, so Wick rotation is a very natural operation in the twistor language.
Congruence of null lines
The fundamental idea of Penrose is that the primary physical structure is not 4-dimensional Minkowski space, but complex twistor 3-dimensional space: twistor equivalents of various physical quantities should be described easier than the 4-dimensional quantities defined in Minkowski space. According to Penrose, many physical field equations just follow from the analyticity conditions in the twistor space. After you deal with a quantity in the twistor space, you reduce it to its equivalent in Minkowski space by an integration over twistors. In other words, you introduce some kind of integral transformation from the complex 3-dimensional twistor space to the real 4-dimensional Minkowski space.
This program is easily realized in the simplest case of free massless fields of various spins: scalar field, spinor, vector field and linearized Einstein equations. These massless fields propagating in 4-dimensional flat spacetime correspond to solutions of Cauchy-Riemann conditions in the twistor space. This fact is not of a physical interest, though, since what you really get is new representations of solutions of linear differential equations.
Next time I am going to discuss a bit how twistors help dealing with solutions of non-linear differential equations and present some examples.
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334. How much should you publish?
As far as I remember, it was believed that one has to publish about 2-3 papers/year during glorious and relaxing PhD years (i.e., about 1 paper per 4-6 months, not a too heavy burden indeed)… This would give necessary 6 publications in the end of the term (in Russia, getting your PhD takes 3 years) for your thesis to be officially considered worth defending. If you were publishing less than 2 papers/year, you were assigned a mark “loser”, which is, I guess, quite reasonable 
Being loser meant that you had to spend another year preparing your thesis, then – another one, until the overall number of your publications would hit the magical number 6. Believe it or not, I happen to know (many) very smart people belonging to this category.
Now, the first question is – how many published papers are you supposed to have in the end of your first postdoctoral position term in order for your career to be considered successful? Does the vacuum expectation value of the number of published papers differ for different institutions and countries? What are your thoughts, what is your personal standard of scientist’s productivity?
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333. Periodic table of elements: video of the day
I’ve just discovered Tom Lehrer for myself – you all certainly knew about this guy, didn’t you? He is just plain amazing… I am trying to learn the song by heart, but failing so far – the rhythm is too fast for me.
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332. NEQNET: last two weeks of March
Finally… This freezing March has come to the end. Why freezing? Well, for example, it featured snow storms stronger than the ones in January/February, how is that? Or temperature dropped below -15 on March 25th. Global warming? Not in Helsinki, Mr. Gore.
In the mean time, the audience of NEQNET has reached 300 people (email subscriptions and our RSS feed), while about 700 people read us on Twitter – your humble correspondent is currently the number 2 most followed person in Finland 
You can subscribe to our daily email updates or RSS feed. You might be also interested to follow me on Twitter, since my Twitter stream contains much more than just activity on NEQNET.
And that’s what happened on NEQNET for the past two weeks…
1. String theory. Field theory. Quantum gravity
1.1. Glueballs and gluelumps as bound states of transverse constituent gluons by Fabien Buisseret (Mons). Fabien explains the physics behind his model of constituent gluon and nicely reviews many other questions in QCD – for example, QCD effective equation of state.
1.2. Holographic hydrodynamics by Miguel Paulos (DAMTP, Cambridge). Miguel is interested in strongly coupled QFT plasmas at finite chemical potential.
2. Cosmology
2.1. Dark matter via many copies of the Standard Model by Alex Vikman and Iggy Sawicki (NYU). As follows from the title, the authors discuss a new model of dark matter based on the large number of SM copies. This crazy idea works surprisingly well, simultaneously solving the hierarchy problem.
3. Physics: other
3.1. Turbulence: Statistical approach 1 and Turbulence: Statistical approach 2. I discuss statistical treatment of the developed turbulence regime developed by Taylor and Reynolds, Kolmogorov scaling and intermittency. The basic conclusion is that equations that appear when the system is treated statistically are not closed, which leads to closure problem familiar to many of us from kinetic theory.
3.2. FDT-violation in colloidal glasses under shear by Matthias Krueger (U. of Konstanz). Matthias briefly explains how FDT can be violated in glassy systems. The paper which this post is based on was recently published in PRL.
3.3. Turbulence: order and disorder in turbulent flow. This post is descriptional rather than theoretical. I explain what kind of ordered structures one can observe in various hydrodynamical problems featuring turbulent behavior.
3.4. Turbulence. Dynamical approach. I discuss approach to the turbulence problem based on chaos theory (in particular, strange attractors). I am especially interested to learn how ordered structures get affected by the transition to developed turbulence.
3.5. Fractional quantum Hall effect in some multicomponent systems. Very nice review of fractional quantum Hall effect (Laughlin states, composite fermions, modern applications) by Zlatko Papic (Belgrad).
3.6. Some properties of the Burgers dynamics with Brownian or white-noise initial velocity by Patrick Valageas (Saclay). This is an in-depth analysis of statistical properties of Burgers turbulence.
4. Fun and stuff
4.1. Scientist?s gadgets: Tablet PC and handwriting formulae recognition, where I explain why purchase of a Tablet PC is at least worth considering for a theoretical physicist. Hopefully, handwriting formulae recognition will soon hit the level where it can be considered useful…
4.2. Richard Hamming?s ?You and your research?. A repost of amazing lecture “You and your research” by Richard Hamming. He explains how very good physicists differ from the ones like your humble correspondent
4.3. Global crisis: one interesting plot. We analyse current US federal deficit and find that it is not that scary as Soros says. Nice discussion in comments.
4.4. Scientist?s gadgets: desktop software. I am trying to convince you that you have to use your desktop effectively (not like Moshe Rozali and Lubos Motl ) I also run a contest – the winners are to get invite codes for BumpTop private beta. These winners were determined today morning – Theoretical Minimum and uunuagedecole. Congratulations, guys!
4.5. House market bubble: brief update. That’s what it is – a bit of analysis of US house market, which is not currently doing very well.
4.6. Global crisis and one more plot to think about – namely, I present the plot of the treasury yield curve and try to figure out what are its correlations with GDP and investment.
4.7. Human Activity in the Web by Filippo Radicchi (Turin), who tries to perform statistical analysis of the user activity on such sites as Google. His main conclusion is that one has to study statistics associated with user groups featuring similar patterns of behavior.
Stay tuned!
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