“Landau” by Maja Bessarab

I have recently read the book by Maja Bessarab, entitled “Landau”.

It is a very small book (~120 pages). As guessed, it is about Lev Davidovich Landau — his life, who he was and how he was. It is written by one of his closest friends, Maja Bessarab. Probably the most valuable information that the book contains is not even the biography of Lev Davidovich (which can easily be found even on wikipedia), but the enormous amount of close, sometimes even word-to-word conversations of Landau with various people (Bessarab, Kora Landau, Niels Bohr, Evgeniy Lifshitz, and many-many others).

I do not know if this book is available in English, but it is definitely worth looking it up. It was published by Moscovskiy Rabochiy (Moscow Worker) in 1971 (although I suspect it may have had multiple reprints, possibly by other publishers).

I will quote some of the most memorable (for me) lines from the book. Will do so in Russian, to contain the spirit of Landau’s genius.

Главное, делайте всё с увлечением, это страшно украшает жинь. (из письма автору)

Есть предметы, по которым стыдно получать оценку выше тройки. (Ландау отцу по поводу своей плохой успеваемости по предмету словестность)

Проблемы важнее решения. Решения могут устареть, а проблемы остаются. (Бор из своих лекций)

Я люблю людей, кроме пресыщенных жизнью ничтожеств. (Джон Рид)

Без экспериментаторов, теоретики скисают. (Ландау своим ученикам)

Учёба — любимое занятие женщины. Я не принадлежу к числу мужчин, которые сильный пол ставят выше слабого. Однако, если бы у меня было столько забот, сколько у вас, я бы никогда не стал физиком. (Дау двум молодым аспиранткам)

Главное в жизни — правда, и во имя правды человек должен быть беспощаден к самому себе. Правда и труд. Бойтесь растратить отпущенное вам время на мелкие, недостойные человека дела. (Ландау ученикам)

Когда имеется конечное число экспериментов и бесконечное число теорий, то существует бесконечное же количество теорий, удовлетворящих конечному числу экспериментов. (Ландау цитирует Бора своим ученикам)

- Но согласитесь, в науке ведь есть необъяснимые явления.
- Нет! Любое явление науки можно объяснить. А жульничество — нельзя. В этом и состоит разница между ними.
(Из интервью)

Главное в жизни — дерзать!

Без вдохновления нет воли, без воли нет борьбы, а без борьбы — ничтожество и произвол. (Николай Пирогов)

Верховным судьёй всякой физической теории является опыт. (Ландау, Румер, “Что такое теория относительности”)

Science Rendezvous Part 1: Invitation

As one of the organisers, I invite all, who lives in Toronto, the Greater Toronto Area or near, or just happens to be at Toronto for a moment, to the first annual Toronto’s science and technology festival: the Science Rendezvous!

This is an all-day, free event! Everyone will find something to raise and feed their interest!

Time: 10 of May. All day, from early morning or so to sunset or so.

Location: Toronto Downtown, University of Toronto St. George campus, St. George street, near Willcocks and College (map).

Specifically, I invite you to our physics part of the Science Rendezvous, which is located in the department of Physics, 80 St. George Street (map).

We will have lots of very cool demonstrations, which I shall not reveal here yet. It is going to be very-very exciting! You’ll have a chance to see real laboratories and what we do there (well, not really “we” — theorists are usually repelled by the labs…)

Further information: official website, UofT Bulletin article, Globe and Mail article.

Please, come by. You’re all very welcome!

Add and expand…

This has been a very busy month. And, sadly, it continues to be. This is the reason I have halted the blog entries, which I do feel ashamed for.

I have written a review article on Mather and Smoot’s 2006 Nobel Prize in physics experiment. I will find a way to publish the article in the upcoming month or so.

To tell the truth, it was a project in one of my courses. The sad thing about it, though, is this. I decided to take an early start and take it rather slow (that is, with no rush), so as to be able to make a substantial amount of research and prepare my work very carefully. Well, I did make a fair amount of research, but the due date had approached far too quickly, so I wasn’t able to organise and write my paper quite as neatly and quite as nicely as I wanted to.

Nevertheless, I think I’ve done by far more than what the project was supposed to cover, so there’s not too many concerns about it. I do, however, want to take the time after the semester’s end to improve, add, slightly reorganise and hopefully perfect the paper. Hence the delay in having it out for easy access.

The name to the paper is “Black Body Form and Anisotropy of the Cosmic Microwave Background Radiation”, which is not too remotely distanced from the Nobel Prize statement. I also will take the time this summer to correct my older papers on string theory and TOKAMAK. Add and expand, add and expand…

Ignorance towards physics?

A couple of days ago I visited my high school that I used to go to before I became a university student. I talked to my physics and chemistry teachers; I also wanted to talk to my analysis teacher, but could not find him, unfortunately.

My physics teacher brought me the terrible news, which I was completely shocked by. The school is semestered (that is, courses are divided up into semesters) and — due to small size of the school and the low interest in physics — there is only one grade 12 (final year) physics course. And truly that is not the most disappointing thing, for there was only one grade 12 physics course when I attended the school, and so is in many other small schools. The sad fact is that the class was scheduled exactly in the same time as grade 12 calculus was scheduled. Of course, all people took calculus and were forced to take physics in night school, let alone those who traded it for summer school. There are 2 (!) people in the class!

This is disastrous! The physics education in Canada is very weak by itself; when school administration does such sort of violence, they are making closer the day, when Canada will not produce home physics students at all!

Bulletin On Mini Black Holes: existence, artificiality and reality

• Laser light creates black holes in the lab: As it is hard to experimentally observe what happens to the light’s wavelength, when it approaches a black hole’s horizon, Ulf Leonhardt at the University of St Andrews, UK, and his colleagues seem to have found an alternative route. By firing two laser beams along an optical fiber, first the slower one and then the faster one (the speed depends on the wavelength), the faster light beam tries chases the first bundle of light. When the fast light beam reaches the slower one, it dramatically drops its speed in order to take the lead; however, if the speed difference is large, then the faster light beam becomes trapped by means of the slower bundle — an effect that is intuitively similar to what happens to the light beam at a black hole’s horizon. The team was able to measure the light’s shift patters, which closely correspond to those predicted by cosmologist at event horizons. [full article here].
• Black Holes at the LHC: I found this article by P. Kanti to be quite informative and relatively easy to follow. It is an nice overall outlook at the black-hole creation at the LHC.
• As CERN will make an attempt at observing — or disproving the existence of — mini black holes, which is one of the consequences of — and hence one of the ways to prove or disprove — the superstring theory, here appeared another absolutely pointless, inconstructive, inconclusive, badly written, and subtly and deliberately offensive article, aimed at “string theory is wrong, get over it…”.

Found online

I post here a couple of extracts from the world of (1) astronomy and astrophysics, (2) biology and archaeology, (3) technology, (4) politics and the world that I have found on the internet.

Astronomy and Astrophysics

1. Discovery of the Candidacy for the Furthest Galaxy: The Hubble telescope has come across a galaxy, presumably 13 billion light-years away, making it a strong candidate for the furthest and hence youngest galaxy ever observed. It has been given the name (or the code, rather) A1689-zD1. The galaxy would have formed only 700 million years after the Big Bang; if this is the case, then this galaxy must be one of the first few that helped end the dark ages of the Universe. The discovery was made by means of the natural magnification, provided by the galaxy cluster Abell 1689. [full article here]. Update: 13 billion light years away is actually so very huge. If you think about it, it amounts to about metres away; that’s 4,000,000,000,000,000,000 metres. And we worry that our work is too far away from our home!
2. Dark-matter powered first stars: When a star emits radiation, it does it through thermonuclear fusion reactions that occur deep inside it and its nucleus. There is a suggestion that the early stars — that existed about 100 to 200 million years after the Big Bang — were predominantly fueled not by fusion, but rather by annihilation. As the Universe was still relatively small at that time, matter and antimatter existed in high proximity (as opposed to, for example, what it is today), this suggestion has a significant base. [full article here].
3. Smaller Version of the Solar System Is Discovered: Scott Gaudi of Ohio State University and his colleagues “said Wednesday that they had found a miniature version of our own solar system 5,000 light-years across the galaxy — the first planetary system that really looks like our own, with outer giant planets and room for smaller inner planets.” The object was named OGLE-2006-BLG-109. “… a planet about two-thirds of the mass of Jupiter and another about 90 percent of the mass of Saturn are orbiting a reddish star at about half the distances that Jupiter and Saturn circle our own Sun. The star is about half the mass of the Sun.” “… warm rocky planets — suitable for life — could exist undetected in the inner parts of the system.” The planets were discovered by means of the microlensing. ” … on March 28, 2006, a star 5,000 light-years away in the constellation Scorpius began to pass in front of one 21,000 light-years more distant, causing it to flash. That was picked up by the Optical Gravitational Lensing Experiment, or Ogle.” The collected data provided the knowledge of “not just the masses of the interloper star and its two planets, but also rough approximations of their orbits”. [full article here; for those who have access to Science articles, here are their results].
4. Beautiful Nebula (photo): (Traffic Alert!!!) view photo.
5. Crab Nebula (photo): (Traffic Alert!!!) view photo.

Biology and Archaeology

1. Modern Birds Existed Before Dinosaur Die-Off: “Modern birds originated a hundred million years ago—long before the demise of dinosaurs, according to new research.” Until recently, fossil records were interpreted as if modern birds originated about 60 million years ago; however, the genetic analyses (based on the concept of molecular clock) suggest that these originated some 40 million year earlier (that being 100 million years ago). Dinosaurs disappeared some 65 million years ago. [full article here].
2. 20 Facts About the Human Genome: Here. Perhaps you will find something you don’t know (I did).
3. Who Eats Who: What a great shot!
4. Finding an Underwater Lake (video): Excellent extract from “The Deep” programme. (Traffic Alert!!!) Watch video.

Technology

1. Air-Fueled Car: “A French engineer has claimed he will be ready to start selling a car with no carbon emissions within a year.” (Traffic Alert!!!) Watch video.
2. Zero Emission Car: Here is a short explanation of the suggestion of collecting the carbon dioxide, emitted by a car, in order to later reuse it. Good idea, but, as someone mentioned it in the comments, the overall energy produced from this ‘recycling’ is probably not going to be much. But then again, we need to see the actual calculations.
3. These are in tight connection with point 3 of the list of 2008’s saver technologies.
4. Information age: How exactly has information and communication technology evolved over time? A very nice photographic timeline (here).

Politics and the World

1. The (supposed) 1980 Soviet particle beam weapon construction site (photo): If Soviet Union indeed ever had a project of developing the particle beam weapon around 1980, the construction site is believed to be captured in this American satellite image.
2. Chicago to Raise the Environmental Awareness by Turning Lights Off: On March 29 from 20:00 to 21:00, as part of the Earth Hour 2008, Chicago will turn the lights off. I wonder what is the estimated cost of saved energy over this hour — must be a very-very large number. If anyone among the readers is from Chicago, I would like to see a few photographs of the city during the hour — that must be magnificent! [reference]
3. View from Mountain Everest: Have you ever stood on “the top of the world”? Are you planning on doing so any time soon? Well, me neither. But at least we can can a sense of what it is like, by taking a look at this splendid panoramic photograph: (Traffic Alert!!!) here.

A Bead Sliding on a Parabola-Shaped Smooth Wire

I present here a beautiful solution (as many, including myself, would find) to a classical problem in mechanics.

A smooth massless wire is bent into a shape of a parabola , where is a positive constant. The wire is oriented vertically, opening upward, and is subjected into a uniform gravitational field of strength , directed downward. The wire rotates with a constant angular velocity about the axis, while a bead of mass is free to slide on the wire without friction. We want to analyse this system for stability.

First, I will solve the problem, and then I will make a few remarks about the solution.

As the bed is confined to the wire, which rotates in , the problem is reduced to a one-dimensional motion of the bead, with rotation and wire’s shape playing the role of holonomic constraints.

As the gravitation field is acting only along the axis, we choose the zero of the potential energy at (id est, at the bottom of the parabola), in which case the potential energy of the system can be written:

Note that the potential energy of the wire plays no role, since the wire is massless and hence it is a mere constraint for the bead’s motion, as has been mentioned previously. The kinetic energy of the system is written as

We can now write down the Lagrangian for the system:

After computing the derivatives , we can write down the Lagrange equation of motion for the system:

An equilibrium can occur only at a fixed point — a point where ;that is, if a material point is placed at a fixed point at rest, it will stay at rest at that point. Such points are found from the Lagrange equation by simply setting :

Let us first analyse the first solution: . Consider small perturbations around . In this case, the Lagrange equation becomes

or

where we have neglected all higher order terms (such as ). The resulting equation has the same form as that describing the simple harmonic motion; hence we can conclude that the stability of the system about point depends solely on the sign of the factor . Thus, there are three cases:

1. the fixed point is stable with a frequency of oscillation ;
2. the fixed point is a separatrix; the period of oscillation is infinitely long (id est, the frequency is zero);
3. the fixed point is unstable.

Let us now discuss the second solution, namely . The solution implies that every point is a fixed point, when this condition is satisfied. It can easily be verified, though, that all points are unstable (or, more correctly, each one is a separatrix). Indeed, suppose we consider the stability of the system at a point . We consider with small perturbations about point . The Lagrange equation of motion rewrites:

(note that )

motion is unstable, unless to begin with.

Remarks: the solution involves Lagrangian mechanics. This particular problem can be solved using simple Newtonian formulation. Such solution would, in principle, be quite easier, for there would be no need to look for auxiliary tools like the Lagrangian and hence no need to take three derivatives of it. However, the Newtonian formulation would be a perfect choice for finding the second solution to the Lagrange equation for fixed points (namely, .) Such arguments are presented here. Indeed, we can see that we here have arrived at the fact that the bead will rotate in a circle of a given radius if and only if

precisely the result found here.

On the other hand, the Newtonian formulation does not reveal the subtle nature of stability of the system in various other configurations, discussed above. This is in opposition to the Lagrangian formulation, which naturally leads to the analysis of these configuration.

One further advantage of the Lagrange formulation is that it possesses a by far greater generality than the Newton’s solution. For example, the above solution can easily be generalised to the case when the wire’s shape is bent into a biquadratic parabola, (where, perhaps surprisingly, one finds two equilibrium points, none of which is located at the origin), or any other analytic smooth function for that matter.

A Short Update and Motivation for Further Takeoff

I sincerely appologise for updating the blog thus rarely. The new semester has started from a tough note, and so it ought to take time for me to obtain a laminar flow, for I would really hate to see any turbulent behaviour.

As some of you may know (and those who have checked out my web page, http://individual.utoronto.ca/nikolaev, for more information), I organise the 2008 Canadian Undergraduate Mathematics Conference (CUMC) that will take place at the University of Toronto some time in July. I have recently found out that the 2008 Canadian Undergraduate Physics Conference will also take place at the University of Toronto some time in October. Knowing that I have gained much experience in organising the CUMC, I thought no longer and found people responsible for the organising the physics conference. I now organise both events. With any further questions, please contact me. If you would like to appear as one of the speakers, please let me know that, too!

Again, I regret that I haven’t been updating the blog too often. I will try to manage my time better so that I will leave a few minutes to scribble a note or two. I have had a few things I was ought to share with the blog, but found no time to actually write them; as a result, I now do not remember what they were…

Also, I have quite a few nice photographs of the University of Toronto campus to show. These will also hopefully appear reasonably shortly.

On another note, I mentioned that apparently University of Toronto Physics Department had a store (here and here). Well, I went there and I looked at it. Umm… I couldn’t find it. Perhaps I was either looking at the wrong place or it was closed. I should ask someone, I think. I’ll let you know.

In the News

UK push for space station modules
A proposal for the UK to join the International Space Station (ISS) project has been put forward by a group of scientists and engineers.
A group of scientists and engineers put forward a proposal for UK to joint the ISS (Internation Space Station) project in that Britain will build and launch two HEMs (Habitation Extension Modules), directed towards improving the living conditions therein. [from BBC NEWS].

BBC NEWS also provide some short information on the proposed HEMs, which I thought I’d paste here, too:

• HEM is a 3.8m x 5.7m cylinder; Modules add 100 cu m to ISS
• HEM-C is a communal area for eating, meeting and socialising
• HEM-D sleeps 6 astronauts with enhanced radiation protection
• Launch on Soyuz-Fregat vehicle with 3 tonnes of supplies
• Room for one ISS Payload Rack for UK experiments
• Launch/build cost: £530 million; other costs about £70m

More details here (pdf file, 380 KB).

It is interesting that UK pulls out their support from particle physics, but will most probably sponsor this project. This all seems as if they rate the importance of scientific discoveries. Of course, ISS is crucial and there is much that humanity can gain from it; but ILC is very important, too, and we should not forget this.

Low energy light bulbs should be handled carefully
Be cautious when disposing your low energy light bulbs (such as the CFT ones) — some may contain a small amount of mercury. In fact, environmental agency in UK called for posting more information about this, since too little people new about the harm these excellent devices may bring when disposed. [from here]

This reminds me of an incident with a CFT light bulb some two years ago. I was twisting a CFT light bulb in, when it suddenly broke in half — I guess it was that kind of light bulbs that break for no particular reason. Knowing its low but measurable toxicity, I got a little scared. Luckily enough, it was a hot-hot summer day with no clouds whatsoever, so I decided to walk out into the yard and stand under the sun for 25 minutes. The idea was that if that light bulb did do something bad to me, then those 25 minutes under open sun would have done two or three hundred times as much, so the effect of a piteous light bulb would be negligible. That’s how I solve problems regarding health ;) I bet my fiancee is ready to kill me herself for my health-related beliefs.

UofT Department of Physics has a department store!? O_O
I have just found out that University of Toronto Department of Physics has a departmental store, where all various kinds of objects of UofT physics logos is sold. Boy, I am going down there tomorrow first thing!

What do you know about Kuiper belt?

The Live Science web site posted a short article, a part of which gives a nice overview of Kuiper belt and current perspective at it.

Here is a short summary on Kuiper belt from the article (which can be found here

Why is there rainbow of colors in the Kuiper belt?
Kuiper belt past Neptune is the suspected home of the comets, which complete their solar orbits as fast as a few decades or at most a few centuries. University of Hawaii astrophysicist David Jewitt says that it is surprising that Kuiper belt shows a very wide range of colours (from slightly blue to very red). The reason for it is unknown, although “Jewitt and his colleagues had suggested that cosmic rays could have made Kuiper belt objects redder, while impacts with rocks could have dug up more pristine matter that made them less red,” he thinks there ought to be another explanation.

What is ultra-red matter?
A material that exists only on about half or all Kuiper belt objects and their immediate progeny, the centaurus (these are icy planetoids orbiting between Jupiter and Neptune that recently escaped from the Kuiper belt). Interesting is that the ultra-red matter does not exist in the inner solar system, which suggests that ultra-red matter is unstable at higher temperatures, as Jewitt explains. He also says that the red colours suggest that this matter may contain organic molecules. A spacecraft could ideally go and take a probe of what it is.

Has the Kuiper belt shrunk?
Calculations suggest that Kuiper belt lost about 99% of its original mass. There are several conjectures as to how and when this happened. One suggests that when Saturn and Jupiter shifted their orbits roughly 4 billion years ago, their gravitational pulls threw Kuiper belt objects out of the solar system. Another suggests that objects pulverised themselves into dust and were swept away buy Sun’s radiation. Another one suggests that the proposition that mass was lost is wrong, in which case there is missing something crucial in our understanding.