I have an accompany these days when I take a walk in the footpath of Rad Lane, Abinger Hammer. It is a sheep dog, with white and patches of black on, probably, her body. I knew sheep dogs are very clever. It was a Japanese animation, Heidi, when I first saw a sheep dog guding sheep in the Alpine montain fields. Next one is a BBC programme called "rural life" featuring people's life in villages and farms. I think it was in Cornwall where one clever sheep dog takes care of sheep for the farmer, who is sitting on a big stone placed in the cliff facing the ocean.
The sheep dog, my recent friend, is owned by a my neighbour farmer (who runs Rad farm, mainly specialises chicken and eggs), but with so much curiosity, she runs from nowhere as soon as she finds my smell to accompany with me for a walk. She is not so obedient to me, of course. Sometimes, she disappears in the corn field. But about 15 minutes later, when I reached the sheep field, she suddenly come back out of howthorn hedges and walk with me, sometimes looking back if I am following her!
She passes through her own farm house, and kindly bring me back to my house. And, after she confirms I am defnitely home,
she finally comes back to her home... How clever and kind this dog is!
Saturday, October 08, 2005
Old gentleman and Super string theory
When I was taking a walk this morning, I met a gentleman, whose age is probably nearly 70 or 80 years old, on a way back to the clock tower in Abinger Hammer from the North Downs. The begining was just a brief exchange of greetings, but gradually our conversation evolved into a comment about colourful British landscape in early autumn (meaning now), global warming, and finally superstring theory! Surprisingly, this old gentleman is thirsty for knowledge, particularly on science. It seems physics is his best interest. I have never met an ordinary people (I mean, non-scientists) who knows that the M-theory implies we are living in the D-brane floating in the 11-dimensional world! I respcet this kind of people, with full of curiosity and a strong will trying to improve themselves.
Surrounded by English myst in October, I guess we have talked more than 30 minutes on the village path, about the fate of the universe. Maybe, blackbirds and robins were singing in the fence of the cow fields, and the sounds were transmitted through the fog. The white sun was about to appear with lights to make the colour of the North Down Hill more vivid. This environment and nice, respectful people.... is the reasons why I sometimes like a life in Britain, doing physics.
Surrounded by English myst in October, I guess we have talked more than 30 minutes on the village path, about the fate of the universe. Maybe, blackbirds and robins were singing in the fence of the cow fields, and the sounds were transmitted through the fog. The white sun was about to appear with lights to make the colour of the North Down Hill more vivid. This environment and nice, respectful people.... is the reasons why I sometimes like a life in Britain, doing physics.
Wednesday, October 05, 2005
Angular momentum in the Lab- and Intr- frames
In finite quantum many-body systems, such as nuclei, metalic clusters and dilute atomic gases in a trap, an approximation of rigid-rotor is useful. As far as rotation is concerned, anuglar momentum is the most important and natural choice for physical quantities in descriptions of these systems. Then, we have to think about the coordinates-space transformation between the Laboratory frame and the Intrinsic frames. (Let us denote Lab-frame and Intr-frame, hereafter.)
The transformation is an ordinary unitary (orthogonal) transformation, so that simply we tend to believe that physics does not change before and after the transformation (in particular, from a quantum mechanical viewpoint). However, Klein noticed more than 50 years ago that the commutatation relation of angular momentum operators are different in the Lab- and Intr-frames. This means that the transformation is not a canonical transformation.
Usually, the commutation relation is given as
[J_m, J_n] = i J_l \eps_{mnl}.
This is the case for the commutation rule in the Lab-frame. However, in the intrinsic frame, the commutation relation is given as
[J_m,J_n] = -i J_l \eps_{mnl}.
Namely, the sign is opposite in the right-hand side.
There are several proofs for the commutators, and they are roughly divided into two groups. One of them is to use differential operator representations, and the commutators are directly calculated. The other type is to use properties of tensors, in particular, with respect to the transformation in the Lab- or Intr-frame. Ring and Schuck, Eisenberg and Gleiner, and Iwanami's nuclear physics textbook employ the former approach, while Bohr and Mottelson the latter (although the detailed proofs are not written in the textbook of BM's....). My former supervisor in Tokyo said to me that the simplest proof he has ever seen is the one by Landau. It was true.... Only one math equation and three lines to explain briefly what has to be done in the proof. As usual, the equation can be derived "easily", according to Landau. I have to confess, at first, I could not understand why this equation can be derived "easily"... But, after having read Eisenberg and Gleiner, I realised that Landau's approach is exactly the same as the Germans', although they spent nearly three pages to demonstrate that "simple" equation.
Anyway, intuitively, this sign change in the intrinsic frame is very difficult to grasp. I heard many good and old professors who are not familar with nuclear structure physics but general nuclear physics say " I don't believe it" or "How come?" I myself tried once to prove this when I was in my PhD course in Tokyo, but I gave up proving the equation because I felt "the proof could eat up my precious time for numerical calculations and time to read recent publications in PRL and PRC in preparation for writing a paper....."
Last week, suddenly, I decided to come back to the old (personally) unsolved problem. The first several days, my calculations just repeated creations of the comments and complaints told by the old professors, that is, "How come?" Next several days, I noticed my physical interpretations about the transformation to the intrinsic frame was wrong and needed to be modified, but the calculations just ended up in a disastrous manner, simply gave nothing meaningful.... Then, finally, a last couple of days, I found my treatment of a rank-\lambda tensor was wrong, particularly, about the Wigner's function... If D(\Omega) is chosen, this is not a tensor at all. But the complex conjugate of D is a tensor!!! In addition, the direction of the transformation is reversed when we change an operator appraoch to a matrix-representation approach. Perphaps, this is the key point why the sign has to be reverted in the intrinsic frame for the angular momentum commutation relation.
Anyhow, it was very painful to complete the proof. I think Klein is great because he noticed the problem and solved correclty. I know this is because he did not have any prejuice, which is often very difficult not to do so. (Oscar Klein is the physicsts who derived the Klein-Gordon equation, Klein-Nishina formula and Kaluza-Klein theory!) Thinking from the first principle is sometimes very important, especially when you want to go beyond the currently established things and concepts. In this sense, I want to believe that my attempt this week is not simple a waste of time...
The transformation is an ordinary unitary (orthogonal) transformation, so that simply we tend to believe that physics does not change before and after the transformation (in particular, from a quantum mechanical viewpoint). However, Klein noticed more than 50 years ago that the commutatation relation of angular momentum operators are different in the Lab- and Intr-frames. This means that the transformation is not a canonical transformation.
Usually, the commutation relation is given as
[J_m, J_n] = i J_l \eps_{mnl}.
This is the case for the commutation rule in the Lab-frame. However, in the intrinsic frame, the commutation relation is given as
[J_m,J_n] = -i J_l \eps_{mnl}.
Namely, the sign is opposite in the right-hand side.
There are several proofs for the commutators, and they are roughly divided into two groups. One of them is to use differential operator representations, and the commutators are directly calculated. The other type is to use properties of tensors, in particular, with respect to the transformation in the Lab- or Intr-frame. Ring and Schuck, Eisenberg and Gleiner, and Iwanami's nuclear physics textbook employ the former approach, while Bohr and Mottelson the latter (although the detailed proofs are not written in the textbook of BM's....). My former supervisor in Tokyo said to me that the simplest proof he has ever seen is the one by Landau. It was true.... Only one math equation and three lines to explain briefly what has to be done in the proof. As usual, the equation can be derived "easily", according to Landau. I have to confess, at first, I could not understand why this equation can be derived "easily"... But, after having read Eisenberg and Gleiner, I realised that Landau's approach is exactly the same as the Germans', although they spent nearly three pages to demonstrate that "simple" equation.
Anyway, intuitively, this sign change in the intrinsic frame is very difficult to grasp. I heard many good and old professors who are not familar with nuclear structure physics but general nuclear physics say " I don't believe it" or "How come?" I myself tried once to prove this when I was in my PhD course in Tokyo, but I gave up proving the equation because I felt "the proof could eat up my precious time for numerical calculations and time to read recent publications in PRL and PRC in preparation for writing a paper....."
Last week, suddenly, I decided to come back to the old (personally) unsolved problem. The first several days, my calculations just repeated creations of the comments and complaints told by the old professors, that is, "How come?" Next several days, I noticed my physical interpretations about the transformation to the intrinsic frame was wrong and needed to be modified, but the calculations just ended up in a disastrous manner, simply gave nothing meaningful.... Then, finally, a last couple of days, I found my treatment of a rank-\lambda tensor was wrong, particularly, about the Wigner's function... If D(\Omega) is chosen, this is not a tensor at all. But the complex conjugate of D is a tensor!!! In addition, the direction of the transformation is reversed when we change an operator appraoch to a matrix-representation approach. Perphaps, this is the key point why the sign has to be reverted in the intrinsic frame for the angular momentum commutation relation.
Anyhow, it was very painful to complete the proof. I think Klein is great because he noticed the problem and solved correclty. I know this is because he did not have any prejuice, which is often very difficult not to do so. (Oscar Klein is the physicsts who derived the Klein-Gordon equation, Klein-Nishina formula and Kaluza-Klein theory!) Thinking from the first principle is sometimes very important, especially when you want to go beyond the currently established things and concepts. In this sense, I want to believe that my attempt this week is not simple a waste of time...
Saturday, August 27, 2005
Meeting friends in Japan
In the August of this year (2005), I was back in Japan, I mean in Tokyo and Nagano. Here in this blog, there is nothing to talk about Nagano because I usually cannot put myself into any kinds of physics research there. Gardening, riding a bicycle to challenge moutain passes, eating Japanese noodles (soba) in Oiwake... there are too many things to do to read even a single physics textbook in my beautiful home village. And, this is nearly the case again for this Summer.
One small difference in this year is that I had two visitors. They are my all friends and junior colleagues in Univ. of Tokyo, Komaba. One (Dr. F) is from New York and the other (Dr. O) from Kyoto. The main purpose for the gathering is to climb a volcano mountain (more precicely, a ridge of the valcano crator of Mt Asama) near my village. However, due to this summer's bad weather dominating most of the eastern part of Japan, we had to give up the climbing in the end. (We could climb one of the parasite volcanos to Mt Asama, called Ko-asama, the day before the ascent to Mt Asama, though.) So that, we had a plenty of time for discussion in my log cabin, my nice summer cottage in Nagano, over a glass of Long Island wine Dr F broght for us from Brook Haven and RIOJA I bought at Sainsbury in Burpham....
One small difference in this year is that I had two visitors. They are my all friends and junior colleagues in Univ. of Tokyo, Komaba. One (Dr. F) is from New York and the other (Dr. O) from Kyoto. The main purpose for the gathering is to climb a volcano mountain (more precicely, a ridge of the valcano crator of Mt Asama) near my village. However, due to this summer's bad weather dominating most of the eastern part of Japan, we had to give up the climbing in the end. (We could climb one of the parasite volcanos to Mt Asama, called Ko-asama, the day before the ascent to Mt Asama, though.) So that, we had a plenty of time for discussion in my log cabin, my nice summer cottage in Nagano, over a glass of Long Island wine Dr F broght for us from Brook Haven and RIOJA I bought at Sainsbury in Burpham....
Saturday, March 26, 2005
Kepler and Newton (Systematics or Singularity)
"This world is unfair" .... Maybe yes.
When you see low-quality papers in highly prestigeous scientific journals, this might be your assessment of the reality. (hope you agree.)
I came back from Manchster, where this year's IOP meeting for nuclear physics was held. On the second day, the conference dinner was organised. I joined the table with a few relatively young academics and had a talk about many things. But particularly, we eagerly debated about the way to carry out physics research. They all have experimental backgrounds and it was only me who was a theoretician. But the point was in common, that is, whether we should focus on systematics or one singular event contaning new physics. The guy from France said that systematic survey is important and most of the research should be spent on the systematics. Another guy from Scotland (i.e., Britain) said we should focus on one particular event containing very new and interesting physics. And I, from Japan, said that the one single event should be studied after looking at the systematics. What I mean, is that the systematics should not be the purpose, but it should be a way to reach or find out the singular events with good and new physics.
Then, we talked about Kepler and Newton. Well, more precisely, we should add Tycho Brahe, the supervisor of Kepler. Tycho spent his entire professional life on the systematic study of the motion of stars, particularly, planets. He left the enormous amount of data collected for many decades. and passed on to Kepler. He then analysed this systematics and found three laws. After 70-80 years, Newton explained the laws with mathematics.
Kepler's work is, needless to say, the work of genius. It is extremely non-trivial to dig out a very small treasure stone (the three laws) embedded by an innumerable numbers of sands and dirty stones (Tycho's data). It is further non-trivial to explain the three laws by a single principle in the name of the theory of gravity. So, Newton is a genius of geniuses. On the contrary, it is obviuos that Tyco's work is nothing but the systematics, which is tedious, boring and painstaking (at least to me). Probably, from the modern standard, this kind of work should be avoided because we can not earn many numbers in pubilcation. However, it is certain that without the work, Kepler and Newton could have nothing to study in the motion of planets.
Darwin said in his famous book, "The origin of Spieces", that we should not forget that every species currently occupying the Earth is the result of so-many deaths and failures of extinct fauna and flora. This means that we are just tree leaves on the top of a thick forest, and below us, there are tremendous number of dead branches and fallen leaves. But without them we could not sit here and see the world.
It is interesting to observe that even today, the styles of scientific studies rarely change: the French and German prefer the systematic studies while the British try to find a special event. Well, History is continuous and rarely faces a phase transition, perphaps.
Tuesday, March 08, 2005
Nuclear physics and Condensed matter physics
I have a visitor from Japan now. He got his PhD degree for his work on physics of metallic clusters as an application of nuclear structure theory. Now he is a post-doc in a Japanese university and studying structure of fullerens with the density functional theory. To many nuclear physicists, solid-state or condensed-matter physicists are a kind of the target of envy: they are richer, have more opportunities, and easier access to publicaions in Phys. Rev. Lett, Nature and Sciences (meaning more publications in these highly prestigeous journals). Of course, some of these things can be purely an imagination by nuclear physicists....
Listening to the inside-stories from the visitor, the condensed matter physics community is not such the Garden of Eden. It is more like a nuclear system consisting of independent particles. That is, the subjects they are interested in are so various and huge that they pay little attention to others' works...Yes, very little interaction between researchers... This comment by the visitor reminded me of my experience in an anuual meeting of the Japanese Physical Society (JPS) about a year ago when I first attended to the session of the condensed matter physics.
There were many presentations and a great number of audience came to listen. But after each presentation few questions were given. It seemed nobody was in the room. To me, the situtation was comfortable for asking my naive questions, such as "Is the GP equation really able to reproduce high-spin states with vortices?" The answers to my questions from the speakers were not so sound as an expert. Instead of giving a good reply reminding the audience of a fact that the questioner (that is, myself) is stupid enough to ask this kind of question, with a deep insight and wide range of knowledge in their physics, it seemed to me that they tried to escape from my "accusation" as soon as possible by saying something confusing me. As a matter of fact, I was a little dissapointed at their responses. The chairman was Professor Ueda, who is well-known for his works on the Bose-Einstein Condensation, and probably knew how to deal with this kind of naive and stupid questions, but he did say very little in order to help their students in the presentation stage, for unknown reasons. Probably, I was stupid enough that he wanted to finish the session as soon as he could and to go to lunch....I don't know.
I then went to the high-energy physics (Hadron Physics) session. I expected more than the condensed matter physics session, but surprisingly the atomosphere was very similar to the previous one. Of course, in comparison to the condensed-matter physics community, the number of the audience in the hadronic physics session is much smaller, but I guess more than 50 people fullhoused the room. Dr. Fukushima from MIT gave an invited talk in the begining, but the reaction fro the audience was not so good. I strongly believe that many of them could not follow what he talked about although I thought his presentation was well-prepared and good-structured so as to make even novices understand to some extent. Again, I was dissappointed a little.
Back in Nuclear Structure Session, surprisingly the atomosphere was very different from the last two sessions. The participants asked many questions and the chairman sometimes had to stop the arguments. The reason was obvious. In contrast to the previous two physics communities, there are more seniour academics taking place in the session at the nuclear structure division. Therefore, the audience well understood the contents spoken by the talkers and they could easily evaluate the value of the talks.
I learned that even inside physics there are very many different worlds. If I went to the sessions such as the material sciences or semi-coductor physics, where the communities are tightly bound to the industry, the atomosphere would be totally different from the others...
Listening to the inside-stories from the visitor, the condensed matter physics community is not such the Garden of Eden. It is more like a nuclear system consisting of independent particles. That is, the subjects they are interested in are so various and huge that they pay little attention to others' works...Yes, very little interaction between researchers... This comment by the visitor reminded me of my experience in an anuual meeting of the Japanese Physical Society (JPS) about a year ago when I first attended to the session of the condensed matter physics.
There were many presentations and a great number of audience came to listen. But after each presentation few questions were given. It seemed nobody was in the room. To me, the situtation was comfortable for asking my naive questions, such as "Is the GP equation really able to reproduce high-spin states with vortices?" The answers to my questions from the speakers were not so sound as an expert. Instead of giving a good reply reminding the audience of a fact that the questioner (that is, myself) is stupid enough to ask this kind of question, with a deep insight and wide range of knowledge in their physics, it seemed to me that they tried to escape from my "accusation" as soon as possible by saying something confusing me. As a matter of fact, I was a little dissapointed at their responses. The chairman was Professor Ueda, who is well-known for his works on the Bose-Einstein Condensation, and probably knew how to deal with this kind of naive and stupid questions, but he did say very little in order to help their students in the presentation stage, for unknown reasons. Probably, I was stupid enough that he wanted to finish the session as soon as he could and to go to lunch....I don't know.
I then went to the high-energy physics (Hadron Physics) session. I expected more than the condensed matter physics session, but surprisingly the atomosphere was very similar to the previous one. Of course, in comparison to the condensed-matter physics community, the number of the audience in the hadronic physics session is much smaller, but I guess more than 50 people fullhoused the room. Dr. Fukushima from MIT gave an invited talk in the begining, but the reaction fro the audience was not so good. I strongly believe that many of them could not follow what he talked about although I thought his presentation was well-prepared and good-structured so as to make even novices understand to some extent. Again, I was dissappointed a little.
Back in Nuclear Structure Session, surprisingly the atomosphere was very different from the last two sessions. The participants asked many questions and the chairman sometimes had to stop the arguments. The reason was obvious. In contrast to the previous two physics communities, there are more seniour academics taking place in the session at the nuclear structure division. Therefore, the audience well understood the contents spoken by the talkers and they could easily evaluate the value of the talks.
I learned that even inside physics there are very many different worlds. If I went to the sessions such as the material sciences or semi-coductor physics, where the communities are tightly bound to the industry, the atomosphere would be totally different from the others...
Monday, February 28, 2005
Plane wave and Spherical Bessel * Spherical Harmonics
It is often said in Japan that teaching is learning. I am always convinced that this saying is true everytime I prepare for lectures and discussions with students. Last week it was the partial wave expansion of plane wave that reminded me of the saying again.
Obvioulsly, the Hamiltonian for a free particle has translational and rotational symmetries. So, linear and angular momenta are good quantum numbers. However, the linear and angular momentum operators do not commute with each other, which means we need to choose one of them for labelling the free-particle wave function. In the scattering problem, linear momentum is usually chosen because of the nature of the scattering experiment (you know, the incident beam is produced with a good linear momentum...). This means the wave function far from the target is a plane wave.
In the vicinity of the target, however, angular momentum plays more important role than linear momentum because the interaction between the target and the beam causes the trajectory of the beam bent. So, in many cases, the plane wave is expanded by wave functions labelled by angular momentum, which has a product form of the spherical Bessel function and the spherical Harmonics.
Then, I had a question. When the flux of the free-particle wave function is calculated with the plane wave, the result is well-known to be the constant velocity (in a non-relativistic limit). Even after a conversion into the spherical polar coordinates, the flux has only \theta (orientation) dependence, and there is no dependence of distance (from the origin). However, with the angular momentum representation ( that is, with spherical Bessel and sherical harmonics), the resultant flux seems r-dependent (that is, dependent on the distance). What is wrong with this?
After analysing several mathematical relations, I found that the spherical Bessel functions satisfies a kind of conditions similar to the completeness condition. But this completeness condition is realised only with the weight factor (2L+1), where L represents angular momentum. I have never seen this in the literatures.
I talked to J. on last Friday about this problem. His expertise is the nuclear reaction theory. He said that he was aware of this problem, but could not give the instant answer. "OK, so this problem is not so trivial." is my impression. He continued that he has seen an article in the Am. J. Phys. discussing this problem many years ago. Maybe, the answer can be obtained from the paper.... if J's information is correct and the paper really exists....
Obvioulsly, the Hamiltonian for a free particle has translational and rotational symmetries. So, linear and angular momenta are good quantum numbers. However, the linear and angular momentum operators do not commute with each other, which means we need to choose one of them for labelling the free-particle wave function. In the scattering problem, linear momentum is usually chosen because of the nature of the scattering experiment (you know, the incident beam is produced with a good linear momentum...). This means the wave function far from the target is a plane wave.
In the vicinity of the target, however, angular momentum plays more important role than linear momentum because the interaction between the target and the beam causes the trajectory of the beam bent. So, in many cases, the plane wave is expanded by wave functions labelled by angular momentum, which has a product form of the spherical Bessel function and the spherical Harmonics.
Then, I had a question. When the flux of the free-particle wave function is calculated with the plane wave, the result is well-known to be the constant velocity (in a non-relativistic limit). Even after a conversion into the spherical polar coordinates, the flux has only \theta (orientation) dependence, and there is no dependence of distance (from the origin). However, with the angular momentum representation ( that is, with spherical Bessel and sherical harmonics), the resultant flux seems r-dependent (that is, dependent on the distance). What is wrong with this?
After analysing several mathematical relations, I found that the spherical Bessel functions satisfies a kind of conditions similar to the completeness condition. But this completeness condition is realised only with the weight factor (2L+1), where L represents angular momentum. I have never seen this in the literatures.
I talked to J. on last Friday about this problem. His expertise is the nuclear reaction theory. He said that he was aware of this problem, but could not give the instant answer. "OK, so this problem is not so trivial." is my impression. He continued that he has seen an article in the Am. J. Phys. discussing this problem many years ago. Maybe, the answer can be obtained from the paper.... if J's information is correct and the paper really exists....
Thursday, February 24, 2005
Snow and Lecture
Last four or five days, we have had snowfall in the southeast England. Even today... Last three years since I came to Britain, I have never seen this kind of weather. I asked my colleague, who has lived here more than five years, if he has seen the similar weather before, but his answer was negative.
Nevertheless, thanks to the Gulf stream (probably), snow melts quickly this year. In fact, it is now at noon and I can still see, through my office windows, snow falling, but there is no snow on the road. When I came to the university this morning, the world was totally white, though.
So, the serious problem this time is the snow on the raod early in the morning, in particular on Thursdays. This is based on a totally selfish reason, that is, I have a lecture of Maths to give from 9:00 am to 11:00 am every Thursday in the Spring semster. So, I need to come to the university by 8:30 am. Around 8 o'clock, air temperature is still low and there is much snow on the road.
Last three years, I have at least one day per year when I needed to fight with snow to come to the university. Two years ago was the most serious. I could not drive a car on that day, but luckily I lived relatively near to the university at that time. So, I can walk to the university. Now, I am living far away from the University. Even by car, it takes about 30 minutes (using high-speed road, similar to freeways), so if heavy snow falls I have a great difficulty to come to Guildford.
They say the global warming is happening. Yes, there are many strange things happening in weather and climate, but sometimes not in a way we expect. Well, if you say "warming", then why so many snow in early spring or end of winter? Of course, I know things are not so easy and complicated because the dynamics that weather follows is highly non-linear. But still, simply from the selfish reason, I hope the "warming" is literally meant as "warming". What I am saying is that I don't like warm winter, but that I want real spring without much snowfall! (I believe today can be regarded as "early spring"...)
In a Korean drama I have recently seen, there was a scene for a couple who went out for a date for the first time to ask personal questions with each other. The questions contained:
"What is your favorite colour?" --- "White"
"What is your favorite season?" ---- "Winter"
Definitely, with 100% surely, I don't belong to that sort of humans. (The drama is "Kyour Yonka", or "冬恋歌", of course...)
Nevertheless, thanks to the Gulf stream (probably), snow melts quickly this year. In fact, it is now at noon and I can still see, through my office windows, snow falling, but there is no snow on the road. When I came to the university this morning, the world was totally white, though.
So, the serious problem this time is the snow on the raod early in the morning, in particular on Thursdays. This is based on a totally selfish reason, that is, I have a lecture of Maths to give from 9:00 am to 11:00 am every Thursday in the Spring semster. So, I need to come to the university by 8:30 am. Around 8 o'clock, air temperature is still low and there is much snow on the road.
Last three years, I have at least one day per year when I needed to fight with snow to come to the university. Two years ago was the most serious. I could not drive a car on that day, but luckily I lived relatively near to the university at that time. So, I can walk to the university. Now, I am living far away from the University. Even by car, it takes about 30 minutes (using high-speed road, similar to freeways), so if heavy snow falls I have a great difficulty to come to Guildford.
They say the global warming is happening. Yes, there are many strange things happening in weather and climate, but sometimes not in a way we expect. Well, if you say "warming", then why so many snow in early spring or end of winter? Of course, I know things are not so easy and complicated because the dynamics that weather follows is highly non-linear. But still, simply from the selfish reason, I hope the "warming" is literally meant as "warming". What I am saying is that I don't like warm winter, but that I want real spring without much snowfall! (I believe today can be regarded as "early spring"...)
In a Korean drama I have recently seen, there was a scene for a couple who went out for a date for the first time to ask personal questions with each other. The questions contained:
"What is your favorite colour?" --- "White"
"What is your favorite season?" ---- "Winter"
Definitely, with 100% surely, I don't belong to that sort of humans. (The drama is "Kyour Yonka", or "冬恋歌", of course...)
Friday, February 18, 2005
Broadband and Physics
Finally, Broadband came to my home. I have waited for today for 5 years.... Before the introduction of Broadband, I cannot edit this blog from home. (I need to come to the university....) But now I can edit at home.
At the University, I feel I am working. I mean, I talk to students, answer the questions from them, printing papers to read, writing e-mails to colleagues and colloaborators... But I have no time to think at the university! So, I prefer to work at home because there is a plenty of time for thinking (but dangerously for sleeping too). When tired from calculations and debugging, I can take a walk around my home, which has nice hills and forests around with beauttiful views of the North Downs (Surrey Hills). Many wild animals such as rabits, foxes, deers, etc. and English wild flowers and trees are also refreshing my mind everytime. So, BT broadband, which allows me to work at home, is extremely useful to me.
I usually prepare my lecture at home. While preparing, many questions appear in mind for the things I thought I understood. These questions make me understand physics much more deeply. I agree, this is the experience of learning from teaching. So, giving lectures to studnets is very rewarding although it is very time consuming and sometimes very hard.
Today, I was preparing a lecture of quantum mechanics for next tuesday. The subject is about the scattering theory. I know there are two representations for the description of a free particle. When linear momentum is given, it is a plain wave. While, when angular momentum is given, it is the spherical Bessel functions with the spherical harmonics. Then, suddenly today, I have a question.... why in the presence of the central potential do we need to think about the partial wave expansion for the scattered wave function? Since the potential is rotationally symmetric, angular momentum is a good quantum number. We should then start from the wave function with good angular momentum! I thought for a while (about an hour?), but could not find the answer. So, I decided to take a bath. Then after 10 minutes or so (even after singing some Japanese old pop music), like Archimedes, the idea came down from the heaven (or somewhere)!
Well, it might be too expensive to take a bath for finding every new idea. But I manage to survive as a lecturer like this, and I like this kind of life very much. Thinking is what I like most, and surprisingly it is my job now! I thank God (and my employers) and the broadband for allowing me this.
At the University, I feel I am working. I mean, I talk to students, answer the questions from them, printing papers to read, writing e-mails to colleagues and colloaborators... But I have no time to think at the university! So, I prefer to work at home because there is a plenty of time for thinking (but dangerously for sleeping too). When tired from calculations and debugging, I can take a walk around my home, which has nice hills and forests around with beauttiful views of the North Downs (Surrey Hills). Many wild animals such as rabits, foxes, deers, etc. and English wild flowers and trees are also refreshing my mind everytime. So, BT broadband, which allows me to work at home, is extremely useful to me.
I usually prepare my lecture at home. While preparing, many questions appear in mind for the things I thought I understood. These questions make me understand physics much more deeply. I agree, this is the experience of learning from teaching. So, giving lectures to studnets is very rewarding although it is very time consuming and sometimes very hard.
Today, I was preparing a lecture of quantum mechanics for next tuesday. The subject is about the scattering theory. I know there are two representations for the description of a free particle. When linear momentum is given, it is a plain wave. While, when angular momentum is given, it is the spherical Bessel functions with the spherical harmonics. Then, suddenly today, I have a question.... why in the presence of the central potential do we need to think about the partial wave expansion for the scattered wave function? Since the potential is rotationally symmetric, angular momentum is a good quantum number. We should then start from the wave function with good angular momentum! I thought for a while (about an hour?), but could not find the answer. So, I decided to take a bath. Then after 10 minutes or so (even after singing some Japanese old pop music), like Archimedes, the idea came down from the heaven (or somewhere)!
Well, it might be too expensive to take a bath for finding every new idea. But I manage to survive as a lecturer like this, and I like this kind of life very much. Thinking is what I like most, and surprisingly it is my job now! I thank God (and my employers) and the broadband for allowing me this.
Thursday, February 17, 2005
Dirac and Wheeler
Here are two textbooks about the general relativity.One was written by Dirac, and the other by Wheeler et al. Although the theme is the same between them, there is the big difference, which is thickness of the books. I think it is correct to assume that this difference is clearly reflecting the difference in the standing point to look at physics. (I mean, simply the difference in their personal characters.....maybe.)
I bought Dirac's book about 10 years ago. This book contains just 100 pages, with large letters and many pages with a lot of white blank. But, still I don't finish reading it. On the other hand, I already read about 50 pages of Wheeler's, which I bought last year. Interestingly, the ratio (R) of the pages I have ever read (P) and the total page (T) is the same for Dirac's and Wheeler's. (Namely, R_dr \simeq R_wh, where R=P/T.) This may explain the conservation of momentum to understand physics???
I bought Dirac's book about 10 years ago. This book contains just 100 pages, with large letters and many pages with a lot of white blank. But, still I don't finish reading it. On the other hand, I already read about 50 pages of Wheeler's, which I bought last year. Interestingly, the ratio (R) of the pages I have ever read (P) and the total page (T) is the same for Dirac's and Wheeler's. (Namely, R_dr \simeq R_wh, where R=P/T.) This may explain the conservation of momentum to understand physics???
Monday, February 14, 2005
Gravity and Wheeler
In Surrey University, BSc students in the final year are required to do a kind of research called the Final Year Project. This year, I took two students to supervise. I gave one of them the review project on the Dirac equation, which is not so difficult to supervise because it is a quantum theory. Topics from Quantum Mechanics are easy to handle to me because all of my research are from it. However, many students are interested in Black Holes for some reasons. Having considered this "demand from the market", I decided to give the other project on the theory of black hole this year.... which was my big mistake.
Personally, I did not spend much time to learn this subject. I think many physics students and academics have similar experiences as mine, except very few. This is because the gravitation theory cannot give us many jobs, unlike Quantum theory. In modern Universities, the emphasis is placed on mastering quantum mechanics and its applications. As a consequence, very few students seriously study the gravitation theory, or the general theory of relativity.
It is, again, J. Wheeler, who motivated me to go for the theory of Black hole... I mean I don't know him personally,
but I have been influenced by his papers, works, books and articles, directly and indirectly. For instance, my current research as a theoretical nuclear physicist is to solve the Hill-Wheeler equation through a numerical approach for the nuclear wobbling motion; It is when I was a high-school student that I learned to know he was the supervisor of R. Feynman, by reading the famous book "surely, you're..."; and as a fatal blow, my former supervisor in Tokyo recommended me to read Wheeler's recent self-biography book "Geons....", which I've read it a few months ago.
You can tell easily from this book that Wheeler is a genius and a real theoretical physicist: his carrer started from nuclear physics, then particle physics (the famous collaboration with his "PhD student" about the QED) and gravitation theory (naming of the "black hole" was given by Wheeler, and his predictions of gravitational wave and worm holes are famous), and finally recently he arrived at quantum computation and quantum information theory! (David Deutsch is his fomer student!)
Well, I am a nuclear physicist. Particle physics is the thing I am already interested in and sometimes apply the concepts into nuclear physics, but the gravitation theory?? I took a lecture of Prof. Ezawa in Tohoku and of Prof. Eguchi in Tokyo. It was nearly ten years ago when I took these lectures.... So, naturally, I don't remeber what the Einstein's equation is as well as the Christoffel symbol... But If Wheeler did before, maybe I can ..... is the starting point of my mistake. It is true, however, that I enjoy relearning this "new" subject a lot. I hope my FYP student also enjoy this subject.
Personally, I did not spend much time to learn this subject. I think many physics students and academics have similar experiences as mine, except very few. This is because the gravitation theory cannot give us many jobs, unlike Quantum theory. In modern Universities, the emphasis is placed on mastering quantum mechanics and its applications. As a consequence, very few students seriously study the gravitation theory, or the general theory of relativity.
It is, again, J. Wheeler, who motivated me to go for the theory of Black hole... I mean I don't know him personally,
but I have been influenced by his papers, works, books and articles, directly and indirectly. For instance, my current research as a theoretical nuclear physicist is to solve the Hill-Wheeler equation through a numerical approach for the nuclear wobbling motion; It is when I was a high-school student that I learned to know he was the supervisor of R. Feynman, by reading the famous book "surely, you're..."; and as a fatal blow, my former supervisor in Tokyo recommended me to read Wheeler's recent self-biography book "Geons....", which I've read it a few months ago.
You can tell easily from this book that Wheeler is a genius and a real theoretical physicist: his carrer started from nuclear physics, then particle physics (the famous collaboration with his "PhD student" about the QED) and gravitation theory (naming of the "black hole" was given by Wheeler, and his predictions of gravitational wave and worm holes are famous), and finally recently he arrived at quantum computation and quantum information theory! (David Deutsch is his fomer student!)
Well, I am a nuclear physicist. Particle physics is the thing I am already interested in and sometimes apply the concepts into nuclear physics, but the gravitation theory?? I took a lecture of Prof. Ezawa in Tohoku and of Prof. Eguchi in Tokyo. It was nearly ten years ago when I took these lectures.... So, naturally, I don't remeber what the Einstein's equation is as well as the Christoffel symbol... But If Wheeler did before, maybe I can ..... is the starting point of my mistake. It is true, however, that I enjoy relearning this "new" subject a lot. I hope my FYP student also enjoy this subject.
Friday, February 11, 2005
Physics and Rain
It is raining today, nearly all day from the morning. Because there was no lecture to give today, I wanted to take a walk in the hill of Abinger Hammer, where my home is. Yes, there was no lecture today and raining... Theoretical Physicists need a calm and comfortable environment for thinking. Today looked a best day. So, I stayed at home until evening.
There is one thing disturbing my mind recently. It is a relation between symmetry and collectivity. I learned when I was a PhD student that a quantum object with perfect roational symmetry cannot rotate. Therefore, the ground states of the magic nuclei such as 16-O and 208-Pb have zero angular momentum I=0. In many (probably, "most of") textbooks, this is explained by words, and with no mathematics. Well, Dirac said that we need to understand physics without relying on mathematics, and Faraday realized what Dirac said in fact... But, As many other students, it is true that I forced myself to swallow this "well-known" fact as a common sense. However, deep in my heart, there have been something which I cannot digest completely.
I think it is very important to understand (or definte carefully) the term "collectivity". For example, what does the collective wave function mean? In nuclear physics, the particle-plus-rotor model answers this question in a phenomenological manner. So, I decided to use this model to think this problem today.
Out of the window, I saw grey clouds come and go with a great speed. Sometimes, the sound of raindrops was magnified on the roof. Although the problem was hard to solve, I enjoyed this time of thinking under this natural rhythm and melody.
There is one thing disturbing my mind recently. It is a relation between symmetry and collectivity. I learned when I was a PhD student that a quantum object with perfect roational symmetry cannot rotate. Therefore, the ground states of the magic nuclei such as 16-O and 208-Pb have zero angular momentum I=0. In many (probably, "most of") textbooks, this is explained by words, and with no mathematics. Well, Dirac said that we need to understand physics without relying on mathematics, and Faraday realized what Dirac said in fact... But, As many other students, it is true that I forced myself to swallow this "well-known" fact as a common sense. However, deep in my heart, there have been something which I cannot digest completely.
I think it is very important to understand (or definte carefully) the term "collectivity". For example, what does the collective wave function mean? In nuclear physics, the particle-plus-rotor model answers this question in a phenomenological manner. So, I decided to use this model to think this problem today.
Out of the window, I saw grey clouds come and go with a great speed. Sometimes, the sound of raindrops was magnified on the roof. Although the problem was hard to solve, I enjoyed this time of thinking under this natural rhythm and melody.
Thursday, February 10, 2005
Physics and Blog
I didn't know what "blog" means just a week ago.
And suddenly, I noticed that many "diaries" by physicists are being replaced by "blogs".So, I decided to try by myself, too.
I know many Japanese physicists have their "research diaries" or "research blogs",and I found also some American physicists do the same thing.It is strange, but I haven't heared of anybody in the UK who is doing this. Maybe there are, maybe not.
I have a feeling that the Japanese and Americans are similar in this point, that is, writing diaries for other people.
What is the reason for this "diary"? They are supposed to be private by definition, aren't they?
I myself think why I want to write this kind of thing in the web, over and over again. I have not yet had the answer, but I can say one thing. I like to write and want them to be read since my elementary school days.
From the fact that my papers are sometimes cited by other physicists,my scientific papers are read by somebody,
which is quite rewarding to me. Unfortunately, it is rare to send messages about the contents of other people's paper
inside the nuclear physics community. (I think the reason is that nuclear physics does not have a central and common big problems everybody tries to attack, unlike particle physics. ) Probably, because of this, I want to show what I am doing and trying to do in my life of research, to other people. I don't know...
漢字もつかえるのだろうか？
And suddenly, I noticed that many "diaries" by physicists are being replaced by "blogs".So, I decided to try by myself, too.
I know many Japanese physicists have their "research diaries" or "research blogs",and I found also some American physicists do the same thing.It is strange, but I haven't heared of anybody in the UK who is doing this. Maybe there are, maybe not.
I have a feeling that the Japanese and Americans are similar in this point, that is, writing diaries for other people.
What is the reason for this "diary"? They are supposed to be private by definition, aren't they?
I myself think why I want to write this kind of thing in the web, over and over again. I have not yet had the answer, but I can say one thing. I like to write and want them to be read since my elementary school days.
From the fact that my papers are sometimes cited by other physicists,my scientific papers are read by somebody,
which is quite rewarding to me. Unfortunately, it is rare to send messages about the contents of other people's paper
inside the nuclear physics community. (I think the reason is that nuclear physics does not have a central and common big problems everybody tries to attack, unlike particle physics. ) Probably, because of this, I want to show what I am doing and trying to do in my life of research, to other people. I don't know...
漢字もつかえるのだろうか？
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