In 1947 Hendrik Casimir, once an assistant of Pauli, was working in applied industrial research at the Philips Laboratory in the Netherlands along with physicist J. T. G. Overbeek. They were analyzing the theory of van der Waals forces when Casimir had the opportunity to discuss ideas with Niels Bohr on a walk. According to Casimir, Bohr ''mumbled something about zero-point energy'' being relevant. This led Casimir to an analysis of zero-point energy effects in the related problem of forces between perfectly conducting parallel plates.
http://www.calphysics.org/zpe.html
Wednesday, November 28, 2007
The Famous Legendary Story of Ramanujan
Here is Chuang's post on an anecdote about Ramanujan:
Ramanujan was sick and was taken care in the hospital. Hardy once came over and talked to Ramanujan about the taxi that he just went on has a truly boring car number: 1729.
Ramanujan replied immediately: "No. This is a very interesting number."
"It is the smallest number expressible as the sum of two cubes in two different ways."
There is even an article on wikipedia telling the story. Before you click on the web page, why not try to find out the two pairs of integers?
1729
Wiki on Ramanujan
I (Chern Chuang) remember that I first time read about this story was reading Prof. 曹亮吉's book: <阿草的葫蘆> in junior high. At that time I was busy hand-making various paper models of uniform polyhedra.
Ramanujan was sick and was taken care in the hospital. Hardy once came over and talked to Ramanujan about the taxi that he just went on has a truly boring car number: 1729.
Ramanujan replied immediately: "No. This is a very interesting number."
"It is the smallest number expressible as the sum of two cubes in two different ways."
There is even an article on wikipedia telling the story. Before you click on the web page, why not try to find out the two pairs of integers?
1729
Wiki on Ramanujan
I (Chern Chuang) remember that I first time read about this story was reading Prof. 曹亮吉's book: <阿草的葫蘆> in junior high. At that time I was busy hand-making various paper models of uniform polyhedra.
Monday, November 12, 2007
E. Teller and C. N. Yang
*Yang began as a student of R. Mullikan
*Then became an experimentalist under Allison.
*The result: “If there is a bang, it’s Yang.”
*Teller: Why don’t you come back and try writing up your proof for a thesis.
*A few days later, Yang returned with three sheet of paper.
*Teller: That’s very good, but why don’t you add the proof for the relationship in the case of half-integer angular momentum valuse.
*A few days later, Yang again showed up in Teller’s office with additional four sheets of paper.
*Teller: The custom in Chicago was that theses should be longer than that.
*A few weeks later, Yang got to eleven pages. Teller said okay.
*Yang submitted them and was granted the doctorate.
*Then became an experimentalist under Allison.
*The result: “If there is a bang, it’s Yang.”
*Teller: Why don’t you come back and try writing up your proof for a thesis.
*A few days later, Yang returned with three sheet of paper.
*Teller: That’s very good, but why don’t you add the proof for the relationship in the case of half-integer angular momentum valuse.
*A few days later, Yang again showed up in Teller’s office with additional four sheets of paper.
*Teller: The custom in Chicago was that theses should be longer than that.
*A few weeks later, Yang got to eleven pages. Teller said okay.
*Yang submitted them and was granted the doctorate.
Thursday, November 1, 2007
薛丁格方程式的來源
這是以前在教物化二時，根據 Moore 的書寫的
Debye suggested Schrodinger to give a talk on the de Broglie thesis. Debye said he doesn't understand it and asked Schroedinger to read it, and see if he can get a nice talk about it.
One month later, most likely at a meeting on December 7, according to the recollection of Felix Bloch (Nobel prize laureate due to his work on the NMR), at the end of meeting of this colloquium:
Debye casually remarked that he thought this way of talking was rather childish. As a student of Sommerfeld he had learned that, to deal properly with waves, one had to have a wave equation... Just a few weeks later [Schrodinger] gave another talk in the colloquium which he started by saying: "My colleague Debye suggested that one should have a wave equation; well, I have found one!"
However, Debye himself had no recollection of ever mentioning the need for a wave equation.
adapted from Walter Moore "A life of Erwin Schrodinger", Cambridge University Press, 1994
﹦﹦﹦﹦﹦﹦﹦﹦﹦﹦﹦﹦﹦﹦﹦﹦﹦﹦﹦﹦﹦﹦﹦﹦﹦
另外，也有這樣的說法
During 1924 and 1925, de Broglie's thesis started to make the rounds of scientific circles in Europe. While visiting Paris, Victor Henri received a copy of the thesis from Langevin who suggested that he ask Schrödinger to look at it. Henri did not understand it very well, so he gave it to Schrödinger who, after two weeks, returned it again with the comment "That's rubbish!" When Henri visited Langevin again and explained what had happened, Langevin replied: "I think that Schrödinger is wrong; he must look at it again." Henri returned to Zurich and told Schrödinger "You ought to read de Broglie's thesis again. Langevin thinks this is a very good work." During this fall of 1925, Erwin Schrödinger was a visitor in the laboratory of Peter Debye in Switzerland. Debye had heard of de Broglie's thesis and asked Schrödinger if he would lead a discussion at one of their regularly scheduled group meetings on the subject. He agreed, and this time, as he worked with the concepts, he soon became an ardent fan, and led a strongly favorable presentation of these ideas in the meeting. Debye, speaking with him afterwards, was cool towards the general ideas and stated that if anything is ever going to come of it someone would need to write down a wave equation for matter. And he certainly didn't see how that was going to happen.
A wave equation for matter! That was the ticket. Schrödinger accepted the unintended challenge and took his mistress up into the Alps over Christmas and New Years, 1925-26. When he descended again in early January, he had it - a wave equation for matter. His work is the foundation of all our modern quantum theory. It is also known as wave mechanics, to distinguish it from Heisenberg's Matrix Mechanics which together form the joint foundation of modern physical theory. Schrödinger's approach is the most common method for studying quantum theory today.
Debye suggested Schrodinger to give a talk on the de Broglie thesis. Debye said he doesn't understand it and asked Schroedinger to read it, and see if he can get a nice talk about it.
One month later, most likely at a meeting on December 7, according to the recollection of Felix Bloch (Nobel prize laureate due to his work on the NMR), at the end of meeting of this colloquium:
Debye casually remarked that he thought this way of talking was rather childish. As a student of Sommerfeld he had learned that, to deal properly with waves, one had to have a wave equation... Just a few weeks later [Schrodinger] gave another talk in the colloquium which he started by saying: "My colleague Debye suggested that one should have a wave equation; well, I have found one!"
However, Debye himself had no recollection of ever mentioning the need for a wave equation.
adapted from Walter Moore "A life of Erwin Schrodinger", Cambridge University Press, 1994
﹦﹦﹦﹦﹦﹦﹦﹦﹦﹦﹦﹦﹦﹦﹦﹦﹦﹦﹦﹦﹦﹦﹦﹦﹦
另外，也有這樣的說法
During 1924 and 1925, de Broglie's thesis started to make the rounds of scientific circles in Europe. While visiting Paris, Victor Henri received a copy of the thesis from Langevin who suggested that he ask Schrödinger to look at it. Henri did not understand it very well, so he gave it to Schrödinger who, after two weeks, returned it again with the comment "That's rubbish!" When Henri visited Langevin again and explained what had happened, Langevin replied: "I think that Schrödinger is wrong; he must look at it again." Henri returned to Zurich and told Schrödinger "You ought to read de Broglie's thesis again. Langevin thinks this is a very good work." During this fall of 1925, Erwin Schrödinger was a visitor in the laboratory of Peter Debye in Switzerland. Debye had heard of de Broglie's thesis and asked Schrödinger if he would lead a discussion at one of their regularly scheduled group meetings on the subject. He agreed, and this time, as he worked with the concepts, he soon became an ardent fan, and led a strongly favorable presentation of these ideas in the meeting. Debye, speaking with him afterwards, was cool towards the general ideas and stated that if anything is ever going to come of it someone would need to write down a wave equation for matter. And he certainly didn't see how that was going to happen.
A wave equation for matter! That was the ticket. Schrödinger accepted the unintended challenge and took his mistress up into the Alps over Christmas and New Years, 1925-26. When he descended again in early January, he had it - a wave equation for matter. His work is the foundation of all our modern quantum theory. It is also known as wave mechanics, to distinguish it from Heisenberg's Matrix Mechanics which together form the joint foundation of modern physical theory. Schrödinger's approach is the most common method for studying quantum theory today.
Shannon's information and von Neumann
Here is the story about the origin of information entropy.
"Despite the narrative force that the concept of entropy appears to evoke in everyday writing, in scientific writing entropy remains a thermodynamic quantity and a mathematical formula that numerically quantifies disorder. When the American scientist Claude Shannon found that the mathematical formula of Boltzmann defined a useful quantity in information theory, he hesitated to name this newly discovered quantity entropy because of its philosophical baggage. The mathematician John Von Neumann encouraged Shannon to go ahead with the name entropy, however, since "no one knows what entropy is, so in a debate you will always have the advantage."
From The American Heritage Book of English Usage, p. 158.
"Despite the narrative force that the concept of entropy appears to evoke in everyday writing, in scientific writing entropy remains a thermodynamic quantity and a mathematical formula that numerically quantifies disorder. When the American scientist Claude Shannon found that the mathematical formula of Boltzmann defined a useful quantity in information theory, he hesitated to name this newly discovered quantity entropy because of its philosophical baggage. The mathematician John Von Neumann encouraged Shannon to go ahead with the name entropy, however, since "no one knows what entropy is, so in a debate you will always have the advantage."
From The American Heritage Book of English Usage, p. 158.
Von Neumann and Fly Puzzle
Here is the famous fly puzzle of Von Neumann I mentioned in class.
Two bicyclists start twenty miles apart and head toward each other, each going at a steady rate of 10 m.p.h. At the same time a fly that travels at a steady 15 m.p.h. starts from the front wheel of the southbound bicycle and flies to the front wheel of the northbound one, then turns around and flies to the front wheel of the southbound one again, and continues in this manner till he is crushed between the two front wheels. Question: what total distance did the fly cover ?
The slow way to find the answer is to calculate what distance the fly covers on the first, northbound, leg of the trip, then on the second, southbound, leg, then on the third, etc., etc., and, finally, to sum the infinite series so obtained. The quick way is to observe that the bicycles meet exactly one hour after their start, so that the fly had just an hour for his travels; the answer must therefore be 15 miles. When the question was put to von Neumann, he solved it in an instant, and thereby disappointed the questioner: "Oh, you must have heard the trick before!" "What trick?" asked von Neumann; "all I did was sum the infinite series."
More stories about von Neumann: see http://stepanov.lk.net/mnemo/legende.html
Two bicyclists start twenty miles apart and head toward each other, each going at a steady rate of 10 m.p.h. At the same time a fly that travels at a steady 15 m.p.h. starts from the front wheel of the southbound bicycle and flies to the front wheel of the northbound one, then turns around and flies to the front wheel of the southbound one again, and continues in this manner till he is crushed between the two front wheels. Question: what total distance did the fly cover ?
The slow way to find the answer is to calculate what distance the fly covers on the first, northbound, leg of the trip, then on the second, southbound, leg, then on the third, etc., etc., and, finally, to sum the infinite series so obtained. The quick way is to observe that the bicycles meet exactly one hour after their start, so that the fly had just an hour for his travels; the answer must therefore be 15 miles. When the question was put to von Neumann, he solved it in an instant, and thereby disappointed the questioner: "Oh, you must have heard the trick before!" "What trick?" asked von Neumann; "all I did was sum the infinite series."
More stories about von Neumann: see http://stepanov.lk.net/mnemo/legende.html
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