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Feynman said that those who claim they understand the Equations (Math) and so they understand the Physics contribute little to Physics and less to Mathematics.
The great mathematician Whittaker (not the serpent one) undertook a two-volume eminently readable study titled: 'The theories of aether and electricity' in which he gave the entire credit of Special Relativity and Lorentz Transformations to neither Einstein nor Lorentz but to his fellow-mathematician Poincare.
When this was pointed out to Einstein he dismissed it saying everyone is entitled to his views.
But he fought back with a set of Thought Experiments beyond the pale of any mathematician. Panofsky & Phillips build Lorentz Transformations from four Thought Experiments in a book which bristles with math otherwise. It also has a Table listing prevalent theories and experimental results in a matrix of about a dozen rows and half a dozen columns. Only STR has 'ticks' in all its entries while the other contending theories have one or more 'crosses'. That sort of settled it. I tried to work out the entire Matrix but had to give up half-way after a month or so.
Let Whittaker and his ilk try it!
This 'Thought' adjective reminds me of RKN' s patriotic Mysore Uncle who started a venture called 'Indian Thought Publications' that came out with a Weekly with articles largely written by the Uncle under various names and styles. I think it also published one or two books of RKN. When ultimately the Uncle lost his steam (as I will presently), RKN dubs it: 'Indian Thoughtless Publications'.
This 'Thought' adjective to 'Experiments' endlessly used to amuse me as it implies all other Experiments as Thoughtless.
Anyway, the QM School of Bohr and everyone else took up this 'Thought Experiments' business full steam, maybe to scare Mathematicians away and settle scores between themselves in all sorts of diverting manner...cats and kings sprouting all over.
Rupak's neighbor in his Chemical Engg B Tech Class, by name Amanullah, gave me a rare and precious gift at the end of the semester: a worn out copy of the original English Version of Heisenberg's: 'Physical Principles of Quantum Theory' bought in a College Street Used Book Outlet. I asked him to keep it for himself but he said he bought another copy for himself and his dad who happened to be a Physics Prof in Patna. Wonderful gift.
I found that in that book circa 1925 Heisenberg derives his famous Uncertainty Product Relations from a series of Thought Experiments...the most Thoughtful and dashing being one deriving the Uncertainty Product of transverse E and B Fields!
My problems with Lorentz Transformations started with our Math Dept at IIT KGP which had a full-blown Course of Relativity in their 4th Year. There was a Campus Buzz brought to my notice by DB that teachers in Math Dept were getting both Length Contraction and Length Dilation depending on whether they used the direct or the inverse transformations...and they sort of were proud of it. Our HoD's daughter Saraswati (who later became Ph D in Math and is now the Principal of a famous College...and was in Tanmoy's batch and learned Fermat's Principle there) barged into my room one morning and insisted once for all to show how to get rid of Length Dilation. I had to ask her to sit down and stick to the definition of length of a moving rod strictly and made her work out the thing either way. She was glad to get the Contraction even if it took a couple more steps.
Eureka for the Math Dept!
Lorentz Transformations can be treacherous even to seasoned Physics Teachers if they forget their definitions. Once our then HoD, MLM, forced me to teach about 40 University and College Physics Teachers from India, Sri Lanka, Bangladesh and Nepal (Pakistan opted out, the loss was mine entirely) in a richly funded UNESCO Summer School. I told MLM that I would hardly venture to lecture them but make them do some Problems and Riddles that teased me and show them how to use the beautiful Problem-Solving Spacetime Software of Edwin Taylor of MIT which was set up in our 4th Year Lab.
The first problem I gave them was to find the distance between two photons in a Boosted Frame when that distance is one meter in the Lab Frame. All of them used Lorentz transformations trivially and got the wrong answer! Spacetime Software did it right.
While doing my Ph D, I got an indefinite integral 'I' of the simplest of Bessel Functions which foxed me. I then passed it on to Dr. A who was a Post-Doc under the most renowned Prof of the Math Dept, Prof AS Gupta. He returned it to me next day saying it can't be done in terms of known functions. A very useful result. I then discovered that I needed only its asymptotic expansion in the Radiation Zone...which I could do by myself.
Similarly I landed up with a 3x3 matrix 'M' involving algebraic (not numerical) elements which I couldn't diagonalize. After a few weeks I passed it on to a colleague of mine in the GG Dept living in our infamous Faculty Hostel who had a renowned math brother at ISI. On the first weekend he dismissed it saying it was a high school problem. On the second weekend he declared it can't be done in terms of algebraic elements. Again a very useful 'no' like the Michelson-Morley thing. I then carried my 'M' on to the next dozen steps and it sort of diagonalized itself!
Heisenberg titled his book 'Quantum Theory'. But it didn't catch on. We still talked of QM I, II, III, IV even when the Quantum adjective started qualifying 'Optics and Electronics'. I used to feel that there should be a new name for just the noun dealing with just the 'Principles' of QM. I then discovered that Levy-Leblond and Balibar came up with a fantastic book titled: 'Quantics'. No equations at all. But full of experimental graphs from the latest Phys Revs using QM as it is used in the cutting-edge labs.
I used and cited the 'Quantics' book in the Abstract of one our EJP Papers. It went like knife through butter without the usual referee comments: maybe Levy-Leblod was its referee!
It all shows as Hilbert said famously:
"Mathematicians and Physicists shouldn't quarrel...they live in different spaces"
...Posted by Ishani
***********************************************************************************************************************
Feynman said that those who claim they understand the Equations (Math) and so they understand the Physics contribute little to Physics and less to Mathematics.
The great mathematician Whittaker (not the serpent one) undertook a two-volume eminently readable study titled: 'The theories of aether and electricity' in which he gave the entire credit of Special Relativity and Lorentz Transformations to neither Einstein nor Lorentz but to his fellow-mathematician Poincare.
When this was pointed out to Einstein he dismissed it saying everyone is entitled to his views.
But he fought back with a set of Thought Experiments beyond the pale of any mathematician. Panofsky & Phillips build Lorentz Transformations from four Thought Experiments in a book which bristles with math otherwise. It also has a Table listing prevalent theories and experimental results in a matrix of about a dozen rows and half a dozen columns. Only STR has 'ticks' in all its entries while the other contending theories have one or more 'crosses'. That sort of settled it. I tried to work out the entire Matrix but had to give up half-way after a month or so.
Let Whittaker and his ilk try it!
This 'Thought' adjective reminds me of RKN' s patriotic Mysore Uncle who started a venture called 'Indian Thought Publications' that came out with a Weekly with articles largely written by the Uncle under various names and styles. I think it also published one or two books of RKN. When ultimately the Uncle lost his steam (as I will presently), RKN dubs it: 'Indian Thoughtless Publications'.
This 'Thought' adjective to 'Experiments' endlessly used to amuse me as it implies all other Experiments as Thoughtless.
Anyway, the QM School of Bohr and everyone else took up this 'Thought Experiments' business full steam, maybe to scare Mathematicians away and settle scores between themselves in all sorts of diverting manner...cats and kings sprouting all over.
Rupak's neighbor in his Chemical Engg B Tech Class, by name Amanullah, gave me a rare and precious gift at the end of the semester: a worn out copy of the original English Version of Heisenberg's: 'Physical Principles of Quantum Theory' bought in a College Street Used Book Outlet. I asked him to keep it for himself but he said he bought another copy for himself and his dad who happened to be a Physics Prof in Patna. Wonderful gift.
I found that in that book circa 1925 Heisenberg derives his famous Uncertainty Product Relations from a series of Thought Experiments...the most Thoughtful and dashing being one deriving the Uncertainty Product of transverse E and B Fields!
My problems with Lorentz Transformations started with our Math Dept at IIT KGP which had a full-blown Course of Relativity in their 4th Year. There was a Campus Buzz brought to my notice by DB that teachers in Math Dept were getting both Length Contraction and Length Dilation depending on whether they used the direct or the inverse transformations...and they sort of were proud of it. Our HoD's daughter Saraswati (who later became Ph D in Math and is now the Principal of a famous College...and was in Tanmoy's batch and learned Fermat's Principle there) barged into my room one morning and insisted once for all to show how to get rid of Length Dilation. I had to ask her to sit down and stick to the definition of length of a moving rod strictly and made her work out the thing either way. She was glad to get the Contraction even if it took a couple more steps.
Eureka for the Math Dept!
Lorentz Transformations can be treacherous even to seasoned Physics Teachers if they forget their definitions. Once our then HoD, MLM, forced me to teach about 40 University and College Physics Teachers from India, Sri Lanka, Bangladesh and Nepal (Pakistan opted out, the loss was mine entirely) in a richly funded UNESCO Summer School. I told MLM that I would hardly venture to lecture them but make them do some Problems and Riddles that teased me and show them how to use the beautiful Problem-Solving Spacetime Software of Edwin Taylor of MIT which was set up in our 4th Year Lab.
The first problem I gave them was to find the distance between two photons in a Boosted Frame when that distance is one meter in the Lab Frame. All of them used Lorentz transformations trivially and got the wrong answer! Spacetime Software did it right.
While doing my Ph D, I got an indefinite integral 'I' of the simplest of Bessel Functions which foxed me. I then passed it on to Dr. A who was a Post-Doc under the most renowned Prof of the Math Dept, Prof AS Gupta. He returned it to me next day saying it can't be done in terms of known functions. A very useful result. I then discovered that I needed only its asymptotic expansion in the Radiation Zone...which I could do by myself.
Similarly I landed up with a 3x3 matrix 'M' involving algebraic (not numerical) elements which I couldn't diagonalize. After a few weeks I passed it on to a colleague of mine in the GG Dept living in our infamous Faculty Hostel who had a renowned math brother at ISI. On the first weekend he dismissed it saying it was a high school problem. On the second weekend he declared it can't be done in terms of algebraic elements. Again a very useful 'no' like the Michelson-Morley thing. I then carried my 'M' on to the next dozen steps and it sort of diagonalized itself!
Heisenberg titled his book 'Quantum Theory'. But it didn't catch on. We still talked of QM I, II, III, IV even when the Quantum adjective started qualifying 'Optics and Electronics'. I used to feel that there should be a new name for just the noun dealing with just the 'Principles' of QM. I then discovered that Levy-Leblond and Balibar came up with a fantastic book titled: 'Quantics'. No equations at all. But full of experimental graphs from the latest Phys Revs using QM as it is used in the cutting-edge labs.
I used and cited the 'Quantics' book in the Abstract of one our EJP Papers. It went like knife through butter without the usual referee comments: maybe Levy-Leblod was its referee!
It all shows as Hilbert said famously:
"Mathematicians and Physicists shouldn't quarrel...they live in different spaces"
...Posted by Ishani
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