Thursday, October 21, 2010
Monday, October 18, 2010
Group theory and Physics
Most of us have group theory in our degree course. Some time ago, I was pretty critical about pure math and its abstract nature ( having nothing to do with reality). I treated them as just mental fantasies, some of which tends to have a structure that agrees with the way nature nature worked.
I went around telling people about some paradoxes in set theory and how Godel's theorem implies that any system based on precise axioms and set of rules is fundamentally flawed. One famous paradox is Russel's paradox.
I now realize that how I felt back then was wrong. I felt that way partly because I am not good at Math and partly because I my thinking was very naive. Which is not really a bad thing, I always learn from my naiveties.
I am now doing a project in Lie Groups under a professor in my college. And I visit a person named Dr. Aravinda from TIFR. He's helping me out with Topology and Differential Geometry. This is amazing because two years ago I didn't think I would find anyone working on these topics ( and also willing to guide me).
Anyway, I thought I'll put up something here that I found worth reading. This is the preface to one of the books that he suggested:
" As a graduate student in experimental physics, I found the study of group theory considered to be a useless "high-brow" luxury. Furthermore all attempts to follow a lecture course resulted in a losing battle with cosets, classes, invariant subgroups, normal divisors and assorted lemmas. It was impossible to learn all the definitions of new terms defined in one lecture and remember them until the next lecture. The result was complete chaos.
It was a great surprise to find later on that (1) Techniques based on group theory can be useful; (2) They can be learned and used without memorizing the large number of definitions and lemmas which frighten the uninitiated.
Angular momentum is presented in elementary quantum mechanics courses without a detailed analysis of the lie group of continuous rotations in three dimensions. The student learns about angular momentum multiplets and coupling angular momenta without realizing that these are irreducible representations of the rotation group.He also does not realize that the algebraic properties of other lie groups can be applied to physical problems in the same way as he used angular momentum algebra, with no need for classes, cosets etc. . . . . . . "
He then goes on to talk about further applications in creation and annihilation operators, and also talks about quasi spin etc..
The book is Lie groups for Pedestrians by Harry Lipkin.
Group theory is actually fun and beautiful ( a word I rarely use) , but again college takes the life out of it. I am actually lucky that this course is handled in my college by an expert in this topic, but even he is constrained because the college requires you to rush through all the theorems within one semester and one is not given enough time to understand the subtleties. But it is always best continue to reflect on it even after the course is done.
P.S: The weekend sessions have been going on. Everybody has just been too busy to put up the summary. We have had three sessions within a span of four days. Karthik made quite a lot of connections in classical mechanics during his class on friday. I conducted a test on saturday on whatever has been done, to judge the understanding so far. Today was Shruthi's session on QM, which was again taken up mostly by Karthik to make known previously unspoken things.
I went around telling people about some paradoxes in set theory and how Godel's theorem implies that any system based on precise axioms and set of rules is fundamentally flawed. One famous paradox is Russel's paradox.
I now realize that how I felt back then was wrong. I felt that way partly because I am not good at Math and partly because I my thinking was very naive. Which is not really a bad thing, I always learn from my naiveties.
I am now doing a project in Lie Groups under a professor in my college. And I visit a person named Dr. Aravinda from TIFR. He's helping me out with Topology and Differential Geometry. This is amazing because two years ago I didn't think I would find anyone working on these topics ( and also willing to guide me).
Anyway, I thought I'll put up something here that I found worth reading. This is the preface to one of the books that he suggested:
" As a graduate student in experimental physics, I found the study of group theory considered to be a useless "high-brow" luxury. Furthermore all attempts to follow a lecture course resulted in a losing battle with cosets, classes, invariant subgroups, normal divisors and assorted lemmas. It was impossible to learn all the definitions of new terms defined in one lecture and remember them until the next lecture. The result was complete chaos.
It was a great surprise to find later on that (1) Techniques based on group theory can be useful; (2) They can be learned and used without memorizing the large number of definitions and lemmas which frighten the uninitiated.
Angular momentum is presented in elementary quantum mechanics courses without a detailed analysis of the lie group of continuous rotations in three dimensions. The student learns about angular momentum multiplets and coupling angular momenta without realizing that these are irreducible representations of the rotation group.He also does not realize that the algebraic properties of other lie groups can be applied to physical problems in the same way as he used angular momentum algebra, with no need for classes, cosets etc. . . . . . . "
He then goes on to talk about further applications in creation and annihilation operators, and also talks about quasi spin etc..
The book is Lie groups for Pedestrians by Harry Lipkin.
Group theory is actually fun and beautiful ( a word I rarely use) , but again college takes the life out of it. I am actually lucky that this course is handled in my college by an expert in this topic, but even he is constrained because the college requires you to rush through all the theorems within one semester and one is not given enough time to understand the subtleties. But it is always best continue to reflect on it even after the course is done.
P.S: The weekend sessions have been going on. Everybody has just been too busy to put up the summary. We have had three sessions within a span of four days. Karthik made quite a lot of connections in classical mechanics during his class on friday. I conducted a test on saturday on whatever has been done, to judge the understanding so far. Today was Shruthi's session on QM, which was again taken up mostly by Karthik to make known previously unspoken things.
Saturday, October 16, 2010
CHANDRASEKHAR CENTENARY LECTURE
Title: From white dwarfs to holography and quantum gravity
Date: 19th Oct, 4:00pm, CHEP Seminar Hall (IISC)
Abstract:
The talk aims to trace the influence of the Chandrasekhar limit
in understanding the physics of gravity. Here
is a summary of the salient points which will be covered
in the talk.
Around the time when Chandrasekhar was born ,
the white dwarf was regarded as a bete noir by astronomers. During
1930-35 , Chandrasekhar proved that massive stars which have
run out their fuel , can not rest in peace as white dwarfs if their mass
exceeds 1.44 times the mass of the Sun , because gravitation will
overwhelm all other forces and they must collapse.
Recalling later developments, in 1982 during the Eddington centenary
lecture Chandrasekhar said " the existence for a limiting mass is
inextricably woven into the present fabric of astronomical tapestry with
its complex designs of stellar evolution , nuclear burning in the
high - density cores of certain stars and gravitational collapse
leading to supernova phenomenon and the formation of neutron stars of
nearly the same mass and of black holes. " .
In the nineteen thirties famous but older physicists disliked the idea
of ultimate collapse and disapproved of singularities of the equations of
physics. Along with the issue of stellar collapse there was also the
parallel problem regarding cosmological singularities present in
models of the Universe . Are singularities rigorous results of equations
of physics or the work of maladroit theorist ? The seminal work of
Raychaudhuri in the fifties , paved the way for Penrose Hawking and
Geroch , to prove a decade later
-1) the inevitability for collapse into black hole by a massive star
on the one hand
2) strengthened the basis of big bang cosmology on the other . It is
consistent with astronomical data to assume that our Universe
began with a singularity .
Today thousands of white dwarfs with mass below Chandrasekhar limit are
known with their structure and properties well understood . They are an
important standard in astronomy. Many stellar mass black holes are known
today.
Classical black holes absorb everything and pose a problem for the second
law of thermodynamics . Hawking's discovery that in quantum theory ,
black holes must radiate resolves this but brings in fresh issues in its
wake , challenging our understanding of interface
between the inside and outside of a black hole .
Speaker: J. Pasupathy.
Affiliation: CHEP
I think we should all attend this lecture. Seems mouthwatering. Ciao
Date: 19th Oct, 4:00pm, CHEP Seminar Hall (IISC)
Abstract:
The talk aims to trace the influence of the Chandrasekhar limit
in understanding the physics of gravity. Here
is a summary of the salient points which will be covered
in the talk.
Around the time when Chandrasekhar was born ,
the white dwarf was regarded as a bete noir by astronomers. During
1930-35 , Chandrasekhar proved that massive stars which have
run out their fuel , can not rest in peace as white dwarfs if their mass
exceeds 1.44 times the mass of the Sun , because gravitation will
overwhelm all other forces and they must collapse.
Recalling later developments, in 1982 during the Eddington centenary
lecture Chandrasekhar said " the existence for a limiting mass is
inextricably woven into the present fabric of astronomical tapestry with
its complex designs of stellar evolution , nuclear burning in the
high - density cores of certain stars and gravitational collapse
leading to supernova phenomenon and the formation of neutron stars of
nearly the same mass and of black holes. " .
In the nineteen thirties famous but older physicists disliked the idea
of ultimate collapse and disapproved of singularities of the equations of
physics. Along with the issue of stellar collapse there was also the
parallel problem regarding cosmological singularities present in
models of the Universe . Are singularities rigorous results of equations
of physics or the work of maladroit theorist ? The seminal work of
Raychaudhuri in the fifties , paved the way for Penrose Hawking and
Geroch , to prove a decade later
-1) the inevitability for collapse into black hole by a massive star
on the one hand
2) strengthened the basis of big bang cosmology on the other . It is
consistent with astronomical data to assume that our Universe
began with a singularity .
Today thousands of white dwarfs with mass below Chandrasekhar limit are
known with their structure and properties well understood . They are an
important standard in astronomy. Many stellar mass black holes are known
today.
Classical black holes absorb everything and pose a problem for the second
law of thermodynamics . Hawking's discovery that in quantum theory ,
black holes must radiate resolves this but brings in fresh issues in its
wake , challenging our understanding of interface
between the inside and outside of a black hole .
Speaker: J. Pasupathy.
Affiliation: CHEP
I think we should all attend this lecture. Seems mouthwatering. Ciao
Thursday, September 30, 2010
Problem 2 and 3
Here are more problems for us to have fun doing...
Problem 2:
It has been stated that Archimedes once saved the Greeks from attack by a Roman fleet by equipping a large number of well trained soldiers with large hand-held plane mirrors and getting them to reflect the sun's rays onto some part of a Roman ship at a distance of 100m, thereby setting it on fire. Comment on the feasibility of such a plan.
You may assume that the mirrors are available, that the solar flux is 1 kW per meter squared, and that the angular diameter of the sun is 0.5 degrees. The ships may be assumed to be wooden. Stefan's constant is 5.7 x 10^(- 8) W m^(- 2)K^(- 4)
Problem 3:
A parabolic mirror is made to focus the sun's disc into a circle of radius 1 cm. Estimate the smallest diameter of such a mirror if it can be used to melt iron. Make any assumptions that are plausible and necessary. Stefan's constant has been given with the above problem, the melting point of iron is 1535 degree celcius, the solar constant at the bottom of the atmosphere is 1 kW per meter squared.
Problem 2:
It has been stated that Archimedes once saved the Greeks from attack by a Roman fleet by equipping a large number of well trained soldiers with large hand-held plane mirrors and getting them to reflect the sun's rays onto some part of a Roman ship at a distance of 100m, thereby setting it on fire. Comment on the feasibility of such a plan.
You may assume that the mirrors are available, that the solar flux is 1 kW per meter squared, and that the angular diameter of the sun is 0.5 degrees. The ships may be assumed to be wooden. Stefan's constant is 5.7 x 10^(- 8) W m^(- 2)K^(- 4)
Problem 3:
A parabolic mirror is made to focus the sun's disc into a circle of radius 1 cm. Estimate the smallest diameter of such a mirror if it can be used to melt iron. Make any assumptions that are plausible and necessary. Stefan's constant has been given with the above problem, the melting point of iron is 1535 degree celcius, the solar constant at the bottom of the atmosphere is 1 kW per meter squared.
Sunday, September 26, 2010
Weekend discussions 3
I have a backlog of a few weekends which I hope to catch up with very soon. Anyway, this post is concerned with our discussions yesterday and the day before. So here it is:
September 25, 2010
Session 1: Shruthi
We continued our foray to understand the necessity of a quantum theory, and Shruthi pointed out a few interesting things like whether we could determine the terminal velocity of a steel ball dropped into liquid helium. Th results were more interesting. I think Shruthi will do a better job of discussing that. We then went back to a concept we were all fuzzy about. Matter waves. Superposition. Wave packets. What we all thought was a trivial thing and went right ahead after thinking we understood it, is now coming back to haunt us. I'm struggling to make the problem itself clear. Maybe someone should open it up for discussion here.
Session 2: Raunaq
He said he'd write this himself.
September 26, 2010
Session 1: Karthik
He started off by getting us to discuss what exactly a linear, homogeneous differential equation means. We then worked through the problem of the damped harmonic oscillator, which we went on to study in a matrix representation, finally giving (atleast me) a good idea of exponentiating a matrix. This was followed by a phase space analysis of the problem, at which point Karthik urged us to read up on the Sine-Gordon equation and elliptic functions. He actually wanted to continue next week, but I made him give an introduction to the Poisson bracket as it was previously agreed that I would continue from there. So he did.
Session 2: Harshini
Well, I didn't get to do most of what I'd planned on doing. I started off by basically showing how the Commutator bracket is connected to the Poisson bracket and went on to discuss how these become operators in quantum mechanics. Actually, the problem was I couldn't show how they become operators. Staying true to our policy of not taking anything for granted, we spent a while talking about whether we've missed something in making the leap from something being a physical quantity in classical mechanics, to becoming an 'operator' in quantum mechanics. It doesn't sound quite so serious when put this way, but we struggled over the details for a bit.
Then we followed in the steps of Schrodinger to "derive" the Schrodinger equation, all the time questioning the rationale behind it, and whether it could be done in a better way. Nothing might come out of it, but its very important that these questions are asked. That's what makes what we're doing worth doing.
And before we leave, an ego-check is always done, so that we know that we're not doing anything path-breaking or earth-shattering in these discussions. But what we are doing, is something different.
September 25, 2010
Session 1: Shruthi
We continued our foray to understand the necessity of a quantum theory, and Shruthi pointed out a few interesting things like whether we could determine the terminal velocity of a steel ball dropped into liquid helium. Th results were more interesting. I think Shruthi will do a better job of discussing that. We then went back to a concept we were all fuzzy about. Matter waves. Superposition. Wave packets. What we all thought was a trivial thing and went right ahead after thinking we understood it, is now coming back to haunt us. I'm struggling to make the problem itself clear. Maybe someone should open it up for discussion here.
Session 2: Raunaq
He said he'd write this himself.
September 26, 2010
Session 1: Karthik
He started off by getting us to discuss what exactly a linear, homogeneous differential equation means. We then worked through the problem of the damped harmonic oscillator, which we went on to study in a matrix representation, finally giving (atleast me) a good idea of exponentiating a matrix. This was followed by a phase space analysis of the problem, at which point Karthik urged us to read up on the Sine-Gordon equation and elliptic functions. He actually wanted to continue next week, but I made him give an introduction to the Poisson bracket as it was previously agreed that I would continue from there. So he did.
Session 2: Harshini
Well, I didn't get to do most of what I'd planned on doing. I started off by basically showing how the Commutator bracket is connected to the Poisson bracket and went on to discuss how these become operators in quantum mechanics. Actually, the problem was I couldn't show how they become operators. Staying true to our policy of not taking anything for granted, we spent a while talking about whether we've missed something in making the leap from something being a physical quantity in classical mechanics, to becoming an 'operator' in quantum mechanics. It doesn't sound quite so serious when put this way, but we struggled over the details for a bit.
Then we followed in the steps of Schrodinger to "derive" the Schrodinger equation, all the time questioning the rationale behind it, and whether it could be done in a better way. Nothing might come out of it, but its very important that these questions are asked. That's what makes what we're doing worth doing.
And before we leave, an ego-check is always done, so that we know that we're not doing anything path-breaking or earth-shattering in these discussions. But what we are doing, is something different.
Weekend Discussions - 2
Our discussion sessions have been going well. I hope we can dedicate more and more time and effort to what's been going on in these sessions. This has really provided us with a good platform where we have the freedom to think and question without having to take anything for granted. So far its been very unconventional. We are in fact unlearning a lot, and these sessions are the only place where this kind of unlearning, I feel, has been welcome. So far, so good.
I will now be putting down here what I have been doing in a little more detail.
Session 1 : Space, time and Structure
Our high school physics begins with Newton's laws of Motion. By the end of MSc. we would have investigated motion a little further and spoken about it in terms of Lagrangian and Hamiltionian. When Einstein came up with his theory of relativity, he showed that space and time actually had a structure. A structure that evolves dynamically. This should perhaps be enough motivation to question about the very structure of the space and time on which motion actually takes place. Doing this won't be an easy task. We can't observe physical effects of time to model its structure, and yet everything that happens is parametrised using time. One big leaps in our understanding of time came when Einstein said that the faster you move in space, the slower you move in time. And this stitches space and time forever. You can't talk about space or time, you can only talk about space-time. Also, he showed that mass has something to do with space-time. The closer you are to a heavy mass, the slower the time flows for you.
We express time as the amount distance travelled with a certain velocity. And velocity as the amount distance travelled in certain time. If you try to talk about the structure of space and time in terms of distance and velocity, this is as far as you'll get. The only thing that can be further broken down here is distance. A space where we can talk about distance between two points is called a metric space. We seem to live on such a space. To be even able to talk about why our space the way it is, we need to talk about a more general space which does not have the notion of distance on it. This general space is known as a topological space. We go on later to define a metric on it.
I hope in the first session I was successful in motivating the reason behind going into some amount of topology and differential geometry. Though these are some purely mathematical structures, I feel that when used by physicists, they should be powerful tools to gain new insights into any physical concept and to look at physics in a unified sense.
Towards the end of the first session we tried entering into a little bit of set theory. And how sets are looked at in a topology. I ended with a few definitions like open and closed sets.
The assignment (which was successfully completed by all) was to look up a few theorems and lemmas, more importantly 'The Axiom of Choice' , Zorn's lemma. Also, to look up how a vector space and an algebra is technically defined. There was another long term assignment given which was to think if it was possible to arrive at the fact that there had to be a observer independent constant velocity given that space and time both are relative in our universe.
References: (1) Naive Set theory by P. Halmos (2) Differential Geometry and Lie Groups For Physicists by Marian Fecko (3) Wikipedia:)
I have spoken for three other sessions, the summary's for which will soon be put up. Our new aim is to be able to make lecture notes as well and turn them in to soft copies.
Karthik has been doing a wonderful job with classical mechanics. He has motivated us to think of a lot of things that haven't been thought of before. Shruthi has been showing failures of classical mechanics and has been trying to bring in the notion of wave-particle duality and making us think as to why a new theory was needed . And Harshini has been dealing with the mathematics of QM and the how's and why's of it. She did a nice derivation today which she will probably summarise later.
I urge everyone to post the summaries of their talks. It really has been a wonderful time discussing and opening our eyes to the fact that we really don't know anything.
ciao
I will now be putting down here what I have been doing in a little more detail.
Session 1 : Space, time and Structure
Our high school physics begins with Newton's laws of Motion. By the end of MSc. we would have investigated motion a little further and spoken about it in terms of Lagrangian and Hamiltionian. When Einstein came up with his theory of relativity, he showed that space and time actually had a structure. A structure that evolves dynamically. This should perhaps be enough motivation to question about the very structure of the space and time on which motion actually takes place. Doing this won't be an easy task. We can't observe physical effects of time to model its structure, and yet everything that happens is parametrised using time. One big leaps in our understanding of time came when Einstein said that the faster you move in space, the slower you move in time. And this stitches space and time forever. You can't talk about space or time, you can only talk about space-time. Also, he showed that mass has something to do with space-time. The closer you are to a heavy mass, the slower the time flows for you.
We express time as the amount distance travelled with a certain velocity. And velocity as the amount distance travelled in certain time. If you try to talk about the structure of space and time in terms of distance and velocity, this is as far as you'll get. The only thing that can be further broken down here is distance. A space where we can talk about distance between two points is called a metric space. We seem to live on such a space. To be even able to talk about why our space the way it is, we need to talk about a more general space which does not have the notion of distance on it. This general space is known as a topological space. We go on later to define a metric on it.
I hope in the first session I was successful in motivating the reason behind going into some amount of topology and differential geometry. Though these are some purely mathematical structures, I feel that when used by physicists, they should be powerful tools to gain new insights into any physical concept and to look at physics in a unified sense.
Towards the end of the first session we tried entering into a little bit of set theory. And how sets are looked at in a topology. I ended with a few definitions like open and closed sets.
The assignment (which was successfully completed by all) was to look up a few theorems and lemmas, more importantly 'The Axiom of Choice' , Zorn's lemma. Also, to look up how a vector space and an algebra is technically defined. There was another long term assignment given which was to think if it was possible to arrive at the fact that there had to be a observer independent constant velocity given that space and time both are relative in our universe.
References: (1) Naive Set theory by P. Halmos (2) Differential Geometry and Lie Groups For Physicists by Marian Fecko (3) Wikipedia:)
I have spoken for three other sessions, the summary's for which will soon be put up. Our new aim is to be able to make lecture notes as well and turn them in to soft copies.
Karthik has been doing a wonderful job with classical mechanics. He has motivated us to think of a lot of things that haven't been thought of before. Shruthi has been showing failures of classical mechanics and has been trying to bring in the notion of wave-particle duality and making us think as to why a new theory was needed . And Harshini has been dealing with the mathematics of QM and the how's and why's of it. She did a nice derivation today which she will probably summarise later.
I urge everyone to post the summaries of their talks. It really has been a wonderful time discussing and opening our eyes to the fact that we really don't know anything.
ciao
Saturday, September 18, 2010
Summary
I haven't checked my mail in over a week, so couldn't respond sooner. Sorry. Anyway, lets get down to business. After much ado, this structure has been finalised for our discussions.
Karthik will be dealing with Classical Mechanics, and following that, Electrodynamics.
Raunaq's is a course in Theoretical Physics. More on that by him.
Shruthi and I will be handling Quantum Mechanics(non-relativistic). between us, as it was decided that all of us will give one lecture per week.
The following is a summary of what has been happening for the past few weeks in our sessions:
September 2, 2010
Session 1: Raunaq
He started by getting us to question the basic notions of space, time and velocity, and it was left to us to prove that if the definitions of the above depend on each other, i.e. they are interrelated, then there must exist a constant velocity, and this velocity turns out to be the maximum velocity anything can have, i.e., the speed of light. We then tested new waters by being introduced to elementary set theory. A lot of mind-bending for us non-mathematicians!
Session 2: Karthik
Another session of questioning and unlearning. We spent the hour talking about our 'definitions' of force, momentum, acceleration and our understanding(or in my case, not!) of Newton's laws. This discussion took up the whole sessions as we analysed these so-called 'basics' and discovered new ways of looking at it.
September 5, 2010
Session 1: Harshini
It was initailly decided that Shruthi and I would handle electrodynamics, before we settled on QM. But we had one session, where we didn't get past Coulomb's law, due to our tendency to analyse every little thing without taking anything for granted. Its not a bad thing at all, for it helps in gaining a better understanding of the subject, and reveals flaws in our understanding. But due to time-constraints, we've decided to cut down on our long-winded discussions.
And oh, this discussion went on for so long, Shruthi didn't even get a chance to talk that day. Sorry S.
September 11, 2010
Session 1: Karthik
Now we dug our teeth into the concept of inertia and this lead to another round of discussion. We managed to proceed to the concept of phase diagrams and their usefulness and importance in Classical Mechanics. Then he introduced the concept of the Lagrangean which started off another round of discussions. Time-management was really becoming a problem now! Again, this was the only session we could have on this day.
September 12, 2010
Session 1: Shruthi
Hers was an introductory lecture to show the need for a new theory at a micro-level. She discussed the problem of black body radiation, the anomalous behaviour of liquid helium under certain conditions, the phenomenon of superconductivity etc. She sent us links to videos of experiments to demonstrate some of these phenomena. This session brought to light many interesting experimental phenomena.
Session 2: Raunaq
We dove right into set-theory, having dutifully completed the assignments we had been given. In this session, we dealt with what actually makes up vector spaces(one of our assignments, actually)and we were then led to an introduction to Lie algebra, followed by some problem-solving. And oh, abstract mathematics caused a lot of brouhaha again.
Karthik will be dealing with Classical Mechanics, and following that, Electrodynamics.
Raunaq's is a course in Theoretical Physics. More on that by him.
Shruthi and I will be handling Quantum Mechanics(non-relativistic). between us, as it was decided that all of us will give one lecture per week.
The following is a summary of what has been happening for the past few weeks in our sessions:
September 2, 2010
Session 1: Raunaq
He started by getting us to question the basic notions of space, time and velocity, and it was left to us to prove that if the definitions of the above depend on each other, i.e. they are interrelated, then there must exist a constant velocity, and this velocity turns out to be the maximum velocity anything can have, i.e., the speed of light. We then tested new waters by being introduced to elementary set theory. A lot of mind-bending for us non-mathematicians!
Session 2: Karthik
Another session of questioning and unlearning. We spent the hour talking about our 'definitions' of force, momentum, acceleration and our understanding(or in my case, not!) of Newton's laws. This discussion took up the whole sessions as we analysed these so-called 'basics' and discovered new ways of looking at it.
September 5, 2010
Session 1: Harshini
It was initailly decided that Shruthi and I would handle electrodynamics, before we settled on QM. But we had one session, where we didn't get past Coulomb's law, due to our tendency to analyse every little thing without taking anything for granted. Its not a bad thing at all, for it helps in gaining a better understanding of the subject, and reveals flaws in our understanding. But due to time-constraints, we've decided to cut down on our long-winded discussions.
And oh, this discussion went on for so long, Shruthi didn't even get a chance to talk that day. Sorry S.
September 11, 2010
Session 1: Karthik
Now we dug our teeth into the concept of inertia and this lead to another round of discussion. We managed to proceed to the concept of phase diagrams and their usefulness and importance in Classical Mechanics. Then he introduced the concept of the Lagrangean which started off another round of discussions. Time-management was really becoming a problem now! Again, this was the only session we could have on this day.
September 12, 2010
Session 1: Shruthi
Hers was an introductory lecture to show the need for a new theory at a micro-level. She discussed the problem of black body radiation, the anomalous behaviour of liquid helium under certain conditions, the phenomenon of superconductivity etc. She sent us links to videos of experiments to demonstrate some of these phenomena. This session brought to light many interesting experimental phenomena.
Session 2: Raunaq
We dove right into set-theory, having dutifully completed the assignments we had been given. In this session, we dealt with what actually makes up vector spaces(one of our assignments, actually)and we were then led to an introduction to Lie algebra, followed by some problem-solving. And oh, abstract mathematics caused a lot of brouhaha again.
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