Happy New Year Everyone!

Wishing you all a very Happy New year :)

Here are my

;-)

Latex Incorporated :)

I have finally been successful at incorporating Latex and we can now type any equation!

$ R_{ \mu \nu } - \frac{1}{2}g_{\mu \nu} R + g_{\mu \nu} \Lambda = \frac{8\piG}{C^4}T_{ \mu \nu} $

See :)
And this is one of my favourite equations.

Using latex is very easy, you just need to know the commands.
Usha ma'am, satyajit, and Raghu are already experts at it :).

Here are a few examples:

$ s = \int L ( q, \dot{q} , t ) dt $

To type this equation, one has to type & s = \int L ( q, \dot{q} , t ) dt &
You just have to replace & with $$.
Any latex commands can be used by enclosing them between $$ .

Similarly

$ \frac{\partial u}{\partial t} = h^2 \left( \frac{\partial^2 u}{\partial x^2} + \frac{\partial^2 u}{\partial y^2}+\frac{\partial^2 u}{\partial z^2} \right) $

is & \frac{\partial u}{\partial t} = h^2 \left( \frac{\partial^2 u}{\partial x^2} + \frac{\partial^2 u}{\partial y^2}+\frac{\partial^2 u}{\partial z^2} \right) &

( again just replace & with $$ )

For those who want to use latex and want to know all the commands, here are some links that will help you:

http://web.ift.uib.no/Teori/KURS/WRK/TeX/symALL.html

http://www.maths.tcd.ie/~dwilkins/LaTeXPrimer/Calculus.html

Have fun :)

Waking Life - Part 1

" There are two kinds of sufferers in this world: those who suffer from a lack of life and those who suffer from an over-abundance of life. I've always found myself in the second category.
When you come to think of it,almost all human behaviour and activity...is not essentially any different from animal behaviour.The most advanced technologies and craftsmanship... bring us, at best, up to the super-chimpanzee level. Actually, the gap between,say, Plato or Nietzsche and the average human...is greater than the gap between that chimpanzee and the average human.The realm of the real spirit, the true artist, the saint, the philosopher, is rarely achieved.

Why so few? Why is world history and evolution not stories of progress...but rather this endless and futile addition of zeroes? No greater values have developed. Hell, the Greeks years ago were just as advanced as we are. So what are these barriers that keep people... from reaching anywhere near their real potential? The answer to that can be found in another question, and that's this:
Which is the most universal human characteristic--
fear or laziness?"
-From the movie "Waking Life"

Latex?

I was thinking of making the blog more technical and this will require us to be able to type equations. So does anyone know if Latex can be incorporated on the blog? Is there any html script or something using which this can be done?
Please let me know thanks.

Mathematical structure of nature

For a while now, the correspondence between a mathematical structure and the way nature behaves has puzzled and amazed me. In other words, Why is it that I can write down equations on a sheets of paper and predict something about a natural object?
Newtonian Mechanics had a certain mathematical structure and Maxwell's Electrodynamics had a certain mathematical structure, and these two structures couldn't co-exist. Just by trying make the equations co-variant, we were able to get great insights into the way nature worked. We could get testable predictions which we were ofcourse verified by experiment.
Quantum Mechanics brought in another mathematical structure which takes into account the relationship between the observer and the observed, and gives us the nature of a measurement.

There may be domains where experimental physics cannot yet reach. There may be some underlying physical phenomena which cannot yet be detected by experiments. To probe into those domains, as of now, we may only have mathematical tools at our disposal.
Here is a paragraph from a book on Quantum Mechanics by Bohm ( Ref 3) that I think is worth mentioning:

" Physicists believe that there is something in nature, or in each restricted domain of it, that may be "understood"; that there is a structure in nature. To "understand" means to bring this structure into congruence with some structure in our mind, with a structure of thought objects, with a structure that has been created by our minds. For physics, this structure of thought objects is a mathematical structure. So to understand part of physical nature means to map its structure on a mathematical structure. To obtain a physical theory, then, means to obtain a mathematical image of a physical system. 
For the domains of quantum physics the mathematical structures are algebras of linear operators in linear spaces. The discovery of this, the fundamental properties of the algebra, and the other basic assumptions of quantum mechanics was a very difficult process. " 

I just hope we have the capability to recognise the true underlying structure of nature( however naive this may sound).


P.s. The references are given in the column on the right.

Academy Lecture

Indian Academy of Sciences
Bangalore

"Chandra: Gentleman, Scholar and Telescope"

Academy Public Lecture by

Professor Roger Blandford
Kavli Institute for Particle Astrophysics and Cosmology
Stanford

Date : Wednesday, 8th December 2010

Time:  6.00 p.m.

Venue: Faculty Hall, Indian Institute of Science, Bangalore

Abstract: Professor Subrahmanyan Chandrasekhar, or "Chandra" as he was widely known, was a singular scientist and intellectual. Blessed with formidable mathematical ability and legendary powers of concentration, he was a scientific leader over an unequalled suite of the most challenging astrophysical disciplines. Although he may be most famous for his youthful discovery of a mass limit for white dwarfs and its famous corollary that black holes must exist, for which he was awarded the 1983 Nobel Prize, his lifetime contributions to mathematical physics, astrophysics and even the humanities, are even greater. The range and durability of his scholarship was memorialised in the naming of the finest imaging X-ray telescope ever launched.  Vignettes from his life will be interspersed with a  description of some of the amazing discoveries made by Chandra X-ray Observatory.

About the speaker: Roger Blandford is director of the Kavli Institute for Particle Astrophysics and Cosmology.  He oversees research that seeks to answer some of our great cosmic questions: What powered the Big Bang? What are dark matter and dark energy? What is happening around black holes?. He is a Fellow of The Royal Society and the American Academy of Arts and Sciences, and a Member of the National Academy of Sciences.


All are welcome

Coffee/tea will be served at 5.30 p.m.

Quantum Cryptography Lecture

Centre for Quantum Information and Quantum Computing
                   Indian Institute of Science
                           Bangalore


Announces its lecture

By

Dr. Prabha Mandayam
Institute for Quantum Information
California Institute of Technology, Pasadena, USA

Title:
" Uncertainty and Complementarity in Quantum Cryptography: Security in the Noisy Storage model"

       On Wednesday the 8th  December, 2010 at 4.00 pm

Venue: Lecture Hall - I, Department of Physics, Indian Institute of Science.

Abstract

Historically, uncertainty relations have played an important role in our understanding of quantum mechanics. Recently, entropic uncertainty relations have gained prominence in the field of quantum information. In particular, they play a crucial role in analyzing the security of quantum cryptographic protocols such as quantum key-distribution and information locking. While optimal entropic uncertainty relations have been obtained for two measurements, not much is known in a general setting with more than two outcomes. We outline a novel construction of symmetric mutually unbiased bases (MUBs), using the 2n generators of the Clifford algebra in dimension d = 2^n.  These bases satisfy the symmetry property that they are cyclically permuted under a unitary transformation. We prove a lower bound for entropic uncertainty relations for any set of MUBs and show that symmetry plays a central role in obtaining tight bounds. Finally, we describe a two-party protocol based on recent cryptographic models  -- the "bounded-storage model" and  the "noisy-storage model" -- whose security is directly related to a lower bound on the average entropy of complementary bases. While the security of most cryptographic systems in use today is based on the premise that certain computational problems are hard to solve for the adversary, these models are based on the physical assumption that no large-scale reliable quantum storage is available to the cheating party. Our protocol achieves security in the bounded-storage model even if the cheating party can store all but a constant fraction of the transmitted information, thus resolving an open question on the achievable physical limits of this model. In the general setting of the noisy-storage model, our protocol extends the range of storage devices for which security can be achieved.

All are Welcome 

DO WE LEARN TO SEE ?

INDIAN INSTITUTE OF SCIENCE

BANGALORE

 

Cordially invites you to a

 

CENTENARY LECTURE

 

by

Prof. Torsten Wiesel
Nobel Laureate

  on

"DO WE LEARN TO SEE ?"


Date  : 15th November 2010
Time  : 4-00 p.m
Venue : Faculty Hall, Main Building


Prof. P. Balaram, Director
  will preside

I saw an interesting video on how groups were used by Garret in his model for a Theory of Everything. Here is the video. The group he used is an exotic Lie group commonly known as E8.

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. 

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

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. 


 

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.

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

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.

Weekend Discussions

In one of my previous posts ( A good weekend), I mentioned bumping into Karthik and how we discussed a lot of random things. One of the things we discussed has led to what I feel is a very wonderful thing.
We decided that it was essential for us to channelize our efforts and make the best of what time we have. Spend a little time learning from each other. To give each other what the education system couldn't give us. This was just an idea, but it is yet to materialize completely. It is easy said than done. But here is the story of what has been done so far.
We decided to tell Shruhi, Harshini, and Raghu about what we had thought about and wanted to see if anything could be done. Shruthi and Harshini were available after GR's class on sunday and as expected they were really enthusiastic about it.

We had to figure out when and where we could meet. Shruthi immediately said that she could make available a place where nobody will disturb us and which is easily accessible to everyone of us. Thank you Shruthi. This is one of the main constraints we would otherwise have had to deal with. Now that the spatial co-ordinates had been decided, we had to zero in on the time co-ordinates. It was again rather quickly decided that we would be meeting on thursdays and Saturdays, between 6 and 8 in the evening. It went as planned for a week, and due to some other practicalities we have decided to meet on saturdays and sundays instead.

Raghu has joined us and we are now a group of five. It is a nice group of people with different mentalities and unique areas of creativity. Some of us are inclined towards theoretical physics, while the others have a more experimentally oriented mind. Each of us will be giving one course. Harshini will probably be summarizing what all has been done so far, and who is doing what etc. And when she does, I urge everyone in the group to comment and add what they learnt from the particular lectures. It will give us all a perspective from the other's  point of view. Harshini has also been recording the lectures for future reference.
All the speakers gave assignments and have been taken up seriously by all present. We have deliberately restricted the discussion to the five of us in order to avoid dilution.

Ego clashes are bound to happen as well. We however hope to minimize this and focus on learning as much as we can and make the most of the time we spend together.

We have had 4 sessions so far, which sums up to a total of 8 hours of lecture. Hope to have many more of such fruitful hours.


PS : Thanks to Michael, a very good friend of mine, we now have a bigger white board. Thank you Michael.

Problem 1

Harshini's post has brought back a few things from when I was a kid. One of the first things that brought to my mind the thought of becoming a scientist was the cartoon Dexter's laboratory. My interests did change but it did invariably come back to physics. I actually even wanted to be a wildlife photographer in 9th standard, but then I realized photography(and for that matter anything else) wasn't really my cup of coffee.

 You find dexter( and some times tom and jerry) mixing up these random chemicals and colourful liquids and surely enough there would eventually be a big bang.I told my mom to get me one of those and she told that they are just cartoons. And then at school in 8th std. , I first heard of an actual explosive chemical reaction. When you put sodium in water it is supposed to react violently and can also be explosive, and our chem teacher said she is going to show it to us in lab. She ended up putting a tiny bit of sodium in water and all you could see was a tiny bubble of fire. And then I thought may be this was as 'explosive' as it gets in real life. I was a bit disappointed.
A few years later I was helping these people build up a lab( for school kids ) and I told them to buy a few things including sodium. I used to get a lot of time alone there to come up with experiments that would excite kids and once my school mate Sneha was around to help and everyone else had gone to have lunch. I slowly slipped in the idea of  trying out the experiment with sodium. I was actually scared of doing it alone and also I wanted a partner in crime if something went wrong.
We filled a small glass beaker with water and I just took up a chunk (as big as a match box!) of sodium and put it in the beaker. Before we could see what was happening , small glass pieces were flying everywhere and the water just vaporized with a huge bang. This is a very memorable event, because a) this was the first time I saw an explosive reaction I had read so much about all through my chemistry classes and b) Not a single glass piece touched us. That actually left us shocked for quite a while. There was not a single place in the room where the glass pieces didn't go, and I had almost no time to move away after putting the sodium. It was pretty unbelievable. For once I wished my lab teacher was around shouting at me as usual to put on the safety glasses which I conveniently forget to carry to college. But I guess we just got lucky and lord murphy was on a holiday I suppose.
After that we used plastic buckets filled with water and put larger chunks of sodium and we showed every kid who walked through the door what " Smoke on the water and fire in the sky" actually looked like.

After experiencing a completely institutionalized learning at college and school, it is really refreshing and revitalizing when things are experienced and learnt in any unconventional ways.
All through school and college we are made to solve problems so that we can get more marks, or get through an entrance exam and have an amazing life ahead. But that's not why take up problems to solve, now is it? So lets try to solve some nice problems just to have fun. I will be posting up a problem as regularly as I can, and Harshini said she will be too. Please do try to spend a few minutes thinking about them, I'm sure it will be worth it. Solutions will be put up eventually. Here is the first one, enjoy :-)

When told that the world record for the pole vault was about 18 feet, the fast-rising athlete Rod told the press, 'Give me a pole long enough, and I will raise the record to 30 feet'. Could he manage it? How high might he get if tried hard?

More things to ponder over a cup of coffee

I was sitting around yesterday without knowing what to do. At this point I usually look towards by book shelf for inspiration. I found it yesterday when I opened the pages of Jearl Walker's "The Flying Circus of Physics". A wonderful book full of problems which the author says himself, "are for fun... What I mainly want to show here is that physics is not something that has to be done in a physics building. Physics and physics problems are in the real, everyday world that we live, work, love and die in."

Here I've stated, word for word, a very curious and interesting problem(like all the others in the book). I don't have an answer, and I haven't looked it up. Thought I'd leave it as an open question for now. And, oh, I've noticed this myself too! But never payed too much attention as I'm too sleepy in the mornings while drinking coffee, and too preoccupied in the evenings. Anyway, it goes like this-

Coffee laced with polygons

If you examine a hot cup of coffee under a strong light that is incident nearly parallel to the surface of the coffee, you will find the surface laced with polygonal cells. They disappear, however, as the coffee cools. You can also destroy the cellular appearance by putting a charged rubber comb (charge it by running it through your hair) near the coffee.

Other liquids show surface designs too. James Thomson, a famous 19th century physicist, noticed the rapidly varying surface designs in a pail of hot soapy water and in strong wines. Later, the Frenchman Bernard was able to make regular patterns in oil surfaces when the oil was heated from below. His regular polygons would slowly evolve into a beautiful hexagonal, honeycomb structure. Still other fluids gave a roll-like appearance. Recently, cellular surface designs were attempted on board spacecraft while under zero gravity.

In these examples, why do rolls and polygons (especially honeycombs) form on the fluid surface? Is the same physics actually responsible for all of the examples? Why do the coffee cells disappear when there is a charged body nearby? Finally, do these several types of surface designs depend on gravity?

The above is listed under the topics- convection, surface tension, nonlinear fluid flow, stability, condensation.

Story of spin

Both Harshini and Shruthi were quite excited about GR’s lectures last Sunday -- which, I was told, revolved mainly around “spin”. I told them I will post an historical account of spin and here it is.

This goes back to 1920’s during which Quantum physics was being intensely explored. Specifying a complete list of quantum numbers associated with electrons in atoms had occupied much of interest. A decisive contribution was made by Wolfgang Pauli (he was 25 year old at that time). Like many theoreticians of the day, Pauli was concerned with understanding the spectral lines emitted by atoms. Bohr’s original model worked only for the relatively simple spectral patterns emitted by hydrogen; but heavier, more complex elements were much harder to understand. For example, Cesium, Sr, and Ba (alkaline earth materials) produce spectral lines that are seen to split into two – they were called doublets. In December 1924, Pauli suggested that a complete set of quantum numbers of an orbiting electron would include its energy, angular momentum (l), and its orientation in space (m); in addition, to explain the alkali doublets, he suggested that there had to be a fourth quantum number, which he referred to – rather unhelpfully – as “Zweideutigkeit” (two-valuedness). During the summer of 1925, Samuel Goudsmit, a young Dutch physicist, was trying to explain Pauli’s ideas to another young countryman, George Uhlenbeck. During such afternoon talks, it occurred to Uhlenbeck that Pauli’s “Zweideutigkeit” was not really another new quantum number, but simply another property of an electron. He suggested that perhaps an electron spins about its axis like a toy top – but unlike a toy top, the spin of the electron would be quantized, and so, it could only “spin” at certain specific values. Looking at Pauli’s formulae, Uhlenbeck and Goudsmit realized that if electrons had a second angular momentum, this would perfectly account for “two-valuedness”. of the alkaline earth metals. The amount of “spin” turned out to be ½ hbar. Both men took their idea to Paul Ehrenfest, Uhlenbeck’s teacher, who made them write up a short paper on spin and then told them to take it to H. Lorentz, the grand old man of Dutch physics.
In 1925, Lorentz was 72, retired, but he still taught a class at Lieden every Monday morning at 11.00 AM. After one such class, Uhlenbeck and Goudsmit showed Lorentz their paper, which was only a few paragraphs long. Lorentz said that it was interesting and he would think about it further. Thinking, for Lorentz, was apparently an active occupation. Two weeks later, Lorentz gave a stalk of papers with long calculations to Uhlenbeck: Lorentz had calculated the speed of the spinning electron with ½ hbar angular momentum to be 10 times that of light!! Uhlenbeck and Goudsmit were most unhappy – they went back to Ehrenfest and said “You better not publish that paper, because Lorentz has shown that it is not correct”. But Ehrenfest had already submitted the paper and the paper was expected to be published within a few days! Later, Bohr, dismissed Lorentz’s objections saying that the faster-than-the-speed-of-light problem disappears when the full quantum theory is applied to a structureless point electron – apparently, Lorentz’s calculations were valid for a classical extended particle with spin ½ hbar. As it turned out, Bohr was correct. The eigenvalues, eigenkets of angular momentum and the matrix representation of angular momentum operators was first obtained in a 1926 paper by Max Born, W Heisenberg and P. Jordan (Zeitschrift fur physic, 35 (1926) 557). It was shown, basing the analysis wholly upon the commutation properties of the angular momentum operators, that there are two types of angular momentum, one with eigenvalues that are only integral multiples of hbar and the other, which can assume half odd integral multiples of hbar values also.

Wise man

Book reviews aren't usually quite as long, and are rarely so touching. This is the tribute of one great man to another, honest admiration, with no hint of envy or self-service. It is full of insight. This is an article published by Freeman Dyson about Feynman in the New York Review of Books

"Great scientists come in two varieties, which Isaiah Berlin, quoting the seventh-century-BC poet Archilochus, called foxes and hedgehogs. Foxes know many tricks, hedgehogs only one. Foxes are interested in everything, and move easily from one problem to another. Hedgehogs are interested only in a few problems which they consider fundamental, and stick with the same problems for years or decades. Most of the great discoveries are made by hedgehogs, most of the little discoveries by foxes. Science needs both hedgehogs and foxes for its healthy growth, hedgehogs to dig deep into the nature of things, foxes to explore the complicated details of our marvelous universe. Albert Einstein was a hedgehog; Richard Feynman was a fox.

Many readers of The New York Review of Books are more likely to have encountered Feynman as a story-teller, for example in his book Surely You’re Joking, Mr. Feynman! than as a scientist. Not many are likely to have read his great textbook The Feynman Lectures on Physics, which was a best seller among physicists but was not intended for the general public. Now we have a collection of his letters, selected and edited by his daughter, Michelle. The letters do not tell us much about his science. For readers who are not scientists, it is important to understand that foxes may be as creative as hedgehogs. Feynman happened to be young at a time when there were great opportunities for foxes. The hedgehogs, Einstein and his followers at the beginning of the twentieth century, had dug deep and found new foundations for physics. When Feynman came onto the scene in the middle of the century, the foundations were firm and the universe was wide open for foxes to explore.

One of the few letters in the collection that discusses Feynman’s science was written to his former student Koichi Mano. It describes the fox’s way of working:

'I have worked on innumerable problems that you would call humble, but which I enjoyed and felt very good about because I sometimes could partially succeed…. The development of shock waves in explosions. The design of a neutron counter…. General theory of how to fold paper to make a certain kind of child’s toy (called flexagons). The energy levels in the light nuclei. The theory of turbulence (I have spent several years on it without success). Plus all the “grander” problems of quantum theory.

No problem is too small or too trivial if we can really do something about it.'"

A Good Weekend

Last few of my weekends have been spent having to attend environmental science classes all through the day. They have come up with a scheme where we are made to complete these compulsory foundation courses by attending them on weekends. This weekend we didn't have any for class for some reason.

I therefore ended up going to BU yesterday and spent some time with friends, playing tt, some problem solving etc. It was a nice break from the usual weekends. I had planned to go to brainstars around 5 in the evening, and then get home at 7 to watch a nice football match. Harshini and Shruthi climbed the bus to go home and then I got on my bike and on my way out I bumped into Karthik. And then all my plans later that evening went down the drain. But it was worth it I must say.

We went to the canteen back in BU and had a good conversation. We spoke about many things ranging from the "scientific outlook" to the nature of mathematics and then inevitably discussed physics. It was nice talking to him about some of the subtle things in physics. We spoke about things like inertia and many other things that we simply take for granted.
The funniest part was when we would talk about seemingly different things and then realize that we were arguing about the same thing. We agreed on quite a lot of things and the best part was when I heard him say that he is " not the only Bakra" after all.
Hope to have more of such reality checks every once in a while.

And now its a nice sunday morning and I made a random choice to read something just until I'm done drinking coffee.

" The tremendous transformation of the scientific view of Nature could only be compared with the change of outlook brought about by Copernicus. It originated, like all really important intellectual revolutions, in places where to all appearance deep tranquillity reigned. The most far-reaching revolution of the twentieth century was born in idyllic circumstances. It came from a picturesque park in Copenhagen, from a quite street in Berne, from the seashore of the island of Heligoland, from the meadows and tree-shaded river at Cambridge, from the Hofgarten in Munich, from the quiet neighbourhood of the Pantheon in Paris, from the peaceful Zurichberg and from the ancient fortifications, along which tall trees now rustle, of the town of Gottingen"
-Brighter than a thousand Suns.

Looking forward to GR's class today, hope its a good one.
Have a nice day!

Ramblings

I was just on the phone talking to Harshini, and she was telling me about the discussion they had in BU today. I asked her, " What do you think about quantum mechanics?", and she said " What do you mean?". I told her that somehow deep down inside I felt Quantum Mechanics was wrong. I really don't know much about Quantum Mechanics to actually say that but then it was just a kind of an intuitive feeling. Anyway, she replied saying, " You Einsteinians!".
Well, I may be a little biased but then I have my reasons. When I first started out reading popular articles as a kid who was fascinated by science, it was quantum mechanics and string theory that seemed more appealing ( the things about teleportation, extra dimensions etc). To be fair, relativity had its own attractions. I started working on special relativity first I guess because of its mathematical simplicity. It's just amazing being able to show that time slows when things move just using high school algebra. But, I have NO idea about how or what drove me to even consider working something as sophisticated as the general theory of relativity. Not to say that I know much about it, I really don't. Considering that I was very weak ( still am ) at mathematics and school physics, it surprises me to no end that I actually had the guts to work out a few things in gtr. I think it was its beauty that blinded me and I just couldn't see any of my weaknesses or any other problems in front of it. I don't know what Einstein's Field equations mean, but still when I look at them I get goosebumps all over me.

How could a man, sitting in a patent office, having never even looked through a binocular predict that the planet mercury's orbit will undergo a shift and give precise calculations showing it? How could he predict that GRAVITY could bend the path of LIGHT? That Gravity could slow down TIME? And the technology was far from even being able to confirm these predictions. And all he knew was that Newton's laws worked pretty well and that the speed of light is same for all inertial observers. To be fair, he also knew that Galileo showed that objects of different masses fall with the same acceleration. Who would have thought that a few facts like these could lead to a theory that predicted black holes, to be only confirmed a few years ago.  Unparalleled elegance, I would say.

I find it really hard to find that I don't have many around me to discuss this with wonderful thing with. Sometimes it seems that happiness is only real when shared. I was the happiest while talking about it during the lecture sessions in BU. Well, I don't think that's going to happen for a while. Entrance exams coming up. Prof. Vishweshwara, Joseph Samuel, Lee Smolin, Carlo Rovelli, Abhay Ashtekar are a few people I know who have done it all in relativity. What I would give to just exchange a few words with them. I was crazy about Chandrashekar sir the moment I heard he had seen Lee Smolin.

Lee Smolin and Carlo rovelli are currently working on Quantum Gravity. Rovelli formulated a new approach known as Relational Quantum Mechanics. Abhay Ashtekar formulated general relativity by creating self-dual variables so that you could have a hamiltonian (a.k.a Ashtekar Variables). And Lee smolin, well, you will be hearing a lot about him from me, and a I will be quoting a lot from his books. And here is the first,
from his book, The Trouble With Physics,

" This is the story of a quest to understand nature at its deepest level. Its protagonists are the scientists who are labouring to extend our knowledge of the basic laws of physics. The period of time I will address - roughly since 1975 - is the span of my own professional career as a theoretical physicist. It may also be the strangest and most frustrating period in the history of physics since Kepler and Galileo began the practise of our craft four hundred years ago.
The story I will tell could be read by some as a tragedy. To put it bluntly - and to give away the punch line - we have failed. We inherited a science, physics, that had been progressing so fast for long that it was often taken as the model for how other kinds of science should be done. For more than two centuries, until the present period, our understanding of the laws of nature expanded rapidly. But today, despite our best efforts, what we know for certain about these laws is no more than what we knew back in the 1970's.
How unusual is it for three decades to pass without major progress in fundamental physics? Even if we look back more than two hundred years, to a time when science was the concern mostly of wealthy amateurs, it is unprecedented. Since at least the late eighteenth century, significant progress has been made on crucial questions every quarter century".   - Lee Smolin (The Trouble With Physics)

Well, in a less elaborate way, all this can be said by quoting G Ramchandra's one sentence "Yen agillapa." We laughed it off then but I think its time for us to do something. Is it the Education system? Is it the research Institutes? Do we even Care?
How long is it just going to be about clearing entrance exams and worrying about how many papers are being submitted per month?
Ofcourse, there are a lot of us who are very optimistic about the system and that it is changing. But I guess hope is a luxury we cannot afford right now. It seems the time has come to use our strengths and collective differences in a harmonious way. To what end? I don't know. But it's the journey that matters, not the destination.

Bongos

Here is a really nice video of Feynman playing the bongos. For some reason I really enjoy watching this:)
Click here to watch

Wonderful:) ... as a follow up to ur post i would like to show an extract from Mlodinow's, "Feynman's Rainbow"...

" When I got to him, Feynman was gazing at a rainbow. He had an intense look on his face, as if he were concentrating. As if he had never seen one before. Or maybe as if it might be his last.
I approached him cautiously.
"Professor Feynman. Hi," I said.
"Look, a rainbow," he said without looking at me.
I joined him in staring at the rainbow. It appeared pretty impressive, if you stopped to look at it. It wasn't something I normally did-in those days.
"I wonder what the ancients thought of rainbows", I mused. There were many myths based on the stars, but I thought rainbows must have seemed equally mysterious.
"All I know," Feynman said, " is that according to one legend angels put gold at its ends and only a nude man can reach it.
"Do you know who first explained the true origin of the rainbows?" I asked.
"It was Descartes," he said. After a moment he looked me in the eye.
" And what do you think was the salient feature of the rainbows that inspired descartes' mathematical analysis?" he asked.
" Well, the rainbow is actually a section of a cone that appears as an arc of the colors of the spectrum when drops of water are illuminated by sunlight behind the observer."
"And?"
"I suppose his inspiration was the realization that the problem could be analysed by considering a single drop, and the geometry of the situation."
"You're overlooking a key feature of the phenomenon," he said.
" Okay, I give up. What would you say inspired his theory?"
"I would say his inspiration was that he thought rainbows were beautiful."
I looked at him sheepishly. He looked at me. " How's your work coming?" he asked.
I shrugged. " It's not really coming."
"Let me ask you something. Think back to when you were a kid. For you, that isn't going too far back. When you were a kid, did you love science? Was it your passion?"
I nodded. " As long as I can remember. "
"Me, too", he said. " Remember, it's supposed to be fun." And he walked on. "


Along with science being fun, I think there is a certain appreciation for beauty inherent in human beings. We cannot define beauty. What we find beautiful is usually something natural. ( Personally, I find Einstein's relativity beautiful, even if eventually it turned out to be wrong).
Curiosity may drive us to do science. The fact that it is fun is another motivation. Whatever it is, these things feed on us. Curiosity transforms itself into a strong driving force that pushes us through the greatest extents. We don't know where our search will lead us, but the journey sure is fun. In the end, I think it is the journey that matters, not the destination. And that I think is one of the most beautiful things about life and physics.

What remains to be answered about present day science is whether this is what still drives every physicist? Or have the motivations changed a bit?

The pursuit of science: its motivations

We have been talking about how Feynman influenced our learning of science and towards our scientific imagination – with the help of a mathematical abstract view, Julius Sumner Miller’s exciting science demonstrations … I felt I should continue this stream of thoughts by adding some observations on the pursuit of science. (These are my compilations from the wonderful book “Truth and Beauty” by Professor S. Chandrashekhar, Penguin Books Ltd (1991) – don’t miss to read this book if you happen to come across). I am aware that I am not offering here any concrete thinking on the “pursuit of science” -- but surely it helps to put things in their places, and it invites deeper thinking on this issue.

“The pursuit of science: its motivations” is a difficult topic because of the variety and the range of the motives of the individual scientists; they are as varied as the tastes, the temperaments, and the attitudes of the scientists themselves. Besides, their motivations are subject to substantial changes during the life-times of the scientists. Indeed it is difficult to discern a common denominator! We may consider some examples to get some better ideas on this. Let us think of Albert Michelson: His main preoccupation throughout his life was to measure the velocity of light with increasing precision. His interest came about almost by accident, when the commander of the United states Naval Academy asked him – he was then an instructor at the Academy – to prepare some lecture demonstrations of the velocity of light. That was in 1878 and it had led to Michelson’s first determination of the velocity of light in 1880. On 7th May 1931, i.e., fifty years later and two days before he died he dictated the opening sentences of a paper, posthumously published, which gave the results of his last measurement! Michelson’s efforts resulted in an improvement in our knowledge of the velocity of light from one part in 3,000 to 1 part in 30,000 – i.e., by a factor of 10. But by 1973, the accuracy had been improved to 1 part in 100000000000 -- a measurement that made obsolete, beforehand, all earlier measurements! Were Michelson’s efforts over fifty years in vain? Leaving that question aside, one must record that, during his long career, Michelson made great discoveries derived from his delight in “light waves and their uses”. Thus, his development of interferometry, leading to the first direct determination of the diameter of a star, is breathtaking. And who does not know the Michelson-Morley experiment, which -- through Einstein’s formulation of the special and the general theory of relativity -- changes irrevocably our formulation of the nature of space and time? It is a curious fact that Michelson himself was never happy with the outcome of his experiment!! Indeed, it is recorded that when Einstein visited Michelson in April 1931, Mrs. Michelson felt it necessary to warn Einstein in a whisper when he arrived: “Please don’t get him started on the subject of the ether”!
When Michelson was asked towards the end of his life, why he had devoted such a large fraction of the time to the measurement of the velocity of light, he is said to have replied “It was so much of fun”! There is no denying that “fun” does play a role in the pursuit of science. What are the other factors? Difficult to say! I leave it open to your own jurisdiction now.

Prof Julius Sumner Miller

It's been my pleasure of late that I'm getting opened to a very necessary scientific outlook, i.e, in the form of "seeing" physics in action everywhere. In this context I ran into several of the blogs of scientists{ students and Profs included} who have poured out their cynicism about the sorry state of science in India and teaching in particular, read and saw more about Feynman. Nevertheless, what I noticed in all, is their enthusiasm to do something "off the track" like us. Something not for the sake of it but for the love towards it.

To this end, I would like to draw your attention to this one of a kind Professor by name Prof Julius Sumner Miller. I don't know how many of you already know him but i ran into him only this day and thought that you ought to know him for his infectious love towards Physics. He has featured in cadbury Dairy Milk chocolate ads {which by the way, I -- guess that even you--would not have seen it}. I accidentally happen to watch his demonstration of Bernoulli's principle and went Eureka!! {not the Archimedes way!!!} So, I would request you all to watch his demonstration of Bernoulli's principle part 1 and 2 -- and a lot more--for the fun of it-- and to know how things work. You can find one of his cadbury ad here.

Scientific imagination

I have a free afternoon session today – no lab work to take care of and no students came with some bothering questions! So, I decided to post what Harshini’s Fine Man says about scientific imagination – which had fired my imagination for sure!

“Let us try to imagine electric and magnetic fields; you may say, “Professor, All this business of electric and magnetic fields is pretty abstract! What is actually happening? Why can’t you explain it? Please give us an approximate description of the electromagnetic waves, even though it may be slightly inaccurate, so that I too can “see” them!” I am sorry – I can’t do that for you. I don’t know how. I have no picture of this electromagnetic field that is in any sense accurate. The only sensible question is, “what is the most appropriate way to look at their effects?” Some people prefer to represent them as field lines and feel that writing vector E and vector B is too abstract! The field lines, however, are only a crude way of describing a field. Field lines cannot efficiently describe superposition of electromagnetic waves. From the mathematical stand point, on the other hand, superposition is easy – we simply add two vectors to get another vector. The field lines have some advantage in giving a vivid picture, but they also have some disadvantages. So, the best way is to use the abstract field idea. That it is abstract is UNFORTUNATE but NECESSARY!

Our science makes terrific demands on the imagination. It appears that scientific imagination requires mathematical view and then its experimental verification. Now, what is a mathematical view?
For example, from a mathematical view, there IS an electric field vector and magnetic field vector at every point in space. This concept is abstract – true, but in some sense the fields are real, because after we are all finished fiddling around with mathematical equations, we can still make the instruments detect electromagnetic signals.

The whole question of imagination is often misunderstood by people in other disciplines. They try to test our imagination in the following way. If someone asks me: “Here is a picture of some people in a situation. What do you imagine will happen next?” I would say “I can’t imagine (because I don’t have enough facts”. So, people think that I have a weak imagination. They overlook the fact that whatever we are allowed to imagine in science must be consistent with EVERYTHING else we know.

The electric and magnetic fields we talk about are not just some happy thoughts which we are free to make as we wish, but ideas which must be consistent with all the laws of Physics we know. We can’t allow ourselves to seriously imagine things, which are obviously in contradiction to the known laws of nature. One has to have the imagination to think of something that has never been seen before, never been heard before. But creating something new, has to be consistent with everything, which has been seen before, is extremely difficult and requires scientific imagination.”

So, tell me if this caught your imagination (poetic – if not scientific) too!

Duality and Reality

After Harshini's post, this is probably going to seem very pale. I've never written anything of this nature before. Please do comment, honest criticism will be well accepted and I will be more than happy to fill in the gaps. I am supposed to be giving a talk tomorrow on "Symmetry in nature and mathematics"in college and that has made me think again about something that I started thinking when I first began working on the General theory of relativity. This post is a result of those rambling thoughts.
It was in the book by Simon Singh, " Fermat's last theorem", where I first read Pythagoras' famous statement - " Everything is a number". This is indeed true. Theoretical physicists and experimental physicists are both trying to get meaningful numbers out of nature. Numbers are one of the most important things that define our reality. Theoretical Physicists have a way of getting to these numbers. Its called duality. Duals are paths to real numbers.
The first time I encountered duality was when I started out on general relativity and had to study tensor calculus [or according to G. Ramachandra, I was just raising and lowering indices ;-) ] There are vectors that are a part of dual vector spaces, the contravariant and covariant vectors. For those who are more into QM , its the Bras and the Kets. They do not make any physical sense individually. You need both to describe a physical quantity. They are the yin and yang of everything. For a long time I wondered why this was true. Why does a description of reality require two different things? Why not three or four? Can I not know the "one" thing knowing which I can know everything else? While working on Quantum Information, I was introduced to a new concept known as distinguishability.

Imagine a universe where you could not distinguish between any two things or events. Imagine not being able to differentiate between the correct answer and the wrong answer. The universe simply could not exist without any distinguishability. And now, while preparing for tomorrow's thought, it seems to me that duality is a consequence of symmetry. Can there be a perfectly asymmetric object?
I have come to realize so far that as long as a mathematical structure defines reality, there is an inherent duality. I may be wrong, but I haven't seen anything that doesn't satisfy my argument. For example, if you want to get rid of the notion of distance between two points, you need to get rid of the metric, which means ur getting rid of the dual vectors and the inner product between them. And the space thus becomes a simple topological space in which there in only a notion of connectedness but no distance.

I am yet to find a reason for this duality in nature to exist. Is it actually there? Or is the duality in our heads? Are our brains wired to think that way? At this point I silence a horrible thought occurring to my head about the struggle towards Quantum Gravity. I have in this post spoken about duality from a theoretical point of view. I will let you answer the question about the duality in experimental physics :) .

More on this and self-duality yet to come.


P.S: It may have no relevance with what I have said, but for some reason I am inclined to end by quoting Niels Bohr - " The opposite of a correct statement is a false statement. But the opposite of a profound truth may well be another profound truth."

A Fine Man Indeed

A funny thing happened in Sharath Sir's class this week. I think I'm one of two people sitting in that class who found it funny. It went like this- He was showing us these slides he'd made as an introduction to Atomic Physics. He chose to quote Feynman, who, in his Lectures said, famously, 'everything is made of atoms'. Sharath Sir repeated that, and then said, quite seriously, "I hope you all know who Feynman is. If you don't...get out of my class and don't come back..". I think the threat was quite real. But nevertheless, funny. You can't talk physics without bumping into Feynman.

My first encounter was a happy accident. I was in a book store, sometime in 8th standard when I came across 'Surely, you're joking Mr. Feynman'. And then my dad came around and told me I had to read it. This, from a doctor who hasn't "studied" physics since he was in Class 12. And yes, after reading it, I almost decided to hang around book stores, grab random people, and ask them to read it too! But I wasn't that insane(yet!).

What is it about Richard P. Feynman that brings out such reactions in us? To use a cliche, like him or hate him(Oh yes, there are those too), you just cannot ignore him. I thought about this for a long time. It is finally becoming clear to me. Feynman, to me, represented what I wasn't, but wished I could be. A free thinker, a free learner, and a free liver(as in life, not the organ, just clarifying).

Much has been said about his 'zest for life', his 'unique style of teaching physics', etc etc that I don't think I'll be able to say anything that hasn't been said before. Feynman for me, personally, embodies the complete man(not Raymond, whoever that is). Aristotle(see footnote) said "The whole is greater than the sum of the parts", and Feynman, you see, is greater than the infinitely many tales about him. He was one of the most outstanding physicists of the 20th century. Leonard Mlodinow says, in Feynman's Rainbow, "..there indeed was no problem in the world of physics into which he couldn't provide the greatest insight..". But he was equally well-known later, for his fun-loving nature, his various eccentricities and the like, having completely smashed away the notion of a scientist being a boring creature that can be found in labs, working on experiments with fuming liquids, or buried neck-deep in huge books, and the only thing more boring than the work was the person doing it. Feynman made science relevant. He made it fun! I actually have much more to say on this matter but will take mercy on the hapless readers(if any), and edge nearer towards an ending. But not just yet.

Feynman probably wasn't born that way, but everything that went on inside his head, and outside, made him who he turned out to be. He didn't have any grand plans for himself, and he certainly never had any grand plans for humanity. He touched millions of lives without even knowing it, by simply having the courage to be himself. Everything else that followed was a consequence of that. And that is the biggest lesson I learned from him. I try everyday to be a little more like Feynman. I try everyday to be a little more like me.

Harshini




P.S. This is the aforementioned footnote. I googled the quote to see who had said it first and found that it was Aristotle. Alongside that, I saw this, and found it interesting: Kurt Koffka: "It has been said: The whole is more than the sum of its parts. It is more correct to say that the whole is something else than the sum of its parts, because summing up is a meaningless procedure, whereas the whole-part relationship is meaningful." (Kurt Koffka, 1935: New York: Harcourt-Brace. p 176). Incidentally, Aristotle meant the same thing too. Whoever interpreted it otherwise, goofed up.

Intro

I'm sure the name of the blog will tell you lots about it. The people who will be invited to co-author the blog are like minded friends. Please feel free to share any insights, experiences, views and ideas with regard to learning in general, physics in particular. Since we share common concerns about our education system, this can be considered a platform for individual expression and action oriented discussion.


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