(Image Courtesy : http://www.photonics.cusat.edu/Article5.html)

Feb 28th is our National Science day ! This day, in the year 1928, C.V. Raman announced to the world his famous discovery, a discovery which would earn him a Nobel prize. You can read about his work in the presentation speech that preceded his nobel lecture. Some excerpts:

The diffusion of light is an optical phenomenon, which has been known for a long time. A ray of light is not perceptible unless it strikes the eye directly. If, however, a bundle of rays of light traverses a medium in which extremely fine dust is present, the ray of light will scatter to the sides and the path of the ray through the medium will be discernible from the side. We can represent the course of events in this way; the small particles of dust begin to oscillate owing to electric influence from the ray of light, and they form centres from which light is disseminated in all directions. The wavelength, or the number of oscillations per second, in the light thus diffused is here the same as in the original ray of light. But this effect has different degrees of strength for light with different wavelengths. It is stronger for the short wavelengths than for the long ones, and consequently it is stronger for the blue part of the spectrum than for the red part. Hence if a ray of light containing all the colours of the spectrum passes through a medium, the yellow and the red rays will pass through the medium without appreciable scattering, whereas the blue rays will be scattered to the sides. This effect has received the name of the “Tyndall effect”.

Lord Rayleigh, who has made a study of this effect, has put forward the hypothesis that the blue colours of the sky and the reddish colouring that is observed at sunrise and sunset is caused by the diffusion of light owing to the fine dust or the particles of water in the atmosphere. The blue light from the sky would thus be light-scattered to the sides, while the reddish light would be light that passes through the lower layers of the atmosphere and which has become impoverished in blue rays owing to scattering. Later, in 1899, Rayleigh threw out the suggestion that the phenomenon in question might be due to the fact that the molecules of air themselves exercised a scattering effect on the rays of light.

In 1914 Cabannes succeeded in showing experimentally that pure and dustless gases also have the capacity of scattering rays of light.

But a closer examination of scattering in different substances in solid, liquid, or gaseous form showed that the scattered light did not in certain respects exactly follow the laws which, according to calculation, should hold good for the Tyndall effect. The hypothesis which formed the basis of this effect would seem to involve, amongst other things, that the rays scattered to the sides were polarized. This, however, did not prove to be exactly the case.

This divergence from what was to be expected was made the starting point of a searching study of the nature of scattered light, in which study Raman was one of those who took an active part. Raman sought to find the explanation of the anomalies in asymmetry observed in the molecules. During these studies of his in the phenomenon of scattering, Raman made, in 1928, the unexpected and highly surprising discovery that the scattered light showed not only the radiation that derived from the primary light but also a radiation that contained other wavelengths, which were foreign to the primary light.

(Image Courtesy : http://www.photonics.cusat.edu/Article5.html)

The National Science day speech of President of India is available here. He starts off with

My greetings to all of you. I am indeed very happy to talk to you on the occasion of National Science Day, which is celebrated on the 28th of February every year, the day in the year 1930, Nobel Laureate Sir CV Raman announced a landmark discovery which is finding applications today in the area of continuous wave all-silicon laser. On this day, the nation pays tribute and expresses its gratitude to all the scientists who have made our dream of using the science and scientific discoveries as vehicles for economic development, a reality. Celebration of Science will attract many young children to take up science as a career. This is the day, our Scientists may like to rededicate themselves to create high quality scientific research output from India and make the nation proud. Science day is the day to remind us that the important ingredient for societal transformation would mainly come from science.

and then goes on to talk about the usual pet topics which are so dear to him – Solar cells and other alternatives that are being explored in energy research. No pure science here though 😦 which in a way is what I expected ..

Indian science, in my opinion, is at crossroads. There is a lot which remains to be done – many tasks waiting for scientists of different hues and world views to take them up. And India with its diversity and intellectual potential has no excuse for not getting them done. To quote the concluding words of this years budget speech,

The young people of India are building castles, it may appear that those castles are in the air, but as Henry David Thoreau said: “If you have built castles in the air, your work need not be lost; that is where they should be. Now put the foundations under them.” It is our duty to put the foundations on which the young can build their castles.

(via nanopolitan )

Today I came across one of my favourite poems in the Bengali Language. It is by Rabindranath Tagore – one of the greatest poets that this subcontinent has ever produced. He is a Nobel Laureate and is the author of the National anthems of both India and Bangladesh.

And this is the poem from Gitanjali


There is an English Version by the poet himself

Where the mind is without fear and the head is held high
Where knowledge is free
Where the world has not been broken up into fragments
By narrow domestic walls
Where words come out from the depth of truth
Where tireless striving stretches its arms towards perfection
Where the clear stream of reason has not lost its way
Into the dreary desert sand of dead habit
Where the mind is led forward by thee
Into ever-widening thought and action
Into that heaven of freedom, my Father, let my country awake

from Rabindranath Tagore’s Geetanjali

In mechanics, the concept of a pseudo-force is a useful one. It allows you to work in frames which are non-inertial and apply there the usual laws of Newton. But, one thing about pseudoforces which is rarely discussed, is the fact that pseudoforces tell you something about the geometry of the space around you.

One has to wait till one learns general relativity to recognise this fact. And even then, it is quite likely that this fact is missed in the rain of tensor indices and four vector algebra 🙂

But the relation between pseudoforces and geometry is a simple one, independent of relativity or gravity. And this relation between pseudoforces and geometry is better discussed first in the familiar Newtonian framework.

    Sidenote : Once you understand how pseudoforces affect geometry, the relation between geometry and gravity- the core idea of GR is self-evident. According to Einstein’s equivalence principle, gravitational forces are indistinguishable from pseudoforces and if pseudoforces affect geometry, gravitational forces should do so too !

    Well, the beauty of the equivalence principle is that by identifying gravitational forces with pseudoforces it connects a lot of seemingly unrelated facts into a beautiful theory. All this factsabout pseudoforces, geometry and gravity fall into place in General relativity which combines all of them by identifying gravitational forces with pseudoforces and making matter affect geometry via gravitational/pseudo-forces

Now, coming back – how do we see that pseudoforces affect geometry, and yeah why haven’t we seen it before when we learnt mechanics ?

I’ll answer the second question first. We haven’t seen it before, because the usual examples chosen for non-inertial frames – accelerating/rotating frames have such a familiar geometry that we tend to overlook the effect of pseudoforces. The geometry of space is same as the usual High-school geometry which applies to inertial frames , so there is not much new to talk about here. Once we realise this, the question how do we see the effect of pseudoforces on geometry has a straightforward answer : Think about more general non-inertial frames !

    Sidenote : By the way, if you take Einstein’s relativity into account, you would see that this is not true – you can prove that there is no non-inertial frame which has the same geometry as the highschool geometry. In particular, in accelerating and rotating frames we would see two additional geometric effects- gravitational redshift and Sagnac effect due to pseudoforces. That indeed is the reason why in relativity, you are forced to acknowledge the effect of pseudoforces on geometry, whether you like it or not.

Now, what do I mean by non-inertial frames more general than accelerating/rotating frames ? Consider, for example, what I call an “expanding” frame – a frame of observers who when seen from an inertial frame are expanding radially outwards from the origin.The frame is defined by the usual convention that according to these set of observers, they are all at rest with respect to each other. If you think about it a bit, you will see why this frame is different from the usual non-inertial frames .

In the case of accelerating/rotating frames, the corresponding observers are in a rigid-body like motion. In particular, this means that the distances between the observers does not change. But, for an expanding frame, the distance between the observers increases with time. It is very simple to convince oneself of this fact- just think of two diametrically opposite observers. The distance between them increases with time. And since distances are absolute in Newtonian framework, these observers will actually see the distance between them increasing, though they are at “rest” with respect to each other (by definition) !

I like this particular example very much, since it brings into a sharp focus our conception of what do we mean by being at rest . If you say that being at rest with respect to some frame means not moving, then these two observers are not moving in the “expanding” frame – they are at rest due to the very way the “expanding” frame has been defined. And the distance between the two observers can still increase, though neither of them is “moving” in this sense ! So, how do the expanding frame’s observers interpret this weird thing they observe ? There is only one way out – in that frame, the space itself is expanding ! Though they are at rest, the space is continuously “created” in between them resulting in the increase of distance.

But, what causes this “creation of space” in this non-inertial frame ? What is that entity which is responsible for the creation of space ? Well, that is easily answered. Remember this golden rule about pseudoforces- “Whatever weird is happening in non-inertial frame, can eventually be blamed on the pseudo forces” ! So, it is the pseudoforce fields that create space.

You can convince yourself by calculating the pseudoforces due to this expansion and by showing that the expanding observers can predict the rate of creation of space by measuring the pseudoforces in this frame. So here we have the first example of effect of pseudoforces on geometry- there are some pseudoforce fields which can create space and increase the distance between the two objects which are at rest. In fact, they can do the reverse thing too, they can “eat up” or “swallow” the space in between two objects at rest.

So in this sense, non-inertial frames are like the wonderlands of Lewis Caroll. If you’ve read “Alice in the Wonderland” you would remember this scene in which the red queen and Alice start running

The most curious part of the thing was, that the trees and the other things round them never changed their places at all : however fast they went, they never seemed to pass anything. …
Alice looked round her in great surprise. `Why, I do believe we’ve been under this tree the whole time! Everything’s just as it was!’
`Of course it is,’ said the Queen, `what would you have it?’
`Well, in our country,’ said Alice, still panting a little, `you’d generally get to somewhere else — if you ran very fast for a long time, as we’ve been doing.’

`A slow sort of country!’ said the Queen. `Now, here, you see, it takes all the running you can do, to keep in the same place.

If you want to get somewhere else, you must run at least twice as fast as that!’

Expanding-frame is a bit like that. You’ve to run in this frame to be at the same distance from something at rest in this frame !

And once you realise this, you are on your way to understand the philosophy behind GR- that space is not a quite thing sitting silently allowing all other things to move. It is not a dead-silent stage for the other actors. The stage called space itself is an actor in the drama. It can be created and eaten up, squished and stretched by the pseudoforces.

In fact, there are only two more steps from here to GR. First, is the realisation that inertial frames need not exist- a spacetime where there is no frame in which pseudoforces vanish everywhere is said to be a “curved” spacetime. So, this realisation can be rephrased as the fact that the spacetime can be “curved”. This terminology comes from the fact that for example, a two-dimensional being over a sphere cannot establish a frame over the sphere in which all the pseudoforces vanish. So, this is one way of defining what do you mean by a curved space-time – you are in a curved spacetime if you cannot establish a single inertial frame everywhere.

The universe we live in is such a space. There are pseudoforce fields that extend all over the universe creating new space – this is what we mean by the expansion of the universe. But unlike the example before, this expansion cannot be gotten rid of. The pseudoforce fields cannot be transformed away everywhere by a change of frame since there are no global inertial frames. And in fact, you can use this to tell about the past of our universe- in the past when all this space was not yet created by the pseudoforce fields, the universe was small and hot, and this is what the BigBang theory is all about.

    And this should clear the confusing question “where did BigBang happen ?” – you see when bigbang happened there was only one place where it could happen – the rest of the space was simply not there !

    And then there are people who think everything in the universe expands – you know from our measuring rods to earth-sun distance to distance between the galaxies. Then they get confused about how we can see the expansion if everything expands. Well, I just tell them – think of this expanding frame and imagine what those non-inertial guys would see. Equivalence principle assures you that what we see in an expanding universe would be very similar.(The only difference is that the pseudoforces cannot be wished away bya frame choice- the efffect of pseudoforces on geometry are very similar.). It is immediately obvious that the measuring rods these people carry would not expand. True there will be a tendency to expand- there will be stresses developed on the rods due to the pseudoforces for example ! But, they won’t expand appreciably unless the pseudoforces are really strong .

Second, is of course the equivalence principle- There is no way to distinguish gravitational forces from the pseudoforces in a general spacetime. So, they are just two different names of the samething. This in turn, means that matter can produce pseudoforce fields which can then eat up space. How cool !

This gives rise to really cool objects called Black Holes ! What happens here is that the matter produces a pseudoforce field which eats up space at a large rate. In fact, it eats up space so fast that invariably any two things inside a blackhole are brought near each other. The rate of eating of space is so high that you can’t even run away ! Remember – there is a limit to how fast you can run since you cannot run faster than light. There is no escape from the interior of a blackhole because eventually the pseudoforces will eat up the space between any two objects and everything will be crushed together. Like the expanding universe case, these pseudoforces which create blackholes cannot be transformed away or gotten rid of by changing frames.

So, in GR you have this picture of space which is active and alive , with birth and death ! The space is like a deep sea on which all ships stand. When the sea is calm and serene, the explorers aboard can delude themselves that they are on the land – That there is a ‘ground’ beneath their feet, that their life is lived over a rock-steady stage. Oh explorers! how far would you delude yourselves ? When the sea comes to her full glory, When her waters drench your clothes, When the platform on which you stand begins to shake, would you still mainatain that you are on land ? Would you still dismiss its dynamical nature ? That, in a way, is the challenge of gravity to anyone who seeks to understand her.

P.S. : Do have a look at this article titled Albert Einstein’s Theory of Relativity- In Words of Four Letters or Less . It talks about the same topic but in a different(and probably better) way.

The Five Years

February 23, 2006

A deep impatience of the half-night,
A furious stare at the red-brick citadels,
A walk with thoughts coursing through the veins,
A deep love, A near-lunatic laugh, A yearning,
Pointed complaints, peripheral rituals,
A journey into the young elite Indian mind,
A life !

A subtle pain not unlike the birth pangs,
A ruthless wall involuntarily dividing what ought to be undivided,
A silent fall of the great and the mighty,
A darkness with a pessimistic sting,
Unattempted greatness, mysterious shadows,
A dissection of life with lazy passion,
A deaf path !

A long road walked with the illustrious,
A whisper in the air penetrating the soul,
A rare music to forget all,
A crazy subject to caress the mind,
Unwatched fountains, smiling faces,
A sleep in the library with quantum field theory,
A richness of theme !

A beautiful morning, the cold nights,
A pursuit for light and deeper understanding,
A moment of silence becoming the voice of the multitude,
A stubborn walk day after day, year after year,
The wonder that is human, effervescence of language,
A watch from the distance, the eternal hand-wringing,
A struggle to connect !

A hesitation to haste, the refusal to hate,
A star-gazing solitude, the rainy afternoons,
A long monologue with relativity,
A perception of the unsure India,
The impersonal institute, the immunised hypocrisy,
A suicide, a drama running in our breath,
A sojourn to relish !

There is Music

February 20, 2006

There is Music ! When the silence of the air is broken, and when the voices summon the deep human feelings through the sonic waves, I find myself standing alone troubled by some deep questions…

There are not many who would go into rhapsody over the Maxwell’s equations, but such a reaction is apparently commonplace in a music audience . Sometimes I wonder – does music touch and celebrate nature in a deeper way than science does ? Or is the very comparison ridiculuous ? And how is it that music is so inclusive – belonging both to the elite and the ignorant decorating the lives of both whereas science still has to tear down its walls ?

Ok, here is the context- there was this “Musical Extravaganza” at the IITK auditorium. And there were voices- voices which glide through music with a deep confidence like the mighty whale in the deep sea, which startle me everytime I hear them – It was the duo Adish and Narasimha. I can but bow in humility and mutter to myself how you can give anything for these voices ! I am not a music aficionado to appreciate them well, so I shall remain demure in my silence…

But deep are the questions, and in a suble way the way of the scientist is same as the voice of the musician.Both are attempts to bring nature and human mind together. And whenever I hear a good music, I feel a tinge of childish jealousy on how for one moment, that music has gone closer to nature than I have 🙂

Tear down this wall !

February 15, 2006

Almost alone among the greatest of human endeavours, Science stands as the common ground, a great unifier of all that is there. And whenever I say this, most people counter that I overstate my case and I somehow underestimate the greatness of the other fields of human endeavour.

But, tell me one other field which is comparable to science
Which interweaves Mathematics and Philosophy, Empirical observations and Technology, along with simplicity and artistic elegance,
Which in one stroke of quantum mechanics relates deep questions about reality to Hilbert-spaces and fibre bundles to the diverse chemistry of the various elements we see around us, to Lasers and superconductors, to the semiconductor technologies that dominate the present technological landscape
Which in one stroke of electromagnetism connects the sensations that course through our nervous system to the strong magnetic fields of distant stars, to the deep ocean rocks which by their patterns of magnetisation tell you about the history of the ancient earth, to the faint starlight that cuts across the darkness with enormous speeds and comes to us traversing mind-boggling distances to decorate our night sky,
Which in one stroke of Evolution unifies the weird-looking monsters of the deep ocean to spiders and ants,to that little mushroom that grows by the roadside, to the food we eat, to that herds of bacteria that rushes into your nose as you breathe

Tell me one other field which relates them all like science does, and you will see me immediately retract my initial claim. Science has achieved something which no other thing had achieved before – and the irony of this whole success is how that achievement is virtually unknown and how people in general are so hesitant to acknowledge this success !

In the public discourse, where many a failure is paraded and applauded as great victories , oddly enough the real success of science is never acknowledged or even when it is acknowledged people are eager to follow it up with a long list of qualifiers – “Science is great, but you see there are other things in life that science doesnot cover you know…” Granted ! But, why this stepmotherly treatment to science alone ? Why don’t I hear with every appreciation of sports something similar ?

When is the last time you heard – ” This guy is a great batsman. But you know there are other things in life that cricket doesn’t cover you know… ” ?
Now,what would you think of a cricket commentator who adds such a sentence after every single appreciation ? You would think the commentator is insane ! But, that is precisely the way many people comment on science !

So, What indeed is the origin of this trend where it is not as fashionable to be a fan of science as to be a fan of some music ? Well, the reasons are not difficult to find. I can safely say that the blame almost completely lies on the scientists themselves. This “unfashionableness” of science in public discourse is the exact mirror image of “unfashionableness” of public discourse in science ! Majority of scientists look down upon popularisation of science – How else do you explain the general apathy towards popular lectures in many academic departments around the world ? How else do you explain the people who accuse some of the best popularisers of science of “playing to the gallery” or “selling science” ?

How else do you explain the looking down of the school teachers by the academic elite ? I think I can safely bet that when I or my fellow colleagues in physics think of what subfield to choose in physics, “physics education ” rarely crosses our minds. You know somehow to all of us, it is there somewhere down-under in our list and most of us even have a problem acknowledging it as a field.

Oh, mysterious indeed are the chains of fashion ! This only reminds me of those of us who would assert (based on fashion of course) the superiority of computer science over physics without knowing either ! To ensure that you don’t mistake me for somebody who decries blindly all that is fashionable, let me put on record this – I do understand that every fashion has a reason behind it, right or wrong ! And yes fashions simplify the world for us – creating for us a virtual reality cast in black and white which tries to mimic the colorful reality. But, what of those who should know better ? If scientists don’t respect science education who else would ? If scientists look down upon popularisation of science who else can attempt to increase the quality of science in public discourse ?

“But,..”- I can hear you counter ” Why should we attempt at all to increase the quality of science in public discourse ? ” Well, rather than me answering it directly I’ll just ask you to read the posts which triggered this post. Read what Carl Zimmer and PZ Myers have to say and especially read the comment section at PZ Myer’s Blog .

(Just so that you can follow the discussion over there – Carl Zimmer is the author of many popular science books related to biology and PZ Myers is a Bio-Prof. And presently biologists are fighting against a ridiculous attempt named “Intelligent Design(ID)” in the U.S. to undermine science and the scientific method in general and evolution theory in particular. It is in this context that Zimmers went to a screening of the movie titled “Flock of Dodos” related to this issue and Zimmer’s post is about his opinions on what was portrayed in it. And PZ Myers is commenting on Zimmer’s post. )

If you read them, you would hopefully realise that there is indeed a strong case to be made for scientists to come down from their ivory towers to addres the public. To quote Zimmers

The evening ended with a student in the back making the case that, like it or not, evolutionary biologists do work that has profound implications for people’s lives. “If I have to quote Spiderman,” he said, “it’s a great power you have. And with great power comes responsibility.”

Great responsibility indeed ! It is hightime that this prison-like wall that the science has erected around itself be brought down. I can understand fences for protection, after all I do understand the dangers of PR in science. But, when the caution to “not to play to the gallery” becomes a paranoia against the “masses”, it is time to cry out- “Oh Scientists ! Tear down this wall !”

Update(18th Feb, 2006) : The debate rages on ! Have a look at the continuing debate at Zimmer’s blog and PZ Myer’s reaction. Just read the points raised on comments- you would see some interesting arguments raised on either side. Indeed as one of the commetators at Zimmer’s Blog says

Carl, you should be particularly proud of your blog today. I think it really shows how valuable blogging can be.

So much for Biology ;)

February 14, 2006

Via Pharyngula, we are informed that there exists The Calvin and Hobbes searchable database.