Back to School

Attending the 4th AKR School on General Relativity  at SINP was a pretty interesting, if exhausting experience. We learned a real lot about GR and Cosmology in the past two weeks, stuff that I'm still trying to digest. 

 The daily schedule was  like this : from 10:15 to 1:30, lectures. Then Lunch. Again from 2:30 to 5:45 tutorials where we worked out problems based on what we learned. It was pretty cool. But it was also pretty tiring, given that SINP is about one and a half hours from me home.

It was also interesting to meet new people. I made some new friends : Irshad from Delhi U, Himadri from Baroda U, Soumi from Brabourne, Dibakar da and Sumit from NBU, Deeptimoy da from TIFR and the gang from SXC. Best of luck to all these people! 

I understand that when speaking of such serious matters as GR and Cosmo, one shouldn't digress to topics of food. But being the shameless foodie that I am, I can't help mentioning that the food was excellent. I can rave about the Ilish machh and Pathar mungsho for days. Sadly, Irshad and Himadri found Bengali preparations too sweet and had a tough time, food-wise. It scares me to think what will happen to me when I step out of my little state, into the big bad world of non-Bengali  khana. Aaaaargh!!!

There, there. Have some mishti doi and don't worry about it. 

About Kashmir

Most Indians have this idea that the whole Kashmiri freedom struggle thing had been a Pakistani conspiracy. The naive Kashmiri is fooled by the sly Pakistani agents into rebellion against India. This, however, is not true. There was a genuine rebellion by Kashmiris against India and most people in the valley still want independence.

If anyone is interested about what was the matter and what is the matter, these are some links which I've found informative and worth reading: 

 Kashmir: The Unending War by Pankaj Mishra

 

Kashmir: A View from India by Tavleen Singh

I have no idea how the problem can be solved, but I think that people need to realise that there is a problem and why it is there. 

About Heisenberg's Uncertainty Principle

Most of us have done sums about falling particles and how long it would take them to fall and things like that. Take this problem for example: If a ball falls from the top of a building (on earth) of height 20 metres at 12 o'clock, where is it at 12:02? The noticeable thing about the question is this : we are saying that if you know the position of the ball at some time, and the environment it is in ( is there something pulling or pushing it? in this case it's earth, pulling it through gravity) , you can tell exactly where you'll find it later. There will be a certain position where it will invariably turn up. It won't , for example, say ' no thank you' and go back to the top of the building. Or that's what we thought.



It turns out that we just can't have enough information to tell you exactly where the ball can be. If you do an experiment with a hundred different balls, it turns out that we get different results, even if all the controllable conditions are kept just same. In one experiment you get 1 (say), in the other 2 or something. These differences are usually small, which is why for large objects like a ball we can neglect it. But the smaller our object gets, the more these differences matter.
But are these things totally random? Can we make any predictions at all? Yes, we can. Tell me where it was initially, and what the environment is, and I can tell you is the probability of finding it at different places. There'll even be a probability of it jumping up again ( though I admit none of its actually saying ' no thank you') . Not as good perhaps as telling you exact locations, but that's the best that can be done. And it's not just true of positions, but any physical quantity that's there : momentum, angular momentum etc. The theory which provides the scheme for working out these probabilities is Quantum Mechanics.

Now to uncertainty. Uncertainty is just the standard deviation (or sometimes half the s.d)calculated from these probabilities. Larger the uncertainty, larger is the range of values we are likely to get for whatever it is that we are measuring. Smaller the uncertainty, smaller is this range of likely results. That's why it's called uncertainty, duh!

So what's theHeisenberg's Uncertainty Relation? It is a result in Quantum Mechanics which says that the product of position uncertainty and momentum uncertainty of our object is always greater than a certain number. So if you find (through experiments) that the standard deviation in position values is small for our object, then it always turns out that the standard deviation in momentum values will be large. It is a statistical rule; narrower the probability distribution for position, wider the pd of m, and vice versa.

So this tells us that there must be something funny between position and momentum; by knowing the uncertainty in one, I can say something about the uncertainty in the other. There is something funny between the two, they are 'observables that do not commute with each other'.

How the uncertainty principle follows from this commutation relation, I'll write in another post.