Posted by Arjendu on January 8, 2008
The term has gotten going, and while there has been nothing major to report, in the spirit of this being a journal, time to record. Everything’s ticking along pretty much as usual, though it’s proved to be a more … um, inertia-filled term to start than usual, for some reason. But, worth remarking:
(1) Quantum mechanics started with a sudden immersion into Hilbert space. A sentence guaranteed to lose all the non-physicists bothering to read this, and some of the physicists as well. Irrespective: I teach quantum from John Townsend’s quantum book, which I have described to colleagues as ‘baby Sakurai’ (where Sakurai is a classic graduate textbook).
It plunges into what’s startling about quantum mechanics immediately with the description of some thought experiments about the spin of atoms, and the response of this spin to magnetic fields. Using this approach, within a single lecture, we had established that it was impossible to describe this spin with the standard or ‘classical’ prescriptions (the way we describe position, speed, etc) and that it was impossible to know the spin in the two different directions simultaneously. Then we set up the mathematical machinery required to start describing everything, and there we were, off on the journey into Hilbert space.
The true structure of Hilbert space is something that’s still being explored in the research world — the ‘explosion’ of research in quantum computing starting in the late ’90s, 70 years after quantum mechanics was discovered/invented shows that we’ve barely begun to figure out the structure of quantum mechanics. My own research is about how Hilbert space turns into real space for sufficiently large or sufficiently warm objects, and why nonlinearity affects this transition, and it is so so wonderfully easy to get lost in there. I do so get a kick out of introducing smart and eager students to this machinery, and the amazing Dirac notation.
(2) I had one of my advisees ask to meet me for lunch. This is an international student who is going through some blues, some of which I can recognize, and some are unique to his life, of course. But here’s this smart, sweet 18-year-old struggling with big issues of identity and of feeling neither at home at Carleton or in his own country, trying to figure out how to reconcile his ‘liberal arts’ choice for major with the notion of being a success, and trying hard in his head to justify the cost — both the true economic cost as well as the emotional ones — of being so far away from family and friends.
And while this is a difficult difficult conversation to have sensibly over lunch in a crowded student eatery, what I want to say to him is what I say to myself all the time: You’ve got to find what makes you happy, hard as that is to do. Because success, money, fame, all that is about happiness. So understand that everything you do is a choice you make about finding your happiness. And you’ve got to understand that decisions about happiness are made in the face of the fact that these are amorphous, morphing, fluid issues, almost guaranteed to later generate a sense of compromise, of loss, of regret. But isn’t it amazing that we belong to a generation, to an economic group that can focus on this issue of happiness, instead merely of survival?
Hah. My student looked puzzled but intrigued to see himself as engaged in an essential struggle, not just a heavy one. And that’s all I had for him at the moment.
(3) And a friend forwarded an obituary for our mutual teacher and hero, Dr. Bhargava.