As you know (if you read my posts), I am doing a Summer Research Fellowship at IIT Madras. As a part of the same I have to work on a problem, something I don’t know much about but is interesting and difficult enough for it to take me two months to get acquainted with. Now that I am almost a month into my fellowship I guess it is time I should tell you about this problem.
What I am working on, officially, is: Quantum to classical transition. What do I mean by that? In brief, we know that quantum particles, which can be understood as particles too small to behave in a manner intuitive to us, for eg. an electron, obey the Schrodinger’s equation, which tells us how the state (wavefunction) of the particle evolves given a Hamiltonian (read: a function describing the energy associated with the system comprising of everything that affects the system). Okay, what I just described is something you might not know if you haven’t taken up quantum mechanics in a somewhat formal way. Anyways, what you do (or should?) know is that particles which are not so small, i.e. macroscopic particles; for eg. you, your house, a ball etc. are governed by Newton’s laws of motion. One might wonder: if every macroscopic thing is made up of a collection of microscopic particles itself, then why do we need two different laws for them? Can’t an averaged out Schrodinger’s equation do the trick, why are Newton’s laws required at all? And for once, let us accept that we do need two laws for some reason, we still fail to understand that why are the two regimes, the quantum and the classical are so different? Understanding the latter might give us some clue about needing two different laws. I won’t go into much detail on this as I plan to write another post discussing the physics behind all that I am working on, starting from the basic difference between the classical and the quantum world and ending with the insights I gained during my fellowship, which ends on July 15.
Having said all that, what am I actually doing currently? Well, my supervisor is kind enough to have given me the freedom to approach this problem in the way I want to. So, instead of working on the problem to the dot, I am looking at the measurement problem in quantum mechanics as a whole (to read more about the measurement problem refer to the Wikipedia article or wait for my future post on the topic, as mentioned earlier), which is a more general form of the quantum to classical transition problem. In doing so, I am studying about the theory of decoherence, which to give you a teaser is elegant to say the least, and the theory of weak continuous measurements. I aim to understand the two in a profound manner as I feel that only then will I be capable of doing something worthwhile using the two.
Given that I have only done a first course in quantum mechanics, working directly on decoherence sure feels like a big leap. But then, the more difficult the task the more I have to gain. So, onwards and upwards !