Thursday, January 31, 2013

Ultimate and conventional Truth- Lagrangian, Noether's Theorem

Today in my Advanced Dynamics class, in the process of showing Noether's Theorem, I found an interesting connection with Buddhism and the play of different generalized coordinates that you can put in the Lagrangian.

The power of the Lagrangian way of doing Classical Mechanics is that one can choose any generalized coordinates to solve the same problem, so some coordinates maybe more suitable to the problem than others. Also if the Lagrangian does not have explicit dependence on one particular coordinate (called cyclic coordinate) in the chosen generalized coordinates, then there will be something that is conserved. Specifically, it's the conjugate momentum of the Lagrangian with respect to the cyclic coordinate. If the generalized coordinate is chosen badly, then one might not see this symmetry and the conserved quantity may not be so obvious.

Let's call the generalized coordinate that we can see the symmetry directly as Q, and the one that we cannot, let's call it q. It might be for example that although q does not reveal the symmetry directly, but the equation of motion that it generates from the Lagrangian might be simple and usable in our everyday life. And the Q form of the Lagrangian might be more troublesome to interpret in its equation of motion form, so a transformation to the q view would make the equation easier to work with.

This is what I see as the duality between conventional truths and ultimate truths as well. (Do note that there is a range of q and Qs, but there is only one ultimate truth, and the conventional truth maybe many, but should not be too complicated either.)

So in the conventional truths, (coordinate q), there exist you, me, I, the car, etc... which makes everyday living and talking (equations of motion) smooth and easy. Yet in this view, we cannot see the conserved quantities of everything. That's where the ultimate truth comes in (coordinate Q) wherein the true nature of the situation is revealed and we see impermanence, non-self and subject to suffering in all things (timelessly-corresponding to the conserved quantities) and yet it is not convenient to operate in purely ultimate truth view. One would have to say: "this 5 aggregates has arisen the wish to go to abandon some water at the particular location wherein the electromagnetic waves are shielded from the light receptors of other 5 aggregates." which in conventional terms is: "I would like to go to the toilet."

No comments:

Post a Comment