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Back after the weekend

Count Photon is a very witty nick name. I wish I'd thought of that! Either way, back to hearing me instead of my friends. Today just passed by thinking about general relativity, lasers and cython. I finally figured out why my cython code was giving seemingly errenous results, because I had forgotten to implicitly typecast a specific constant that I was in the earlier buggy version, calling directly from the function. Every numeric operation in cython has to be between values that are typecast is something that I learnt out of this so far.

The morning was spent in awe at what was being taught as part of a general relativity and cosmology course that I am taking this semester. By simply varying/extremizing the action of a free particle in space, we arrived at the equations of it's motion. No field, nothing! It was beautiful to see that a function derivative of the metric that describes the space(time) describes the equations of motion. It was also interesting to note that the equations of motion become that for a free particle when we are working in inertial coordinates in flat space time and non-inertial coordinates or curved space time will both have non zero derivatives of the metric tensor, which in itself has dependence on the coordinate system.

Later, it was interesting to understand how the gaussian envelope shape in the spectral domain arises. The gaussian envelope is a sum of individual lorentzian line shapes for the individual modes that a laser can support and the lorentzian shapes themselves are because of inhomogenous emissions from oscillators in the gain medium. It was exciting to see a sound theoretical framework to prove this and to understand the theory behind active and passive mode locking. Marvelous feats of engineering, such solutions are always thought stimulating and great examples of applied science.

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