News for hackers. Stuff that matters.

A comment on Schrödinger equation emerges mathematically from classical mechanics (2012). Parent comment

Re:Schrödinger equation emerges mathematically from classica... by EvgeniyZh on Saturday December 23, 2023 @02:31AM (#38742366)
> then you kind of already accept that (ordinary, classical) light somehow knows the time it takes to go along all possible paths, then chooses the minimum

But it doesn't, minimum (or more precisely extremum) is a local quality. Basically light goes by the path with zero derivative because otherwise neighboring pathes interfere. Feynman lectures touch on it relatively early [1] which I think is nice

[1] https://www.feynmanlectures.caltech.edu/I_26.html#Ch26-S5

[ Parent | on HN ]
Re:Schrödinger equation emerges mathematically from classica... by alecst on Saturday December 23, 2023 @04:49AM (#38742962)
It is not local. That’s what’s wild about it. It’s a minimum over all paths. Re-read that section you posted.
[ Parent | on HN ]
Re:Schrödinger equation emerges mathematically from classica... by EvgeniyZh on Saturday December 23, 2023 @07:37AM (#38743801)
> In other words, the principle is that light takes a path such that there are many other paths nearby which take almost exactly the same time.

> the wavelength tells us approximately how far away the light must “smell” the path in order to check it.

For the same reason, it doesn't even have to minimum at all, it should be extremum.

[ Parent | on HN ]