2018-02-24

[public] 1.40M views, 58.2K likes, 449 dislikes audio only

3Blue1Brown

The meaning of the uncertainty principle in the context of Fourier transforms

Help fund future projects: https://www.patreon.com/3blue1brown

An equally valuable form of support is to simply share some of the videos.

Special thanks to these supporters: http://3b1b.co/uncertainty-thanks

For more on quantum mechanical wave functions, I highly recommend this video by udiprod:

https://youtu.be/p7bzE1E5PMY

Minute physics on special relativity:

/youtube/video/1rLWVZVWfdY

Main video on the Fourier transform

/youtube/video/spUNpyF58BY

Louis de Broglie thesis:

http://aflb.ensmp.fr/LDB-oeuvres/De_Broglie_Kracklauer.pdf

More on Doppler radar:

Radar basics: https://www.eetimes.com/document.asp?doc_id=1278808

There's a key way in which the description I gave of the trade-off in Doppler radar differs from reality. Since the speed of light is so drastically greater than the speed of things being detected, the Fourier representation for pulse echoes of different objects would almost certainly overlap unless it was played for a very long time. In effect, this is what happens, since one does not send out a single pulse, but a whole bunch of evenly spaced pulses as some pulse repetition frequency (or PRF).

This means the Fourier representation of all those pulses together can actually be quite sharp. Assuming a large number of such pulses, it will look like several vertical lines spaced out by the PRF. As long as the pulses are far enough apart that the echoes of multiple objects on the field from different targets don't overlap, it's not a problem for position determinations that the full sequence of pulses occupies such a long duration. However, the trade-off now comes in choosing the right PRF. See the above article for more information.

Music by Vincent Rubinetti:

https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown

Thanks to these viewers for their contributions to translations

Hebrew: Omer Tuchfeld

------------------

3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted on new videos, subscribe, and click the bell to receive notifications (if you're into that).

If you are new to this channel and want to see more, a good place to start is this playlist: http://3b1b.co/recommended

Various social media stuffs:

Website: https://www.3blue1brown.com

Twitter: https://twitter.com/3Blue1Brown

Patreon: https://patreon.com/3blue1brown

Facebook: https://www.facebook.com/3blue1brown

Reddit: https://www.reddit.com/r/3Blue1Brown