The more general uncertainty principle, regarding Fourier transforms

The meaning of the uncertainty principle in the context of Fourier transforms
An equally valuable form of support is to simply share some of the videos.

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

Minute physics on special relativity:

Main video on the Fourier transform

Louis de Broglie thesis:

More on Doppler radar:

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:

Thanks to these viewers for their contributions to translations
Hebrew: Omer Tuchfeld

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Various social media stuffs:

[bluebrown]

Attentive viewers may have noticed that I broke a promise from the last video to talk about Fourier inversion. I still plan for that to come at some point, perhaps in the context of a video on Laplace transforms, or perhaps after it.

[samtukua]

Why is it that when I can't understand something, a YouTuber comes out no less than a month later with a beautiful explanation of it. My FBI guy must really care. I love you man.

[marcni]

Great video as always! As a physicist, I just want to point out something that usually bothers me about some phrasings of the uncertainty principle (which you were careful to also do in the last minutes of the video). When people say "you can't know the position and momentum of a particle", you really need to bring the probabilistic interpretation of quantum mechanics to make sense of that. It certainly does not mean that you can't measure both quantities. If you have a certain localized quantum state (with low position uncertainty) and measure its momentum, you will get a definite result in your detector. It is only when you prepare the same localized state and measure its momentum again that you realize the result is now different than before (and repeating this process many many times you'll conclude indeed that the uncertainty of the momentum is large). This has to do with particles in quantum mechanics not being described by its classical state (which is characterized entirely by its position and momentum) but by its wave function. That popular phrasing of the uncertainty principle in a way extrapolates by saying that the particle "has" a position or momentum a priori, which is a little misleading (or at least debatable in the various interpretations of quantum mechanics).

[ElectronFieldPulse]

I don't know if you ever read the comments, but I just want you to know that you make the world a better place with your videos. You allow people like me to gain knowledge about subjects that I have always been interested in. In a very tangible sense, the world gets better with each video that you make. I want to sincerely thank you for the effort you put into these and help you have given to so many people. Bravo!

[diegopablogordillovaras]

I love these videos. I finally understood the mathematical meaning of the uncertainty principle. And I didn’t comment those other videos, but your Linear Algebra series was excellent. I can’t tell you enough how many times in my life I was multiplying matrices without having any single idea of what it meant. Thank you!!

[jackr]

I have 24 credit hours left to get my Bachelors in Electrical engineering, and I can confidently say that I have never heard these concepts explained so clearly. Your past two 20 minute videos have given me more clarity in my field of study than every professor I have ever had combined. Absolutely incredible. #3Blue1Brown>CollegeEducation

[alexanderf]

I remember when someone first told me that the uncertainty principle was due to certain aspects of a particle being Fourier transforms of each other. Totally changed my understanding of it from "impossible to understand" to "reasonable but unexpected".

[spyguy]

Another one of my favorite explanations of the uncertainty principle is taking a picture of a pool table. With a fast shutter speed, you can tell exactly where all the pool balls are, but you can’t tell how fast they’re going. With a slow shutter speed, you can use the motion blur to determine how fast each pool ball is moving, but it’s much harder to say where each ball exactly is.

[Superphilipp]

You are a shockingly good teacher. I've never seen anything like it.

[frego]

As an engineering student, even the first seconds of the video blew my mind. I got the gist of the idea (even tho I still don't understand it fully), but the connection between the mathematics and these physics phenomena have never been made for me. This video is truly amazing. I would be so happy if all my professors were only half as good as explaining stuff as you. Truly amazing.

[bobtivnan]

Who says the sequel is never as good as the original. Great follow up to the previous video! I think 50 years from today, educators will point back to you and say- this is how we learned to effectively explain complex ideas. You have really set the bar with your style.

[JonathanRichetti]

"A particle momentum is somehow a sheet of music describing how it moves though space." How to do poetry with physics and math. Thanks for the video.

[aj]

Please do more physics oriented videos. I love seeing the mathematical intuition behind it!

[GnuReligion]

My physics instructors have told me that we know that lumps of mass are basically a big standing wave ... this video makes the concept more tangible. My favorite on your channel so far.

[DeFlekkie]

I really believe the world could be in a profoundly more advanced place if we had more teachers like you. (or more people had acces to those limited set of teachers). Think of all the people that could benefit from these learnings and deep understandings.

I studies applied physics in engineering, but your video's on algebra, linear algebra and this on on the *unsharpness* principle really bring my insight in these topics to a whole new level. I feels really wierd to realise how much I did nót grasp things in a fundamental way when I was studying this and at the same time still was able to pass these exams. Makes me wonder how many people finish with a physics degree but do not have the deep insights that you are presenting and teaching in these series of online videos.

Glad to be a patreon supporter btw, the world needs more of you.
Thank you so much.

[shockminerx]

You deserve a lot more subscribers. Your videos explain everything so well and are presented beautifully. I hope more people are interested math/physics from watching your videos!

[jpdoane]

Great video as always. Although a minor correction regarding doppler-range tradeoff for radar: Good range resolution does not require a short-duration pulse, but on a highly localized auto-correlation function, which requires wide bandwidth due to uncertainty principle. Although time duration and bandwidth are inversely related for the wavelet signals you are using, you can use other waveforms that have both long duration (for good doppler resolution) and wide bandwidth (for good range resolution). A typical example would be a repeating set of chirps. But for a given constraint on the waveform’s time-bandwidth product, the range and doppler resolutions are fundamentally limited due to the reasons you described in the video.

[alexsims]

HOW ARE YOU SO GOOD AT EXPLAINING THINGS?!

[joanpascualribes]

The way a relationship is established between the Fourier transform and the essence of our reality is gorgeous. Thank you for sharinng this kind of content. The way it is explained and the animations are just brilliant.

[paradox]

I’ve been searching for an intuitive explanation to why the Heisenberg uncertainty principle works for a long time and this is the most beautiful and logically consistent explanation I’ve ever seen. I’ve never had such a high understanding of the uncertainty principle, you made it as simple as you possibly could but no simpler. I think too many of us just accept the facts of quantum mechanics without diving into why they work and the logic and intuition used to build them, why is the hardest question to answer but when it is it leads to a fundamental understanding that births new creative intuitive theories. Thank you for this video.