Uncertainty principle? It's not about quantum.

Very interesting. As a quantum chemist, I never understood how this Fourier intuition ties with the general stament of the uncertainty principle, which holds for any two operators that do not commute with each other. I mean, when you look at the proof as presented in many QM textbooks, it basically involves some algebraic manipulation and some tricks, but I guess I am missing the big picture.

Keep it up! 🖒🏽👏🏽🌐

Genese Harris

Awesome!

3blue1brown

I reconstructed some FFT graphs using python and matplotlib. <a href="https://www.instagram.com/p/Bf7ynrenrc6/?taken-by=khmccurdy" rel="nofollow noopener" target="_blank">https://www.instagram.com/p/Bf7ynrenrc6/?taken-by=khmccurdy</a>

Kevin McCurdy

Can you help explain this article? How much does this contribute if at all to holographic or simulated reality? <a href="https://www.google.com/amp/s/aeon.co/amp/ideas/you-thought-quantum-mechanics-was-weird-check-out-entangled-time" rel="nofollow noopener" target="_blank">https://www.google.com/amp/s/aeon.co/amp/ideas/you-thought-quantum-mechanics-was-weird-check-out-entangled-time</a>

Hi Sohan, thanks for the detailed writeup. The only way to improve is with well thought-out and well intentioned criticism like this, so I really do appreciate it. I can see what you mean where if someone took the spring analogy too literally, as opposed to just interpreting it as a standing for a generic phenomenon involving cycles over time, it runs the risk of insinuating that the "wave" of a wave function is like that of a rope or water. I certainly agree that the crux of whether or not HUP is intuitive comes down to position and momentum being conjugate, and the analysis with SR is what did it for me. But perhaps it just ended up too rushed and lacking detail in the time I was willing to allot it for this video. Even just a sentence or two about how it's okay if that fact seems counterintuitive may have helped the narrative. Again, thanks for the thoughtful feedback.

3blue1brown

I know this is a few days late, but I just recently got a chance to watch this video and I wanted to add my two cents. Unfortunately, this video was a bit of a letdown for me. I thought that the classical portion was great and super well-motivated, but your claim that the quantum uncertainty principle can be made intuitive strikes me as very misleading. Yes, the Heisenberg uncertainty principle can be viewed as a simple consequence of the fact that position and momentum space are related by a Fourier transform, but I think the premise that position and momentum are conjugate variables is EXTREMELY non-intuitive. It seems to me that the conclusion of your video was a bit too strong. This could cause misconceptions such as the idea that the quantum-mechanical wavefunction is a physical wave in the same way that a sound wave is. My other issue with this video was that the discussion of the mass-spring system didn't actually help me understand de Broglie's original argument. It seemed as though you were recapping de Broglie's thesis for people who had already read it rather than summarizing the argument for an audience who had never seen it before. Making this section of the video stronger may have helped clear up the issues I mentioned earlier (possibly better motivating the relation between position and momentum). Overall, I felt like the presentation of the uncertainty principle itself was solid, but the surrounding discussion of quantum mechanics was muddled and seemed to imply that the subject only appears non-intuitive because people who study it haven't thought hard enough about classical wave phenomena. I hope this criticism is constructive, and I'd be happy to discuss it with you further if any of my points aren't clear (or if you disagree about any of them). I'm a huge fan of your content and I hope to see you discuss more topics outside of pure math in the future!

Sohan

Glad to hear the video hit so many of your interests, thanks!

3blue1brown

Very cool - this is the first new video since I signed up as a sponsor. I've been studying QM on a formal mathematical level for about a year, after years of more popular-level interest, and am fairly new to Fourier transforms and how the uncertainty principle is intrinsic to wave mechanics as opposed to a specific QM concept. This video lays this out very nicely. I'm also a hobbyist musician and music buff, and am well aware of how percussion instruments are considered "indefinite pitch", but had never before thought of drum shots vs. piano tones in terms of the uncertainty principle. This is great!

Yet again this is the best explanation of this topic I have ever seen. Well worth my PatreonBux. For the record, this was previously the one that set the high bar for me: <a href="https://www.youtube.com/watch?v=p7bzE1E5PMY" rel="nofollow noopener" target="_blank">https://www.youtube.com/watch?v=p7bzE1E5PMY</a> And I found that one through viascience and his excellent (though a bit more involved) lectures.

PeetieGonzalez

Hmm, it's essentially the same code as for the blue dot-cloud distribution.

3blue1brown

Thanks!

3blue1brown

Thanks! I had fun putting that together.

3blue1brown

Thanks! For what it's worth, my strategy moving forward is to use Patreon funds to bring on more talented math communicators, allowing for some combination of higher quality and higher quantity on this channel. You will see the first products of this in the upcoming two videos. My hope is that the marginal value of dollars pledges on this page is just as high as it would be for a smaller page.

3blue1brown

Let's hope you're right! This is the thought that inspires me the most.

3blue1brown

I wasn’t supporting you on Patreon, you already have lots of patrons and I prefer to focus on people with fewer ones. But after this video it was impossible not to become a patron. What an amazing video, really! Congrats and thank you for that!

Fabio Bobrow

You can delve so much deeper into this topic. If you look into gamma spectroscopy, you get peaks where isotopes release gammas. The accuracy (called resolution) of these peaks increases as the efficiency decreases. This means it takes a lot more time and many more measurements to get a very accurate picture of the spectrum. You can also observe the Phenomenon in information theory. Really, what you are doing when you are detecting quantum particles is you are transferring information from the particle itself. The Fourier Transform is really showing us the two types of information we can detect from a particle. Chebyshev is actually the one who gave us the exact formula of the maximum and minimum amount of "certainty" you can have when looking at frequency space and time space. Just as an aside, you mentioned that photons change in time, but actually the definition of a photon is that all of its information is in the space domain. Electron information, for example is present in both space and time (positive time), whereas positron information is present in space and negative time.

Benjamin BairMoshe

Your little graphic with the turqoise position cloud varying in diameter, and the origin for zillions of momentum vectors varying in direction, is just a superb depiction of ... Unsharferelation! (my new favourite word)

Chris Jennings

It was just fantastic!

I liked very much specially in the end of the video when you described locality and velocity using a red arrow and a blue sphere. It was great! Very good, Grant!

This is brilliant, thanks for your great work!!!

Jonathan Fuzaro Alencar

Wow, that turned out even better than I could have imagined. Well done! Also, I might be just seeing it wrong, but I think you might not have done \pm 2\sigma on the momentum bracket size

Evan Miyazono

How do non-commutative variables come into play?