Cadwhiskeron Hacker News • Recommends
On “The Fourier Uncertainty Principles [pdf] (2021)”
The clearest, most intuitive explanation of the Fourier Uncertainty Principle that I have come across is by Grant Sanderson of 3Blue1Brown. link to this video
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#fouriertransform#uncertaintyprinciple#quantummechanics
The more general uncertainty principle, regarding Fourier transforms
3Blue1Brown
8.7M subscribers • 42 videos on Hallway
- Recommended by 7 people: 7 on Hacker News.
- A classic. People kept recommending it from 2019 to 2025.
- Presented by Grant Sanderson, creator of 3Blue1Brown
Intermediate. Assumes working knowledge.
2.3M views8 years ago7 recommendations
Computer scienceGraphics and audioMath for programmersComputation and complexity
Grant Sanderson explains how the Heisenberg uncertainty principle arises naturally from the mathematics of Fourier transforms and wave packets.
The meaning of the uncertainty principle in the context of Fourier transforms Help fund future projects: patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: 3b1b.co/uncertainty-thanks For more on quantum mechanical wave functions, I highly recommend this video by udiprod: youtu.be/p7bzE1E5PMY Minute physics on special relativity: youtu.be/1rLWVZVWfdY Main video on the Fourier transform youtu.be/spUNpyF58BY Louis de Broglie thesis: aflb.ensmp.fr/LDB-oeuvres/De_Broglie_Kracklauer.pdf More on Doppler radar: Radar basics: 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: 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: 3b1b.co/recommended Various social media stuffs: Website: 3blue1brown.com Twitter: twitter.com/3Blue1Brown Patreon: patreon.com/3blue1brown Facebook: facebook.com/3blue1brown Reddit: reddit.com/r/3Blue1BrownWhy it's here
7 people recommend thisWhat people say. Recommended as the clearest and most intuitive explanation of the Fourier uncertainty principle.
pdkl95on Hacker News • Recommends
On “Why have so many physicists shrugged off the paradoxes of quantum mechanics?”
…. A short wave packet only a few wavelengths long correlates with a narrow (precise) range of positions, but also correlates well with a very wide range of frequencies due. A Heisenberg-like uncertainty exists any time you are working with weave packets with length near the wavelength. 3Blue1Brown gives a very good example using Doppler radar. 1 link to this video 2 link…
chriswarboon Hacker News • Recommends
On “Why have so many physicists shrugged off the paradoxes of quantum mechanics?”
…not, without hitting it with a photon and hence triggering the bomb (50% of the time, at least). - The actual reason, the uncertainty principle ( link ), doesn't require any notion of observation at all, let alone interaction. It's a simple property of waves (the relationship between duration and frequency). 3blue1brown did a nice video on this link to this video…
Kednicmaon Hacker News • Recommends
On “A Physicist Trying to Fix Quantum Mechanics”
In many cases, Wikipedia actually lists the analogy for classical probability theory. For several theorems, the proof for Hilbert spaces can be directly brought to the classical world. The main difference to keep in mind is that we have amplitudes, not probabilities, and they can be negative or complex. We recover typical probability theory by taking norms/squares of amplitudes. The uncertainty principle follows via doing signal analysis on Fourier-transformed wavefunctions. A fun professional treatment from Baez et al. is 0, and 3blue1brown has an excellent two-video visual explanation 12. The uncertainty principle turns out to be a special case of the sampling theorem (yes, that one!…
uoaeion Hacker News • Recommends
On “Is the Schrödinger Equation True?”
This may help answer some of your question, though I recognize it does not address it directly: link to this video (3b1b on the Heisenberg uncertainty principle and how it arises) Think of a free neutron as the wave envelope, rather than any of the bumps in the wave.
nextaccounticon Hacker News • Recommends
On “An Interactive Guide to the Fourier Transform”
Yes, but that's because the momentum is the fourier transform of the position and vice versa So there's an uncertainty principle for signal processing, entirely because of the fourier transform and not because of quantum mechanics See this video link to this video
ben_won Hacker News • Recommends
On “Project Hyperion: Interstellar ship design competition”
The reason Trek has it is likely a common misunderstanding of QM: it's not only that we cannot record both position and momentum, the information does not exist in the first place . It's easier to see why if you think about Fourier transforms: link to this video TLDW: an infinitely long wave does not (cannot) have any definite location, but it does have a definite periodic wavelength; conversely, a single impulse noise (a shockwave from e.g. a bullet or an explosion) has a definite location (in the direction of motion and at any given point in time) but no meaningful wavelength. The more you constrain the possibility space of one, the looser the other becomes in a physical sense, not just the informati…
jerfon Hacker News • Mentions
On “Superdeterminism may help us overcome the current crisis in physics”
The limitations of the Fourier transform are intimately tied to the uncertainty principle: link to this video Reality does appear to be limited by the limitations of the Fourier transform.
krastanovon Hacker News • Mentions
On “What is a photon? (2017)”
It is a neat trick actually. If you superimpose a few of these waves with frequencies that are fairly close, then you will see how they cancel out in the distance, while they reinforce each other in the center. This is called a "wave packet". 3blue1brown was somewhat useful, somewhat tangential video on the topic link to this video The more rigorous way to say "superimpose a few of these waves", is to say that there is some uncertainty in the frequency. This uncertainty in the frequency lets you have more certainty about the position (the wave packet is centered somewhere, instead of being completely distributed the way an infinite plane wave is)
wruzaon Hacker News • Mentions
On “Physics Without Probability (2015) [video]”
The uncertainty is not exclusive to QM and is a property of any ‘wavy’ system, it seems. It is inherent. Here is the example: link to this video — if you want to defeat QM, attack its wave-part. It would be nice to have much better (deterministic, measurable) physics, but some properties just emerge from a fundamental level and you can’t do much about it (monster group etc). Nature and maths don’t care about our confusion and convenience. >should have refuted it and looked for something better instead Afaik, the time when theories were driven by ideas is over. Today it’s petabytes of data that you can’t really argue with over a mailbox, only discuss. (I’m just a layman physicist with deep interest, but…
westurneron Hacker News • Mentions
On “An animated introduction to Fourier series”
"The more general uncertainty principle, regarding Fourier transforms" by 3blue1brown link to this video From link : > Convolution is in fact multiplication in Fourier space (this is the convolution theorem 1) which says that Fourier transforms convert convolutions to products. 1. link : >> In mathematics, the convolution theorem states that under suitable conditions the Fourier transform of a convolution of two functions (or signals) is the pointwise product of their Fourier transforms. More generally, convolution in one domain (e.g., time domain) equals point-wise multiplication in the other domain (e.g., frequency domain). Other versions of the convolution theorem are applicable to various Fou…
u/currentscurrentsin r/compsci • Mentions
On “My theory on why magic does not 'work on computers'”
It is the latter, sorry.
The uncertainty principle actually applies to any kind of wave, quantum or not. It's a limitation of how accurately
waves can be measured rather than a magical property of quantum objects. Check out this 3blue1brown video for more information.