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The more general uncertainty principle, regarding Fourier transforms

3Blue1Brown · 2.3M views · 2018-02-25 · 18:07

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Overview

3Blue1Brown shows how the uncertainty principle arises from Fourier transforms. A wave packet cannot be narrow in both position and frequency, so the principle is a property of waves rather than of measurement.

On Hacker News

HN recommends it as the clearest visual explanation that uncertainty is intrinsic to waves, separate from measurement disturbance.

Recommended by 7 HN people across 6 months · HN mentions 2019–2025

Topics

Information theory & signal processingQuantum physicsRecreational & visual math
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fourier transformuncertainty principlewave packetsquantum mechanicssignal processing3blue1brown

What people said

Cadwhisker · 2024-09 · Strong recommendation

The clearest, most intuitive explanation of the Fourier Uncertainty Principle that I have come across is by Grant Sanderson of 3Blue1Brown. [VIDEO]

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ben_w · 2025-08 · Recommendation

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: [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 information you have about it .

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nextaccountic · 2023-12 · Recommendation

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 [VIDEO]

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Sources

Video by 3Blue1Brown, played through YouTube.

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