Name: Defining uncertainty
Duration: 11 min
Description: A ten-minute segment of MIT 8.04 (Spring 2016) that defines the Δ precisely: the standard deviation of an observable in a given state, built from expectation values. It is this section's ensemble definition on the blackboard, a property of the state rather than of any one blurry measurement.

In the course

Supports Chapter 8

08Unit 2 · Wave–Particle DualityHeisenberg's Uncertainty Principle

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10 videos · 5 h 5 min

Lecture · MIT
11. Uncertainty Principle and Compatible Observables (continued)
MIT OpenCourseWare · Barton Zwiebach
MIT 8.05, the lecture after the one in the Lecture Hall. It opens on the energy-time relation, read as this section reads it: Δt is how fast a state can change, not a spread of clock readings. Zwiebach then uses the uncertainty principle to put a floor under a ground-state energy, section 6's argument made rigorous. The second half, on diagonalizing operators, is chapter 14 material.
- Ch 08
Lecture · MIT
Lecture 4: Expectations, Momentum, and Uncertainty
MIT OpenCourseWare · Allan Adams · 2013
The lecture from MIT 8.04 Quantum Physics I (Allan Adams, 2013) that goes with Chapter 8. The whole course is in the Lecture Hall.
- Ch 08
Lecture · MIT
10. Uncertainty Principle and Compatible Observables
MIT OpenCourseWare · Barton Zwiebach · 2013
The lecture from MIT 8.05 Quantum Physics II (Barton Zwiebach, 2013) that goes with Chapter 8. The whole course is in the Lecture Hall.
- Ch 08
Course · MIT
Quantum Physics I
MIT OpenCourseWare · Allan Adams · 2013
Allan Adams' celebrated course starts from superposition and the experimental facts, builds the wavefunction, operators and the Schrödinger equation, then tours scattering, hydrogen, identical particles and band structure before closing on entanglement and Bell's theorem. Calculus and a little linear algebra are enough to keep up.
- Ch 01
- Ch 04
- and 14 more chapters
Course · MIT
Quantum Physics I
MIT OpenCourseWare · Barton Zwiebach · 2016
The same course rebuilt as 115 short segments of roughly ten to twenty minutes, each devoted to one idea, so you can watch exactly the concept a chapter needs. Barton Zwiebach is meticulous: every step on the board is justified.
- Ch 04
- Ch 06
- and 8 more chapters
Explainer · YouTube
What is the Heisenberg Uncertainty Principle? - Chad Orzel
TED-Ed
Chad Orzel's animated TED-Ed lesson sets up the whole session in under five minutes: you can never pin down an object's exact position and exact speed together, because everything behaves as both a particle and a wave. Watch for the wave argument at its heart, which Parts 2 and 3 turn into precise mathematics.
- Ch 08
Explainer · YouTube
The more general uncertainty principle, regarding Fourier transforms
3Blue1Brown
Grant Sanderson shows that the uncertainty principle is a general fact about Fourier transforms long before it is a fact about particles: a brief sound has no crisp pitch, and Doppler radar must trade sharp range against sharp speed. The quantum chapter starts at about 10:24. Watch it beside Part 3 and the lab's wave builder.
- Ch 08
Explainer · Fermilab
Demystifying the Heisenberg Uncertainty Principle
Fermilab
Fermilab's Don Lincoln traces the principle to the wave nature of matter and the link between wavelength and momentum, with Fourier pictures of square and bell-shaped pulses. A good second pass on Parts 2 and 3, and on this chapter's central claim that the limit lives in the wave, not in the instruments.
- Ch 08
Demo · YouTube
Heisenberg's Uncertainty Principle Explained
Veritasium
Section 1's single slit in four minutes: a laser shone through a slit that is made narrower and narrower. Watch what the spot on the screen does as the slit closes, and connect it to slit width times sideways momentum spread ≈ h. The description calls the principle a limit on measuring; section 2 sharpens that into a property of the state.
- Ch 08
Explainer · YouTube
The Uncertainty Principle: What Does It Mean, How Does It Work?
Sabine Hossenfelder
The jump lands on her chapter 'Is Uncertainty All About Waves?', the question this section answers with Fourier's bargain; 'What's Quantum About It?' (9:02) then asks what quantum mechanics adds. Compare her answer with the lesson's: p = ħk turns a fact about every wave into a fact about momentum. Rewind to 2:00 for what quantum uncertainty means.
- Ch 08