What is the uncertainty principle?

Some pairs of questions about a particle can't both have sharp answers at the same time. The famous pair is where the particle is and how it's moving. Make one sharper and the other spreads out.

Werner Heisenberg put the idea into words in 1927. Later that year Earle Kennard proved the exact limit. Take the spread in a particle's position and the spread in its motion, multiply them, and the answer can never fall below a fixed tiny amount set by Planck's constant (chapter 1).

That's the most common myth, and Heisenberg helped start it. His first explanation pictured a microscope whose light knocks the electron as it looks.

But the limit doesn't come from the measuring. It's built into the quantum state itself, before anyone looks. A state with a perfectly sharp position simply has no single speed for any instrument to find.

You've met this already. In chapter 2, a photon polarised at 45° gives a certain answer to the diagonal question but only odds for the vertical one. No careful handling changes that. In 1929 Howard Robertson showed the same rule holds for any pair of questions that clash like this.

Because the limit is tiny. For a grain of sand, or anything else you can see, the blur is far smaller than an atom and nobody could ever detect it. For an electron squeezed inside an atom, it's big enough to shape everything.

• Atoms don't collapse. Squeezing an electron's wave into a smaller space makes its motion more energetic, so there's a lowest rung it can't fall below (page 1b).
• Nothing is perfectly still. Even cooled to absolute zero, an atom held in a trap keeps a minimum jiggle, because a perfectly still atom would need a sharp position and a sharp motion at once.
• You can choose where the blur goes. You can't beat the limit, but you can move the uncertainty from one property into the other. Since 2019 the LIGO detectors have used this trick, called squeezed light, to measure the one property they care about more sharply (page 4b).