Physics Laws & Theorems
Advanced

Heisenberg Uncertainty Principle

Position and momentum cannot both be known with unlimited precision.

Formula

Δx Δp≥ℏ2\Delta x \, \Delta p \ge \frac{\hbar}{2}

Variables

\Delta xPosition uncertainty
\Delta pMomentum uncertainty
\hbarReduced Planck

Example

Pin down an electron’s position precisely and its momentum becomes hopelessly uncertain.

Did You Know?

You cannot know a particle's exact position and momentum at once — nature has a built-in fuzziness.

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