Math Playground
Physics

Heisenberg uncertainty

Position and momentum — you can't pin both down at the same time.

You cannot simultaneously know a particle's position and momentum to arbitrary precision.

Try this
1
Δx · Δp ≥ ℏ/2 — pin down position and momentum gets fuzzier = minimum Δp ≈ 5.27e-26 kg·m/s
Heisenberg's uncertainty principle

ℏ ≈ 1.055 × 10⁻³⁴ J·s. Squeeze Δx towards zero and Δp must blow up to keep the product above ℏ/2.

This isn't about clumsy instruments. A particle simply doesn't *have* a perfectly sharp position and momentum at the same time — the limit is built into the quantum description of nature.

Watch out

It's not 'measuring one disturbs the other' in a billiard-ball sense. Even an unmeasured particle has linked spreads in position and momentum; observing just forces the trade-off into the open.

Uncertainty principle

It's not a measurement limitation — it's a property of the universe.