The Double-Slit Experiment
Fire particles — photons, electrons, even large molecules — at a barrier with two narrow slits, and let them land on a screen behind it. If particles behaved classically, you'd see two bright bands, one behind each slit. Instead, you get an interference pattern: alternating bright and dark stripes, the signature of a wave passing through both slits at once and interfering with itself.
The strange part isn't the pattern — it's what happens when you send particles through one at a time. Individually, each particle lands at a single point, like a particle should. But over thousands of individual, isolated arrivals, the interference pattern builds up anyway. Whatever each particle is doing, it isn't simply "going through one slit or the other."
Add a detector that determines which slit each particle actually went through, and the interference pattern disappears — you get the two classical bands back. Gaining which-path information destroys the wave behavior. This single result carries most of the weight behind superposition and wave–particle duality.