Quantum entanglement
When several particles share a state that cannot be described separately — the resource that makes quantum computers more powerful than classical ones.
Einstein, Podolsky and Rosen raised the phenomenon in 1935 as an argument that quantum mechanics must be incomplete; Einstein called it spooky action at a distance. John Bell showed in 1964 that the question could be settled experimentally, and the experiments have consistently favoured quantum mechanics.
No information travels faster than light — the measurement outcomes are random individually, and the correlation only appears once they are compared over an ordinary channel. Computationally, however, entanglement is decisive: without it quantum algorithms can be simulated efficiently classically, and the entire advantage disappears.