In 1935 Einstein, Podolsky, and Rosen published a paper meant to demonstrate the incompleteness of quantum mechanics: two particles prepared in a joint state and separated by arbitrary distance would have correlated properties, with a measurement on one instantaneously fixing the other. Einstein called it "spooky action at a distance." The argument went unsettled for thirty years. In 1964 John Bell, a Northern Irish physicist at CERN, derived an inequality that any local realistic theory must satisfy — and quantum mechanics violates it. Experiments by Aspect (1982), Zeilinger (1990s+), and most decisively the loophole-free Delft experiment (2015) have shown that nature violates Bell's inequality. The world is non-locally correlated. Einstein was right that quantum mechanics has the feature he disliked, and wrong that this was a reason to reject it.
Entanglement is a quantum correlation between systems that has no classical counterpart. Two particles are entangled when their joint quantum state cannot be written as a product of individual states — measurements on one are statistically correlated with measurements on the other in a way that depends on the choice of measurement bases. The canonical example is a pair of spin-½ particles in the singlet state |ψ⁻⟩ = (|↑↓⟩ − |↓↑⟩)/√2. Measuring the spin of one along any axis yields a 50/50 outcome; measuring the other along the same axis yields exactly the opposite with probability 1, regardless of distance. Measure along different axes and the probabilities are determined by the angle between them — and they violate the Bell inequalities that any local hidden-variable theory must satisfy. Bell's theorem (1964): no local realistic theory can reproduce all the predictions of quantum mechanics. Loophole-free experiments (Hensen et al., Giustina et al., 2015) closed the locality and detection loopholes simultaneously, providing what is considered definitive refutation of local realism. The 2022 Nobel Prize went to Aspect, Clauser, and Zeilinger. Entanglement does not allow faster-than-light signaling: the random outcome on one side, viewed alone, is just noise; the correlations are revealed only when observers compare notes (which requires light-speed communication). Causality is preserved operationally, but the underlying mechanism is not classically intelligible. Entanglement is generated by interaction and destroyed by decoherence (entanglement with the environment, which traces out unobserved degrees of freedom). Quantum information theory treats entanglement as a resource — quantifiable, transferable, fungible — and uses entanglement entropy as the basic measure.
Quantum cryptography (the BB84 and E91 protocols) exploits entanglement to enable provably secure communication: any eavesdropping disturbs the correlations in detectable ways. Quantum teleportation (Bennett et al., 1993, demonstrated dozens of times since) uses an entangled pair plus classical communication to transmit an arbitrary unknown quantum state. Quantum computing derives much of its power from entanglement: an n-qubit entangled state spans a 2ⁿ-dimensional Hilbert space. Quantum sensing uses entangled probe states (NOON, squeezed) to measure with precision beyond the classical standard quantum limit. Entanglement entropy has become a fundamental probe in condensed-matter physics and quantum gravity (the ER=EPR conjecture identifies entanglement with wormhole geometry). The phenomenon Einstein called spooky is, a century later, the central resource of quantum technology.