Quantum Entanglement
Quantum entanglement is the situation in which two or more systems have a joint quantum state that cannot be written as a product of separate states for each part. Neither subsystem then has a state of its own; only the pair does. Measurements on the two parts, however far apart, show correlations that no assignment of independent local properties can reproduce.
The standard account
Schrödinger coined the term Verschränkung in 1935, in response to the Einstein–Podolsky–Rosen paper, and called it "not one but rather the characteristic trait of quantum mechanics". The formal definition is simple: a state of a composite system is entangled if it is not separable — not a product state, and not a statistical mixture of product states.
Three properties are worth stating exactly, because entanglement is routinely described in ways that are stronger than the physics:
- The correlations are not explicable locally. This is the content of Bell's Theorem, and it is established experimentally, most decisively by the loophole-free tests of 2015.
- No information is transmitted. The no-communication theorem is a proved result: the statistics observed at one wing are entirely unaffected by what is done at the other. Entanglement cannot be used to signal, at any speed. Descriptions of entanglement as instantaneous communication are simply wrong, and this wiki should not repeat them.
- It is monogamous. The more strongly two systems are entangled with each other, the less either can be entangled with a third. This is a theorem, and it is why entanglement-based cryptography works.
Entangled photon pairs are routinely produced by spontaneous parametric down-conversion in a nonlinear crystal, entangled ions by shared motional modes, entangled solid-state spins by heralded photon interference. Practical consequences include quantum key distribution — Ekert's 1991 protocol uses Bell violation itself as the security test — quantum teleportation, proposed by Bennett and colleagues in 1993 and first demonstrated in 1997, and the entanglement distribution between ground stations over 1200 km apart achieved by the Micius satellite in 2017. Entanglement degrades rapidly through interaction with an environment; this decoherence is why the effect is hard to maintain and why it is not visible in everyday objects.
What is not settled is what entanglement is. That question is the measurement problem, and it is open. Whether the quantum state is a physical thing or a bookkeeping device, whether measurement outcomes are unique, and whether the correlations reflect a real physical connection or a limit on what can be said, are all matters on which competent physicists disagree — and the disagreement is not currently decidable by experiment.
On this wiki
Entanglement is one of the most-requested topics in this collection and one of the most attacked. The work catalogued here divides roughly into three approaches.
Entanglement as a real connection through a medium. If space contains a physical medium, correlations between distant systems need not be spooky. Duncan W Shaw takes this line explicitly in "Maxwell's Aether: A Solution to Entanglement", and Peter Kohut's "Quantum Entanglement, Its Nature and Manifestations" derives it from his quantum-dipole structure, in which every dipole stands in relation to every other, so that connectedness is built into the geometry rather than added to it. Both belong to the wider Aether programme catalogued here.
Entanglement as a formal or logical artefact. Domina Eberle Spencer's "The Holor Representation of Entanglement" recasts the mathematics in holor form, and "Interpretation of Quantum Mechanics and Entanglement with Multivalued Logic" attacks the problem through non-classical logic rather than through physics.
Entanglement versus relativity. Augusto Garuccio's "Entangled States and the Compatibility Between Quantum Mechanics and Relativity" addresses the real point of friction: the correlations do not permit signalling, so no operational contradiction with relativity arises, yet no Lorentz-invariant account of what happens is available either. That is a genuine open problem and not a manufactured one.
Experimental work. Carroll O Alley and collaborators report down-conversion experiments in "Experiments with Entangled Two-Photon States From Type-H Parametric Down Conversion: Evidence for Wave-Particle Duality". The critical experimental literature — Caroline H Thompson on coincidence counting, Al F Kracklauer on local models — is gathered at Bell's Theorem and EPR Paradox, and the chronological caution stated there applies here too: objections resting on detector inefficiency were answered in 2015.
A note on what a good critique here would have to do. Entanglement is now a working technology, not merely a prediction: entangled states are prepared, distributed, verified and consumed in laboratories every day. Any alternative account offered on this wiki has to reproduce the observed correlations quantitatively — the CHSH value near 2√2, the angle dependence, the monogamy — and not merely offer a picture in which correlation is unmysterious.