On the Einstein-Podolsky-Rosen paradox.¶
Bell, J. S. (1964). On the Einstein-Podolsky-Rosen paradox. Physics Physique Fizika, 1(3), 195-200.
Cited by¶
5 citations across 5 artifacts.
Each citation links to the sentence it supports in the citing article.
Primes¶
- Correlation
- Physics: Quantum correlations between entangled particles whose measurement outcomes co-vary more tightly than any classical (local hidden-variable) model permits, as quantified by violations of Bell's (1964) inequality — a case where the correlation is real and exact yet carries no transmissible signal or local cause between the sites.
This sourceDerives the inequalities any local hidden-variable theory must satisfy; quantum correlations between entangled particles violate them, so the correlation cannot be reduced to a local common cause — yet carries no transmissible signal.
- Physics: Quantum correlations between entangled particles whose measurement outcomes co-vary more tightly than any classical (local hidden-variable) model permits, as quantified by violations of Bell's (1964) inequality — a case where the correlation is real and exact yet carries no transmissible signal or local cause between the sites.
- Entanglement
- Classical local-realistic theories bound |S| ≤ 2 (CHSH bound); quantum mechanics permits |S| ≤ 2√2 (Tsirelson bound).
This sourceProves that no local hidden-variable theory can reproduce all quantum predictions, introducing the first Bell inequality that quantifies entangled correlations (the CHSH/Tsirelson-bound framing follows from this).
- Classical local-realistic theories bound |S| ≤ 2 (CHSH bound); quantum mechanics permits |S| ≤ 2√2 (Tsirelson bound).
- Non-Locality
- In physics it is foundational: Newtonian gravity was an explicit action at a distance, field theory replaced the bare jump with a mediating field but quantum entanglement reinstated genuine non-locality — measurement outcomes on separated particles are correlated in ways no local hidden-variable account can reproduce, the content of Bell's theorem.
This sourceProves that no local hidden-variable theory can reproduce all quantum-mechanical predictions; measurement correlations on entangled particles violate an inequality any locally-mediated account must satisfy.
- In physics it is foundational: Newtonian gravity was an explicit action at a distance, field theory replaced the bare jump with a mediating field but quantum entanglement reinstated genuine non-locality — measurement outcomes on separated particles are correlated in ways no local hidden-variable account can reproduce, the content of Bell's theorem.
- Stochasticity vs. Determinism
- No hidden variables (local realism) have survived empirical tests, as Bell (1964) demonstrated by deriving inequalities that any local hidden-variable theory must satisfy.
This sourceDerives the inequalities that any local hidden-variable theory must satisfy: subsequent experimental violations rule out deterministic local-realist completions of quantum mechanics, leaving genuine ontological stochasticity.
- No hidden variables (local realism) have survived empirical tests, as Bell (1964) demonstrated by deriving inequalities that any local hidden-variable theory must satisfy.
- Wave-Particle Duality
- T5 — Operational Definition vs. Ontological Commitment:
This sourceBell's theorem and experimental closure of locality and realism loopholes rule out local hidden-variable theories that would restore classical particle ontology.
- T5 — Operational Definition vs. Ontological Commitment:
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