Two entangled particles are separated to distant detectors, and their measurement outcomes are found to violate the Bell inequality. The 'matched gloves' explanation — particles carry pre-set correlated values from preparation — predicts:
ACorrelations that exactly match quantum mechanics, since pre-set values correctly describe quantum entanglement
BCorrelations that satisfy the Bell inequality, which quantum mechanics exceeds
CStronger correlations than quantum mechanics, since pre-set values would determine outcomes with certainty
DNo correlations at all, since the particles are no longer in contact at the time of measurement
Any local hidden variable theory — including the pre-set gloves model — must produce correlations satisfying the Bell inequalities. Quantum mechanics violates these bounds for certain measurement angle combinations. The gloves model handles the aligned-detector case correctly (100% correlation) but fails at intermediate angles, where quantum correlations are roughly 40% stronger than any local pre-shared information can produce.
Question 2 Multiple Choice
Bell's theorem establishes that quantum mechanics cannot be explained by any theory that assumes both:
ASuperposition and unitarity
BDeterminism and time-reversal symmetry
CLocality and realism (particles have definite properties prior to and independent of measurement)
DCompleteness and consistency of the wave function
Bell's argument requires exactly two assumptions: (1) locality — the measurement choice at one detector cannot influence the outcome at the other; (2) realism — particles have definite values for observable properties before measurement. Together these imply the Bell inequalities. QM violates them. So at least one assumption must fail — no theory can be simultaneously local and realistic while reproducing quantum predictions.
Question 3 True / False
Experiments that confirm violations of Bell inequalities prove that no local hidden variable theory can explain the observed quantum correlations.
TTrue
FFalse
Answer: True
This is the empirical upshot of Bell's theorem. Bell showed that local hidden variable theories are constrained by his inequalities. Experiments from Clauser and Freedman (1972) through loophole-free tests in 2015 confirm correlations that violate Bell inequalities and match quantum predictions. The violations are not subtle. Local hidden variable theories are empirically ruled out — the strangeness of quantum entanglement is a feature of the world, not a failure of imagination.
Question 4 True / False
Bell's theorem proves that quantum mechanics is non-local — measurements on entangled particles involve faster-than-light causal influences between the detectors.
TTrue
FFalse
Answer: False
Bell's theorem proves that at least one of {locality, realism} must fail — it does not specify which. Many physicists respond by abandoning realism (particles lack definite values before measurement) while maintaining a form of locality. Even in explicitly non-local interpretations like Bohmian mechanics, the non-local influences cannot be used to transmit information faster than light — the no-signaling theorem holds in all empirically adequate interpretations. Bell's theorem rules out LOCAL REALISM, not locality alone.
Question 5 Short Answer
What are the two assumptions Bell's argument makes, and what follows if experiments confirm that Bell inequalities are violated?
Think about your answer, then reveal below.
Model answer: Bell's argument assumes (1) locality: the measurement setting at one detector cannot causally influence the outcome at the other; (2) realism: each particle possesses definite values for the measured observable prior to and independent of measurement. Together these constrain the correlations any such theory can produce — the Bell inequalities. Quantum mechanics predicts correlations that violate these bounds for certain angle combinations. Loophole-free experiments confirm the violations. The logical consequence: at least one assumption must be false. Either nature is non-local (measurement choices or outcomes at one detector affect the other in some sense) or realism fails (particles do not have pre-existing definite values). Bell's theorem does not determine which must be abandoned — that requires additional interpretational choices — but it proves no theory maintaining both can match the data.
The philosophical depth of this result cannot be overstated: the pre-quantum intuition that correlations must arise from either direct causation or common causes (local hidden variables) is empirically refuted. The correlations between entangled particles are irreducibly non-classical.