Problem
Classical mechanics is deterministic: given the initial condition, the future evolution is known. Quantum mechanics provides probabilities. Is quantum probability of the same nature as a dice roll, or is it something different? Discuss, citing Bell’s inequalities.
Solution
Classical probability (dice). In a dice roll, probability is epistemic: it arises from our ignorance. In principle, knowing exactly the forces, velocities and friction, we could predict the outcome. Probabilities cover hidden but well-defined variables: the die already has a determined outcome that we simply do not know.
Quantum probability. Quantum probability is of a different, fundamental nature. Before measurement, a quantity (for example a photon’s polarisation or a spin) does not possess a predetermined value: it is genuinely undefined. The outcome is not “already written and hidden”, but is generated by the act of measurement (collapse of the wave function).
Bell’s role. One might object: perhaps there still exist hidden variables that make everything predetermined, as with the die. Bell’s inequalities (1964) turn this question into an experiment. Every local hidden-variable theory must respect an inequality between the correlations measured on pairs of particles at different angles. Quantum mechanics instead predicts correlations that violate that inequality.
Experimental verdict. Experiments (Aspect 1982, and the “loophole-free” tests of 2015) show violation of Bell’s inequalities, in agreement with quantum mechanics. Conclusion: quantum randomness is not like that of the die. There are no local hidden variables that predetermine outcomes; indeterminacy is an intrinsic property of nature, not a limit of our knowledge.
Collegamenti
Argomenti: Quantum physics Concetti: Entanglement · Wave-particle duality