Bell nonlocality, signal locality and unpredictability (or What Bohr could have told Einstein at Solvay had he known about Bell experiments)

Abstract

The 1964 theorem of John Bell shows that no model that reproduces the predictions of quantum mechanics can simultaneously satisfy the assumptions of locality and determinism. On the other hand, the assumptions of \emph{signal locality} plus \emph{predictability} are also sufficient to derive Bell inequalities. This simple theorem, previously noted but published only relatively recently by Masanes, Acin and Gisin, has fundamental implications not entirely appreciated. Firstly, nothing can be concluded about the ontological assumptions of locality or determinism independently of each other -- it is possible to reproduce quantum mechanics with deterministic models that violate locality as well as indeterministic models that satisfy locality. On the other hand, the operational assumption of signal locality is an empirically testable (and well-tested) consequence of relativity. Thus Bell inequality violations imply that we can trust that some events are fundamentally \emph{unpredictable}, even if we cannot trust that they are indeterministic. This result grounds the quantum-mechanical prohibition of arbitrarily accurate predictions on the assumption of no superluminal signalling, regardless of any postulates of quantum mechanics. It also sheds a new light on an early stage of the historical debate between Einstein and Bohr.

Substantially modified version; added HMW as co-author

References in corpus (4)

• Random Numbers Certified by Bell's Theorem
• No Signalling and Quantum Key Distribution
• Contextuality for preparations, transformations, and unsharp measurements
• General properties of Nonsignaling Theories

Cited by in corpus (27)

• The Two Bell's Theorems of John Bell
• No $\psi$-epistemic model can fully explain the indistinguishability of quantum states
• Measurement-device-independent randomness from local entangled states
• Quantum Correlations and Quantum Non-locality: a review and a few new ideas
• Understanding quantum mechanics: a review and synthesis in precise language
• Randomness? What randomness?
• Can observed randomness be certified to be fully intrinsic?
• The wavefunction as a true ensemble
• Quantum discord is Bohr's notion of non-mechanical disturbance introduced in his answer to EPR
• A Toy Model for Local and Deterministic Wave-function Collapse
• Nonlocal quantum information transfer without superluminal signalling and communication
• Self-testing of binary Pauli measurements requiring neither entanglement nor any dimensional restriction
• Single system based generation of certified randomness using Leggett-Garg inequality
• Classical-hidden-variable description for entanglement dynamics of two-qubit pure states
• Extending quantum mechanics entails extending special relativity
• Taxonomy for Physics Beyond Quantum Mechanics
• Bell's Theorem, Accountability and Nonlocality
• Several foundational and information theoretic implications of Bell's theorem
• The operational reality of quantum nonlocality
• Certified Random Number Generation using Quantum Computers
• Epistemic Boundaries and Quantum Uncertainty: What Local Observers Can (Not) Predict
• Role of nonclassical temporal correlation in powering quantum random access codes
• The Hardy's nonlocality argument
• Quantum and Classical Frontiers of Noise
• What does it take to solve the measurement problem?
• Security of Device-independent Quantum Key Distribution under Sequential Attack
• Quantum interpretations, causality and quantum computation