Bell's Theorem: A Fundamental Principle Unifying Quantum Mechanics and the Uncertainty Principle

Thomas A. Brody

Jacques Poitevineau, Yves‐Henri Sanejouand

We show that the proofs of Bell’s theorem regarding the Einstein, Podolsky, Rosen paradox about incompleteness of Quantum Mechanics implicitly use a negation of Heisenberg’s uncertainty principle, for particles taken separately. Moreover, we show that the entanglement of the pair of particules, hidden variables and locality property are not necessary to establish the theorem. In other words, the theorem only speaks about Heisenberg’s principle and its experimental violation is simply another demonstration of the fundamental character of this principle. Therefore, the paradox is still alive and abandoning the locality property, as often advocated, is premature.

Eric G. Cavalcanti

In the early stages of the famous debates between Einstein and Bohr on the foundations of quantum mechanics, Einstein attempted to devise thought experiments aiming at showing that arbitrarily accurate predictions of incompatible physical quantities was possible, in violation of Heisenberg's uncertainty principle. Bohr was able to defend quantum mechanics from those attacks by showing that a careful application of the uncertainty principle to the experimental apparata as well as the measured system lead to consistent results. Could Bohr have given an independent argument for the irreducible unpredictability implied by the uncertainty principle? The celebrated 1964 theorem of John Bell shows that no model that reproduces the predictions of quantum mechanics can simultaneously satisfy the ontological concepts of locality and determinism. However, nothing can be concluded from Bell's theorem alone about locality by itself or determinism by itself--it is possible to reproduce quantum-mechanical predictions with deterministic models which violate locality as well as indeterministic models which satisfy locality. On the other hand, there's almost universal agreement that the epistemic form of locality--signal locality, or the impossibility of faster-than-light communication--must hold in a relativistic universe. By making a similar distinction between determinism and the epistemic concept of predictability, I show that signal locality plus the bare observed phenomena of Bell inequality violations lead to the remarkable conclusion that Nature is fundamentally unpredictable. This result grounds the quantum-mechanical prohibition of arbitrarily accurate predictions on the principle of relativity, regardless of any postulates of quantum mechanics.

Gordon Watson

Wen-Xiang Chen

We introduce an innovative approach to the generalized Bell's theorem by employing complex analysis tools, specifically Laurent series residues and winding numbers. This method extends beyond traditional two-measurement settings, demonstrating that the uncertainty principle's threshold can be reduced below 1/2 in scenarios with more than two measurement settings. By constructing a complex function that encapsulates measurement correlations and analyzing its singularities and topological properties, we establish a novel connection between quantum non-locality and quantum uncertainty. This framework not only provides deeper insights into the foundational aspects of quantum mechanics but also opens new avenues for exploring quantum correlations using advanced mathematical techniques.

Pavel Vyacheslavovich Kurakin, Георгий Геннадьевич Малинецкий