Small Probability Space Formulation of Bell’s Theorem

Gordon Watson

John F. Clauser

Henry Krips

John F. Clauser

Lopez, C.

The standard formulation of Quantum Mechanics violates locality of interactions and the action reaction principle. An alternative formulation in an extended phase space could preserve both principles, but Bell's theorems show that a distribution of probability in a space of local variables can not reproduce the quantum correlations. An extended phase space is defined in an alternative formulation of Quantum Mechanics. Quantum states are represented by a complex va\-lued distribution of amplitude, so that Bell's theorems do not apply.

Marek Czachor

Bell's theorem is a conflict of mathematical predictions formulated within an infinite hierarchy of mathematical models. Inequalities formulated at level k ∈ Z are violated by probabilities at level k+1. We are inclined to think that k=0 corresponds to the classical world, while k=1 — to the quantum one. However, as the k=0 inequalities are violated by k=1 probabilities, the same relation holds between k=1 inequalities violated by k=2 probabilities, k=-1 inequalities violated by k=0 probabilities, and so forth. By accepting the logic of the Bell theorem, can we prove by induction that nothing exists?