How the Quantum Sorites Phenomenon Strengthens the Bell Argument and How a Random-Matrix Collapse Dynamics Answers It

Abstract

Bell proved that no theory of pre-existing local values can reproduce the predictions of quantum mechanics, but his proof leaves the culprit ambiguous: one may reject either of two independence conditions, Outcome Independence or Parameter Independence, and most commentators have found Outcome Independence the safer sacrifice. The first part of this paper presents, in a form adapted to spin-1/2 particles in the singlet state, an argument (Forster 2014) that removes the ambiguity: using a chained family of experiments in which quantum mechanics predicts an extreme pattern of correlations -- the quantum Sorites phenomenon -- a contradiction is derived without ever assuming Outcome Independence. Under the resulting theorem, anyone who holds that hidden variables could improve on the quantum probabilities must give up Parameter Independence itself. That looks like a heavy price, because Parameter Independence appears to be protected twice over: rejecting it seems to put superluminal influences into spacetime, and its statistical shadow -- the No-Signaling condition -- is experimentally beyond reproach The second part of the paper shows that the price is payable. In the random-matrix collapse dynamics proposed by Kryukov, measurement is a random walk of the quantum state, and the hidden variable is not a stock of values fixed at the source but the random stream that drives the walk -- like the stored random numbers of a computer simulation, with the measurement settings playing the role of seeds. In that framework Parameter Independence is false while Outcome Independence and No-Signaling are both true, and one can say exactly how the Sorites argument is blocked, why the violation involves no process propagating in spacetime, and why the influence of one wing's setting on the other wing's outcome -- demonstrated here in a simulation -- can never be used to send a message.