In the paper the proof of the non-locality of quantum mechanics, given recently by H. Stapp and D. Bedford, and appealing to the GHZ example, is analyzed. The proof does not contain any explicit assumption of realism, but instead it uses formal methods and techniques of the Lewis calculus of counterfactuals. To ascertain the validity of the proof, a formal semantic model for counterfactuals is constructed. With the help of this model it can be shown that the proof is faulty, because it appeals to the unwarranted principle of Elimination of Eliminated Conditions (EEC). As an additional way of showing unreasonableness of the assumption (EEC), it is argued that yet another alleged and highly controversial proof of non-locality of QM, using the Hardy example, can be made almost trivial with the help of (EEC). Next the question is considered whether the validity of the proof in the GHZ case can be restored by adopting the assumption of partial realism. It is argued that although this assumption makes the crucial step of the original reasoning valid, it nevertheless renders another important transition unjustified, therefore the entire reasoning collapses.
Problem- Many attempts have been made, starting from Quantum mechanics (QM), to prove the non-viability of hidden-variable (HV) solutions, and to justify the unnaturalness of QM explanations over physical realism. In particular, Colbeck & Renner (C&R) (2011) claimed to prove that no extension of quantum theory can exist with better predictive power than quantum mechanics itself. This implies that QM is an ideal theory, and that physical realism should be abandoned. Purpose- This paper critiques this proof. Approach- Logical considerations are used to examine the premises in the proof. Findings- The C&R proof is show to be capable of entirely the opposite interpretation that its authors intended, namely that a new deeper physics may exist based on physical realism, but that it will definitely not be quantum theory or even an extension thereof. Also, the proof is falsified by presenting a viable theory of internal structures (hidden-variable solution) with demonstrably better ontological explanatory power than QM. Implications- QM is interpreted as an approximate stochastic representation of a deeper dynamic behaviour at the finer scale. Originality- This work predicts that physical realism still applies, and that hidden-variable solutions still have vitality as the way forward for fundamental physics.