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Problem: Superposition and entanglement are coherent effects, which can be quantified by quantum mechanics (QM), but lack descriptive explanations. They are typically analysed with inequality methods, and the results favour QM and reject physical realism and hidden-variable solutions. In particular, Colbeck & Renner (2011) showed that no extension of quantum theory can exist with better predictive power than quantum mechanics itself. Purpose: The purpose here is to critically evaluate from a conceptual and philosophical perspective the ontological underpinnings of the inequality approach. The current work is speculative in nature as it is based on a conjectured non-local hidden-variable (NLHV) design for particles, and does not yet have a mathematical formalism. Nonetheless this is worth attempting for the philosophical questions it poses about the nature of reality, and the pointers it gives to possible future directions in fundamental physics. Findings: The premises of the C & R proof (that particles are points, that locality exists, that quantum theory is correct) are inconsistent, hence invalidate its conclusion. We also show that superposition and entanglement may be qualitatively explained if particles were to have the internal structure proposed by the Cordus NLHV theory. Originality: The ability to explain superposition and entanglement conceptually in terms of physical realism is relevant because it rebuts the claim that it is impossible that such a hidden-variable theory could exist. This is significant because previously it has been believed that these phenomena are explainable by QM only.

A Physical Basis for Entanglement in a Non-Local Hidden Variable Theory