Problem: Several measurement effects, including superposition and entanglement, lack descriptive explanations though can be quantified by quantum mechanics (QM). Historical applications of the inequality method appear to favour QM and reject physical realism and hidden-variable (HV) solutions. In particular, Colbeck & Renner showed that no extension of quantum theory can exist with better predictive power than quantum mechanics itself. Purpose: This paper critiques the inequality method and the C&R proof. Approach: Logical considerations are used to examine the premises of the proofs. Findings: The analysis shows the inequalities are based on circular reasoning. They are premised on particles being zero-dimensional points, and then conclude that particles are incapable of having internal structure. The inequalities are falsified by showing that a non-local hidden-variable (NLHV) solution does exist to explain superposition and entanglement, without using quantum theory. In this new Cordus theory particles are proposed to have a specific internal structure. These structures provide the causality for behaviours including spin, polarisation, charge, frequency, matter-antimatter species differentiation, superposition, and entanglement. Originality: The ability to explain superposition and entanglement is especially relevant because it rebuts the C&R claim that it is ‘impossible’ that such a hidden-variable theory could exist. This is significant because these quantum phenomena have historically been considered to be only explainable with quantum mechanics.This shows that fundamental physics may be explained from the basis of physical realism after all. Implications: New physics based on NLHV principles can explain multiple phenomena, and suggests a way to better understand coherent phenomena.
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