The True Relation of Photon Pairs:Independent Particles under Initial-State Constraints and the Falsification of the "Quantum Entanglement" Collapse Hypothesis

This paper aims to clarify the true physical relation of photon pairs and to falsify the "entanglement collapse" hypothesis that standard quantum mechanics imposes upon them. Bell experiments violating Bell's inequality only rule out "local independent hidden variables," and are not a sufficient condition for proving "superposition plus wave-function collapse." The physical definition of entanglement in standard quantum mechanics is: subsystems are strongly correlated, the system is inseparable, and the individual subsystem has no definite independent physical state; its mathematical expressions are the non-factorizability of pure-state wave functions and the non-convex-combination of mixed-state density matrices. The physical definition and mathematical expressions are fully aligned: the individual subsystem cannot be written as a separate expression and has no definite independent physical state. Operationally, it is also absolutely impossible to realize an individual measurement of the subsystem. However, in Bell experiments, photon pairs are separately and individually measured on spatially separated detectors, which directly falsifies the premise that "the photon pair is in an entangled state." Stripping away mysticism, the true relation of two photons is a linear equation with two unknowns (independent particles under an initial-state constraint); the three-photon logic (a linear equation with three unknowns) proves that after measuring one photon, the other two still have not collapsed into definite values and must still be measured individually to obtain their states—"wave-function collapse into a definite value" is purely fictitious in algebraic logic.