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.
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.
A critical reconsideration of the EPR (Einstein-Podolsky-Rosen) paper shows that the EPR argument can be developed without using the concept of `element of physical reality', thus eliminating any philosophical element in the logical chains of the paper. Deprived of its philosophical ornament, the EPR argument plainly reduces to require what quantum mechanics can not do: to assign definite values to two incompatible physical quantities. Hidden variables theories built up according to Bell - type theorems are formulated on the basis of the assumption that the locality condition implies the statistical independence between two measurements space - like separated. This assumption is valid only with the additional one that statistical dependence between two measurements requires a causal connection between them. This additional assumption rules out the possibility that statistical dependence may due to an intrinsic property of the physical system under study. Therefore, hidden variables theories are built up with a restriction which leads them to be disproved by experiment. Quantum mechanical non - locality, invoked for describing EPR - type experiments, is strictly connected to the hypothesis (NDV hypothesis) according to which the twin photons of entangled pairs do not have a definite polarization before measurements. Both hypotheses are used only for describing EPR experiments and not for making predictions. Therefore, they can be dropped without reducing the predictive power of quantum mechanics concerning entangled photons pairs. Furthermore, both hypotheses can be experimentally tested by a modification of a standard experimental apparatus designed for studying entangled photons pairs.
EPR showed that two particles emitted from a source can be entangled by a shared wavefunction where two non-commuting observables (position, momentum) can be simultaneously real, leading to a contradiction with quantum mechanics (two non-commuting variables can not be simultaneously real). John Bell derived an inequality where any local hidden variables prediction is bounded and quantum mechanics can violate the inequality. Bell tests on correlated photon pairs showed a clear violation of the Bell inequality and agreement with quantum mechanics. This study revealed that the Bell inequality holds at any individual instances in a given system but it does not hold over the entire population. The Bell inequality is not an incompatibility criterion for local hidden variables vs quantum mechanics rather it is a criterion for an individual nature vs population dynamics. The nonlocality prediction given by wavefunction is a system approximation and local causality (photon polarization) provides a complete description of the Bell tests. The paper concludes with great satisfaction that the measurement of two correlated photons at a distance was a local cause (photon-filter interaction did not violate the special theory of relativity).
Bell's inequality is widely regarded as the death knell of local hidden variable theories. However, this paper points out that Bell's argument implicitly relies on an overly narrow assumption about what constitutes a "local hidden variable"—namely, that hidden variables must assign measurement outcomes to each particle independently at the moment of measurement. This paper proposes that the deterministic correspondence established between entangled particles at the moment of their creation, and determined by initial conditions, can itself serve as a local hidden variable. As long as the polarization direction of the photons is not altered, this correspondence persists indefinitely. It is independent of whether a measurement is performed, and requires no superluminal communication to sustain. From this perspective, quantum entanglement experiments do not violate special relativity; the violation of Bell's inequality merely rules out a specific class of hidden variable models, not all forms of local realism.
Bell inequalities are intended to formulate mathematically the argument of the thought-experiment proposed by Einstein, Podolsky and Rosen (EPR) in the Einstein-Bohr Debate. Devised to test Bell inequalities against quantum mechanics for resolving the Einstein-Bohr debate, Bell experiments are purportedly modern versions of the EPR experiment. However, there exists a fatal logical flaw in Bell experiments. Because of the logical flaw, Bell experiments differ essentially from the EPR experiment, and quantum correlation in the EPR experiment is not "quantum entanglement" in Bell experiments; the latter is not physically meaningful. In addition to the logical flaw in Bell experiments, a physical constraint imposed on measuring individual quantum objects is violated by all Bell inequalities, which makes Bell inequalities physically meaningless. Unlike Bell experiments, the EPR experiment will not violate any physical constraint, and the EPR argument has no logical flaw. Consequently, the experimental invalidation of Bell inequalities is not evidence for falsifying the two fundamental hypotheses for scientific research, i.e., locality and realism, underlying the EPR experiment, and by no means can Bell experiments resolve the Einstein-Bohr debate. Stemming from abandoning either locality or realism or both, the so-called new applications of quantum mechanics, including various quantum information technologies, are all ineligible and doomed to failure, for they attempt to exploit physically meaningless "quantum superposition" or "quantum entanglement", treating them as physical resources "out there" in the real world.
Abstract. For unit vectors a, b, entanglement requires that spin measurements satisfy those just given for a≠b. Bell’s hidden variable quantum mechanical local particle with a=b cannot provide the values for a≠b and, hence, the values for an entangled particle system. The perception that any hidden variable quantum mechanical description of an entangled system of particles is non-local depends on Bell’s inappropriate definition of locality, which excludes entanglement for a distant particle, and the condition that a=b, which does not give the values for a≠b as required to give the quantum mechanical expectation values, when entanglement occurs for systems that are close, not distant, and ignores that entanglement is a local phenomenon. Expecting the condition a=b and a local particle analysis with no distant entangled particle to give the quantum mechanical result is absurd. Any disentanglement of once entangled particles moving apart sets the spin measurements at those given for a≠b if a≠b and those given for a=b if a=b. Any subsequent measurement of the set values agrees with those for a≠b if a≠b and those given for a=b if a=b just as if the particles are entangled still. In examples where Bell’s inequality is supposedly violated, the conditions for which the inequality is true are not met. There is no contradiction.
The original Bell inequality was obtained in a statistical derivation assuming three mutually cross-correlated random variables (four in the later version). Given that observations destroy the particles, the physical realization of three variables from an experiment producing two particles per trial requires two separate trial runs. One assumed variable value (for particle 1) occurs at a fixed instrument setting in both trial runs while a second variable (for particle 2) occurs at alternative instrument settings in the two trial runs. Given that measurements on the two particles occurring in each trial are themselves correlated, measurements from independent realizations at mutually exclusive settings on particle 2 are conditionally independent, i.e., conditionally dependent on particle 1, through probability. This situation is realized from variables defined by Bell using entangled particle pairs. Two correlations have the form that Bell computed from entanglement, but a third correlation from conditionally independent measurements has a different form. When the correlations are computed using quantum probabilities, the Bell inequality is satisfied without recourse to assumptions of non-locality, or non-reality.