Locally real states of electromagnetic radiation derived from the underlying quantum mechanical formalism are shown to provide an alternative basis for definite polarized states of the widely accepted probabilistic interpretation. The locally real states traverse common loop configurations without invoking non-local superposition. Correlated photon pairs represented by the locally real states are consistent with the underlying quantum mechanical formalism independent of Bell's inequality and without invoking entanglement. Replacement of interdependent non-local probabilistic states with the locally real states yields independence of those states. A novel loop configuration provides differential testability of the representation of the locally real states relative to the probabilistic interpretation with the prediction of a unique polarization state.
Locally real states of electromagnetic radiation derived from the underlying quantum mechanical formalism are shown to provide an alternative basis for definite polarized states of the widely accepted probabilistic interpretation. The locally real states traverse common loop configurations without invoking non-local superposition. Correlated photon pairs represented by the locally real states are consistent with the underlying quantum mechanical formalism independent of Bell's inequality and without invoking entanglement. Replacement of interdependent non-local probabilistic states with the locally real states yields independence of those states. A novel loop configuration provides differential testability of the representation of the locally real states relative to the probabilistic interpretation with the prediction of a unique polarization state.
A locally real representation of quantum mechanics deduced from the underlying quantum formalism is presented here. The representation is based upon Mirell's local hidden variable theory, an LHVT, [doi: 10.1103/PhysRevA.65.032102] that provides correlations in agreement with reported Bell experiments. Conversely, the non-local phenomenon of entanglement is necessarily invoked by the Copenhagen Interpretation of that formalism for those reported experiments by maintaining that the formalism is complete. Although a broad class of LHVT's has been disproven by Bell's inequality, Mirell's LHVT is identifiable as a special exempted case by its inherent inclusion of the property of enhancement. Clauser and Horne [doi: 10.1103/PhysRevD.10526] showed that LHVT's with the property of enhancement are not testable by Bell's inequality. In order to address that lack of testability, the representation presented here substantially expands on Mirell's earlier LHVT by self-consistently demonstrating locally real photon state transits of common loop configurations, transits that necessarily invoke non-local superposition under the Copenhagen Interpretation of the quantum formalism. We then analyze those locally real transits and deduce methods to re-engineer the loop configurations to achieve selected output state distributions and show that these re-engineered configurations are predicted by the present representation to yield novel distributions of locally real states. Conversely, the Copenhagen Interpretation predicts corresponding output distributions for these re-engineered configurations that are unremarkable. Those mutually disparate output distributions provide the experimentally testable basis for definitively falsifying either the present locally real representation or the completeness of the original quantum formalism as postulated under the Copenhagen Interpretation.
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-state experiments with pairs of polarization-entangled photons are interpreted without any hinge on non-local mechanisms. The presented model rests on a careful analysis of published experimental findings. These foundations are implemented into a standard quantum mechanical treatment that obeys the purely local nature of each polarization preparation in the course of a measurement process. Polarization entanglement is ascribed to the generation of indiscernible photon pairs while undistorted propagation maintains this interrelation. Thus, the proposed approach assigns the essential characteristics of polarization entanglement to each constituent of an entangled pair. Accordingly, space-time separated polarization preparations lead to consistent probabilities of joint detection events. The obtained results agree with those of previous non-local models and thus reproduce the experimentally required violations of the Bell inequality. Since the presented approach lacks any non-local phenomenon, hidden variables are rendered superfluous, too.
Stochastic optics may be considered as simply a local realistic interpretation of quantum optics and, in this sense, it is a first step in the reinterpretation of the whole of quantum theory. However, as it is not possible to interpret all the details of quantum theory in a local realistic manner, as shown by Bell's theorem, minor changes are introduced in the formalism with the consequence that the new theory makes different predictions in some special cases. In stochastic optics, the quantum-operator formalism is simply considered a formal way of dealing with stochastic fields. In particular, the quantum zero point is taken as a real random electromagnetic radiation filling the whole of space. This radiation noise has the same nature as light signals, the only difference being the greater intensity of the latter. We assume that photon detectors have an intensity threshold just above the level of the noise, thus detecting only signals. Transmission of radiation through polarizers follows Malus's law, but the interplay of signal and noise leads quite naturally to the prediction that the detection probability of some signals is enhanced, which is known to be a necessary condition for the violation of the empirically tested Bell inequalities. In our view, correlated photon pairs are pairs of light signals supercorrelated in polarization, in the sense that, as well as the signal, the accompanying noise is also correlated. Thus stochastic optics allows predictions for the empirical correlations very close, but not identical, to the quantum ones. The theory is applied to the analysis of all experiments designed to test the Bell inequalities by measuring polarization correlations of photon pairs. The predictions agree with quantum optics and experiments within statistical errors, except for the Holt-Pipkin experiment. In this case, the experimental results agree with stochastic optical predictions within two standard deviations while violating quantum optics by four.
Since John Bell has established his famous inequality and several independent experiments have confirmed the distinct polarization correlation of entangled photons predicted by quantum mechanics it is evident that quantum mechanics cannot be explained by local realistic theories. Actually, the observed polarization correlation can be deduced from wave optical considerations. The correlation has its origin in the phase coupling of the two circularly polarized wave packets leaving the photon source simultaneously. The experimental results violate Bell's inequality although no non-local interactions have to be assumed. In consequence the principle of locality remains valid in the scope of quantum mechanics. However, the principle of realism has to be replaced by the less stringent principle of contextuality.
As discussed below, Bell's inequalities and experimental results rule out commutative hidden variable models as a basis for Bell correlations, but not necessarily non-commutative probability models. A local probability model is constructed for Bell correlations based on non-commutative operations involving polarizers. As in the entanglement model, the Bell correlation is obtained from a probability calculus without explicit use of deterministic hidden variables. The probability calculus used is associated with chaotic light. Joint wave intensity correlations at spatially separated polarization analyzers are computed using common information originating at the source. When interpreted as photon count rates, these yield quantum mechanical joint probabilities after the contribution of indeterminate numbers of photon pairs greater than one is subtracted out. The formalism appears to give a local account of Bell correlations.