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On Superposition and Entanglement of Polarized Photons

Eugen Muchowski

Published Jul 8, 2024• 0 citations
Publisher

Abstract

It is shown that the superposition and entanglement of polarized photons can be explained by a local realistic model without introducing a hidden parameter. The basis of the modeling is that only relations between states of photon beams are predefined and not the states themselves. The actual state before a measurement has to be selected by a polarizer.

DOI
10.32388/5g09pg.2

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It is shown that the superposition and entanglement of polarized photons can be explained by a local realistic model without introducing a hidden parameter. The basis of the modeling is that only relations between states of photon beams are predefined and not the states themselves. The actual state before a measurement has to be selected by a polarizer.
Polarized photons have properties that can be explained, among others, by their indistinguishability. This includes superposition and entanglement. We propose that the superposition state can be understood as the entirety of all mixtures of indistinguishable perpendicularly polarized photon beams. The photon beams, whose polarization correspond to the position of the polarizer, are filtered out by selection using a polarizer. There are no nonlocal effects with the entangled photons. This is because the physical states of the photons are defined before each measurement. The model replicates the predictions of quantum mechanics for entangled photons and also explains entanglement swapping and teleportation. The superposition of indistinguishable photon beams can be experimentally demonstrated using a Mach-Zehnder interferometer. This explains how the polarization of the input state reappears at the output of the Mach-Zehnder interferometer.
A system of two polarized photons in singlet state appears as being in one of two product states independent of any measurement. These states depend on the selected polarization angles. With the polarizers on either side perpendicular to each other, both photons pass the polarizers without any disturbance. Action at a distance is therefore not needed to explain the results of the measurements. In general, the elements of physical reality demanded by EPR are the polarization states of the two photons of the entangled pair. As these are local elements in the regions of space of the polarizers the EPR paradox for the case of entangled photons can be regarded as resolved.
Entangled quantum systems can connect to the environment via a Bell state measurement. This applies, for example, to teleportation and entanglement swapping. Although the results are well understood, it is not entirely clear whether they involve nonlocal action or whether they are predetermined. This can best be decided from a model, provided it predicts the key measurement results. Models based on the fact that the partners of an entangled pair have the same value of a statistical parameter cannot be applied here. This is because the partner particles of the resulting entangled states after a teleportation or an entanglement swapping never had contact before. The question then is, what connects entangled photons? Therefore, this paper presents a local realistic model that reproduces the quantum mechanical predictions for expectation values with polarization measurements, but is not based on shared statistical parameters. Instead, the coupling of the entangled particles is based on initial conditions and conservation of spin angular momentum. The model refutes Bell's theorem and also explains teleportation and entanglement swapping in a local way. The manuscript is thus a step forward toward a complete theory describing quantum physical reality as thought possible by Einstein, Podolsky, and Rosen.
Entangled photons leaving parametric down-conversion sources exhibit a pronounced polarization correlation. The data violate Bell's inequality thus proving that local realistic theories cannot explain the correlation results. Therefore many physicists are convinced that the correlation can only be brought about by non-local interactions. Some of them even assume that instantaneous influences at a distance are at work. Actually, assuming a strict phase correlation of the photons at the source the observed polarization correlation can be deduced from wave optical considerations. The correlation has its origin in the phase coupling of circularly polarized wave packets leaving the fluorescence photon source simultaneously. The enlargement of the distances between photon source and observers does not alter the correlation if the polarization status of the wave packets accompanying the photons is not changed on their way from the source to the observers. At least with respect to the polarization correlation of entangled photons the principle of locality remains valid.