The reason for the misunderstanding of the violation of Bell's inequality. Polarizer

The main reason for the misunderstanding is the basis of the occurrence of probabilities, but an erroneous interpretation of the principle of operation of polarizers is also extremely important.

Let's consider the currently generally accepted definition of the term polarizer. A polarizer is an optical device that converts natural (unpolarized) light, oscillating in all directions, into plane polarized light that passing waves with only a certain orientation of the oscillation vector.

However, polarizers are not devices that filter out part of the light wave, leaving only the polarized part. This is proved to us by experimental data on the passage of a multitude of polarizers deflected at small angles. For example, light is absolutely unable to pass through three consecutive polarizers positioned at angles of \(0^o\), \(45^o\), \(90^o\) (between the transmission axes of the polarizers) based on the generally accepted definition of the term polarizer. However, experimental studies show that light partially passes through them. Why?

The reason is that polarizers are devices that non-linearly absorb, pass or not pass through themselves and re-emit photons. All this depends on the orientation of the photons in space, that is, their polarization, and on the atoms of the polarizers with which the photons interact.

We know perfectly well that the electrons in atoms are not static and revolve around the nuclei. Also, the nuclei of atoms themselves are not static. The sizes, energies, locations, and other characteristics of electrons and other particles in atoms are comparable to those of photons, which in each particular experiment changes the result of the interaction of a photon with a polarizer. All this leads to different results in a series of interactions of each of the photons with the polarizer. This introduces an additional change in "probability" (alters and distorts statistics). The polarizer changes the value of the "message" in a pair of entangled photons. This is unacceptable, based on the conditions of the experiment to verify the violation of Bell's inequality, since polarizers should not change the "probabilities" (change the value of the "message" in a pair of entangled photons).

In fact, polarizers change the polarization of photons during their nonlinear transmission and re-emission. A single photon with a well-defined axis of polarization interacts with the polarizer statistically in different ways due to the motion of atoms, electrons and other elementary particles of the polarizer. The probability of a photon passing through the polarizer is \(cos^2(\alpha)\) (experimentally coincides with Malus' law). Where \(\alpha\) is the angle between the transmission axis of the polarizer and the axis of polarization of the photon before the interaction. And due to the fact that in experiments to verify Bell's inequality we set an additional angle between the axes of polarization for a pair of polarizers, then for one polarizer we get the law \(cos^2(\alpha)\), and for the second \(cos^2(\alpha-\beta)\). Where \(\beta\) is the angle between the transmission axes of a pair of polarizers from the experiment. Even worse, our polarizers are different and the states of the atoms are also different. Therefore, each polarizer will change the value of the "message" in a pair of entangled photons in different ways for each specific experiment from a series of experiments. This is unacceptable, based on the conditions of the experiment to verify the violation of Bell's inequality (Bell's theorem postulates that there are no additional "probabilistic" factors: The measurement outcome is determined by the pre-existing state. It is not introducing new, random errors (statistical uncertainty) during the extraction. This is directly contradicted by the fact that the atoms of polarizers are in different states and act differently on photons, changing their ability to pass / reflect during each specific interaction). Additionally, it is extremely important to note that after the photon passes through the polarizer, its axis of polarization coincides with the axis of transmission of the polarizer. This is confirmed experimentally by the almost complete absence of a decrease in the intensity of the photon beam (after the first polarizer) when passing through multiple polarizers with matching transmission axes. The residual decrease in the intensity of the photon beam is most likely due to the direct collision of photons with polarizer atoms and inaccuracy in the manufacture of polarizers. Based on all this, it is now possible to understand the reasons for what is happening in an experiment with three consecutive polarizers positioned at angles of \(0^o\), \(45^o\), \(90^o\) (between the transmission axes of the polarizers). After passing through the first polarizer, the polarization axes of the transmitted photons coincide with the transmission axis of the first polarizer. We obtain that the angle between the axes of photon polarization and the transmission axis of the second polarizer is \(45^o\). Therefore, half of the remaining photons will pass through the second polarizer, since \(cos^2(45^o)=0.5\). After passing through the second polarizer, the polarization axes of the transmitted photons coincide with the transmission axis of the second polarizer. We obtain that the angle between the axes of photon polarization and the transmission axis of the third polarizer is \(45^o\). Therefore, half of the remaining photons will pass through the third polarizer, since \(cos^2(45^o)=0.5\). This fully corresponds to all experimental data and explains everything in this experiment and in other experiments with polarizers, too.

Unfortunately, we cannot avoid statistics now due to the imperfection of technical means that would allow us to know the locations and other characteristics of the elementary particles of the polarizers. Having this information for each specific photon interacting with the polarizer, we could predict its further behavior.

As a result, due to an erroneous interpretation of the functioning of polarizers, all conclusions about the violation of Bell's inequality are also erroneous.

Addition: Interference, diffraction and interpretation of experimental results