Last Update March 26 2019

There are two schools of thoughts concerning entangled particles:

- Along Bohr's thinking is Quantum Mechanics in which statistics and uncertainty rule. Uncertainty rules because entangled pairs are all identical to each other; no matter where or when emitted any entangled pair occurs under the same and unique quantum state made of eight simultaneous yet incompatible constitutions. When a particle of any pair is measured one of these eight outcomes haphazardly pops out; and the measured particle is instantaneously instructing over distance the companion particle to comply, a phenomenon known as non-locality; at that very time the pair's quantum state and its uncertainty vanish.
- Along Einstein, Podolsky, Rosen or EPR paper [1] published in 1935 is conventional physics, or local realism, which asserts that behind quantum statistics and uncertainty are hidden variables; without questioning Quantum mathematics and statistical results EPR nevertheless challenges both uncertainty and nonlocality concepts attached to it.

Later in 1964, well after above controversy was mathematically confirmed and before any experiments were run, John Stewart Bell came up with his famous inequalities [2], establishing that should future physical experiments justify Quantum Mechanics, as summarized in section 1 above, there would be no hidden variables; that would contradict EPR and no Classical or local theory would ever be established.

In the 1980s physical experiments ran by Alain Aspect [3], and many others since, have definitely justified quantum statistics predictions.

Since then, in accordance with Bell's inequalities, the consensus is that there is no hidden variable and no local theory can be established; in essence declaring above EPR's conclusions wrong.

In 1980 N.D. Mermin wrote a paper [4] about Quantum Mechanics, which you might want to read; it explains in much more details and in simple terms Quantum Mechanics uncertainty and non-locality.

Challenging Bells' claim, and at same time justifying EPR prediction, this web page provides a local equation conforming to physical experiments just as Quantum Mechanics does; the equation provided describes the behavior of each and every individual particle of each and every individual entangled pair, a feature abolishing uncertainty.

And in the process Bell's inequalities are turned into equalities.

While entangled pairs are either two photons or two electrons particles in Quantum Mechanics, for simplicity this non-quantum or local interpretation deals with electrons only.

And very specifically, according to Mermin's article [Page 942], the measures indicate that the two electrons of any pair are identical: "The detectors flash the same colors when they have the same settings because the particles carry the same instructions." This physical outcome, which is part of Quantum Mechanics, is also adopted as is in this non-quantum local physics; when measured both electrons magnetic orientations or tilts of an entangled pair are identical. As such a pair graphical representation, represents also both electrons tilts of the pair.

Note regarding the orientations of the 2 particles of an entangled pair. Overlap this line with your mouse pointer.

The particles orientations are angles counted positively counterclock wise with respect to their trajectory. The origin being at the Emitter C.

As such the observer on the right side of Figure 2 will measure a particle oriented at 60 degrees to have an orientation of 60 degrees. Yet the observer on the left of Figure 2 will see the entangled particle of the same pair oriented at 180 plus 60 degrees or 240 degrees.

This writer thinks that might be the reason for which entangled pairs are sometimes referred as being made of 2 complementary particles.

The interpretation of the measures is such that it ends up providing the right information whether the 2 particles are considered to be complementary or having identical orientations.

As such the observer on the right side of Figure 2 will measure a particle oriented at 60 degrees to have an orientation of 60 degrees. Yet the observer on the left of Figure 2 will see the entangled particle of the same pair oriented at 180 plus 60 degrees or 240 degrees.

This writer thinks that might be the reason for which entangled pairs are sometimes referred as being made of 2 complementary particles.

The interpretation of the measures is such that it ends up providing the right information whether the 2 particles are considered to be complementary or having identical orientations.

Figure 2 clearly emphasizes this local interpretation in which each electron's tilt is specifically determined.

In contradiction Quantum statistical mechanics asserts that the electrons have no magnetic orientation at all; all pairs share an identical and unique

In Figure 3 the angles ΘA and ΘB (read theta) are the orientations respectively given to Detector A and Detector B magnets.

Figure 3 illustrates the measurement of a single entangled pair emitted with a 30

If electron north pole matches detector North Pole, the detector flashes GREEN (or G) as Detector A does. When they do not match, they flash RED (R) as Detector B does.

And no matter the number of pairs considered, this reasoning applies.

The detectors orientations Θ

This situation, in which

In order to match the physical measures and Quantum Mechanics statistics when the detectors are set 120

When the detectors are oriented 120

Figure 4 illustrates Equation 2; Equation 2 predicts the behavior of each electron of each pair; while conforming to Quantum statistics, Equation 2 is dethroning the concept of uncertainty.

And as already mentioned, because the 2 electrons of any pair when measured have identical deflection, each grey and black lines in Figure 4 represent a pair orientation as well as each electrons orientations of that pair.

In this interpretation the 2 electrons of any pair are acting in concert, not because one particle is instructing the other to comply over distance (Quantum Mechanics nonlocality interpretation), but because, before the measures take place, their individual yet common tilts have each been re-oriented in an equal amount as provided by Equation 2.

Please note that the 0

Equation 2 abolishes the former local

Equation 2 local reorientation implies the following:

- To start with while roaming within an emitter the electrons' tilts are
*evenly distributed*across the 360^{0}spectrum. - By the time the measures take place though the two electrons' magnetic orientations of any pair have been re-oriented as per Equation 2; the pairs are now measured
*unevenly re-oriented*across the 360^{0}spectrum and that differs from Bell's theorem in which*evenly distributed*angles instead are in force. - The two electrons of any entangled pair have identical magnetic spin axis tilt, and each pair has a different tilt from any other pair. While the identical tilt is integral part of Quantum Mechanics, the pairs' specific tilt attribute departs frankly from the universal quantum state applying to all pairs at all times. Note that even though the two electrons of a pair are emitted with identical tilts they might flash different colors depending on the detectors respective orientations as is the case Figure 3.
- Figure 5 illustrates the electrons uneven distribution once reoriented. The reciprocal symmetries appearing within the 4 quadrants 0
^{0}to 90^{0}, 90^{0}to 180^{0}, 180^{0}to 270^{0}and 270^{0}to 360^{0}determine the one quarter three quarters colors distribution when the detectors are set 120^{0}apart. These paramount symmetries are concealed throughout Quantum Mathematics.

A particularly interesting feature regarding each of these four quadrants is that the electrons emitted within each of these quadrants are reoriented within the same quadrant's limits. - It may be said that the electrons and their reorientations play the role of EPR's hidden variables.
- Please note that the reference chosen, namely the Electron's trajectory, coinciding to the horizontal, can be changed with respect to that horizontal line; while the numerical values would all be shifted by a common factor, the physical reorientations occurring in the 4 quadrants, and their coinciding statistics, will remain physically unchanged.

More precisely the 2 detectors zero's (0) origins specifically chosen as coinciding with the electrons' trajectory are irrelevant as far as the statistical results are concerned; and these origins are also irrelevant as far as this gravimotion's classical interpretation is concerned. These origins could bee chosen at 10 degrees or 90 degrees instead of 0 degree with respect to the electrons trajectory, this gravimotion's classical interpretation would remain the same just as quantum statistics would.

The fundamental factor is the difference of orientations between the 2 detectors, just as expressed in equation 1 and below in Appendix A Equation 3.

In gravimotion the measures do not switch an*uncertainty*into a*certain outcome*as is the case in quantum theory. And that highlights or explains Quantum Mechanics extraordinary alchemy, erroneously interpreted as*uncertainty*and*non-locality*.

A computer simulation is of the essence; one has been set on this site; any one can trigger it and use it; for instance one can choose to set the angles of the two detectors 120

The solution is to observe that in order to emit electrons that are evenly distributed in all directions the emitter must be neutral, preventing any deviation at emission; a detector on the other hand, in order to measure the electrons orientations, must be polarized; that difference most likely is then creating the electron's appropriate reorientations.

Note that these reorientations are at the image of refraction, which involves the deflection of the appearance of a rod partly immerged under water; the words reorientation and reoriented, rather than refraction and refracted, have been used in this web page as magnetic effects rather than indices of refraction are involved.

In the following description 360 pairs are considered to be emitted; the first pair is emitted with a 1

As already mentioned because the upper and bottom halves are symmetrical the following is treating the top half only.

And as shown in paragraph "2.5 Bell's theorem local interpretation" the grey and white shades, whether the upper or lower half circumferences are concerned, coincide to one third two third distribution.

In accordance with Equation 2 though the 15 electrons emitted within the 135

In the end the 120 electrons making the former 0

And the 60 electrons making the former 120

Whether 360 pairs or millions of pairs are considered this reasoning remains valid.

Another goal is to provide as best as possible a physical explanation of the phenomenon as done in section 6 above.

Both Quantum Equation 1 and local Equation 2 are correctly cloning reality.

Equation 1

This incompatibility vanishes noting that Equation 1

When the detectors are set 120

Nonlocality, which states that when one electron is measured the other complies at distance, then cannot refer to the colors measured. Nonlocality must then refer to the fact that the statistics do not coincide to the expected outcome; non locality is a byproduct of unexplained statistics and vanishes with Equation 2.

Based on the wrong

This interpretation has the definite advantage to confirm that Einstein and colleagues mathematics is right after all. The hidden variable is evidently the particles individual orientation.

Phys. Rev. 47, 777-780 (1935).

Also available on internet at: EPR

[2] Bell, J.S.: On the Einstein Podolsky Rosen paradox. Phys. 1, 195-200 (1964)

Available on internet at: Bell's inequalities

[2 a] For everybody explanation: Bell's inequalities for everybody

[3] Aspect, A., Grangier, P., Roger, G.: Experimental realization of Einstein-Podolsky-Rosen-Bohm Gedanken experiment: a new violation of Bell's inequalities. Phys. Rev. Lett. 49, 91-94 (1982) Available on Internet: Alain Aspect experiments

[4] American Journal Of Physics; Volume 49; Number 10; Page 940; October 1981.

Bringing home the atomic world: Quantum mysteries for anybody. By N.D.Mermin.

Also available on internet: Mermin's paper

As noted in "3. Local Mathematics Conforming to Experiment" the detectors orientations are irrelevant. We can then choose Detector B as being the

Both Equation 1 and its

Equation 3 modifies θ

In these conditions one quarter to three quarters distribution will be measured provided the emitted electrons are evenly distributed over the full 360

In the end Quantum Mechanics extraordinary alchemy mends nicely with local reality.

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