Last Update April 20 2022

In the following classical physics is also referred to as

Beware the following so-called

A pair of entangled particles is made of 2 complementary particles emitted at same time by one emitter in two opposite directions, and analyzed within two receivers equidistant from the emitter.

There are two schools of thoughts concerning the measures of entangled pairs:

- Along Bohr's thinking is Quantum Mechanics in which statistics, called probabilities in the litterature, and uncertainty rule. Uncertainty rules because entangled pairs, at time of emission, are all identical to each other; no matter where, no matter when emitted all entangled pairs have and will be occurring under a unique and identical 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 [Ref. 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 mental 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 [Ref. 2], establishing that should future physical experiments justify Quantum Mechanics, as summarized in section 1 above, there would be no hidden variables and no Classical or local theory would ever be established.

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

Since then the consensus in science is that there is no hidden variable, Einstein equation is dismissed, and no local theory will ever be established.

Science physics and mathematics loses some of its prestige as two valid mathematical theories, EPR and Bell's inequalities, are contradicting each other.

This page restores Science's great stature, it demonstrates that Einstein, Podolsky and Rosen are right, without negating Quantum Statistical mathematics; the physical results can be justified using *local reality*, showing *non locality* is not mandated by statistics.

Beware, in quantum Mechanics the orientations of the particles are non existent until the measures occur; and that is so primordial to most physicists that some told me the following is irrelevant and is not to be considered.

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.

Figure 1 illustrates the physical experiments. It consists of two detectors' magnets A and B on either sides of an emitter C of entangled pairs of electrons. The detectors magnets are graphically represented by a circumference and a diameter line delineating the North Pole, labeled with a capital "N", from the South Pole "S" represented in grey. In Figure 1 detector A is oriented at 0

Important note: in Quantum Mechanics'

It turns out that these two specific orientations, and more specifically the difference 120 degrees between the two detectors is, as explained below, at the base of the controversy.

In

Figure 2 represents 12 electrons, which angular tilts are represented counter clockwise with respect to their trajectory.

In this

In contradiction Quantum 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 the 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.

Note that entangled pairs are made of 2 complementary particles, meaning their tilts are 180 degrees apart. For easier presentation and comprehension, the graphs and this text are handling pairs having identical tilts instead. I found out that pairs with identical tilts are providing as good results as complementary pairs even though forbidden in quantum theory.

Please note also, in quantum mechanics, the complementary appellation excludes angular values, keeping it purposely undefined.

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

The detectors orientations Θ

This situation, in which

Provided the pairs are evenly distributed, those with tilts between 0

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

When the detectors are oriented 120

Note, the origin chosen to refer the detectors, as well as the origin chosen to refer the electrons orientations, when making the measures, are both irrelevant.

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

The red and green lines and angles in Figure 4 represent individual electrons orientations and reorientations of any pair before the measures take place.

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

And the 120

Yet as already mentioned the 120 degrees difference is the situation in which the

Equation 2 abolishes the former local

A computer simulation is of the essence; one has been set; click:

Adopting the trajectory of the entangled pairs for angular reference here is what is happening:

- To start with the two electrons of any entangled pair are emitted having opposite orientations.

Please recall, this angular relation between the 2 electrons at emission is not part of Quantum Mechanics; the claim made in Quantum Mechanics is that the particles have no specific angular orientations until the measures occur, at which time the uncertainty desappears, their orientations appear providing the measured results.

- Within its own detector each electron is individually diffracted; that is, its angular orientation is deviated by an angle provided by local Equation 2.

Please take note that nothing is happening until the measures are taking place; showing that quantum mechanics argument, namely that everything is happening at time of measure, cannot be used to justify

A few conditions must be in effect in order to obtain both wrong and correct statistics coinciding to Bell's inequalities; the pairs have to be evenly distributed across the entire 360 degrees sector. And to comply exactly with both one third , one quarter distributions the number of pairs emitted must be an entire number of quarters and thirds at same time; for instance emitting a total of 12 or 24 or 360 pairs, which are numbers evenly divided by 3 and by 4, are acceptable.

Local equation 2 simply nullifies the wrong

I have been told this Entanglement Computer Simulation I wrote is concerning a specific case, and not the general phenomenon and as such is irrelevant.

My answer is that my program precisely simulates Alain Aspect experiment, which is the quintessential case on which all of Quantum Mechanics sprouted up.

The fact of the matter is any computer simulation based on Quantum Mechanics Equation 1

In science the pairs make one complementary entity until measured, the word complementary specifically excluding any physical characteristics. In quantum mechanics the 2 electrons of any pair, until measured, are not distinguishable, and more specifically devoid of any angular orientation; even though the emitting of any pair, that is science's physical emission process, specifically suggests that the 2 particles' orientations are at 180 degrees from each other.

Contrary to quantum science I am using entangled pairs occurring as 2 individual particles; the 2 particles having either opposite or identical magnetic orientations that I call tilts; the pairs' tilts differing from pair to pair.

My computer simulation showed that both cases, identical orientations and opposite (180 degrees) orientations within pairs provide the correct answers, even though pairs of identical particles (opposite of complementary) are forbidden in quantum mechanics.

When the pairs have identical tilts, 25 percent of them flash the same color 75 percent flash differing colors; when the 2 particles are oriented 180 degrees apart (coinciding to quantum mechanics complementary definition) 75 percent of them instead flash the same color, 25 percent flash differing colors; the quantum ratio one quarter, three quarters departing from one third two thirds remaining nevertheless in force in both complementary and non-complementary situations.

Such distinction being apparently kept hidden in physical experiments.

So I dug deeper and looked in more detail at Bell's inequalities in order to come up with an argument that can no longer be denied by those believing in non-locality; that is an argument that does not disprove Quantum Mechanics fundamentals.

In Wikipedia's page labeled 'Bell's theorem' [Ref. 6] is the following:

"

Now that is a whole new ballgame! Now

And to answer that question I had to find out what is meant by

I found an explanation through another Wikipedia article conveniently labeled

"

Recalling section 'A' above, which states that the 2 particles of any entangled pair are generated having opposite directions, a feast by the way that requires specific emissions processes using specific atoms, any particle of any entangled pair in

Entangled pairs are emitted as 2 particles of opposite directions. The point is that these 2 opposite directions for each pair remain in effect no matter the distance up to their measures; and that abolishes the instant communication between the 2 particles, which in Quantum Mechanics is required to provide the final results.

Furthermore Quantum mechanics 25% prediction relies on the fact that the 2 detectors are oriented at 120 degrees from each other ; that is another 2 individual parameters, which can be separated by huge distances yet acting in concern that is acting in a

These specific, within pairs orientations and detectors orientations, are implementing this so-called

The irony is that quantum-entanglement is not the only reason behind the controversy; another imperative factor, behind the measures, is the diffraction phenomenon overlooked in science.

Another goal is to provide as best as possible a physical explanation of the phenomenon as done in section 4 above.

Both Quantum Equation 1 and local Equation 2 are correctly cloning reality. Showing that Equation 1 does not mandate

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 quantum statistics, which are correct, do not coincide to the expected local (and wrong) outcome used by Bell; non locality is a byproduct of unexplained statistics and vanishes with Equation 2.

In the end Bell's famous theorem leads toward conciliation as shown in section 5 above.

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

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

Also available on the 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

[5] See On how the 33% distribution is set ignoring the particles orientations

[6] Quote found Dec 19 2019 on Wikipedia at Wikipedia, the free encyclopedia title: Bell's theorem

[7] Quote also found Dec 19 2019 on Wikipedia at Wikipedia, the free encyclopedia title: Quantum entanglement

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

Both Equation 1 and its

Equation 3 modifies θ

In these conditions one quarter identical measures instead of one third identical measures will occur, 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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