Last Updated June 28 2018

By 1935 Quantum Mechanics *statistical* interpretation of reality and the inherent *uncertainty* attached to it were well established.

Yet these Quantum *Statistics* were at odds with Classical mathematics; and no experiments could be run that would confirm either theory.

That year Einstein, Podolsky, and Rosen, in a paper called EPR, demonstrated that hidden variables were underlying Quantum Mechanics *statistics*, in effect denying the *uncertainty* tied to these statistics.

Almost thirty years later in 1964 John Stewart Bell in a paper now called "Bell's Inequalities" challenged EPR.

Bell's inequalities stated that should Quantum *statistics* prevail there would be no hidden variables.

Alain Aspect experiments in the 1980's definitely justified Quantum Mechanics theory.

As a consequence in science, *uncertainty* became fact of life, and EPR's hidden variables were dismissed.

Reversing this trend, in 2017 this author uncovered the hidden variable behind Quantum *statistics*, and provided *explicit* mathematics describing the phenomenon, altogether discrediting *uncertainty* and Bell's famous inequalities.

Nevertheless physicists accomplished breathtaking measures and made astonishing discoveries concerning these entangled pairs; first the 2 particles of any entangled pair are identical twins; all entangled pairs are furthermore identical to each other; all entangled pairs occur under a common format, which is independent of the particles characteristics.

This common and universal format, called Quantum State, which provides exclusively

Rather than relying on

And to emphasize the discripency between Quantum and Classical Physics these angular orientations are ignored and play no role in Quantum Mechanics.

In Figure 1, the two tilted red-green patterns labeled with an "n" (for North Pole) represent two particles of an entangled pair

Figure 2 illustrates the experiment's fundamental features; two detectors are set on either sides of the Emitter; these detectors are polarized entities akin to magnets represented here by colored circles with a diameter separating the North Pole (N) half circumference represented in GREEN from the South (S) pole represented in RED. The Left Detector is oriented at Θ

The words "should be flashing" and "expected to flash" have been used because, as shown in the following,

Having in mind that the 2 particles of any pair have identical orientation, Figure 3 shows that all of the pairs oriented from 0

Yet the pairs oriented from 0

All in all only one third of the pairs between 0

And for the pairs oriented from 180

In this Classical *explicit* interpretation, one third of the pairs should flash identical colors; two thirds of the pairs should flash differing colors.

This text is in red as experiments ran later proved this *explicit reasoning* to be wrong!

In the early 20th century Quantum mechanics following Equation providing

The detectors orientations Θ_{LD} and Θ_{RD} can be each given any values from 0^{0} to 360^{0}; Quantum Mechanics Equation 1 provides the probability of pairs yielding same colors.

When the detectors angles are set at Θ_{LD} = 0^{0} and Θ_{RD} = 120^{0}, as in Figures 2 and 3, Quantum mechanics (Equation 1) predicts that same colors (either GREEN GREEN or RED RED) will be flashed one-quarter of the times, instead of one-third of the time, and opposite colors (either RED GREEN or GREEN RED) will be flashed three-quarters of the time, instead of two-thirds of the time.

This text is in green as experiments ran later proved this Quantum *Statistics* to fit reality.

These *statistical* predictions are definitely contradicting the *explicit* outcome.

By 1925 both the Classical *explicit* outcome and this contradictory Quantum Mechanics *statistical* prediction were well established.

No physical experiments were yet performed though; nobody knew whether the *explicit* explanation or this Equation 1 contradictory *statistics* would be confirmed by experiments.

Furthermore in order to depart from our human *explicit* reasoning, the two particles of any pair would have to communicate and comply with each other instantly over distance at time of measure; and that contradicts Einstein's relativity in which no signal can be transferred faster than light.

This aspect of Quantum Mechanics has been given the name of nonlocality.

While justifying Quantum mathematics

In 1964 John Stewart Bell took the initiative; he came up with his famous inequalities, establishing that should future physical experiments justify Quantum Mechanics

The first physical experiments and undisputable measures that occurred in the 1980's definitely showed that Quantum

Now according to Bell's famous Inequalities, which has been the consensus for over the next 50 years, not only our human

In Equation 2 the particles' reorientations bring to mind the refraction phenomenon, 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 specifically used in this web page to point out that the pheonomenon studied is not refraction.

Provided the pairs are evenly distributed when emitted, those with tilts between 0In order to match the physical measures and Quantum Mechanics

Equation 2 contradicts Bell's inequalities, which states that no

When the detectors are oriented 120^{0} apart as in Figure 3, the particles evenly tilted from 0^{0} to 135^{0} when emitted will be, according to Equation 2, reoriented and measured between 0^{0} and 120^{0} by both Detectors; these *explicit* reorientations precisely coincide with the physical measures and Quantum mechanics *statistics*.

This *explicit* Interpretation is written in green because it is in agreement with both experiments and Quantum Mechanics *statistics*.

Please note that the 0

Equation 2 abolishes the former

Whereas Quantum Mechanics provides the overall correct distribution of the measures at once, which is with a simple and single calculation using Equation 1,

- Equation 2 requires 5 mathematical operations to find out the reorientation of a single particle; and these five operations would have to be successively repeated a great number of times on a great number of particles to be chosen evenly distributed over the 360
^{0}spectrum. - Finally besides these cumbersome calculations, each calculated reorientation would have to be confronted to both detectors and compiled to verify that the results provided by Equation 2 agree with Quantum Mechanics Equation 1
*statistical*results.

The reorientations shown Figure 4 have been attained using above application; it illustrates *explicit* mathematics Equation 2; and as already mentioned, because the 2 particles of any pair when measured have identical orientations, each red and green lines in Figure 4 represent a pair orientation as well as each particle's orientation of that pair.

As a final note, the particles' reorientations occur most likely while crossing the air-to-detector boundary.

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

Equation 2, which predicts precisely the particles' individual behaviors, abolishes the

And that is going along EPR's hidden variables that disavow

When the detectors are set 120

Nonlocality, which states that when one particle is measured the other complies at distance, then cannot refer to the colors measured. Nonlocality must then refer to the fact that the

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 orientations.

From a purely logical point of view, should

And from a very practical point of view please note that

As a final note, while we know with certainty that life on Earth has a finite time span, meaning that we know with certainty that we will die, we human are nevertheless not given the ability to precisely predict all aspects of our own future. In spite of the Natural Laws, that among other rule with certainty over entangled pairs, our human brain can only be uncertain about many other things.

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