Quantum Mechanics Explicit Interpretation

Last Updated June 28 2018

Abstract

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.

1. Introduction

Quantum mechanics relies on entangled pairs of electrons or photons. Amazingly nobody knows about the materialistic reality that is the physical constitution of either the electron or the photon particle.
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 statistical information, suggests and at the same time embodies uncertainty.
Rather than relying on explicit mathematics, which handles known variables as done in Classical Physics, Quantum Mechanics is relying on statistical mathematics.

2. Classical Explicit Interpretation and Predictions

In this section we are leaving the Quantum World made of statistics and are describing instead the explicit aspect of entangled pairs. The measures show that the particles involved are polarized, having a magnetic North Pole pointing or oriented in any direction within the full spectrum extending from 00 to 3600 (read zero degree to three hundred and sixty degrees); these angular orientations are explicitly, that is individually, detected and measured.
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 explicitly oriented at 600. The 2 particles have been emitted from the Emitter represented in the center; the left particle is travelling toward the left, the right particle toward the right, both remaining oriented at 600 until measured.

Particle 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 ΘLD = 00 (read theta LD) while the Right Detector is oriented at ΘRD = 1200. When a particle's North Pole matches its detector's North Pole (in GREEN) as illustrated in left of Figure 2, the detector should be flashing a GREEN signal. When the particle's and detector's North pole do not match, as is the case in the Right Detector, a RED signal should be flashed.

Particle Pair

The words "should be flashing" and "expected to flash" have been used because, as shown in the following, this explicit reasoning turns out to contradict both Quantum Mechanics predictions and physical experiments.

Having in mind that the 2 particles of any pair have identical orientation, Figure 3 shows that all of the pairs oriented from 00 to 1800 should flash GREEN in the Left Detector.
Yet the pairs oriented from 00 to 1200, or two thirds of the top half circle should flash RED in the Right Detector. Only the pairs oriented from 1200 to 1800, or one third of the top half circle should flash GREEN in the Right Detector.
All in all only one third of the pairs between 00 and 1800 should flash identical GREEN signals, two thirds should flash different GREEN / RED signals
And for the pairs oriented from 1800 to 3600 one third should flash identical RED signals, two thirds should flash different RED / GREEN signals.

Particle Pair

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!

Note that these explicit angular orientations are expressed in a statistical format involving population's thirds. This is done on purpose, it allows for the comparison between this explicit interpretation and Quantum statistical interpretation.

3. On how Quantum Mechanics Contradicts Classical Explicit Predictions

Should mathematics not be your bag, simply ignore Equation 1 and jump to the paragraph printed in green color below.
In the early 20th century Quantum mechanics following Equation providing statistical information had been set:

Particle Pair

The detectors orientations ΘLD and ΘRD can be each given any values from 00 to 3600; Quantum Mechanics Equation 1 provides the probability of pairs yielding same colors.

When the detectors angles are set at ΘLD = 00 and ΘRD = 1200, 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.

4. How the Quantum Statistics Get Justified Beforehand

The first fundamental aspect of above predictions is that should Quantum Mechanics prevail, explicit reasoning would become wrong; Figure 3 distributions and explicit reasoning would all become irrelevant.
Uncertainty would then rule.

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.

Facing such novelties, Einstein, Podolsky, and Rosen came up in 1935 with their famous paper now called EPR demonstrating that behind Quantum statistics, there are hidden variables that explain the particles' individual behaviors.
While justifying Quantum mathematics statistical results, EPR nevertheless challenges both uncertainty and nonlocality.

5. The Experiments and Consequences

During a number of years no experiments were run that could determine whether Quantum statistics or explicit mathematics would rule. Both theories were still plausible. When one of the two would take over the mathematical validity of the other would have to be disqualified.
In 1964 John Stewart Bell took the initiative; he came up with his famous inequalities, establishing that should future physical experiments justify Quantum Mechanics statistical predictions, the explicit explanation (2. above) would not only become irrelevant, but in addition no explicit explanation at all could physically be discovered.

The first physical experiments and undisputable measures that occurred in the 1980's definitely showed that Quantum statistics were ruling over the explicit explanation.
Now according to Bell's famous Inequalities, which has been the consensus for over the next 50 years, not only our human explicit interpretation is wrong, but no hidden variables will ever be uncovered.

6. New Explicit Mathematics Complying with Experiments and Proving Bell's Conclusion Wrong

In 2017 this author came up with explicit Mathematics Equation 2 (below) outperforming Quantum Mechanics achievement in that, besides conforming to Quantum statistics, it brings to light the individual behavior of each particle, a feast banished by Bell's theorem.

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 00 and 1350 represent three quarters of those between 00 and 1800. The remaining pairs between 1350 and 1800 make the remaining quarter. And an identical distribution applies to the circumference's lower half.
In order to match the physical measures and Quantum Mechanics statistics when the detectors are set 1200 apart, it suffices to come up with an equation that modifies the pairs tilted between 00 and 1350 to angles tilted between 00 and 1200. This reorientation occurs as follows:

Particle Pair

Equation 2 contradicts Bell's inequalities, which states that no explicit explanation can be given.

When the detectors are oriented 1200 apart as in Figure 3, the particles evenly tilted from 00 to 1350 when emitted will be, according to Equation 2, reoriented and measured between 00 and 1200 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.

In this interpretation the 2 particles of any pair are acting in concert, not because one particle is instructing the other to comply instantly 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 00, 1200 detectors setting as used in all of the above, is not restrictive; the 2 detectors can be set at any of two values other than 00 and 1200; in all cases explicit mathematics Equation 2 provides reoriented values that fit the experiments, just as Quantum mechanics Equation 1 does.
Equation 2 abolishes the former wrong explicit one third two thirds distribution used by Bell and not conforming to reality and replaces it by a correct explicit one quarter three quarters distribution conforming to reality and Quantum statistics.

7. Computer Simulation

The explicit mathematical Equation 2 predicts the exact behavior of each particle of each pair, a break actually forbidden by Bell's famous inequalities.
Whereas Quantum Mechanics provides the overall correct distribution of the measures at once, which is with a simple and single calculation using Equation 1, explicit Equation 2 requires much more work:
  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 3600 spectrum.
  2. 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.
A computer simulation is of the essence; one has been set; anyone can trigger and use it; for instance one can choose to set the angles of the two detectors 1200 apart and choose to emit 360 pairs; the program displays the individual 360 particles tilts when emitted and their respective reoriented angles over the full circumference along with their equivalent statistics, the later conforming to Quantum Mechanics statistics. Just right click this link and "open in new tab" : Entanglement Computer Simulation.

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.

Particle Pair

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

8. Conclusion

The ultimate goal is to refute both uncertainty and nonlocality concepts, while appreciating Quantum Mechanics statistical interpretation.
Another goal is to provide as best as possible a physical explanation of the phenomenon as done above.

Statistics does not mandate uncertainty
Equation 2, which predicts precisely the particles' individual behaviors, abolishes the uncertainty associated to Quantum Equation 1 statistics.
And that is going along EPR's hidden variables that disavow uncertainty without denying Quantum statistics.

Nonlocality is unreasonably commended
When the detectors are set 1200 apart, a pair emitted at 600, as shown Figure 2, is measured GREEN by one detector and RED by the other; all in all the two particles of a pair maybe measured differently. Yet such not complying colors were witnessed by human operators even before Equation 2 came into play.
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 statistics do not coincide to the expected outcome; nonlocality is a byproduct of unexplained statistics and vanishes with Equation 2.

Bell's inequalities revisited
Based on the wrong one third same colors to two thirds different colors distribution, Bell's famous inequalities are simply dismissed.

EPR's hidden variables reinstated
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 uncertainty rule it would mean that uncertainty is uncertain or unreliable... uncertainty cannot rule; on the other hand certainty, a very plausible alternative, allows itself to rule.
And from a very practical point of view please note that quantum uncertainty always ends up to be metamorphosed into local or explicit certainty that is Classical Physics.

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.

More about Bell's Inequalities

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