Anti Heisenberg—The End of Heisenberg’s Uncertainty Principle

In contrast to many other physical theories, quantum mechanics is generally regarded as above any theory we have ever had and perhaps the best candidate for a universal and fundamental description of objective realty as such. Heisenberg’s uncertainty principle is not the only aspect of the conceptual difference between quantum and classical physics but is certainly one of the most important and famous aspects of quantum mechanics. As we will see, quantum mechanics as a theory and especially Heisenberg’s uncertainty principle challenges not only our imagination but violates some fundamental principles of classical logic as such. Heisenberg’s uncertainty principle is refuted.

• Relativity Theory
• Quantum Theory
• Unified Field Theory
• Causality

1. Introduction

First and foremost, by starting from radical and controversial assumptions, Heisenberg himself attributed a general and far-reaching status to his own uncertainty principle. We are prepared to be confronted with Heisenberg’s most radical step.

“Weil alle Experimente den Gesetzen der Quantenmechanik und damit der Gleichung (1) unterworfen sind, so wird durch die Quantenmechanik die Ungültigkeit des Kausalgesetzes definitiv festgestellt.” [1]

Translated into English:

“Because all experiments are governed by the laws of quantum mechanics and thus far by equation (1), it is therefore that quantum mechanics has established the invalidity of the principle of causality definitively.”

We are faced with the necessity of a radical revision of the foundation for the explanation and description of objective reality as such. We shall not go too deeply into this matter but it is precisely this requirement which prevents us from being able to take into account that Heisenberg’s uncertainty principle can be treated as mathematically and logically consistent.

2. Material and Methods

Logically or mathematically, Heisenberg’s uncertainty principle is formulated as a non strict inequality.

2.1. Definitions

2.1.1. Definition: Strict Inequalities

In terms of algebra, a strict inequality possesses either the symbol > (strictly greater than) or < (strictly less than). A strict inequality is without an equality condition. In general, it is

while the notation a < b means that “a is strictly less than b”. In the same respect, it is

while the notation a > b means that “a is strictly greater than b”.

2.1.2. Definition: Non-Strict Inequalities

In contrast to strict inequalities, a non strict inequality is an inequality where the inequality symbol is ≥ (either greater than or equal to) or ≤ (either less than or equal to). Consequently, a non strict inequality is an inequality which has equality conditions too. In terms of algebra, we obtain

The notation a ≤ b means that “a is either less than or equal to b”. Equally it is

The notation a ≥ b means that “a is either greater than or equal to b”. A non strict inequality can lead to a either or fallacy, a so called “black or white” fallacy.

2.1.3. Definition: Heisenberg’s Uncertainty Principle

A preliminary and simplistic formulation of the quantum mechanical uncertainty principle for momentum and position can be found in Heisenberg’a article of 1927, entitled as “Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik” as

“Im Augenblick der Ortsbestimmung… verändert das Elektron seinen Impuls unstetig. Diese Änderung ist um so größer, je kleiner die Wellenlänge des benutzten Lichtes, d. h. je genauer die Ortsbestimmung ist… also je genauer der Ort bestimmt ist, desto ungenauer ist der Impuls bekannt und umgekehrt” [1] .

Translated into English:

“When the position is determined… the electron undergoes a discontinuous change in momentum. This change is the greater the smaller the wavelength of the light employed, i.e., the more exact the determination of the position… thus, the more precisely the position is determined, the less precisely the momentum is known, and conversely.”

Let us now move to another question about Heisenberg’s uncertainty principle. Speaking, as it is often done, Heisenberg himself did not provide a general and exact derivation of his uncertainty principle. Finally, on a more formal level, we note that the first mathematically exact formulation of Heisenberg’s uncertainty principle is due to Kennard [2] . In particular, in his Chicago Lectures Heisenberg himself pointed out that Kennard’s proof “does not differ at all in mathematical content” [3] from the argument he had presented earlier. Finally, the only difference is that Kennard’s proof “is carried through exactly” [3] . Heisenberg’s uncertainty principle often reads as

where σ(p) is the standard deviation of momentum, σ(X) is the standard deviation of position, h is Planck constant and π is the mathematical constant. Heisenberg’s explanation of the relationship between position and momentum is not defined as an equality in the sense that. Heisenberg explains the relationship between position and momentum as a non-strict inequality as. Thus far and contrary to expectation, Heisenberg is not demanding that two different terms either or are needed to fulfill his above non-strict inequality. Heisenberg demands that the same term must fulfill the non-strict inequality. The logical form of Heisenberg’s uncertainty principle is either

is true or

is true. From Equation (7) follows that

The following table is able to illustrate the last relationship (Table 1).

Table 1

Heisenberg’s uncertainty principleas a strict inequality

	>	1

Due to Equation (8), Heisenberg’s uncertainty principle demands that

2.1.4. Definition: Heisenberg’s Term H

In general, we define Heisenberg’s term H as

Under conditions of Equation (9) Heisenberg’s term H has to be greater than zero or it is

2.2. Axioms

Axiom I. (Lex identitatis).

To avoid any kind of a logical fallacy, the following theory is based on the axiom:

3. Results

3.1. Theorem: Heisenberg’s First Way to Define the Number 1

Claim.

Heisenberg’s uncertainty principle defines the number 1 as

Direct proof.

Due to our Axiom I, it is

We multiply the equation before by the term and do obtain the relationship

According to Equation (6), this is equivalent with

Under these conditions, Heisenberg’s term H is not needed or can be set to H = 0 to define the number +1. In general, Heisenberg’s uncertainty principle defines the number +1 under conditions of Equation (6) as

Quod erat demonstrandum.

3.2. Theorem: Heisenberg’s Second Way to Define the Number 1

Claim.

Heisenberg’s uncertainty defines the number 1 in the same respect in a second way as

Direct proof.

Due to our Axiom I, it is

We add 0 to Equation (19) and do obtain the relationship

Using the same term as before, Equation (20) can be rearranged as

and simplified in general as

Heisenberg’s term is defined as. Thus far, the number +1 is the same and does not depend under conditions. Consequently, even under conditions of Equation (7) it is possible to define the number +1. Heisenberg’s uncertainty principle defines the number +1 under conditions of Equation (7) and due to Equation (10) and Equation (11) as

Quod erat demonstrandum.

The following table may illustrate this relationship (Table 2), which is equivalent with Table 3.

Table 2

Heisenberg’s uncertainty and the number 1

References

1. Heisenberg, W.K. (1927) über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik. Zeitschrift für Physik, 43, 172-198. http://dx.doi.org/10.1007/BF01397280

2. Kennard, E.H. (1927) Zur Quantenmechanik einfacher Bewegungstypen. Zeitschrift für Physik, 44, 326-352. http://dx.doi.org/10.1007/BF01391200

3. Heisenberg, W.K. (1930) The Physical Principles of Quantum Theory. University of Chicago Press, Chicago, 15-19.

4. Recorde, R. (1557) The Whetstone of Witte. John Kyngstone, London, 238.

5. Harriot, T. (1631) Artis analyticae praxis ad aequationes algebraicas nova expedita et generali methodo resolvendas. Robertum Barker, London, 10. http://dx.doi.org/10.3931/e-rara-9120

6. Tanner, R.C.H. (1962) On the Role of Equality and Inequality in the History of Mathematics. The British Journal for the History of Science, 1, 159-169. http://dx.doi.org/10.1017/S0007087400001333

7. Barukcic, J.P. and Barukcic, I. (2016) Anti Aristotle—The Division of Zero by Zero. Journal of Applied Mathematics and Physics, 4, 749-761. http://dx.doi.org/10.4236/jamp.2016.44085

8. Barukcic, I. (2011) Anti Heisenberg—Refutation of Heisenberg’s Uncertainty Relation. American Institute of Physics—Conference Proceedings, 1327, 322. http://dx.doi.org/10.1063/1.3567453

9. Barukcic, I. (2014) Anti Heisenberg—Refutation of Heisenberg’s Uncertainty Principle. International Journal of Applied Physics and Mathematics, 4, 244-250. http://dx.doi.org/10.7763/IJAPM.2014.V4.292