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Algemeen Nederlands Tijdschrift voor Wijsbegeerte

Hoe zeker is Heisenbergs onzekerheidsprincipe?

Jeanne Peijnenburg, David Atkinson

Published Feb 1, 2021• 0 citations
Publisher

Abstract

Abstract How certain is Heisenberg’s uncertainty principle? Heisenberg’s uncertainty principle is at the heart of the orthodox or Copenhagen interpretation of quantum mechanics. We first sketch the history that led up to the formulation of the principle. Then we recall that there are in fact two uncertainty principles, both dating from 1927, one by Werner Heisenberg and one by Earle Kennard. Finally, we explain that recent work in physics gives reason to believe that the principle of Heisenberg is invalid, while that of Kennard still stands.

DOI
10.5117/antw2021.1.006.peij

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Abstract How certain is Heisenberg’s uncertainty principle? Heisenberg’s uncertainty principle is at the heart of the orthodox or Copenhagen interpretation of quantum mechanics. We first sketch the history that led up to the formulation of the principle. Then we recall that there are in fact two uncertainty principles, both dating from 1927, one by Werner Heisenberg and one by Earle Kennard. Finally, we explain that recent work in physics gives reason to believe that the principle of Heisenberg is invalid, while that of Kennard still stands.
Heisenberg’s uncertainty principle is a milestone of twentieth-century physics. We sketch the history that led to the formulation of the principle, and we recall the objections of Grete Hermann and Niels Bohr. Then we explain that there are in fact two uncertainty principles. One was published by Heisenberg in the Zeitschrift für Physik of March 1927 and subsequently targeted by Bohr and Hermann. The other one was introduced by Earle Kennard in the same journal a couple of months later. While Kennard’s principle remains untarnished, the principle of Heisenberg has recently been criticized in a way that is very different from the objections by Bohr and Hermann: there are reasons to believe that Heisenberg’s formula is not valid. Experimental results seem to support this claim.
One of the fundamental cornerstone of quantum mechanics is the Heisenberg uncertainty principle. This principle is so fundamental to quantum theory that it is believed that if a single phenomenon that could violate it is found then the whole building of quantum mechanics will fall apart. However, since the formulation of the uncertainty principle until today there is not clear and universal agreement in its formulation or interpretation. Even Heisenberg was not clear about the exact meaning of p1 and x1 in their first formulation of the uncertainty relations [1]:
The uncertainty principle was first formulated by W. Heisenberg in the year 1927, which showed that certain physical values such as the position and the momentum of a particle, and also the time and the energy, cannot be specified with an arbitrary precision, something that was far from experiences in physics before the principle was discovered. In the same year, Kennard showed the same principle using a rigorous mathematical formalism, which has motivated further research of the principle in many different mathematical contexts. Using the fundamental results of Fourier analysis, and respecting the mathematical formalism of quantum mechanics, we present many different formulations of the uncertainty principle. We observe the principle for a single function – its qualitative, quantitative, operator and entropic formulations, for Gabor and wavelet systems of functions, and finally, generally for finite abelian groups, and more specifically for cyclic groups of prime order.
Abstract Heisenberg’s uncertainty principle states that: The product of the uncertainties in the simultaneous specifications of two °complementary observables can never be less than a small quantity of the order of h. The precise form of the principle is given in Box U.1. It implies that as one observable is constrained to have a more precise value, so its partner becomes more ill-defined. An experiment designed to measure the two observables simultaneously will be able to determine one precisely only at the expense of losing information about the other (see °duality). The principle was established by Werner Heisenberg in 1927, as a consequence of his formulation of °matrix mechanics.
The preceding study of this series, A Theoretical Deconstruction of the Uncertainty Principle, showed, by structural analysis, that the Heisenberg uncertainty principle is neither a theorem of matrix mechanics nor a primitive property of nature, but a product of a Tier-3 translation. The present paper asks a different and limited question: when, by whose hands, and through which channels did that product acquire the rank of a principle? Its historical claims rest on the record alone. The original form of 1925 broke with the analytic description of mechanics at the level of quantities and their rule of multiplication, but borrowed its procedure, its characteristic relation, and its model systems from classical analytic mechanics, and was thereby carried back into the description it had left. The paper of 1927 reverses the direction of the 1925 programme: it re-establishes kinematic concepts, with materials from classical optics and kinematics, in order to make the theory intuitive. The relation was published in that paper together with an addendum that placed it under Bohr’s forthcoming framework of complementarity; the exact inequality now taught under Heisenberg’s name is due to Kennard and was adopted by Heisenberg only in 1930; the name “principle” was conferred by other authors in 1928–1929 and does not appear in the German original of Heisenberg’s own 1930 lectures; and the label “Copenhagen interpretation” dates from 1955. We then compare the uncertainty relation and its thought experiment with relativity and the equivalence principle, and its hidden premises with the explicit hypotheses of Gödel’s theorem, and we record that present-day interpretations of quantum mechanics, though divided, are formulated on one formalism. A symbolic reading of the story, offered as illustration and not as evidence, is confined to a single section. Appendix C expresses the result in the vocabulary of Operatiology V5. Version 2: Section 8 (the symbolic reading) was minimally revised to prevent misreading of the arrangement of the persons in the story, and a revision history was added as an appendix; all other content is unchanged.
oday the so-called Copenhagen Interpretation of quantum mechanics dominated description of the physical world still denies the possibility to assign exact simultaneous values to (all) physical quantities. A prime example is claimed to be the fundamental and universal relationship between position and momentum of a particle. According to Heisenberg's quantum mechanical uncertainty principle for position and momentum, the more precisely the momentum (position) of a particle is given, the less precisely can one say what its position (momentum) is and vice versa.\nThe purpose of this publication is to provide a mathematical proof that Heisenberg's uncertainty principle for position and momentum is refuted under any circumstances. As we shall see, accept Heisenberg's uncertainty principle as valid then you must accept too that +0 = +1, which is a logical contradiction. Thus far, it is possible to derive a logical contradiction out of Heisenberg's uncertainty principle. Heisenberg's uncertainty principle is refuted.