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On the Nature of the Change in the Wave Function in a Measurement in Quantum Mechanics

Douglas Michael Snyder

Published Oct 26, 2020• 8 citations
Publisher

Abstract

Generally a central role has been assigned to an unavoidable physical interaction between the measuring instrument and the physical entity measured in the change in the wave function that often occurs in measurement in quantum mechanics. A survey of textbooks on quantum mechanics by authors such as Dicke and Witke (1960), Eisberg and Resnick (1985), Gasiorowicz (1974), Goswami (1992), and Liboff (1993) supports this point. Furthermore, in line with the view of Bohr and Feynman, generally the unavoidable interaction between a measuring instrument and the physical entity measured is considered responsible for the uncertainty principle. A gedankenexperiment using Feynman's double-hole interference scenario shows that physical interaction is not necessary to effect the change in the wave function that occurs in measurement in quantum mechanics. Instead, the general case is that knowledge is linked to the change in the wave function, not a physical interaction between the physical existent measured and the measuring instrument. Empirical work on electron shelving that involves null measurements, or what Renninger called negative observations (Zeitschrift fur Physik, vol. 158, p. 417), supports these points. Work on electron shelving is reported by Dehmelt and his colleagues (Physical Review Letters, vol. 56, p. 2797), Wineland and his colleagues (Physical Review Letters, vol. 57, p. 1699), and Sauter, Neuhauser, Blatt, and Toschek (Physical Review Letters, vol. 57, p. 1696). Originally appeared in arXiv on December 19, 1995. It can be accessed at arXiv:quant-ph/9601006 .

DOI
10.31234/osf.io/j63pn

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On the Nature of the Change in the Wave Function in a Measurement in Quantum Mechanics

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Generally a central role has been assigned to an unavoidable physical interaction between the measuring instrument and the physical entity measured in the change in the wave function that often occurs in measurement in quantum mechanics. A survey of textbooks on quantum mechanics by authors such as Dicke and Witke (1960), Eisberg and Resnick (1985), Gasiorowicz (1974), Goswami (1992), and Liboff (1993) supports this point. Furthermore, in line with the view of Bohr and Feynman, generally the unavoidable interaction between a measuring instrument and the physical entity measured is considered responsible for the uncertainty principle. A gedankenexperiment using Feynman's double-hole interference scenario shows that physical interaction is not necessary to effect the change in the wave function that occurs in measurement in quantum mechanics. Instead, the general case is that knowledge is linked to the change in the wave function, not a physical interaction between the physical existent measured and the measuring instrument. Empirical work on electron shelving that involves null measurements, or what Renninger called negative observations (Zeitschrift fur Physik, vol. 158, p. 417), supports these points. Work on electron shelving is reported by Dehmelt and his colleagues (Physical Review Letters, vol. 56, p. 2797), Wineland and his colleagues (Physical Review Letters, vol. 57, p. 1699), and Sauter, Neuhauser, Blatt, and Toschek (Physical Review Letters, vol. 57, p. 1696).

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Generally a central role has been assigned to an unavoidable physical interaction between the measuring instrument and the physical entity measured in the change in the wave function that often occurs in measurement in quantum mechanics. A survey of textbooks on quantum mechanics by authors such as Dicke and Witke (1960), Eisberg and Resnick (1985), Gasiorowicz (1974), Goswami (1992), and Liboff (1993) supports this point. Furthermore, in line with the view of Bohr and Feynman, generally the unavoidable interaction between a measuring instrument and the physical entity measured is considered responsible for the uncertainty principle. A gedankenexperiment using Feynman's double-hole interference scenario shows that physical interaction is not necessary to effect the change in the wave function that occurs in measurement in quantum mechanics. Instead, the general case is that knowledge is linked to the change in the wave function, not a physical interaction between the physical existent measured and the measuring instrument. Empirical work on electron shelving that involves null measurements, or what Renninger called negative observations (Zeitschrift fur Physik, vol. 158, p. 417), supports these points. Work on electron shelving is reported by Dehmelt and his colleagues (Physical Review Letters, vol. 56, p. 2797), Wineland and his colleagues (Physical Review Letters, vol. 57, p. 1699), and Sauter, Neuhauser, Blatt, and Toschek (Physical Review Letters, vol. 57, p. 1696). Originally appeared in arXiv on December 19, 1995. It can be accessed at arXiv:quant-ph/9601006 .
Generally a central role has been assigned to an unavoidable physical interaction between the measuring instrument and the physical entity measured in the change in the wave function that often occurs in measurement in quantum mechanics. A survey of textbooks on quantum mechanics by authors such as Dicke and Witke (1960), Eisberg and Resnick (1985), Gasiorowicz (1974), Goswami (1992), and Liboff (1993) supports this point. Furthermore, in line with the view of Bohr and Feynman, generally the unavoidable interaction between a measuring instrument and the physical entity measured is considered responsible for the uncertainty principle. A gedankenexperiment using Feynman's double-hole interference scenario shows that physical interaction is not necessary to effect the change in the wave function that occurs in measurement in quantum mechanics. Instead, the general case is that knowledge is linked to the change in the wave function, not a physical interaction between the physical existent measured and the measuring instrument. Empirical work on electron shelving that involves null measurements, or what Renninger called negative observations (Zeitschrift fur Physik, vol. 158, p. 417), supports these points. Work on electron shelving is reported by Dehmelt and his colleagues (Physical Review Letters, vol. 56, p. 2797), Wineland and his colleagues (Physical Review Letters, vol. 57, p. 1699), and Sauter, Neuhauser, Blatt, and Toschek (Physical Review Letters, vol. 57, p. 1696).
In the well known Copenhagen interpretation of Quantum mechanics, advocated by N. Bohr, the physical objects and the experimental results can be described only in a macroscopic language, leaving any possible microscopic description as unspeakable. This point of view has been deepened by C. Rovelli in the relational interpretation of Quantum mechanics. Most of the alternative interpretations, which try a detailed microscopic description of physical phenomena and of their evolution, have in common the explicit introduction of the wave function as the basic element of the theory. These interpretations require the notion of quantum state as the fundamental concept of the theory, which is the typical unspeakable physical element according to the Copenhagen interpretation. The two basic physical entities are intimately bound together by the integrity of the wave function. These interpretations are usually indicated as realistic. It is well known that the use of the wave function and its time evolution in the description of the physical processes leads unavoidably to some difficulties or so-called paradoxes. The measurement problem is at the center of these difficulties, mainly because it requires the introduction of the reduction process of the wave function, which is not included explicitly within the mathematical formalism of Quantum Mechanics. In this paper we build up and propose a model which goes beyond the standard formalism and which is able to solve the measurement problem and all the other difficulties which, in a way or in another, are related to it.
Introduction It is not exaggeration to claim that one of the major divides in the foundations of non-relativistic quantum mechanics derives from the way physicists and philosophers understand the status of the wave function. On the instrumentalist side of the camp, the wave function is regarded as a mere instrument to calculate probabilities that have been established by previous measurement outcomes. On the other “realistic” camp, the wave function is regarded as a new physical entity or a physical field of some sort. While both sides agree about the existence of quantum “particles” (the so-called theoretical entities), and therefore reject the radical agnosticism about them preached by van Fraassen (1980), the various “realistic” (and consequently, instrumentalist) philosophies of quantum mechanics are typically formulated in different, logically independent ways, so their implications need to be further investigated. For instance, on the one hand it seems plausible to claim that a realistic stance about the wave function is not the only way to defend “realism” about quantum theory. One can support a “flash” or a “density-of-stuff ” ontology (two variants of GRW), or an ontology of particles with well-defined positions (as in Bohmian mechanics), as primitive ontologies for observer-independent formulations of quantum mechanics (Allori, Goldstein, Tumulka and Zanghí, 2008). “Primitive ontologies”, as here are understood, are not only a fundamental ground for other ontological posits, but also entail a commitment to something concretely existing in spacetime (see also Allori, 2013). On the other hand, however, it is still debated whether such primitive ontologies can be autonomous from some form of realism about the wave function (Albert, 1996). In order to discuss this problem, we begin with a preliminary clarification of the meaning of “realism” and “instrumentalism” in physics, which are often subject to ideological and abstract discussions that often have little to do with the practice of physics (Section 9.2).
This report investigates the flawed foundations of standard quantum theory based on a misunderstanding of the role of measurement. The report is major part of a research programme (UET) based on a new theory of the electromagnetism (EM), centered exclusively on the interaction between electrons. All the previous papers to date in this series have presented a realistic view of the dynamics of two or more electrons as they interact only between themselves. This paper now posits a theory of how this microscopic activity is perceived by human beings in attempting to extract information about atomic systems. The standard theory of quantum mechanics (QM) is constructed on only how the micro-world appears to macro measurements - as such, it cannot offer any view of how the foundations of the world are acting when humans are not observing it (the vast majority of the time) - this has generated almost 100 years of confusion and contradiction at the very heart of physics. All human beings (and all our instruments) are vast collections of electrons, our information about atomic-scale can only be obtained destructively and statistically. This theory now extends the realistic model of digital electrons by adding an explicit measurement model of how our macro instruments interfere with nature's micro-systems when such attempts result in human-scale information. The focus here is on the connection between the micro-world (when left to itself) and our mental models of this sphere of material reality, via the mechanism of atomic measurements. The mathematics of quantum mechanics reflects the eigenvalues of the combined target system plus equipment used for measurement together. Therefore, QM has constructed a theory that inseparably conflates the ontological and epistemological views of nature. This standard approach fails to examine isolated target systems alone. It is metaphysically deficient. This investigation concludes that the Quantum State function (Ψ) is not a representation of physical reality, within a single atom, but a generator function for producing the average statistical results on many atoms of this type. In contrast, the present theory builds on the physical reality of micro-states of single atoms, where (in the case of hydrogen), a single electron executes a series of fixed segments (corresponding to the micro-states) across the atom between a finite number of discrete interactions between the electron and one of the positrons in the nucleus. The set of serial segments form closed trajectories with real temporal periods, contra to Heisenberg’s ‘papal’ decree banning such reality because of his need to measure position and momentum at all times. This is the first paper in the multi-paper series (UET7n), which is dedicated to analyzing, criticizing and replacing existing theories of quantum mechanics.
Quantum mechanics describes physical systems through probabilistic wave functions, accounting for phenomena such as wave–particle duality and the uncertainty principle. Although the mathematical formalism of quantum mechanics is well established, conceptual understanding of how quantum entities transition between wave-like and particle-like behavior remains an active area of research. In this work, quantum mechanical principles are re-examined from an interaction-based perspective, emphasizing the roles of environmental coupling, measurement geometry, and energy exchange. Using the photoelectric effect, de Broglie relations, and Heisenberg’s uncertainty principle as foundational elements, a conceptual framework is proposed in which particle identity emerges dynamically from wave interaction with matter and measurement constraints. This interpretation provides an intuitive bridge between classical reasoning and quantum behavior while fully preserving the standard mathematical structure of quantum mechanics...........Please check the attachment for details