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arXiv:quant-ph/0210050

Can Quantum Mechanics be Cleared from Conceptual Difficulties?

Volodymyr Krasnoholovets

Published Oct 8, 2002• 1 citation
arXivHTMLPDF

Abstract

The major conceptual difficulties of quantum mechanics are analyzed. They are: the notion "wave-particle", the probabilistic interpretation of the Schroedinger wave ψ-function and hence the probability amplitude and its phase, long-range action, Heisenberg's uncertainty principle, etc. The probabilistic formalism is developed in the phase space, but not in the real one. Elimination of the difficulties is likely if we are able to develop quantum mechanics in the real space. Such a theory in fact can be constructed, however, it should proceed from deepest first principles starting from the notion of a 4D space-time, the notion of a massive particle in the space, the principles of the motion of a particle, etc. The theory should be characterized by short-range action that automatically means the introduction of a quantum mechanical force. It is shown that the aforementioned force makes it evident and, moreover, is able to appear on the macroscopic scale. A simple experiment, the express test, which in fact proves the macroscopic manifestation of quantum mechanical force, is proposed for the demonstration in the quantum curriculum.

DOI
10.48550/arxiv.quant-ph/0210050

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The major conceptual difficulties of quantum mechanics are analyzed. They are: the notion "wave-particle", the probabilistic interpretation of the Schroedinger wave ψ-function and hence the probability amplitude and its phase, long-range action, Heisenberg's uncertainty principle, etc. The probabilistic formalism is developed in the phase space, but not in the real one. Elimination of the difficulties is likely if we are able to develop quantum mechanics in the real space. Such a theory in fact can be constructed, however, it should proceed from deepest first principles starting from the notion of a 4D space-time, the notion of a massive particle in the space, the principles of the motion of a particle, etc. The theory should be characterized by short-range action that automatically means the introduction of a quantum mechanical force. It is shown that the aforementioned force makes it evident and, moreover, is able to appear on the macroscopic scale. A simple experiment, the express test, which in fact proves the macroscopic manifestation of quantum mechanical force, is proposed for the demonstration in the quantum curriculum.
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Still today the discussion about the foundations, physical interpretation, and real scope of quantum mechanics has never ceased. It would be wrong to dismiss these issues as mere philosophical problems, because questions of consistency and interpretation are not devoid of practical utility. We present the foundations and main properties of a positive definite phase space quantum mechanics. A new quantization procedure is proposed as well. This new interpretation/formulation eliminates conceptual and technical difficulties from quantum mechanics: (i) many paradoxes typical of the wave-particle duality, EPR experiments, macroscopic superpositions, and collapse of wavefunctions disappear; (ii) the elimination of the wavefunctions from quantum theory is in line with the procedure inaugurated by Einstein with the elimination of the ether in the theory of electromagnetism; (iii) it is useful in considering the classical limit, can treat mixed states with ease, and brings certain conceptual issues to the fore; (iv) confirms the ensemble interpretation of the wavefunctions, derives its statistical interpretation, corrects the temporal dependence of the old wavefunctions, and considers pure classical states --localizable states-- beyond the Hilbert space; (v) the quantum equation of motion is of the Liouville kind and star-products are not needed, simplifying the formalism; and (vi) eliminates the hypothetical external quantum field of the pilot wave interpretation, solving its problems on the status of probability, and correcting well-known inconsistencies of the Bohm potential. Finally, we offer some perspectives on future developments and research in progress.
I consider in this book a formulation of Quantum Mechanics. Usually QM is formulated based on the notion of time and space, both of which are thought a priori given quantities or notions. However, when we try to define the notion of velocity or momentum, we encounter a difficulty as we will see in chapter 1. The problem is that if the notion of time is given a priori, the velocity is definitely determined when given a position, which contradicts the uncertainty principle of Heisenberg. We then set the basis of QM on the notion of position and momentum operators as in chapter 2. Time of a local system then is defined approximately as a ratio ∣x∣/∣v∣|x|/|v|∣x∣/∣v∣ between the space coordinate xxx and the velocity vvv. In this formulation of QM, we can keep the uncertainty principle, and time is a quantity that does not have precise values unlike the usually supposed notion of time has. The feature of local time is that it is a time proper to each local system, which is defined as a finite set of quantum mechanical particles. We now have an infinite number of local times that are unique and proper to each local system. Based on the notion of local time, the motion inside a local system is described by the usual Schrodinger equation. We investigate such motion in a given local system in part II. This is a usual quantum mechanics. After some excursion of the investigation of local motion, we consider in part III the relative relation or motion between plural local systems. In the final part IV, we will prove that there is at least one Universe wave function ϕ\phiϕ in which all local systems have local motions and thus local times. This concludes our formulation of Quantum Mechanics.
I consider in this book a formulation of Quantum Mechanics. Usually QM is formulated based on the notion of time and space, both of which are thought a priori given quantities or notions. However, when we try to define the notion of velocity or momentum, we encounter a difficulty as we will see in chapter 1. The problem is that if the notion of time is given a priori, the velocity is definitely determined when given a position, which contradicts the uncertainty principle of Heisenberg. We then set the basis of QM on the notion of position and momentum operators as in chapter 2. Time of a local system then is defined approximately as a ratio ∣x∣/∣v∣|x|/|v|∣x∣/∣v∣ between the space coordinate xxx and the velocity vvv. In this formulation of QM, we can keep the uncertainty principle, and time is a quantity that does not have precise values unlike the usually supposed notion of time has. The feature of local time is that it is a time proper to each local system, which is defined as a finite set of quantum mechanical particles. We now have an infinite number of local times that are unique and proper to each local system. Based on the notion of local time, the motion inside a local system is described by the usual Schrödinger equation. We investigate such motion in a given local system in part II. This is a usual quantum mechanics. After some excursion of the investigation of local motion, we consider in part III the relative relation or motion between plural local systems. In the final part IV, we will prove that there is at least one Universe wave function ϕϕϕ in which all local systems have local motions and thus local times. This concludes our formulation of Quantum Mechanics.
The previous chapters contain many examples of the successful application of quantum mechanics to the solution of real physical problems. These represent only a small sample of the wide range of experimental results, spanning just about all areas of physics and chemistry and beyond, that have been successfully explained by quantum theory. So far at least, no quantum-mechanical prediction has been experimentally falsified. Despite these successes, however, many scientists have considered the basic conceptual framework of the subject to be unsatisfactory, and repeated attempts have been made to reinterpret quantum mechanics, or even replace it with a different theory whose philosophical and conceptual basis could be considered more acceptable. In the present chapter we shall explain the reasons for this dissatisfaction and outline some of the reinterpretations and alternative approaches that have been devised. Inevitably many of the questions that arise in this area are matters of opinion rather than fact and, for this reason, some physicists consider that they belong more properly to the realm of philosophy than of physics. However, the conceptual basis of quantum mechanics is so fundamental to our whole understanding of the nature of the physical universe that it should surely be important for physicists to understand the nature of the problems involved, if nothing else.1,2 16.1 THE CONCEPTUAL PROBLEMS In this section we outline some of the main areas of difficulty with a view to more detailed discussion later in the chapter.