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Which Version of Quantum Mechanics is the Right One

Jiří Souček

Published May 1, 2015• 1 citation
OpenAlex

Abstract

In this article we consider four versions of quantum mechanics (QM), which form four different theories and which have the same experimental consequences (one of them is the standard QM). We consider six fundamental problems as criteria for the evaluation of these theories. The most successful is the modified QM introduced in [1] and described in the axiomatic form in [2], which solves all six problems. The least successful is the standard QM, which does not solve any of considered problems. (It seems that the standard QM is unable to solve any of these problems.) Other two theories solve some of problems and did not solve some other problems. On the base of this result we recommend to abandon the standard QM and to accept the modified QM as the right QM, since both variants have the same experimental content and the differences rest only in theoretical considerations.

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•Jan 1, 1998•0 citations
In this article we consider four versions of quantum mechanics (QM), which form four different theories and which have the same experimental consequences (one of them is the standard QM). We consider six fundamental problems as criteria for the evaluation of these theories. The most successful is the modified QM introduced in [1] and described in the axiomatic form in [2], which solves all six problems. The least successful is the standard QM, which does not solve any of considered problems. (It seems that the standard QM is unable to solve any of these problems.) Other two theories solve some of problems and did not solve some other problems. On the base of this result we recommend to abandon the standard QM and to accept the modified QM as the right QM, since both variants have the same experimental content and the differences rest only in theoretical considerations.
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.
Abstract Over a dozen constructions have been proposed to untangle the foundations of quantum mechanics (QM). The authors have spent a lot of energy in establishing formal solutions but, to the best of my knowledge, have not carefully examined the methodological problems that arise before beginning a theoretical construct in QM. This paper argues on the following methodological obstacles: 1. The definitional and computational formulas. 2. The different theories of probability. We have also tried to solve problems 1 and 2, but the complete illustration of this attempt exceeds an article’s length, so this paper is limited to presenting 1 and 2, and discussing the intellectual and formal assumptions that should be necessary to unify the theories of probability.
In July 1925, exactly one century ago, Werner Heisenberg created Quantum Mechanics (QM) as an invariant-operational formalism by taking as a standpoint the intensive patterns that had been already observed by experimentalists in the lab. One of the few drawbacks of this proposal was the impossibility to conceptualize it in classical terms. Attempting to restore a somewhat classical spatiotemporal representation, six months later, Erwin Schrödinger would present a formalism grounded on a wave equation in configuration space. Taking as a standpoint Schrödinger’s wave mechanics together with the methodological guide of Bohr and logical positivists, Dirac would present in 1930 an axiomatic re-formulation of the theory of quanta that would become known as the “standard” version of QM (SQM). This new version of the theory, that is still today taught in physics classrooms all around the world, would become accepted regardless of its inconsistent narrative as a “recipe” intended (but unable) to predict (binary) measurement outcomes. After pointing out some of the many problems of SQM, in this work we propose to go back to Heisenberg’s matrix mechanics (and also to his understanding of physical theories). We will argue that his matrix mechanics, as an operationally-invariant standpoint, opens the door to a tensorial enlargement of the mathematical formalism capable to account for new phenomena.
Quantum mechanics, one of the most successful theories in the history of science, was created to account for physical systems not describable by classical physics. Though it is consistent with all experiments conducted thus far, many of its core concepts (amplitudes, global phases, etc.) can not be directly accessed and its interpretation is still the subject of intense debate, more than 100 years since it was introduced. So, a fundamental question is why this particular mathematical model is the one that nature chooses, if indeed it is the correct model. In the past two decades there has been a renewed effort to determine what physical or informational principles define quantum mechanics. In this paper, recent attempts at establishing reasonable physical principles are reviewed and their degree of success is tabulated. An alternative approach using joint quasi-probability distributions is shown to provide a common basis of representing most of the proposed principles. It is argued that having a common representation of the principles can provide intuition and guidance to relate current principles or advance new principles. The current state of affairs, along with some alternative views are discussed.
From the dichotomy nonlocality vs which is the consequence of Bell Inequalities (BI) we shall choose the non-realism. We shall present here the modified Quantum Mechanics (modQM) in the axiomatic form. ModQM was introduced in [5] and we shall show its non-realism in the description of an internal measurement process. ModQM allows the restoration of locality, since BI cannot be derived in it. In modQM it is possible to solve: the measurement problem, the collapse problem, the problem of a local model for EPR correlations (see[5]). ModQM is a unique explicit realization of non-realism in QM. ModQM should be preferred as an alternative to the standard QM mainly since it restores the locality.
We discuss the axiomatic basis of quantum mechanics and show that it is neither general nor consistent, since its axioms are incompatible with each other and moreover it does not incorporate the magnetic quantization as in the cyclotron motion. A general and consistent system of axioms is conjectured which incorporates also the magnetic quantization. 1 The neccessity of quantum mechanics (QM) was a result of experimental data for the energy spectrum of atoms which could not be explained in accord with the laws of classical mechanics. Nevertheless in the axiomatic basis of QM there are axioms which are not supported by the experimental results, since the whole system of axioms (1) is introduced only as a ”plausible generalization ” of the first axiom [1]: