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CRC Press eBooks

1 On the Interpretation of Quantum Mechanics

L.D. Faddeev, L.A. Khalfin, I.V. Komarov

Published May 21, 2004• 0 citations
Publisher

Abstract

The modern physics is characterized by deeper and deeper penetration into the laws of the world of atoms and other minute particles of matter. These laws require not only new experimental techniques to be developed, but also new notions to formulate them. To describe atomic phenomena new methods that are completely different from those used to investigate larger objects of our world are required. The new problem of description of atomic objects is of particular practical importance since the arising notions could be applied to other fields of knowledge. Therefore on the ground of the modern physics some questions of the philosophical character arise. We are going to consider them here.

DOI
10.1201/9780203643204-43

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The modern physics is characterized by deeper and deeper penetration into the laws of the world of atoms and other minute particles of matter. These laws require not only new experimental techniques to be developed, but also new notions to formulate them. To describe atomic phenomena new methods that are completely different from those used to investigate larger objects of our world are required. The new problem of description of atomic objects is of particular practical importance since the arising notions could be applied to other fields of knowledge. Therefore on the ground of the modern physics some questions of the philosophical character arise. We are going to consider them here.
The subject of my talk is the relations between the mathematical theory of extremal problems and the physical theory of quanta.1 The theory of quanta, or quantum mechanics, studies phenomena in the world of bodies of atomic scale. It turned out that the usual notions of motion and the usual methods of description of a mechanical system were inapplicable for such bodies. One needed to find another formulation of the basic laws of nature instead of the old one based on observations of bodies containing a very large number of atoms. The drastic revision of all usual notions of mathematics and physics was required. As a result of this revision and due to the efforts of several scientists such formulation has been found and the theory, which is as elegant and complete as the Newton mechanics is, has been created. This new theory — the new quantum mechanics — contains the Newton mechanics as a limiting case. Although some particular questions and problems remain open, the basic principles and the mathematical technique of the new theory can be considered to be completely established.
Niels Bohr himself pointed out to similarity of some philosophic approaches in quantum mechanics and in Buddhism. Some modern interpretations of quantum mechanics go even closer to the Buddhist approach, such as Everett interpretation and, specifically, the recent 'Extended Everett Concept' developed by M.B. Mensky. The present paper shows that both Buddhist thinkers and modern physicists, using very different methods, arrived basically at the same description of reality we live in. This is the point where the parallel worlds of Buddhism and Physics unexpectedly touched each other, and the deeper meaning of this contact is yet to be appreciated by both parties. NeuroQuantology | March 2013 | Volume 11 | Issue 1| Suppl 1 | Page 123-128
The difficulties of the old quantum theory were largely dispelled by the development of quantum mechanics in the 1920s. First Heisenberg (1925) developed the rather abstract matrix mechanics and soon after Schro¨dinger (1926; see also Eckart, 1926) developed the physically more appealing wave mechanics. Subsequently he showed them to be mathematically equivalent. The physicists were greatly relieved; now they had once again a mathematical formalism that enabled the results of experiments to be calculated. It was possible to move forward. It is certainly a very elegant and indeed beautiful formalism, and does enable the results of many physical measurements to be calculated with great accuracy. It is used daily by atomic and nuclear physicists; there is no other way to make calculations. From the earliest days there has been intense debate about the interpretation of quantum mechanics, and it shows no signs of being settled; if anything it is becoming more intense over the years. As Penrose has remarked, no one understands quantum mechanics. Feynman (1967; see also Sykes, 1994) also admitted that ‘nobody understands quantum mechanics’, and Einstein once remarked: ‘I have thought a hundred times as much about the quantum problems as I have about general relativity theory’ (Pais, 1994, p. 57). It should therefore be evident that the most that can be done here is to try to show where the real difficulties lie, and how the failure to recognize that quantum mechanics is an essentially statistical theory has led to a series of confusing quantum paradoxes. It is just these paradoxes that have often been used to support theological speculations. It is useful to ask what ‘understanding quantum mechanics’ actually means. Certainly it means being able to calculate the results of many measurements. The same applies to Newton’s theory of gravitation, which we understand in the sense that we can use it as a basis of calculation, although we do not really understand the gravitational force itself. Very often, especially in modern physics, the mathematical formalism does not give us the sort of intuitive physical feeling for what is going on that we often obtain from classical mechanics. Perhaps we can never achieve more than this for quantum mechanics. In classical mechanics we can assume that a property that is measured objectively exists prior to the interaction of the measuring apparatus with the observed system. Quantum mechanics, however, ‘is incompatible with the proposition that measurement discovers some unknown but pre-existing property’ (Peres, 1997, p. 14). There is an important distinction between mysteries and absurdities. We may be forced to live with mysteries, but there is no reason why we should put up with absurdities such as the wave-particle duality, tunnelling through potential barriers, acausal events and the collapse of the wave function. These are the quantum paradoxes that will be discussed later on. They arise within the Copenhagen interpretation of quantum mechanics and are solved by other interpretations. These alternative interpretations enable us to make conjectures about what is going on, even though we cannot understand it in detail. This is acceptable and a stimulus to further research. It is certainly difficult enough to understand quantum mechanics, but there is no need to try to visualize logical absurdities in the effort to do so. Quantum mechanics is a mathematical formalism that makes it possible to calculate the results of some experiments. Anything more than this, such as questions about the interpretation of what is measured and whether it tells us what is actually going on in the system being studied, belongs to philosophy. Thus we are concerned here with what is essentially a philosophical debate; if it were just a matter of physics the debate would have been settled long ago. One of the difficulties is that it invokes the results of experiments and uses the language of quantum mechanics. Inevitably this language uses philosophical terms and then it is easy to give the impression that the philosophical propositions are in some way entailed by the physical results. These in turn can influence theological thinking. In order to be quite clear which arguments are justified and which are not, it is essential to separate the three levels of discourse: physical, philosophical and theological. Our task is to relate these together, and this immediately raises the traditional problems of the philosophy of science, including the relation of experiment to theory, and of theory to explanation. We begin by discussing experiments, distinguishing between those that are real and those that are imaginary.
What is it about quantum mechanics that continues to make its interpretation so difficult and controversial? It is now more than 70 years after its inception and at least half a century since the verification of its predictions of physical phenomena that range from the motion of electrons in solids to the basic structure and properties of the atomic nucleus. After reading the first half of this book one could be forgiven for believing that it has been just our unwillingness or inability to understand properly what Niels Bohr said from the beginning, and to update these ideas in the light of later experience. The aim of the present book is to do just this: to restate the Copenhagen interpretation and to show us how it has been developed to take modern results and ideas into account.
The quantum mechanics instituted a completely new mathematical language. This change in physics required physicists and philosophers to rethink the concepts by which reality could be represented, since classical notions were limited in the understanding of atomic phenomena. The French philosopher G. Bachelard and the German physicist W. Heisenberg are authors who have discussed the major changes that have occurred in physics and have dealt with the problem of language in quantum mechanics. In this article, the objective is to resort to the arguments of both authors to evidence relations between their ideas about the referred subject. It is noteworthy that Bachelard and Heisenberg criticize the application of the usual language and philosophical concepts of modernity in the new physics, but, through his notion of rupture, the French philosopher proposes that quantum mechanics be restricted to mathematical language. This idea runs counter to Bohr's principle of complementarity, which Heisenberg acknowledges in the understanding of quantum phenomena and an interpretation of quantum physics.