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新量子論.現状と課題

Yoshifumi Ito

Published Dec 24, 2004• 0 citations
OpenAlex

Abstract

Even if there was a pioneering work [1], it becomes about 11 years since we really began to investigate the new quantum theory. Thus, in this article, we wish to summarize the research of the new quantum theory in these 11 years. In the section 1, we give a more clear and evident formulation of Ito [2], [3]. In the section 2, we give a more precise representation of Ito-Kayama [6], [7]. In the section 3, we summarize the papers [8], [9], [10]. In the section 4, we mention the philosophical consideration of the new quantum theory. In the section 5, we mention several problems of the new quantum theory.

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Even if there was a pioneering work [1], it becomes about 11 years since we really began to investigate the new quantum theory. Thus, in this article, we wish to summarize the research of the new quantum theory in these 11 years. In the section 1, we give a more clear and evident formulation of Ito [2], [3]. In the section 2, we give a more precise representation of Ito-Kayama [6], [7]. In the section 3, we summarize the papers [8], [9], [10]. In the section 4, we mention the philosophical consideration of the new quantum theory. In the section 5, we mention several problems of the new quantum theory.
Abstract The modern version of quantum theory—now known as “quantum mechanics”— was born and grew to maturity in just five years, between 1925 and 1930. More was accomplished during those five years than in the preceding twenty-five years, or, for that matter, in the seventy years that have followed. Progress before 1925 was constantly hampered by conceptual doubts. Paradoxes such as the wave-particle duality—the contradiction between the Einstein particle theory of light and the classical wave theory—were disturbing and limiting. But by 1925 these difficulties had, perhaps from familiarity, become less inhibiting. Theorists stopped worrying about the conceptual strangeness of the quantum realm, and began to make a new physics with the strangeness incorporated in it. Once the conceptual barriers were passed, progress was astonishingly rapid. For those who had the vision, it was as if a great fog had lifted. Suddenly it was possible to see in many directions with a clarity no one could have anticipated.
The history of the quantum theory has received rather uneven treatment from professional historians of science. There has been a great deal of emphasis on the early period from 1900 to 1926, during which time the classic formulations of the so-called old and new quantum theories were laid down. But there have been many important subsequent improvements in the underlying theory, its applications and interpretation. The present article attempts a more balanced perspective on the whole theory from the initial inception to its ongoing development. The subject is necessarily a technical and mathematical one, and no account, worthy of any pretensions to accuracy, can avoid reference to some technical matters. An attempt has been made to keep these to a minimum, but it is not entirely possible to eliminate them. This probably helps to explain why the more recent history has largely been dealt with by practising physicists, rather than by historians.
Some observations are presented on the well-known article by Vladimir Fock, "Quantum Physics and Philosophical Problems," published in 1971. In this article, which crowns and summarizes for Western readers a long and complicated reflection on the foundations of quantum mechanics (QM), Fock illustrates his "minimal" interpretation of this theory. By minimal we mean that it only uses concepts related to the operational aspects of the measurement procedures, avoiding any mention to definite quantum onthologies (Bell's beables). It is argued that, by taking into account the time reversal invariance of the microscopic processes and introducing the notion of irreversibility in an appropriate manner, Fock's description becomes an anticipation of the "transaction" notion introduced by Cramer a decade later.
Some observations are presented starting with the well-known article by Vladimir Fock “Quantum Physics and Philosophical Problems”, published in 1971. In this article, which summarizes for Western readers a long and complicated reflection of the foundations of quantum mechanics (QM), Fock illustrates his “minimal” interpretation of this theory. By minimal, we mean that it only uses concepts related to the operational aspects of the measurement procedures, avoiding any mention of definite quantum ontologies (Bell’s beables). It is argued that, by taking into account the time reversal invariance of the microscopic processes and introducing the notion of irreversibility in an appropriate manner, Fock’s description becomes an anticipation of the “transaction” notion introduced by Cramer a decade later. So, the concept of “collapse” does retain the features of a QM “freak” postulate to become a new way to look at the elementary quantum processes.
Now that we have reached the end of our brief tour through the early history of quantum theory, we need to stop and consider some important themes. From a historical point of view, a distinction can be drawn between ‘old quantum theory’ and the full quantum theory that we now use. Old quantum theory was in essence a patchwork cobbled together from classical physics with a few quantum ideas thrown in. e works of Planck, Einstein, Bohr, and Sommerfeld can be classed as old quantum theory. is is not meant to undermine the tremendous achievements that old quantum theory represents, but simply to underline its standing as a stage on the way to a fully formed quantum theory, which slowly emerged from the works of Heisenberg, Schrödinger, Born, and Dirac.
In this note, we present a table with a summary of recent developments in quantum mechanics. If you not have studied our papers carefully already [1–4], then this paper will not make much sense and the equations could easily be misunderstood, so we strongly encourage the reader to become familiar with this material first. We will possibly write a long paper on this topic later, but it may be helpful to present the essence of both old and new QM, as we understand it today. This is useful for both tracing the history of ideas related to QM in mathematical form and for creating an opportunity to compare equations and analyze their similarities and differences.