Abstract This chapter focuses on Paul Dirac’s introduction of a verbally explicit description of scattering in terms of two successive emission and absorption processes, each coupled to a transition of the atom, not obeying energy conservation and located on the level of probability amplitudes. Historical actors called these energy non-conserving transitions “virtual transition” later on. I will contextualize Dirac’s introduction of this verbal model in reference to his research at the time, his interpretation of quantum theory and his rather pragmatic to flexible approach to mostly philosophical aspects of the interpretation of quantum theory. According to my argument, one of the most important reasons for Dirac to come up with this description was its usefulness in the practice of theory. A comparison between Dirac’s concepts and the concepts of the old quantum theory shows that neither the “intermediate states” of the light quantum point of view nor the “virtual” entities of the BKS theory had an important influence on Dirac.
Abstract This chapter focuses on Paul Dirac’s introduction of a verbally explicit description of scattering in terms of two successive emission and absorption processes, each coupled to a transition of the atom, not obeying energy conservation and located on the level of probability amplitudes. Historical actors called these energy non-conserving transitions “virtual transition” later on. I will contextualize Dirac’s introduction of this verbal model in reference to his research at the time, his interpretation of quantum theory and his rather pragmatic to flexible approach to mostly philosophical aspects of the interpretation of quantum theory. According to my argument, one of the most important reasons for Dirac to come up with this description was its usefulness in the practice of theory. A comparison between Dirac’s concepts and the concepts of the old quantum theory shows that neither the “intermediate states” of the light quantum point of view nor the “virtual” entities of the BKS theory had an important influence on Dirac.
Abstract Prior to the development of matrix and wave mechanics, virtual entities figured prominently in the so-called BKS theory. According to some historians, the virtual oscillators of the BKS theory and their mathematical representations are directly connected to the concepts of virtual transitions/states. I will analyse the meaning of the term “virtual” in BKS, discuss the theory’s most important conceptual building blocks and its impact on dispersion theoretic accounts, most importantly the Kramers-Heisenberg paper of 1925. Then I will turn to a development that has nearly faded from sight: Shortly before the development of quantum mechanics, but from a light quantum point of view, physicists developed the idea that scattering and dispersion is composed of successive emission and absorption processes through “intermediate states”. The discussion of both of these strands, BKS and the light-quantum viewpoint, will serve as basis for the further development and for an important question to be answered in the following: Was there a generative connection between virtual oscillators and what came to be known as virtual transitions?
The relationship between physical notions and the structures expressing them is an issue of primary importance the history and philosophy of pre-modern natural philosophy and of modern science. Historical evidence suggests that, when investigating the relationship between physics and mathematics, one should pay attention to the material, sensually perceivable forms mediating it: spoken or written words, drawings, artefacts, descriptions of experimental set-ups or, as the case discussed the present paper, symbolic notation. The reason for this is that, historically, physical notions and their expressions have very often been developed as one, and only distinguished from each other at a later stage. This was for example the case with what we today regard as mathematical and classical mechanics, which were developed the course of the eighteenth century as the discipline of the analysis of motion. When considered from a later point of view, both the physical notions and the concepts involved historical developments appear as being in flux, vague, and, as far as the side is concerned, non-rigorous. In such cases, verbal description, mechanical artefacts or symbols do not simply mediate between physical notions and structures, as might be the case at a later stage, but represent both of them one, allowing the historical actors to construct and manipulate physical-mathematical meaning by following, at times, their physical reasoning and, at times, their criteria of rigour. The history of quantum mechanics offers many examples of how new physics and new mathematics can emerge as one, with symbolic notation playing a central role shaping both. Among the many creators of quantum theory, Paul Dirac was particularly sensitive to questions of notation:
The first objective of this chapter is to briefly review some of the basic ideas about the structure of matter, in particular the concepts of microscopic physics, in order to recall the knowledge gained in previous physics (and chemistry) courses and make it more precise. Our review will be very concise, and most statements will be made without any proof or detailed discussion. A second objective is to give a brief description of some of the crucial stages in the early development of quantum physics. We shall not follow the strict historical order of this development or present the arguments used at the beginning of the last century by the founding fathers of quantum mechanics; rather, we shall stress the concepts which we shall find useful later on. Our last objective is to give an elementary introduction to some of the basic ideas, like those of a quantum particle or energy level, that will reappear throughout this text. We shall base our review on the Bohr theory, which provides a simple, though far from convincing, explanation of how energy levels are quantized and how the spectrum of the hydrogen atom arises. This chapter should be reread later on, once the basic ideas of quantum mechanics have been made explicit and illustrated by examples. From the practical point of view, it is possible to skip the general considerations of Sections 1.1 and 1.2 at the first reading and begin with Section 1.3, returning to those two sections later on as needed.
Abstract This chapter gives an overview of the theory of optical absorption and emission in atoms at the level appropriate to introductory quantum and atomic-physics texts. The aim is to provide an introduction to the more advanced treatment of these topics given later in the book, especially in Chapters 9 and 10. It is assumed that the reader is reasonably familiar with the concepts, and so the material is only developed in summary form. Readers who are less well acquainted with these topics may find it helpful to refer to the bibliography for further details.
[This paper is part of the Focused Collection in Investigating and Improving Quantum Education through Research.] Evidence from physics education research suggests that the introduction of a formalistic description of quantum phenomena can be beneficial to student learning, particularly in terms of helping students move away from naive realist views of quanta or space-time descriptions of quantum phenomena. However, the mathematical requirements for mastering quantum formalism are typically far beyond the scope of secondary school education. Therefore, in previous research, we have proposed a reduced Dirac notation tailored to the capabilities of secondary school students, which is included in a novel teaching-learning sequence. However, the cognitive processes of students when confronted with an introduction to quantum physics via a reduced Dirac notation have not been thoroughly investigated: In particular, it seems important to investigate whether this approach is actually beneficial to students’ learning and to explore the learning difficulties students are likely to encounter in such a setting. This paper contributes to this research gap by reporting the findings of an acceptance survey: N = 14 learners participated in one-on-one interviews following a protocol consisting of four cyclical phases (information phase, acceptance evaluation, paraphrasing phase, and application phase). The findings of our study indicate that the instructional elements within our new teaching-learning sequence were generally well accepted by students but also revealed learning difficulties that students may encounter. Thus, on the one hand, the findings of this study pave the way for future research on students’ learning of quantum physics using Dirac notation. On the other hand, the in-depth findings reported here may guide teachers in designing learning environments that introduce Dirac notation at the upper secondary school and introductory university levels. Published by the American Physical Society 2024
This chapter presents the origins of the transformation theory and related concepts. It shows how, in 1925, a procedure initiated by Werner Heisenberg was developed by himself, Max Born, Pascual Jordan, and a little later by Paul Dirac, into a new system of quantum theory—the first complete system of quantum theory which physics has possessed. A little later Erwin Schrödinger developed the “wave mechanics” from an entirely different starting point. This accomplished the same ends, and soon proved to be equivalent to the Heisenberg, Born, Jordan, and Dirac system. On the basis of the Born statistical interpretation of the quantum theoretical description of nature, it was possible for Dirac and Jordan to join the two theories into one, the “transformation theory,” in which they make possible a grasp of physical problems which is especially simple mathematically.