Constructing Quantum Mechanics

Anthony Duncan & Michel Janssen

Reviewed by Jan Faye

Constructing Quantum Mechanics, Volume 1: The Scaffold 1900–1923
Anthony Duncan and Michel Janssen
Oxford: Oxford University Press, 2019, £65.00
ISBN 9780198845478

As a philosopher of science interested in scientific methodology, one can take either a top-down or a bottom-up approach to understanding the development of science. The first approach rests on the assumption that scientists have to follow some logical and methodological standards—for example, falsification—while they produce their discoveries. The second approach relies on the scientific practice as revealed by the history of science. In this case, the philosopher may attempt to isolate the implicit principles that successfully guide the scientific work. Nowadays, most philosophers of science subscribe to the latter approach because they have become more interested in connecting philosophical analyses to the actual research process in order to understand the achievements of science.

The present book, Constructing Quantum Mechanics, may help these philosophers to understand the early quantum theory. It is a masterpiece of scholarship on what happened among the physicists who were preoccupied by the relationship between radiation and matter. It begins with a full presentation of Planck’s derivation of a new law for the spectral distribution of black-body radiation, in which he introduced a hitherto unknown relation containing the constant h. At that time, Planck did not attempt to make any interpretation; this didn’t appear until Einstein re-used h in his postulation of light quanta in order to explain the fluctuation in the black-body radiation at high frequencies and found evidence of these light quanta in the photoelectric effect. The book then moves on to Rutherford and co-workers’ study of the atomic structure and how Bohr’s quantitative model of the atom gradually emerged while he was a post-doctoral researcher with Rutherford in Manchester. The final chapters are dedicated to the guiding principles behind the attempt to extend Bohr’s model to atoms with more than one electron and the successes and failures of this improved model.

Two things stand out from the title of this book. The first is that it is the first of a series (of two books, where the second covers the period between 1923 and late 1927). The second is the use of ‘scaffold’ and ‘constructing’ in the title, which refers to the claim that quantum mechanics is a theoretical construction around the scaffold of classical physics. As the authors write in the preface (p. v):

Our starting point can be compared to that of someone first encountering an arch. This person will wonder how it was built and come to realize that it was done with the help of a scaffold. If we think of quantum mechanics as an arch, we can likewise say that it was put together with the help of a scaffold, provided in this case by elements of the theory it replaced […] Decisions about which strands in the development of quantum mechanics we cover in detail and which ones we treat more cursorily (if at all) were informed by our assessment, in hindsight, of their relative importance for the scaffold on which the arch was erected. However, our analysis of the strands selected for detailed discussion is given entirely in terms of insights and concepts available to the historical actors at the time. To find meaningful historically sensitive answers to our central question, we scrupulously adhered to this methodological principle.

The authors’ historiographical method would not hold up if Kuhn’s incommensurability thesis were true. With a lot of mathematical calculations, the authors painstakingly demonstrate how the development of the first quantum theory slowly grew out of classical physics. Their rich exposition reveals how the three main figures mentioned above, together with the many other physicists around them, used classical physics to understand the structure of the atom and the dynamical laws for the atomic spectra as far as possible. Sometimes the principles of classical physics fell short in those cases where the quantum of action had a function to play. However, all actors described the problems using the conceptual framework and the mathematical tools they had inherited from classical physics, and they were able to use those concepts and tools to grasp the results of the supporting experiments.

One of the first philosophers to introduce history of physics for the benefit of understanding scientific practice and progress was Kuhn. Trained as a physicist and then self-educated as a historian of science, he studied and published a book on the Copernican Revolution. And partly based on these studies, he wrote his landmark treatise The Structure of Scientific Revolutions ([1962]), in which he introduced concepts like paradigm, normal science, puzzle solving, anomalies, revolutions, and incommensurability. Given that in 1900 Planck had to introduce the constant that was to carry his name in order to account for black-body radiation and that this discontinuity signalled the beginning of a physical revolution, one might have expected Kuhn to have used the theoretical framework he developed in the Structure in his later book on the topic, Black-Body Theory and the Quantum Discontinuity ([1984a]). However, the latter book contains any of those concepts introduced in Structure, as if Kuhn did not believe in the adequacy of his reconstructive analysis (though he later found that the black-body theory was a nice example of the Structure’s explanatory scheme; Kuhn [1984b]). Nevertheless, many historians of science have complained that Kuhn’s analysis—in spite of the fact that it was informed by primary sources—has the character of a rational reinterpretation than a presentation of the inconsistencies and incoherence that govern much scientific research.

Every living philosopher of science has read Kuhn and, I guess, parts of his work are to be found in the syllabus of every introduction to philosophy of science class around the world. Although I had my earliest training in philosophy of science by reading Russell Hanson, Kuhn, Feyerabend, and Popper, I have always wondered why Kuhn thought that succeeding paradigms were incommensurable. This holds for quantum mechanics as well as the Copernican Revolution. Reading Duncan and Janssen’s book is one long confirmation of this scepticism.

The initial success of Bohr’s revolutionary model of the hydrogen atom consisted in its capacity to derive the spectral lines of hydrogen and helium ions, based on certain quantization conditions and the correspondence principle. This was later improved upon by Sommerfeld, who, among other things, re-described Bohr’s circular electron orbits as elliptical and introduced Ehrenfest’s adiabatic principle. Roughly speaking, this improved Bohr–Sommerfeld model had some explanatory success, such as accounting for the relativistic fine structure, X-ray spectra, and the Stark effect, whereas three other phenomena—the complex multiplet structure of spectra, the anomalous Zeeman effect, and the spectrum of helium—became nails in the model’s coffin. The authors describe this development step-by-step, explaining the reasoning and calculations behind the successes and failures, as well as the preliminary attempts to find a successor to the first quantum theory.

Constructing Quantum Mechanics is first and foremost a meticulous historical work about the early quantum mechanics, which will appeal in particular to historians of physics. It presents a rigorous calculation of all major or minor suggestions of correcting and improving quantum physics. I also think that there are features that should interest philosophers of science, and not only philosophers of physics. The first feature is one upon which I already have touched: by providing the conceptual framework and the mathematical tools required, classical physics acted as a scaffold for the development of quantum mechanics. I think the authors’ view of the history aligns completely with the view of Bohr’s principle of correspondence, a leading principle in the construction of the first quantum theory and later in the formulation of the matrix mechanics. Bohr had worked in experimental physics as a young student and never lost sight of experimental practice. The principle of correspondence came from his recognizing that quantum theory should yield the same experimental data as classical physics in the limit—something that would be impossible if those data could only be grasped in terms of incommensurable concepts.

In the formulation of the quantification conditions of his own model, Bohr used the correspondence principle by requiring that the discrete behaviour of electrons in his model must—for very high values of quantum number—correspond to the continuous radiation of a free electron determined by classical theory. Moreover, when Bohr later became preoccupied with the interpretation of the successor to his own quantum theory, the principle of correspondence re-emerged as an epistemological claim that the use of classical concepts like position and momentum, although complementary, were urgently needed to understand the outcome of experiments within the domain of quantum mechanics. The use of the classical concepts in quantum mechanics had to be restricted to the context of experiments, in contrast to how these concepts were used in classical physics.

The second methodological feature from Duncan and Janssen’s book of interest to philosophers of science is that the construction of a new paradigm is not the result of a bold alternative conjecture, but rather piecemeal alterations of the old paradigm when the scientist tries to deal with contradictions. Often when a scientist overcomes one contradiction, another flaw emerges in connection with the paradigm. In fact, internal contradictions in the reasoning behind the new hypothesis are acceptable so long as the proposal produces empirical data and helps the scientist to move forward. From the beginning, the Bohr model was not consistent or, in Ehrenfest’s words, it was ‘ganz kanibalish’ (completely monstrous)¹Quoted by Duncan & Janssen (p. 27); yet Ehrenfest realized Bohr had been successful in his derivation of the Balmer series and Sommerfeld in his derivation of the relativistic fine structure. Hence, the model could not be quite off track. Hence, all these flaws, anomalies, inconsistences, failures, and ad hoc assumptions, together with the principle of correspondence, were a positive rather than a negative procedural boost to the formulation of what is now considered the standard quantum mechanics.

There is a reason why professional historians and historians of science hesitate when people posit counterfactual hypotheses about history. Such hypotheses are unverifiable, and usually they ignore a great number of facts that seem insignificant but which all have determined the course of history. In spite of this, counterfactual history is sometimes entertained. For one, Cushing ([1994]) once imagined what would have happened if Bohm’s theory of quantum potential had appeared before the standard quantum mechanics. Indeed, history of science is partly contingent on whether scientists foster the right ideas at the decisive moment and partly on the level of technological capability. I think that Constructing Quantum Mechanics fully documents that research prior to the development of Bohr’s model and Heisenberg’s matrix mechanics was not concerned with the problems that would have led to Bohm’s theory. Instead, that theory had to await other breakthroughs before scientific progress could be made.

All this raises the question of whether the transformation of physics at the beginning of last century should be called a scientific revolution. In a certain sense, it doesn’t matter. Whether scientific changes are revolutionary or evolutionary is not a matter of real concern. However, if one follows Kuhn and defines a scientific revolution as a replacement of one paradigm with another, paradigms that are mutually incommensurable not only with respect to their content of meaning but also with respect to the values that rule scientific judgements, then the rise of the new quantum mechanics does not constitute a revolution. Indeed, the well-known physicist Steven Weinberg ([1998]), who corresponded with Kuhn, hinted that the transition from classical physics to quantum mechanics does not have the character of a revolution in Kuhn’s sense. The authors of Constructing Quantum Mechanics do not pose this kind of question; nonetheless, their scholarly treatment of the history confirms Weinberg’s observation.

Undoubtedly, the present book will stand out as a valued reference work for historians of modern physics in the years to come. In addition, philosophers of science will find numerous examples of how scientists reason in practice and how they estimate the value of their own considerations.

Jan Faye
University of Copenhagen
faye@hum.ku.dk

References

Cushing, J. T. [1994]: Quantum Mechanics. Historical Contingency and the Copenhagen Hegemony, Chicago, IL: Chicago University Press.

Kuhn, T. S. [1962]: The Structure of Scientific Revolutions, Chicago, IL: Chicago University Press.

Kuhn, T. S. [1984a]: Black-Body Theory and the Quantum Discontinuity, 1894–1912, Chicago, IL: Chicago University Press.

Kuhn, T. S. [1984b]: ‘Revisiting Planck’, Historical Studies in the Physical Sciences, 14, pp. 231–52.

Weinberg, S. [1998]: ‘The Revolutions That Didn’t Happen’, The New York Review of Books, 8 October, pp. 48–52.