Quantum Mechanics in Context:
Pascual Jordan's 1936 Anschauliche Quantentheorie
Pascual Jordan’s 1936, Anschauliche Quantentheorie: Eine Einführung in die moderne Auffassung der Quantenerscheinungen (Jordan 1936a), is an unusual and complicated textbook authored by an unusual and complicated working physicist in an unusual and complicated setting. Jordan was one of the founders of modern quantum mechanics and quantum field theory, but by 1936 he was no longer a major contributor to quantum physics, his attention and effort being diverted, in part, by a growing interest in the relationship between biology and quantum physics. Jordan had been a member of the Nazi party since 1933 and for some years before that had published conservative philosophical and cultural screed under the pseudonym, “Ernst Domeier,” in the journal Deutsches Volkstum (Beyler 2009), but he remained an ardent supporter of modern theoretical physics, openly promoting the work of
The book, Anschauliche Quantentheorie, embodies as many tensions and complexities as does its author. As the title suggests, the book aims to provide an intuitive introduction to the quantum theory, explicitly analogous to the intuitive introduction to geometry then famously on offer in
It is difficult to gauge the audience for and impact of Jordan’s Anschauliche Quantentheorie. There was no English translation, nor was there a second edition. The German edition had a limited circulation in North America after being reprinted in 1946 by J. W. Edwards, of Ann Arbor, under the Alien Property Act. For the German-speaking audience it would have competed mainly with the 1929 Wellenmechanische Ergänzungsband of the fifth edition of
Still, Jordan’s Anschauliche Quantenmechanik stands out and deserves our attention as one of the most important textbooks of its era precisely because of all the tensions and complexities it embodies, it being, in this respect a reflection of its times, and also because its author was, along with Sommerfeld, Born, Heisenberg, Pauli, and Dirac, one of the most important shapers of modern quantum mechanics.
11.2 Pascual Jordan in 1936
That Jordan never won a Nobel Prize in physics is a puzzle. Some blame his inability to give elegant lectures because of a stutter; some blame his pro-Nazi politics or his support, after World War II, for a German nuclear weapons program; some blame the fact that Born misplaced Jordan’s 1925 manuscript in which
But by May of 1936, when Jordan completed work on the manuscript of Anschauliche Quantentheorie, his most significant contributions to the quantum theory were in the past. Jordan was then developing an interest in the relationship between physics and biology, an interest that first found expression in his 1932 paper, “Die Quantenmechanik und die Grundprobleme der Biologie und Psychologie” (Jordan 1932, see also Jordan 1934), and would continue to the end of his life. An interest in the relationship between biology and physics was shared with a number of other physicists who had worked on quantum theory, such as Schrödinger, whose What Is Life? appeared in 1944 (Schrödinger 1944), and Max Delbrück, who had turned to biophysics at
One year before completing his manuscript Jordan had been promoted to Ordinarius at Rostock University, at the comparatively young age of thirty-two. But Rostock, where Jordan had worked since his appointment as Extraordinarius in 1929, was not the kind of high-status post one might have expected for a physicist of such early achievement and promise. Jordan’s stutter, which made lecturing difficult, was surely part of the reason for this. After 1933, his awkward relationship with the Nazi party—a party member but a dissenter from the assault on Jewish physics—would have been an added impediment to a call to a more prestigious chair.
Jordan’s early training in physics and mathematics was at the Technische Hochschule in his native Hannover. In 1923 he went to Göttingen, where he did a dissertation under
It was not just physics, however, that drew Jordan’s attention in Göttingen. As mentioned, he was trained in mathematics and was, briefly, an Assistent with Courant. The Göttingen mathematics tradition centered around
Another major influence on Jordan was the development of logical empiricism and the Vienna Circle.5 Claiming the heritage of
The movement was heavily involved with theoretical physics.
That a young physicist like Jordan, with a broad-ranging and restive intellect, should be drawn to logical empiricism is, thus, not very surprising. Many of Jordan’s contemporaries evinced similarly strong philosophical interests, though not all of them followed Jordan in his attachment to positivism.
As significant as the impacts of
A final fact of note about Jordan in 1936 is that, by then, he was no longer hiding his political musings behind a pseudonym. In the series of articles that he had published in the early 1930s in the conservative, nationalist journal, Deutsches Volkstum under the name “Ernst Domeier” (Domeier 1930a; 1930b; 1930c; 1930d; 1931a; 1931b; 1932), Jordan complained about Marxism, secularism, and the baleful cultural effects of liberal democracy of the Weimar variety, and he had championed science and technology as engines of positive social transformation.12 After Hitler’s ascent to power in 1933, and after Jordan joined the Nazi party in May of that year, he felt comfortable voicing such views under his own name, starting with an article in the spring of 1933 in the Rostock university newspaper on “Die Wandlung der Universität” (Jordan 1933a), and continuing in 1935 in a booklet, Physikalisches Denken in der neuen Zeit (Jordan 1935c), published by the same press that was responsible for Deutsches Volkstum, as well as additional articles in that journal (Jordan 1935a; 1935d). But Jordan did not follow the lead of the anti-Semitic proponents of “Deutsche Physik,” such as
What is most important for our purposes in Jordan’s political writings is his arguing that science, properly understood—which is to say, interpreted in line with antimetaphysical positivism and Bohr’s principle of complementarity—undermines Marxist materialism and opens the door for both religion and a kind of descriptivist vitalism in biology. It is here, in Jordan’s political writings, that the many different strands of his thinking begin to entwine into a somewhat coherent, if highly idiosyncratic world view. It is the politics that provides the glue. Here is where the physics, the biology, and the philosophy combine. While the politics is kept discreetly in the background in Jordan’s Anschauliche Quantentheorie, understanding the book’s many idiosyncrasies is impossible without an appreciation of the political context.
11.3 The Book
Jordan’s Anschauliche Quantentheorie is a brief, 332 pages, book divided into five chapters
1“Die Grundexperimente der Quantenphysik” [“The Basic Experiments of Quantum Physics”]15
2“Theoretische Analyse der quantenphysikalischen Grundexperimente” [“Theoretical Analysis of the Basic Experiments of Quantum Physics”]
3“Quanten- und Wellenmechanik” [“Quantum and Wave Mechanics”]
4“Mehrkörpertheorie und Elementarteilchen.” [“Many-body Theory and Elementary Particles”]
5“Atome und Organismen” [“Atoms and Organisms”]
and introduced by seven pages of introduction, Vorbemerkungen (“Preliminary Remarks”). It is not a typical textbook in many respects. It is not, for example, the kind of text from which the novice student will learn how to solve problems. Nor does it aim to provide a comprehensive survey of all major topics. Instead, the book emphasizes conceptual and mathematical fundamentals, though in a manner quite different from
Jordan announces his philosophical agenda in the introduction: “The overall epistemological orientation that finds expression in modern quantum theory—and that, conversely, receives its most significant support from the quantum theory—has been designated by the author in writings on this subject as ‘positivistic’” (Jordan 1936a, vii). What does “positivistic” mean?
What I will defend is the epistemological orientation of
Bohr and Heisenberg. For me, the writings of Ernst Mach have formed an indispensable preparation for understanding these modern quantum physical conceptions, and the kinship of Mach’s ideas with them seems to me more essential than the differences. (Jordan 1936a, vii–viii)
That anti-positivists such as
The essential and decisive principle of positivist epistemology—the restriction of admissible propositions to those that can be reduced to experimentally testable propositions—seems to me to be characterizable, furthermore, as a sensible adaptation of the same principle that forms the starting point for
Hilbert’s foundational investigations in mathematics, and that Hilbert calls the “finite standpoint.” (Jordan 1936a, viii)
Positivism famously opposes unscientific metaphysics and so is incompatible with “dogmatic materialism.” Jordan warns the reader that some authors confuse the issue by using the term “positivism” in other ways.
If modern quantum physics is a straightforward expression of positivism, then its content must be fixed in virtually every detail by definitive experimental results. The task of chapter 1, “The Basic Experiments of Quantum Physics,” is to exhibit this empirical basis. What is sought is an
inductive construction16 of the theory that makes clear the necessary givenness [zwangsläufige Gegebenheit] of its fundamental concepts and fundamental assumptions by means of direct experimental results […] in which the character of quantum physics appears […] pure and undisguised. (Jordan 1936a, 1–2)
No surprise, therefore, that the chapter begins with black-body radiation and the
With the empirical basis thus secured, Jordan turns in chapter 2 to the “Theoretical Analysis of the Basic Experiments of Quantum Physics.” The main tool is the correspondence principle, which Jordan describes as “the most important idea in all of quantum theory.” Jordan notes that the correspondence principle is not like the energy, entropy, and relativity principles, which are “laws of nature in completely worked out formulation.” It is, instead, “a guide to the detection of still unknown laws of quantum phenomena,” which cannot be given a “mathematically precise expression” (Jordan 1936a, 51). And even now—1936—when we possess a mathematically refined quantum formalism, the correspondence principle is still crucial as a guide in figuring out the “meaning” of the formalism. It does this by exhibiting a “comprehensive and close analogy between classical theory and quantum theory” (Jordan 1936a, 52).
How far Jordan thinks he can push arguments based on the correspondence principle is illustrated by his introduction of electron spin. Analysis of the anomalous Zeeman-effect requires the introduction of the
The introduction of this half-integral spin-moment of an electron […] can be characterized as a departure from the image of the electron simply as a mass-point; there exists a certain correspondence-like analogy to a body rotating around an internal axis, in which, in addition to the angular momentum of its center-of-mass motion, there is another angular momentum of the proper rotation. But the significance of this analogy should not be over-valued: Basically, we are concerned here with relationships that cannot be understood according to classical analogies. With respect to the doubling of the statistical weights required by the introduction of the spin-moment, it would be more prudent to speak of a non-classical “two-valuedness” (
Pauli). (Jordan 1936a, 100)
One might worry that the
That there are, of course, limits to the usefulness of classical analogies in quantum physics is an essential part of the other major idea that
The exposition that follows is unsurprising in that Jordan presents wave and particle models as complementary descriptions of quantum phenomena, and works out more precisely the examples of position and momentum as well as energy and time as complementary magnitudes. In a standard manner, wholly in the spirit of Bohr, Jordan points to the physical incompatibility of measurement contexts as the basis of complementarity.
Chapter 3, “Quantum and Wave Mechanics,” is the technical heart of the book. As one might expect from a mathematician such as Jordan, it is written at a comparatively high level of abstraction, though a few standard examples and applications—the harmonic oscillator, angular momentum, the hydrogen atom—are worked out in detail. Nowhere else in the textbook literature available in the mid-1930s would one have found such a succinct, lucid, indeed eloquent presentation of the fundamental mathematics of quantum physics. Matrix and wave mechanics are developed in detail. Their equivalence is demonstrated in a reasonably intuitive way, without the elaborate algebraic apparatus one might have expected from Jordan.17 The two are then subsumed under the broader framework of statistical transformation theory, and the power of that formalism is exhibited through its application to the problem of electron spin. The level of abstraction was higher still in von Neumann’s Mathematische Grundlagen der Quantenmechanik (von Neumann 1932), but in no way could it be taken to provide an “intuitive” introduction to the theory.
Chapter 3 presents non-relativistic quantum mechanics in a closed, mathematical form. Chapter 4 turns to the messy business of relativistic quantum mechanics, quantum field theory, and nuclear physics. Jordan had as much or more claim to authority on these topics than any of his contemporaries; still, it was a challenge to write such a chapter in 1936.
Jordan does a good job of bringing order to this confused material. His discussions are clear and to the point. Especially nice are the presentations of quantum statistics and second quantization. But Jordan himself emphasizes the incomplete state of things in 1936. He introduces the chapter by declaring, modestly, that its aim is “to make clear how far we have come and what we are still lacking” (Jordan 1936a, 179). The chapter can be read with profit today as a kind of historical snapshot of physics in the making. This is true even with respect to the one bit of self-indulgence that mars an otherwise balanced and dispassionate presentation, namely, the nine pages that Jordan devotes to his own neutrino theory of light, an idea first introduced by de Broglie
A little self-indulgence at the end of chapter 4 is an apt prelude to chapter 5, “Atoms and Organisms,” where the unique intellectual personality of Jordan comes into full view. The chapter contains three sections: § 1. “Die positivistische Methode” [“The Positivistic Method”]; § 2. “Kausalität, Statistik und Finalität” [“Causality, Statistics, and Finality”]; and § 3. “Die Aufbau der realen Welt” [“The Construction of the Real World”].
Section one begins with a reiteration of Jordan’s positivist view of the quantum theory, asserting again, as at the beginning of the book, that the principles of quantum mechanics, at least “within the limits of the non-relativistic theory,” are “unavoidable consequences of the empirically given.” Non-relativistic quantum mechanics is said to constitute “a consistent, closed, conceptual structure in which no fundamental problem remains unsolved and in whose framework every possible question appears as a clearly defined mathematical problem” (Jordan 1936a, 271). But the new theory stands in such “stark contrast” to classical physics that its proper, “intuitive” understanding requires our overcoming of classical “prejudices” through “a thorough, methodological-epistemological analysis” (Jordan 1936a, 272).
Central to that epistemological analysis are two distinctions famously asserted by Vienna Circle logical empiricists: (a) the distinction between genuine problems and “pseudo-problems” (Scheinprobleme) (Carnap 1928); and (b) the distinction between meaningful and meaningless propositions (Carnap 1932). Pseudo-problems are those inaccessible to scientific investigation because of the nature of the scientific method. Mathematics affords many examples of pseudo-problems, such as puzzles about the nature of imaginary numbers and infinitesimals. In physics, says Jordan, we have
This view does away with the whole tangled mess [Wust] of the countless, well-known pseudo-problems that must arise out of any attempt to find an explanation for the laws arrived at via the correspondence principle by means of detailed models for the “course” or “mechanism” of quantum jumps. (Jordan 1936a, 276)
Recognizing pseudo-problems as what they are requires, in turn, one’s understanding the distinction between meaningful and meaningless propositions. Meaningful propositions are those that are either true or false, and in such a way that deciding between these alternatives is a “solvable problem.” Moreover, the only meaningful propositions are those “that refer directly to sense experiences” or can be shown to be “equivalent” to such basic empirical propositions through “definitions and terminological stipulations” (Jordan 1936a, 276–277). Einstein’s analysis of distant simultaneity is the famous example from physics, for the assertion that two distant events are simultaneous, without specification of a frame of reference, lacks empirical content.
Jordan’s main reason for promoting this positivist perspective on the epistemology of quantum mechanics is revealed in the next section, “Causality, Statistics, and Finality.” Quantum mechanics is a non-deterministic theory. In this respect it differs fundamentally from the deterministic classical physics of Newton (and
For a positivist like Jordan, teleology cannot be a metaphysical thesis. It is, instead, a claim about the appropriate descriptive vocabulary for biology. For the description of biological structures and processes the language of purposiveness is “indispensable,” which means, says Jordan, “that the teleological point of view is an indispensable element of biological concept formation” (Jordan 1936a, 287). That the teleological mode of description can be made to work scientifically is further demonstrated by the fact that it can be given clear mathematical formulations. Thus, the idea of purposiveness can be expressed mathematically in the form of variational problems. The related and equally indispensable concept of “wholeness” or the “indivisibility of individual organisms” can be expressed in the form of integral equations (Jordan 1936a, 290–291).
Jordan goes on to discuss an array of more specific questions concerning the relationship between quantum physics and biology. Mendel’s research into combining ratios proves that discreteness plays a fundamental role in biological processes. That random quantum jumps play a role in biology is suggested by the evidence then accumulating for mutations induced by radiation so weak that no more than a single photon could be involved. That randomness at the quantum level can have effects at the biological level is suggested by the possibility of individual, quantum-scale events “directing” mesoscopic and macroscopic biological processes. And if quantum randomness can be “amplified” to the macroscale in this manner, then quantum randomness might be an explanation for our subjective sense of free will. What does this all imply for the fraught question of the reducibility of biology to physics? Jordan has an interesting answer. He suggests that, instead of regarding biology as a complicated, macroscopic limit of microphysics, it might be more appropriate to regard microphysics as the “simplified limit case of the organic, characterized as a minimum of the generation of integral whole,” by which he means just that the properties of macroscopic biological structures and processes commonly represent statistical averages that result from the integration of individual atomic processes. Thus biological laws may be seen, by comparison with the laws of the inorganic, as “the more comprehensive and general” (Jordan 1936a, 302).
Jordan’s Anschauliche Quantentheorie concludes with section three of chapter 5, a highly philosophical discussion of “The Construction of the Real World.” The section begins with a long quotation from Planck’s widely read 1931 essay, “Positivismus und reale Aussenwelt” (Planck 1931), in which Planck defends an unabashedly metaphysical version of realism and denounces positivism for its denial of the existence of an objective, external reality. Jordan brushes off
Thus formulated, however, the realism question receives an affirmative answer within the framework of classical physics, but after the development of the quantum theory, it receives a definitive negative answer because of quantum indeterminism. And this is connected, in turn, with
Letting go of the classical notion of physical reality also has implications for the way we think of the relationship between the physical and the organic. Bohr had famously extended the principle of complementarity to describe the relationship between physics and biology. Beyond a certain limit, only the dead organism can be dissected and its parts studied in isolation and detail. The living organism can be studied only as an organic whole.
With good reason one might say that these last paragraphs of Jordan’s Anschauliche Quantentheorie represent the reductio ad absurdum of his larger philosophical project. But simply to dismiss the book because it ends in such silliness would be to miss the book’s larger significance. For there are two ways in which the book affords, in fact, an interesting perspective on its author and the many contexts in which the book lives.
There is, first, the fact that Jordan and his Anschauliche Quantentheorie probably did more than any other person and text to establish the association between
There is, second, the fact that the only way to make Jordan’s odd mixing of quantum mechanics, positivism, and vitalism at all coherent is to embed the whole in the political context of Germany in the mid-1930s. For it is Jordan’s politically driven opposition to materialism that ties all of the pieces together. And therein lies a great irony. For it is Jordan, a member of the Nazi party, who in this way secured the popular association of quantum mechanics with a positivism that otherwise bore almost exclusively a left-liberal, even socialist political stamp.
Abbreviations and Archives
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Pittsburgh, PA, USA,
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See, for example, (Zilsel 1935), which elicited reactions from Hans Reichenbach, Otto Neurath, Moritz Schlick, and Philipp Frank.
Corry (2004) is a helpful resource on the Hilbert program more generally but, especially, the unique way in which the Göttingen physics and mathematics communities interacted under Hilbert’s patronage.
Stadler (1997) provides the most comprehensive recent history of the Vienna Circle and logical empiricism.
For more on logical empiricism’s roots in the defense of relativity against neo-Kantian critiques, see (Howard 1994).
For more on the curiously intimate relationship between theoretical physics and philosophy of science at the beginning of the twentieth century, see (Howard 2004b).
Tanona (2002) and Bokulich’s 2009 “Three Puzzles about Bohr’s Correspondence Principle,” Philsci Archive, are helpful recent discussions.
Unless otherwise indicated all English translations are by the author.
Unless otherwise indicated, all emphasis is in the original.
For example, there is no mention of the Stone-von Neumann theorem.