In early 1927, Pascual Jordan published his version of what came to be known as the Dirac-Jordan statistical transformation theory. Later that year and partly in response to Jordan, John von Neumann published the modern Hilbert space formalism of quantum mechanics. Central to both formalisms are expressions for conditional probabilities of finding some value for one quantity given the value of another. Beyond that Jordan and von Neumann had very different views about the appropriate formulation of problems in the new (...) theory. For Jordan, unable to let go of the analogy to classical mechanics, the solution of such problems required the identification of sets of canonically conjugate variables, i.e., p’s and q’s. Jordan ran into serious difficulties when he tried to extend his approach from quantities with fully continuous spectra to those with wholly or partly discrete spectra. For von Neumann, not constrained by the analogy to classical physics and aware of the daunting mathematical difficulties facing the approach of Jordan ), the solution of a problem in the new quantum mechanics required only the identification of a maximal set of commuting operators with simultaneous eigenstates. He had no need for p’s and q’s. Related to their disagreement about the appropriate general formalism for the new theory, Jordan and von Neumann stated the characteristic new rules for probabilities in quantum mechanics somewhat differently. Jordan was the first to state those rules in full generality, von Neumann rephrased them and then sought to derive them from more basic considerations. In this paper we reconstruct the central arguments of these 1927 papers by Jordan and von Neumann and of a paper on Jordan’s approach by Hilbert, von Neumann, and Nordheim. We highlight those elements in these papers that bring out the gradual loosening of the ties between the new quantum formalism and classical mechanics. (shrink)

This paper re-evaluates the formative year of quantum mechanics—from Heisenberg’s first paper on matrix mechanics to Schrödinger’s equivalence proof—by focusing on the role of radiation in the emerging theory. We argue that the radiation problem played a key role in early quantum mechanics, a role that has not been taken into account in the standard histories. Radiation was perceived by the main protagonists of matrix and wave mechanics as a central lacuna in these emerging theories and continued to contribute to (...) the theoretical development and conceptual clarification of quantum mechanics. Studying the interplay between quantum mechanics and radiation, the paper provides an account of (a) how quantum mechanics was able to connect to its empirical basis in spectroscopy and (b) how Schrödinger’s equivalence proof emerged from his explorative calculations on the emission of radiation. (shrink)

Using newly uncovered archival sources, this essay traces the meteoric rise and fall of the peculiar interdisciplinary German scientific journal Physis, founded by the physicist Pascual Jordan and the biologist Adolf Meyer-Abich in 1941. Launched when victory for Nazi Germany seemed certain, Physis was intended by Jordan and Meyer-Abich to be a premier international journal for all sciences suitable for the new “German-led Europe” forged by conquest. Yet the journal was simultaneously a vehicle for institutionalizing Jordan’s remarkably prescient vision of (...) the future of the scientific enterprise in Hitler’s state—a vision nearly identical to what is now termed “big science,” yet suitably “Nazified” for wartime Germany. Behind the scenes, Physis was accompanied by a campaign of intrigue, through which Jordan and Meyer-Abich hoped to find a patron for the journal and big science among the various power centers of the Nazi state. These efforts failed, yet they nevertheless demonstrate that big science is not inherently democratic. (shrink)

We discuss the early career of John H. Van Vleck, one of the earliest American quantum theorists who shared the 1977 Nobel prize with his student Philip W. Anderson and Sir Nevill Mott. In particular, we follow Van Vleck's trajectory from his 1926 Bulletin for the National Research Council on the old quantum theory to his 1932 book, The Theory of Electric and Magnetic Susceptibilities. We highlight the continuity of formalism and technique in the transition from dealing with spectra in (...) the old quantum theory to dealing with susceptibilities in the new quantum mechanics. Our main focus is on the checkered history of a numerical factor in the so-called Langevin-Debye formula for the electric susceptibility of gases. Classical theory predicts, under very general conditions, that this factor is equal to 1/3. The old quantum theory predicted values up to 14 times higher. Van Vleck showed that quantum mechanics does away with this "wonderful nonsense" and restores the classical value 1/3 under equally general conditions. The Langevin-Debye formula thus provides an instructive example of a Kuhn loss in one paradigm shift that was regained in the next. In accordance with the expectation of Thomas S. Kuhn that textbooks tend to sweep Kuhn losses under the rug, Van Vleck did not mention this particular Kuhn loss anywhere in his 1926 NRC Bulletin. Contrary to Kuhn's expectations, however, he put the regained Kuhn loss in susceptibility theory to good pedagogical use in his 1932 book. Kuhn claimed that textbooks must suppress, truncate, and/or distort the prehistory of their subject matter if they are to inculcate the exemplars of the new paradigm in their readers. This claim is not borne out in this case. We argue that it is ultimately because of the continuity of formalism and technique that we draw attention to that Van Vleck could achieve his pedagogical objectives in his 1932 book even though he devoted about a third of it to the treatment of susceptibilities in classical theory and the old quantum theory in a way that matches the historical record reasonably well. (shrink)

The laser, first operated in 1960, produced light with coherence properties that demanded explanation. While some attempted a treatment within the framework of classical coherence theory, others insisted that only quantum electrodynamics could give adequate insight and generality. The result was a sharp and rather bitter controversy, conducted over the physics and mathematics that were being deployed, but also over the criteria for doing good science. Three physicists were at the center of this dispute, Emil Wolf, Max Born’s collaborator on (...) a canonical text on optics as a branch of classical electromagnetism, Roy J. Glauber, a student of Julian Schwinger and a high-energy particle theorist, and Leonard Mandel, both experimentalist and theorist and versed in the physics of photodetection. The story told here is thus one of three distinct research trajectories and of the explosion that occurred when, pushed into the well-financed field of laser studies, these trajectories collided. (shrink)

Once one of the main protagonists of history of science, the historiography on quantum theory has recently gone through a process of reconfiguration of methods, research questions and epistemological framework. In this paper, I review the recent developments and propose some reflections on its future evolution.

The main aim of this work is to relate integrability in QFT with a complete particle interpretation directly to the principle of causal localization, circumventing the standard method of finding sufficiently many conservation laws. Its precise conceptual-mathematical formulation as “modular localization” within the setting of local operator algebras also suggests novel ways of looking at general (non-integrable) QFTs which are not based on quantizing classical field theories.Conformal QFT, which is known to admit no particle interpretation, suggest the presence of a (...) “partial” integrability, referred to as “conformal integrability”. This manifests itself in a “braid-permutation” group structure which contains in particular informations about the anomalous dimensional spectrum. For chiral conformal models this reduces to the braid group as it is represented in Hecke- or Birman-Wenzl-algebras associated to chiral models.Another application of modular localization mentioned in this work is an alternative to the BRST formulation of gauge theories in terms of stringlike vectorpotentials within a Hilbert space setting. (shrink)

The celebrated Dreimännerarbeit by Born, Heisenberg and Jordan contains a matrix-mechanical derivation by Jordan of Planck’s formula for blackbody fluctuations. Jordan appears to have considered this to be one of his finest contributions to quantum theory, but the status of his derivation is puzzling. In our Dreimenschenarbeit, we show how to understand what Jordan was doing in the double context of a Boltzmannian approach to statistical mechanics and of the early ‘statistical interpretation’ of matrix mechanics.