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A relational ontology interpretation of quantum physics, based on a reconstruction and further elaboration of Niels Bohr’s philosophy-physics, offers an account of quantum physics that makes claims about the larger physical world, not merely the outcome of laboratory experiments. While Newtonian physics supports an ontology consisting of individual entities that precede their interactions (relata precede relations), quantum physics resists such a metaphysics of individualism, and instead supports the understanding that reality is made of relations: that relata come into being only through and as constitutive parts of their intra-actions (that is, relata only exist within relations). On this agential realist account, the nature of nature is an ongoing dynamism of intra-activity through which the world is differentially articulated, and some of those articulations are what we call measurements.

Quantum theory and functional analysis were created and put into essentially their final form during similar periods ending around 1930. Each was also a key outcome of the major revolutions that both physics and mathematics as a whole underwent at the time. This paper studies their interaction in this light, emphasizing the leading roles played by Hilbert in preparing the ground and by von Neumann in bringing them together during the crucial year of 1927, when he gave the modern, abstract definition of a Hilbert space and applied this concept to quantum mechanics (consolidated in his famous monograph from 1932). Subsequently, I give a very brief overview of three areas of functional analysis that have had fruitful interactions with quantum theory since 1932, namely unbounded operators, operator algebras, and distributions. The paper closes with some musings about the role of functional analysis in actual physics.

While Bohr developed his views independently of any direct philosophical influence, his reflection on the relationship between epistemology and semantics was remarkably in phase with the philosophical avant-garde of his time. Bohr borrowed some concepts and ideas from the neo-Kantian and pragmatist traditions, but what sharply distinguishes his approach from those of other philosophising physicists is the peculiar focus on language (along with a dismissive attitude towards foundationalist concerns, which echoes Wittgenstein’s in some respects). Bohr was convinced of the need to draw a general lesson from quantum mechanics – a lesson that went beyond the theory’s empirical content and concerned the very nature of objectivity and knowledge. Specifically, he thought that understanding quantum mechanics implied a rigorous analysis of the semantic presuppositions of physics and that such an analysis revealed the existence of well-entrenched representational preconceptions, which placed undue limitations upon the account of rational practices.

It will be presented in this chapter a historical account of the consistent histories interpretation of quantum mechanics based on primary and secondary literature. Firstly, the formalism of the consistent histories approach will be outlined. Secondly, the works by Robert Griffiths and Roland Omnès will be discussed. Griffiths’ seminal 1984 paper, the first physicist to have proposed a consistent-histories interpretation of quantum mechanics, followed by Omnès’ 1990 paper, were instrumental to the consistent-histories model based on Boolean logic. Thirdly, Murray Gell-Mann and James Hartle’s steps to their own version of consistent-histories approach, motivated by a cosmological perspective, will then be described and evaluated. Gell-Mann and Hartle understood that spontaneous decoherence could path the way to a concrete physical model to Griffiths’ consistent histories. Moreover, the collective biography of these figures will be put in the context of the role played by the Santa Fe Institute, co-founded by Gell-Mann in 1984 in Santa Fe, New Mexico, where Hartle is also a member of the external faculty.

This chapter explores Chien-Shiung Wu’s contributions to experimental philosophy in American twentieth-century physics. While the Wu-Shaknov (WS) experiment helped reopen discussions on the EPR argument through Bohm and Aharonov’s work, the Kasday-Ullman-Wu (KUW) experiment tested the local hidden variables models and the usual quantum mechanics. Both contributions teach us about the different ways physicists, experiments, and data can enrich scientific culture.

This article focuses on applications of random matrix theory (RMT) to both classical optics and quantum optics, with emphasis on optical systems such as disordered wave guides and chaotic resonators. The discussion centres on topics that do not have an immediate analogue in electronics, either because they cannot readily be measured in the solid state or because they involve aspects (such as absorption, amplification, or bosonic statistics) that do not apply to electrons. The article first considers applications of RMT to classical optics, including optical speckle and coherent backscattering, reflection from an absorbing random medium, long-range wave function correlations in an open resonator, and direct detection of open transmission channels. It then discusses applications to quantum optics, namely: the statistics of grey-body radiation, lasing in a chaotic cavity, and the effect of absorption on the reflection eigenvalue statistics in a multimode wave guide.

This chapter examines physicists’ uses of concepts of classical and modern after the 1911 Solvay Council. British physicists soon recognised a significant challenge to ‘classical electrodynamics’ following the work of Planck and Poincaré, which Bohr incorporated in his 1913 theory of the atom. Yet this language was contingent, and Sommerfeld and Bohr dropped it during the war. An examination of work in Germany and post-war Nobel Prizes explains their subsequent return to it, and the development of still more general concepts of classical physics. Celebrations of Planck, Einstein’s role in ‘deepening classical theory’, and the internationalisation of interest led by 1922 to the promotion of a general concept of ‘classical physics’ with quantum theory being widely identified as a central feature of ‘modern physics’. In turn, this cultural work facilitated the incorporation of a rich variety of concepts of classical theory in the subsequent development of quantum mechanics.

This article focuses on the use of a Bayesian approach that combines simulations and physical observations to estimate cosmological parameters. It begins with an overview of the Λ-cold dark matter (CDM) model, the simplest cosmological model in agreement with the cosmic microwave background (CMB) and largescale structure analysis. The CDM model is determined by a small number of parameters which control the composition, expansion and fluctuations of the universe. The present study aims to learn about the values of these parameters using measurements from the Sloan Digital Sky Survey (SDSS). Computationally intensive simulation results are combined with measurements from the SDSS to infer about a subset of the parameters that control the CDM model. The article also describes a statistical framework used to determine a posterior distribution for these cosmological parameters and concludes by showing how it can be extended to include data from diverse data sources.

This article discusses some applications of concepts from random matrix theory (RMT) to condensed matter physics, with emphasis on phenomena, predicted or explained by RMT, that have actually been observed in experiments on quantum wires and quantum dots. These observations range from universal conductance fluctuations (UCF) to weak localization, non-Gaussian thermopower distributions, and sub-Poissonian shot noise. The article first considers the UCF phenomenon, nonlogarithmic eigenvalue repulsion, and sub-Poissonian shot noise in quantum wires before analysing level and wave function statistics, scattering matrix ensembles, conductance distribution, and thermopower distribution in quantum dots. It also examines the effects (not yet observed) of superconductors on the statistics of the Hamiltonian and scattering matrix.

This chapter addresses the question of how the Danish capital Copenhagen became the embodiment of the philosophical implications of quantum physics, and it discusses some of Niels Bohr’s main ideas in this Copenhagen Interpretation, including complementarity. The chapter suggests that the combination of a favourable Danish science policy with Bohr’s eminent skills as fundraiser and in scientific leadership, paved the way for the small hitherto scientifically peripheral Kingdom of Denmark to be able to foster one of Europe’s leading scientific centers in the interwar years, viz. the Institute for Theoretical Physics. With respect to the interpretation of quantum mechanics the chapter emphasises that Bohr saw quantum physics as an epistemological rather than an ontological theory. Bohr’s focus on the role of measurement in quantum physics is outlined, and how this was discussed and elucidated in Copenhagen through idealised thought experiments. The chapter concludes with a brief review of how the physicists in Copenhagen responded to the new critique and development of the interpretation of quantum physics after the Second World War.

The term, “Copenhagen Interpretation,” is used to designate a set of ideas associated with leading thinkers clustered around Niels Bohr and the Bohr Institute in Copenhagen. Foremost among those ideas are (1) complementarity, (2) a necessary role for classical modes of description, (3) the completeness of quantum mechanics, (4) objective indeterminacy, (5) wave-particle duality, (6) measurement-induced, wave-packet collapse, (7) a disturbance analysis of indeterminacy, and (8) a privileged role for the subjective observer in the quantum realm. Widely assumed to represent the position of Bohr, himself, a number of these ideas were to be found more commonly in the writings of Werner Heisenberg, and members of the Copenhagen community were sometimes badly divided over their status and validity. This article surveys the historical development of these ideas and their eventual coalescence as key ingredients of the Copenhagen interpretation, with an emphasis on the physical considerations that drove that development.

According to quantum mechanics, an oscillator at zero absolute temperature will continue to vibrate with a zero-point energy. This non-classical phenomenon was predicted by Max Planck in 1911, but for a long time it was contested and remained hypothetical. Only in experiments with molecular spectra from 1924 was the zero-point energy confirmed experimentally, and the following year it emerged as a consequence of quantum mechanics. Although Walther Nernst claimed that also vacuum was filled with zero-point energy, specialists in quantum physics denied that this was the case. Nonetheless, with the discovery of the Casimir effect predicted in 1948 Nernst’s idea was vindicated. Later still, the zero-point energy of free space turned up in the vacuum energy or so-called dark energy associated with Einstein’s cosmological constant. The chapter offers a history of the concept of zero-point energy with a focus on the period from 1911 to about 1928.

One of the most striking features of the development of quantum mechanics is the intensity of the debate about its physical meaning that accompanied its development. The dissent laid in the competition between the Göttingen proponents of matrix mechanics and Schrödinger, as well as in the criticism of both formalisms by the “older generation” of physicists, like Einstein, Sommerfeld, and Planck. The establishment of a unified formalism and its physical interpretation was an important goal for the group around Bohr and the Göttingen physicists. It seemed to be reached in the statistical theory, its mathematical codification by von Neumann, and its epistemological defense by Bohr. However, no full agreement was reached. The early history of the dissent from the orthodoxy up to the debates at the Solvay conference is often seen as the result of preestablished metaphysical commitments. We stress a different reading, they were debates about promising research strategies.

This chapter investigates how Japanese scientists and other intellectuals responded to foundational questions of quantum mechanics from the late 1920s to the early 1940s. Avoiding a culturalist approach, it emphasizes diverse local intellectual and historical contexts of the Japanese debates over quantum mechanics, which involved not only scientists, but also science journalists, Marxists, and Kyoto school philosophers. Starting with Nishina Yoshio’s early encounter with Niels Bohr’s complementarity, it examines how Japanese physicists incorporated (or not) conceptual issues of quantum mechanics into their textbooks, education, and research. It discusses how science writers, such as Ishiwara Jun, wrote about them, and how intellectuals with different philosophical standpoints, in particular Marxists such as Taketani Mituo and Kyoto Scholl philosophers such as Tanabe Hajime debated over them in response to incidents like the publication of the Einstein-Podolsky-Rosen paper in 1935 and Bohr’s visit to Japan in 1937.

For over one-hundred years, Solvay Councils have brought to Brussels some of the world’s most prominent scientists to interrogate seemingly intractable problems. These elite conferences have often been portrayed as battlegrounds for scientific immortality and furnaces of rational discourse that forged scientific consensus on quantum theory. Although the conference proceedings certainly give us a record of formative scientific debates, a contextualized historical analysis allows us to understand the power of social and rhetorical forces on the outcomes of these Solvay gatherings. In particular, the Solvay Councils of 1927 and 1930 were reflections of, and catalysts for, a broader ongoing social process that overcame deep political divides and a divergence of approaches to quantum theory. The result was a forced convergence around a tentative quantum consensus that was instrumental in silencing interpretation debates for decades to come.

After having played a fundamental pioneer role in the birth of quantum physics by unveiling non classical properties and formulating a first coherent theoretical approach, Einstein was far less enthusiastic about the constitution of quantum mechanics as proclaimed in 1927. From then on he constantly argued against the pretention of its founders and proponents to have settled a definitive and complete physical theory for the quantum domain. His arguments are analysed, situated in the context of the dominant “complementarity interpretation” and following their evolution with time. They are centered on an “uncompleteness” of the quantum theory with respect to reality and objectivity, exigencies which were at the core of his own program since the start. In the light of further advances in quantum physics, it is then shown how Einstein’s objections have played a decisive role in the clarification of specific quantum concepts such as local non-separability (entanglement and non-locality), while maintaining that of an individual quantum physical system. Through these, it has been possible to deepen the understanding and applications of quantum correlations and the connection between the quantum and classical descriptions (decoherence with consequences as to the “measurement problem”).

We will show that the views of Einstein (and of Podolsky and Rosen), Bohm and Bell about “hidden variables” and nonlocality have been systematically misrepresented and misunderstood by a large number of physicists.

The change that quantum statistics produced in the concept of microphysical entities was not the result of an experimental discovery, a logical inference, nor a choice between preformed conceptual models. It was, rather, the result of uncoordinated efforts to reach a physical understanding of the evolving mathematical-theoretical apparatus by modifying and rearranging familiar ideas about particles. This chapter examines the history of early interpretations of quantum statistics, from Einstein’s first deciphering of Bose’s formal procedure to the earliest attempts to make sense of the formalism that unified Bose-Einstein and Fermi-Dirac statistics with the quantum mechanics of multi-particle systems. The fragmentary and discordant views of this early period highlight the interpretive flexibility of the formal apparatus. The first extended articulations of a new, unified conception of particles emerged only after WWII, as signalled by Dirac’s 1945 proposal of the two new foundational categories of “bosons” and “fermions”.

Textbooks are both classic and subaltern subjects in the history of quantum physics. They featured prominently in path-breaking projects such as Sources for History of Quantum Physics and in Thomas Kuhn’s theoretical challenge. They have subsequently occupied a well-defined, but epistemologically marginal place in contemporary scholarship on quantum mechanics. In contrast, this chapter presents textbooks and pedagogy as a driving force in the making of quantum theory, by reconsidering old and new contributions to the history and philosophy of quantum mechanics in a different framework stressing the intersections of research, lecturing, and writing in the making of standard knowledge. Moreover, it advocates for a more methodologically reflexive use of scientific publication genres as sources. Through historiographical reflection, some exemplary case studies, and an appeal to historical craft, this chapter proposes new ways of understanding the making of quantum mechanics as disciplinary knowledge.

This chapter presents arguments for why and how what often are considered mere applications of the new formalism in the early phase of the development of quantum mechanics is relevant to the study of the history of its interpretations. It argues that the often-made cut between foundations and applications is largely artificial and how this is connected to the actors’ own purviews regarding the open-ended fate of quantum mechanics in statu nascendi. It then presents examples of early developments that, besides being applications of the new theory to new phenomena, also had significant interpretational import. This implies a somewhat wider view on what the interpretation of quantum mechanics consists of, and how it is connected to attempts at understanding the meaning of the new theory and its implications more broadly. There is untapped potential in more thoroughly studying the early applications of quantum mechanics for historians, philosophers, and physicists.