The birth of Bohr's complementarity: The context and the dialogues

This paper starts from the observation that the major hallmarks in the history of quantum mechanics centrally involved light and radiation. Consequently, we ask how precisely did concepts and ideas from radiation theory define the creation of quantum mechanics? And why was it a quantum theory of mechanics and not a quantum theory of electrodynamics that was crafted in the years 1925/26? Following these questions, this paper provides a reading of the history of the old quantum theory from the perspective of radiation. We argue that both wave and matrix mechanics, while emerging from widely different trajectories, emerged as spin-offs from nascent, ultimately unsuccessful quantum theories of radiation. We discuss the epistemological implications of this development for the historical and philosophical analysis of quantum mechanics and quantum field theory.

We go through Bohr's talk about complementary features of quantum theory at the Volta Conference in September 1927, by collating a manuscript that Bohr wrote in Como with the unpublished stenographic report of his talk. We conclude – also with the help of some unpublished letters – that Bohr gave a very concise speech in September. The formulation of his ideas became fully developed only between the fifth Solvay Conference, in Brussels in October, and early 1928. The unpublished stenographic reports of the Solvay Conference suggest that we reconsider the role that discussions with his colleagues possibly had on Bohr's final presentation of the complementary sides of atomic physics in his 1928 papers.

This chapter discusses paraconsistent logics (PL) and paraconsistency. PL are the logics of inconsistent but nontrivial theories. A deductive theory is paraconsistent if its underlying logic is paraconsistent. A theory is inconsistent if there is a formula (a grammatically well-formed expression of its language) such that the formula and its negation are both theorems of the theory; otherwise, the theory is called consistent. A theory is trivial if all formulas of its language are theorems. In a trivial theory “everything” (expressed in its language) can be proved. If the underlying logic of a theory is classical logic, or even any of the standard logical systems such as intuitionistic logic, inconsistency entails triviality, and conversely. This chapter discusses da Costa's C-logics. This chapter elaborates on paraconsistent set theories, and shows, in particular, how they accommodate inconsistent objects, such as the Russell set. Ja´skowski's discussive logic is examined, and it is showed how it can be used in the formulation of the concept of partial truth. The chapter also examines annotated logic, and some of its applications.

The received view on the contributions of the physics community to the birth of molecular biology tends to present the physics community as sharing a basic level consensus on how physics should be brought to bear on biology. I argue, however, that a close examination of the views of three leading physicists involved in the birth of molecular biology, Bohr, Delbrück, and Schrödinger, suggests that there existed fundamental disagreements on how physics should be employed to solve problems in biology even within the physics community. In particular, I focus on how these three figures differed sharply in their assessment of the relevance of complementarity, the potential of chemical methods, and the relative importance of classical physics. In addition, I assess and develop Roll-Hansen’s attempt to conceptualize this history in terms of models of scientific change advanced by Kuhn and Lakatos. Though neither model is fully successful in explaining the divergence of views among these three physicists, I argue that the extent and quality of difference in their views help elucidate and extend some themes that are left opaque in Kuhn’s model.

This paper examines the development and meaning of Heisenberg's notion of wave–particle equivalence and the way in which it differs from Bohr's more widely known notion of wave–particle complementarity. According to the statistical interpretation of the wave function, developed by Born and Pauli in 1926, the electron is treated as a particle, though it cannot be assigned a well-defined position and momentum at a given time. On the other hand, from the vantage point of quantum electrodynamics developed by Jordan, Klein and Wigner in 1927–1928, the electron is described as a quantized matter wave in three-dimensional space. Heisenberg brought these two empirically equivalent approaches together in his 1929 Chicago lectures. Whereas Bohr argued that it was necessary to use wave and particle descriptions alternatively in different experimental arrangements, Heisenberg insisted that one could interpret the quantum-mechanical equation of motion in terms of either a wave ontology or a particle ontology. Clarifying the differences between Bohr and Heisenberg provides a deeper insight into the divergent views which formed the so-called ‘Copenhagen interpretation’ of quantum mechanics.

This chapter discusses paraconsistent logics (PL) and paraconsistency. PL are the logics of inconsistent but nontrivial theories. A deductive theory is paraconsistent if its underlying logic is paraconsistent. A theory is inconsistent if there is a formula (a grammatically well-formed expression of its language) such that the formula and its negation are both theorems of the theory; otherwise, the theory is called consistent. A theory is trivial if all formulas of its language are theorems. In a trivial theory “everything” (expressed in its language) can be proved. If the underlying logic of a theory is classical logic, or even any of the standard logical systems such as intuitionistic logic, inconsistency entails triviality, and conversely. This chapter discusses da Costa's C-logics. This chapter elaborates on paraconsistent set theories, and shows, in particular, how they accommodate inconsistent objects, such as the Russell set. Ja´skowski's discussive logic is examined, and it is showed how it can be used in the formulation of the concept of partial truth. The chapter also examines annotated logic, and some of its applications.