Slobodan Perovic

A recent rethinking of the early history of Quantum Mechanics deemed the late 1920s agreement on the equivalence of Matrix Mechanics and Wave Mechanics, prompted by Schrödinger's 1926 proof, a myth. Schrödinger supposedly failed to prove isomorphism, or even a weaker equivalence (“Schrödinger-equivalence”) of the mathematical structures of the two theories; developments in the early 1930s, especially the work of mathematician von Neumann provided sound proof of mathematical equivalence. The alleged agreement about the Copenhagen Interpretation, predicated to a large extent on this equivalence, was deemed a myth as well. In response, I argue that Schrödinger's proof concerned primarily a domain-specific ontological equivalence, rather than the isomorphism or a weaker mathematical equivalence. It stemmed initially from the agreement of the eigenvalues of Wave Mechanics and energy-states of Bohr's Model that was discovered and published by Schrödinger in his first and second communications of 1926. Schrödinger demonstrated in this proof that the laws of motion arrived at by the method of Matrix Mechanics are satisfied by assigning the auxiliary role to eigenfunctions in the derivation of matrices (while he only outlined the reversed derivation of eigenfunctions from Matrix Mechanics, which was necessary for the proof of both isomorphism and Schrödinger-equivalence of the two theories). This result was intended to demonstrate the domain-specific ontological equivalence of Matrix Mechanics and Wave Mechanics, with respect to the domain of Bohr's atom. And although the mathematical equivalence of the theories did not seem out of the reach of existing theories and methods, Schrödinger never intended to fully explore such a possibility in his proof paper. In a further development of Quantum Mechanics, Bohr's complementarity and Copenhagen Interpretation captured a more substantial convergence of the subsequently revised (in light of the experimental results) Wave and Matrix Mechanics. I argue that both the equivalence and Copenhagen Interpretation can be deemed myths if one predicates the philosophical and historical analysis on a narrow model of physical theory which disregards its historical context, and focuses exclusively on its formal aspects and the exploration of the logical models supposedly implicit in it.

Advancing the reductionist conviction that biology must be in agreement with the assumptions of reductive physicalism (the upward hierarchy of causal powers, the upward fixing of facts concerning biological levels) A. Rosenberg argues that downward causation is ontologically incoherent and that it comes into play only when we are ignorant of the details of biological phenomena. Moreover, in his view, a careful look at relevant details of biological explanations will reveal the basic molecular level that characterizes biological systems, defined by wholly physical properties, e.g., geometrical structures of molecular aggregates (cells). In response, we argue that contrary to his expectations one cannot infer reductionist assumptions even from detailed biological explanations that invoke the molecular level, as interlevel causal reciprocity is essential to these explanations. Recent very detailed explanations that concern the structure and function of chromatin—the intricacies of supposedly basic molecular level—demonstrate this. They show that what seem to be basic physical parameters extend into a more general biological context, thus rendering elusive the concepts of the basic level and causal hierarchy postulated by the reductionists. In fact, relevant phenomena are defined across levels by entangled, extended parameters. Nor can the biological context be explained away by basic physical parameters defining molecular level shaped by evolution as a physical process. Reductionists claim otherwise only because they overlook the evolutionary significance of initial conditions best defined in terms of extended biological parameters. Perhaps the reductionist assumptions (as well as assumptions that postulate any particular levels as causally fundamental) cannot be inferred from biological explanations because biology aims at manipulating organisms rather than producing explanations that meet the coherence requirements of general ontological models. Or possibly the assumptions of an ontology not based on the concept of causal powers stratified across levels can be inferred from biological explanations. The incoherence of downward causation is inevitable, given reductionist assumptions, but an ontological alternative might avoid this. We outline desiderata for the treatment of levels and properties that realize interlevel causation in such an ontology

Focusing on the discovery of weak currents, the current debate on the theory-ladenness of observation in modern physics might be too narrow, as it concerns only the last stage of a complex experimental process and statistical methods required to analyze data. The scope of the debate should be extended to include broader experimental conditions that concern the design of the apparatus and different levels of the detection process. These neglected conditions often decisively delimit experiments long before the last stage has been reached, thus predetermining the extent of the dependence of data production on the theory. I explain the nature of these conditions and the theory-ladenness tendencies they produce, noting how they affect the last stage of the data analysis and providing some relevant examples.

H. Collins has challenged the empiricist understanding of experimentation by identifying what he thinks constitutes the experimenter’s regress: an instrument is deemed good because it produces good results, and vice versa. The calibration of an instrument cannot alone validate the results: the regressive circling is broken by an agreement essentially external to experimental procedures. In response, A. Franklin has argued that calibration is a key reasonable strategy physicists use to validate production of results independently of their interpretation. The physicists’ arguments about the merits of calibration are not coextensive with the interpretation of results, and thus an objective validation of results is possible. I argue, however, that the in-situ calibrating and measurement procedures and parameters at the Large Hadron Collider are closely and systematically interrelated. This requires empiricists to question their insistence on the independence of calibration from the outcomes of the experiment and rethink their position. Yet this does not leave the case of in-situ calibration open to the experimenter’s regress argument; it is predicated on too crude a view of the relationship between calibration and measurement that fails to capture crucial subtleties of the case.

A recent rethinking of the early history of Quantum Mechanics deemed the late 1920s agreement on the equivalence of Matrix Mechanics and Wave Mechanics, prompted by Schrödinger’s 1926 proof, a myth. Schrödinger supposedly failed to achieve the goal of proving isomorphism of the mathematical structures of the two theories, while only later developments in the early 1930s, especially the work of mathematician John von Neumman (1932) provided sound proof of equivalence. The alleged agreement about the Copenhagen Interpretation, predicated to a large extent on this equivalence, was deemed a myth as well. If such analysis is correct, it provides considerable evidence that, in its critical moments, the foundations of scientific practice might not live up to the minimal standards of rigor, as such standards are established in the practice of logic, mathematics, and mathematical physics, thereby prompting one to question the rationality of the practice of physics. In response, I argue that Schrödinger’s proof concerned primarily a domain-specific ontological equivalence, rather than the isomorphism. It stemmed initially from the agreement of the eigenvalues of Wave Mechanics and energy-states of Bohr’s Model that was discovered and published by Schrödinger in his First and Second Communications of 1926. Schrödinger demonstrated in this proof that the laws of motion arrived at by the method of Matrix Mechanics could be derived successfully from eigenfunctions as well (while he only outlined the reversed derivation of eigenfunctions from Matrix Mechanics, which was necessary for the proof of isomorphism of the two theories). This result was intended to demonstrate the domain-specific ontological equivalence of Matrix Mechanics and Wave Mechanics, with respect to the domain of Bohr’s atom. And although the full-fledged mathematico-logical equivalence of the theories did not seem out of the reach of existing theories and methods, Schrödinger never intended to fully explore such a possibility in his proof paper. In a further development of Quantum Mechanics, Bohr’s complementarity and Copenhagen Interpretation captured a more substantial convergence of the subsequently revised (in light of the experimental results) Wave and Matrix Mechanics. I argue that both the equivalence and Copenhagen Interpretation can be deemed myths if one predicates the philosophical and historical analysis on a narrow model of physical theory which disregards its historical context, and focuses exclusively on its formal aspects and the exploration of the logical models supposedly implicit in it.

Weinert defends a distinctively anti-Kuhnian position on scientific revolutions, predicating his argument on a nuanced and clear case analysis. He also builds on his previous work on eliminative induction that he sees as the central scientific method in the rise of revolutionary theories. The treatment of social sciences as revolutionary offers the key elements of a promising ambitious project. His botched attempt to portray the Darwinian view of mind as a brand of emergentism is the only weak point if this insightful book