This paper critically examines the view of quantum mechanics that emerged shortly after the introduction of quantum mechanics and that has been widespread ever since. Although N. Bohr, P. A. M. Dirac, and W. Heisenberg advanced this view earlier, it is best exemplified by J. von Neumann’s argument in Mathematical Foundations of Quantum Mechanics (1932) that the transformation of “a [quantum] state … under the action of an energy operator … is purely causal,” while, “on the other hand, the state … which may measure a [given] quantity … undergoes in a measurement a non‐casual change.” Accordingly, while the paper discusses all four of these arguments, it will especially focus on that of von Neumann. The paper also offers an alternative, noncausal, view of the quantum‐mechanical situation and considers the differences between the ensemble and the Bayesian approaches to quantum mechanics from this perspective.
This paper critically examines the view of quantum mechanics that emerged shortly after the introduction of quantum mechanics and that has been widespread ever since. Although N. Bohr, P. A. M. Dirac, and W. Heisenberg advanced this view earlier, it is best exemplified by J. von Neumann’s argument in Mathematical Foundations of Quantum Mechanics (1932) that the transformation of “a [quantum] state … under the action of an energy operator … is purely causal,” while, “on the other hand, the state … which may measure a [given] quantity … undergoes in a measurement a non‐casual change.” Accordingly, while the paper discusses all four of these arguments, it will especially focus on that of von Neumann. The paper also offers an alternative, noncausal, view of the quantum‐mechanical situation and considers the differences between the ensemble and the Bayesian approaches to quantum mechanics from this perspective.
Abstract The Bohr and von Neumann views on the measurement process in quantum mechanics have been interpreted for a long time in somewhat controversial terms, often leading to misconceptions. On the basis of some textual analysis, I would like to show that—contrary to a widespread opinion—their views should be taken less inconsistent, and much closer to each other, than usually thought. As a consequence, I claim that Bohr and von Neumann are conceptually on the same side on the issue of the universality of quantum mechanics: hopefully, this might contribute to a more accurate history of the measurement problem in quantum mechanics.
A history of the discovery of quantum mechanics and paradoxes of its interpretation is reconsidered from the modern point of view of quantum stochastics and information. It is argued that in the orthodox quantum mechanics there is no place for quantum phenomenology such as events. The development of quantum measurement theory, initiated by von Neumann, and Bell's conceptual critics of hidden variable theories indicated a possibility for resolution of this crisis. This can be done by divorcing the algebra of the dynamical generators and an extended algebra of the potential (quantum) and the actual (classical) observables. The latter, called beables, form the center of the algebra of all observables, as the only visible (macroscopic) observables must be compatible with any hidden (microscopic) observable. It is shown that within this approach quantum causality can be rehabilitated within an extended quantum mechanics (eventum mechanics) in the form of a superselection rule for compatibility of the consistent histories with the statistically predictable future. The application of this rule in the form of the nondemolition principle leads to the statistical inference of the von Neumann projection postulate, and also to the more general quantum information dynamics for instantaneous events, spontaneous localizations (i.e. quantum jumps), and state diffusions (i.e. continuous trajectories). This gives a dynamical solution, in the form of a Dirac boundary value problem and reduced filtering equations, of the notorious decoherence and measurement problems which was tackled unsuccessfully by many famous mathematicians and physicists starting with von Neumann, Schroedinger and Bohr.
ABSTRACT The paper aims to bridge the history of quantum theory with its philosophical implications. The focus is not only on the scientific underpinnings of quantum mechanics (these theories emerged as ‘ad hoc’ responses to experimental anomalies) but also on the philosophical ramifications of its probabilistic nature and indeterminacy, which differ from classical realism. The paper examines Dirac's, Bell's, and modern views, focusing on how quantum mechanics (QM) challenges traditional notions of causality, objectivity, and truth while embracing epistemological and metaphysical perspectives. Debates over collapse theories and hidden variables are discussed, as well as Putnam's philosophical outlook, which includes his trenchant involvement with realism, logic, and the measurement problem. Finally, the paper proposes that QM represents a philosophical revolution that renews our understanding of reality, knowledge, and scientific explanation, rather than simply serving as a physical theory for assessing the prospects of quantum philosophy by connecting it to broader aspects such as relativity, causality, and scientific realism.
It is argued here that a causal account of the behavior of quantum systems can coherently be given within the context of the Basic interpretation of quantum mechanics of Dirac and von Neumann when extended to include positive-operator-valued measures and to include effects as observables. This account is most naturally provided via the notion of probabilistic causation, in particular, as an extension of von Neumann's conception of mathematical causation in mechanics which was intended to generalize aspects of the Laplacian notion to include quantum mechanics.
This work develops a conceptual framework for the foundations of quantum physics, linking two main approaches: the algebraic formulation and quantum probability. Rather than proposing new axioms or theories, the text reorganizes and synthesizes existing models, highlighting their assumptions, conceptual structures, and operational significance. The analysis begins with von Neumann's measurement theory and its subsequent developments by Mackey, emphasizing the role of experimentally feasible procedures and the need for a statistical model grounded in laboratory practice. The work adopts an operational perspective, according to which physical quantities are defined solely through experimental measurement methods, and the corresponding probabilistic measures are derived from measurement outcomes. The introduction critically examines the limitations of purely mathematical formulations - such as the algebraic method - when separated from experimental interpretation. The text argues for a clear distinction between axioms, postulates, and presuppositions, and for a reconstruction of quantum theory that respects both empirical constraints and conceptual clarity.
Overall, the goal is to provide a coherent path from operational principles to algebraic structures, offering a basis for an axiomatic reformulation of quantum mechanics that remains faithful to physical practice.
Abstract The book starts with a description of classical mechanics then discusses the quantum phenomena that require us to give up our commonsense classical intuitions. We consider the physical and conceptual arguments that led to the standard von Neumann-Dirac formulation of quantum mechanics and how the standard theory explains quantum phenomena. This includes a discussion of how the theory’s two dynamical laws work with the standard interpretation of states to explain determinate measurement records, quantum statistics, interference effects, entanglement, decoherence, and quantum nonlocality. A careful understanding of how the standard theory works ultimately leads to the quantum measurement problem. We consider how the measurement problem threatens the logical consistency of the standard theory then turn to a discussion of the main proposals for resolving it. This includes collapse formulations of quantum mechanics like Wigner’s extension of the standard theory and the GRW approach and no-collapse formulations like pure wave mechanics, the various many-worlds theories, and Bohmian mechanics. In discussing alternative formulations of quantum mechanics we pay particular attention to the explanatory role played by each theory’s empirical ontology and associated metaphysical commitments and the conceptual trade-offs between theoretical options.