First, this article considers the nature of quantum reality and the concept of realism in quantum theory, in conjunction with the roles of locality, causality, and probability and statistics there. Second, it offers two interpretations of quantum mechanics, developed by the authors of this article, the second of which is also a different theory of quantum phenomena. Both of these interpretations are statistical. The first interpretation, by A. Plotnitsky, “the statistical Copenhagen interpretation,” is nonrealist, insofar as the description or even (...) conception of the nature of quantum objects and processes is precluded. The second, by A. Khrennikov, is ultimately realist, because it assumes that the quantum-mechanical level of reality is underlain by a deeper level of reality, described, in a realist fashion, by a model, based in the pre-quantum classical statistical field theory, the predictions of which reproduce those of quantum mechanics. Moreover, because the continuous fields considered in this model are transformed into discrete clicks of detectors, experimental outcomes in this model depend on the context of measurement in accordance with N. Bohr’s interpretation and the statistical Copenhagen interpretation, which coincides with N. Bohr’s interpretation in this regard. (shrink)
Reading Bohr: Physics and Philosophy offers a new perspective on Niels Bohr's interpretation of quantum mechanics as complementarity, and on the relationships between physics and philosophy in Bohr's work, which has had momentous significance for our understanding of quantum theory and of the nature of knowledge in general. Philosophically, the book reassesses Bohr's place in the Western philosophical tradition, from Kant and Hegel on. Physically, it reconsiders the main issues at stake in the Bohr-Einstein confrontation and in the ongoing debates (...) concerning quantum physics. It also devotes greater attention than in most commentaries on Bohr to the key developments and transformations of his thinking concerning complementarity. Most significant among them were those that occurred, first, under the impact of Bohr's exchanges with Einstein and, second, under the impact of developments in quantum theory itself, both quantum mechanics and quantum field theory. The importance of quantum field theory for Bohr's thinking has not been adequately addressed in the literature on Bohr, to the considerable detriment to our understanding of the history of quantum physics. Filling this lacuna is one of the main contributions of the book, which also enables us to show why quantum field theory compels us to move beyond Bohr without, however, simply leaving him behind. (shrink)
This article aims to contribute to the ongoing task of clarifying the relationships between reality, probability, and nonlocality in quantum physics. It is in part stimulated by Khrennikov’s argument, in several communications, for “eliminating the issue of quantum nonlocality” from the analysis of quantum entanglement. I argue, however, that the question may not be that of eliminating but instead that of further illuminating this issue, a task that can be pursued by relating quantum nonlocality to other key features of quantum (...) phenomena. I suggest that the following features of quantum phenomena and quantum mechanics, distinguishing them from classical phenomena and classical physics— the irreducible role of measuring instruments in defining quantum phenomena, discreteness, complementarity, entanglement, quantum nonlocality, and the irreducibly probabilistic nature of quantum predictions—are all interconnected, so that it is difficult to give an unconditional priority to any one of them. To argue this case, I shall consider quantum phenomena and quantum mechanics from a nonrealist or, in terms adopted here, “reality-without-realism” perspective. This perspective extends Bohr’s view, grounded in his analysis of the irreducible role of measuring instruments in the constitution of quantum phenomena. (shrink)
This article is concerned with the role of fundamental principles in theoretical physics, especially quantum theory. The fundamental principles of relativity will be addressed as well, in view of their role in quantum electrodynamics and quantum field theory, specifically Dirac’s work, which, in particular Dirac’s derivation of his relativistic equation of the electron from the principles of relativity and quantum theory, is the main focus of this article. I shall also consider Heisenberg’s earlier work leading him to the discovery of (...) quantum mechanics, which inspired Dirac’s work. I argue that Heisenberg’s and Dirac’s work was guided by their adherence to and their confidence in the fundamental principles of quantum theory. The final section of the article discusses the recent work by D’Ariano and coworkers on the principles of quantum information theory, which extend quantum theory and its principles in a new direction. This extension enabled them to offer a new derivation of Dirac’s equations from these principles alone, without using the principles of relativity. (shrink)
Following Niels Bohr's interpretation of quantum mechanics as complementarity, this article argues that quantum mechanics may be seen as a theory of, in N. David Mermin's words, “correlations without correlata,” understood here as the correlations between certain physical events in the classical macro world that at the same time disallow us to ascertain their quantum-level correlata.
This article considers the relationships between the character of physical law in quantum theory and Bohr’s concept of complementarity, under the assumption of the unrepresentable and possibly inconceivable nature of quantum objects and processes, an assumption that may be seen as the most radical departure from realism currently available. Complementarity, the article argues, is a reflection of the fact that, as against classical physics or relativity, the behavior of quantum objects of the same type, say, all electrons, is not governed (...) by the same physical law in all contexts, specifically in complementary contexts. On the other hand, the mathematical formalism of quantum mechanics offers correct probabilistic or statistical predictions in all contexts, here, again, under the assumption that quantum objects themselves and their behavior are beyond representation or even conception. Bohr, in this connection, spoke of “an entirely new situation as regards the description of physical phenomena that, the notion of complementarity aims at characterizing.” The article also considers the relationships among complementarity, entanglement, and quantum information, by basing these relationships on this understanding of complementarity. (shrink)
This article explores the relationships between the philosophical foundations of quantum field theory, the currently dominant form of quantum physics, and Deleuze's concept of the virtual, most especially in relation to the idea of chaos found in Deleuze and Guattari's What is Philosophy?. Deleuze and Guattari appear to derive this idea partly from the philosophical conceptuality of quantum field theory, in particular the concept of virtual particle formation. The article then goes on to discuss, from this perspective, the relationships between (...) philosophy and science, and between their respective ways of confronting chaos, a great enemy but also a great friend of thought, and its greatest ally in its struggle against opinion. (shrink)
The point of departure for this article is Werner Heisenberg’s remark, made in 1929: “It is not surprising that our language [or conceptuality] should be incapable of describing processes occurring within atoms, for … it was invented to describe the experiences of daily life, and these consist only of processes involving exceedingly large numbers of atoms. … Fortunately, mathematics is not subject to this limitation, and it has been possible to invent a mathematical scheme—the quantum theory [quantum mechanics]—which seems entirely (...) adequate for the treatment of atomic processes.” The cost of this discovery, at least in Heisenberg’s and related interpretations of quantum mechanics, is that, in contrast to classical mechanics, the mathematical scheme in question no longer offers a description, even an idealized one, of quantum objects and processes. This scheme only enables predictions, in general, probabilistic in character, of the outcomes of quantum experiments. As a result, a new type of the relationships between mathematics and physics is established, which, in the language of Eugene Wigner adopted in my title, indeed makes the effectiveness of mathematics unreasonable in quantum but, as I shall explain, not in classical physics. The article discusses these new relationships between mathematics and physics in quantum theory and their implications for theoretical physics—past, present, and future. (shrink)
Following Asher Peres’s observation that, as in classical physics, in quantum theory, too, a given physical object considered “has a precise position and a precise momentum,” this article examines the question of the definition of quantum variables, and then the new type (as against classical physics) of relationships between mathematics and physics in quantum theory. The article argues that the possibility of the precise definition and determination of quantum variables depends on the particular nature of these relationships.
Andrei Khrennikov's book returns us to the old question of whether reality, either material or mental, may be fundamentally mathematical. This question, however, creates difficulties for those not suitably trained in mathematics. While this was already a problem for the Greeks, the exceedingly abstract and complex character of modern mathematics makes it especially acute now. Khrennikov's book confronts its readers with one of the more arcane areas of modern mathematics, namely p-adics and the p-adic version of the mathematics used in (...) classical and quantum physics. At the same time, by dealing with Freudian and related theory, the book focuses primarily on the human mind rather than the material world or the brain as a physical object. Thus, while harking back to Greek thought on the possibly mathematical nature of mental reality, the project is unusual from a contemporary point of view. These days, the more usual role of mathematics lies in investigation of the biological, chemical, and physical bases of mental processes, including exploration of the possibility of their quantum origin . While using analogous mathematics, Khrennikov's project shifts the focus to the mathematical modeling of mental, rather than physical, processes. Andrei Khrennikov, Classical and Quantum Mental Models and Freud's Theory of Unconscious Mind, Vaxjo, Sweden: Vaxjo University Press, 2002, xix+207pp., ISBN 91-7636-315-5. (shrink)
Many commentators have remarked in passing on the resonance between deconstructionist theory and certain ideas of quantum physics. In this book, Arkady Plotnitsky rigorously elaborates the similarities and differences between the two by focusing on the work of Niels Bohr and Jacques Derrida. In detailed considerations of Bohr’s notion of complementarity and his debates with Einstein, and in analysis of Derrida’s work via Georges Bataille’s concept of general economy, Plotnitsky demonstrates the value of exploring these theories in relation to each (...) other. Bohr’s term complementarity describes a situation, unavoidable in quantum physics, in which two theories thought to be mutually exclusive are required to explain a single phenomenon. Light, for example, can only be explained as both wave and particle, but no synthesis of the two is possible. This theoretical transformation is then examined in relation to the ways that Derrida sets his work against or outside of Hegel, also resisting a similar kind of synthesis and enacting a transformation of its own. Though concerned primarily with Bohr and Derrida, Plotnitsky also considers a wide range of anti-epistemological endeavors including the work of Nietzsche, Bataille, and the mathematician Kurt Gödel. Under the rubric of complementarity he develops a theoretical framework that raises new possiblilities for students and scholars of literary theory, philosophy, and philosophy of science. (shrink)
Taking as its point of departure the question of light vis-à-vis the question of being in Derrida's work, this article discusses Derrida's radical conceptions of khoral spatiality and alterity, by linking his first book on Edmund Husserl's “The Origin of Geometry” and his early critique of Emmanuel Levinas to his exploration of the ethico-political problematics, in part, again, via Levinas, in his latest works. The article also considers Derrida's reading of Kafka in “Before the Law,” decisive for his analysis of (...) the problematics in question and for our understanding of the relationships between “geometry and democracy.” These relationships, the article argues, are an essential concern of much of Derrida's work and of our culture, from the pre-Socratics on. (shrink)