For many years, Arkady Plotnitsky has written extensively about the interpretation of quantum mechanics, and his source of inspiration has undoubtedly been Niels Bohr’s philosophy to which he has returned time and again in order to make clear what Bohr said and meant. More than many other philosophers, Plotnitsky’s work shows a deep understanding of quantum mechanics and of Bohr’s thinking especially. In the present paper, he attempts to give a rational reconstruction of what he sees as Heisenberg’s Pythagorean revolution. This he explains as Heisenberg’s aim in his search for a theory. Heisenberg was looking for “a strictly predictive theory of quantum phenomena (only probabilistically predictive on the experimental grounds), without requiring this theory to represent the ultimate reality responsible for quantum phenomena. This is the form of Pythagorean view that this article advocates under the heading of the ‘reality-without-realism’ (RWR) Pythagorean view, also possible in mathematics”. Unfortunately, I think that Plotnitsky’s rational reconstruction misses some important historical facts just as I think the expression “ultimate reality” is unfortunate. Rejecting that our physical theories represent a world beyond the phenomena does not imply that there is something left to be represented in the future.
For many years, Arkady Plotnitsky has written extensively about the interpretation of quantum mechanics, and his source of inspiration has undoubtedly been Niels Bohr’s philosophy to which he has returned time and again in order to make clear what Bohr said and meant. More than many other philosophers, Plotnitsky’s work shows a deep understanding of quantum mechanics and of Bohr’s thinking especially. In the present paper, he attempts to give a rational reconstruction of what he sees as Heisenberg’s Pythagorean revolution. This he explains as Heisenberg’s aim in his search for a theory. Heisenberg was looking for “a strictly predictive theory of quantum phenomena (only probabilistically predictive on the experimental grounds), without requiring this theory to represent the ultimate reality responsible for quantum phenomena. This is the form of Pythagorean view that this article advocates under the heading of the ‘reality-without-realism’ (RWR) Pythagorean view, also possible in mathematics”. Unfortunately, I think that Plotnitsky’s rational reconstruction misses some important historical facts just as I think the expression “ultimate reality” is unfortunate. Rejecting that our physical theories represent a world beyond the phenomena does not imply that there is something left to be represented in the future.
The innovations to physics introduced by Werner Heisenberg and Niels Bohr via quantum mechanics presented them with epistemological and metaphysical challenges with which they were perpetually engaged. Among Heisenberg’s innovations are the complex-valued quantum state-transition probability amplitudes, and among Bohr’s the non- trivial role of the measuring environment in the procurement of data. In his article, Arkady Plotnitsky examines the responses of these two natural philosophers to these challenges through the lens of Pythagoreanism in terms of the rational and the irrational. He argues that Bohr’s philosophical stance is of the Reality-without-Realism sort in that Bohr holds quantum reality to be unrepresentable, and that Heisenberg’s is of the Pythagorean-realist sort in that Heisenberg comes to hold reality to be representable, but only by mathematics. Here, I argue that Heisenberg’s later representation of reality can be characterized as neo- Aristotelian because, among other relevant things, he intentionally develops quantum potentiality, which is essential to his late interpretation of the quantum formalism, as a quantification of Aristotle’s potentia.
This article considers a revolutionary transformation – physical, mathematical, and philosophical – of modern physics brought about by Heisenberg’s invention of quantum mechanics (QM). While physical and mathematical aspects of Heisenberg’s invention have been extensively commented on, and while they are essential for this article, considering the transformative philosophical aspects of Heisenberg’s thinking is rare. This article fills this lacuna through the concept of reality without realism (RWR) and the corresponding interpretations of QM, and philosophical implications of this concept.
Following the view of several leading quantum-information theorists, this paper argues that quantum phenomena, including those exhibiting quantum correlations (one of their most enigmatic features), and quantum mechanics may be best understood in quantum-informational terms. It also argues that this understanding is implicit already in the work of some among the founding figures of quantum mechanics, in particular W. Heisenberg and N. Bohr, half a century before quantum information theory emerged and confirmed, and gave a deeper meaning to, to their insights. These insights, I further argue, still help this understanding, which is the main reason for considering them here. My argument is grounded in a particular interpretation of quantum phenomena and quantum mechanics, in part arising from these insights as well. This interpretation is based on the concept of reality without realism, RWR (which places the reality considered beyond representation or even conception), introduced by this author previously, in turn, following Heisenberg and Bohr, and in response to quantum information theory.
The article reconsiders quantum theory in terms of the following principle, which can be symbolically represented as QUANTUMNESS → PROBABILITY → ALGEBRA and will be referred to as the QPA principle. The principle states that the quantumness of physical phenomena, that is, the specific character of physical phenomena known as quantum, implies that our predictions concerning them are irreducibly probabilistic, even in dealing with quantum phenomena resulting from the elementary individual quantum behavior (such as that of elementary particles), which in turn implies that our theories concerning these phenomena are fundamentally algebraic, in contrast to more geometrical classical or relativistic theories, although these theories, too, have an algebraic component to them. It follows that one needs to find an algebraic scheme able make these predictions in a given quantum regime. Heisenberg was first to accomplish this in the case of quantum mechanics, as matrix mechanics, whose matrix character testified to his algebraic method, as Einstein characterized it. The article explores the implications of the Heisenberg method and of the QPA principle for quantum theory, and for the relationships between mathematics and physics there, from a nonrealist or, in terms of this article, “reality-without-realism” or RWR perspective, defining the RWR principle, thus joined to the QPA principle.
Complementarity and Deconstruction: Plotnitsky's Analysis and Beyond Makoto Katsumori Akita University The philosophical thought of the modern physicist Niels Bohr (1885–1962), which revolves around the concept of complementarity, has long been a major subject of historical and philosophical inquiry. Many prior studies of Bohr's complementarity, however, seem to be limited by the fact that they largely proceed within the conceptual frames of the "mainstream" philosophy of science. This being the case, his radical questioning of traditional scientific and philosophical notions—such as the unambiguity of concepts and words—has not been adequately addressed, insofar as these notions are uncritically presupposed by the commentators themselves. In other words, Bohr's thought has often been interpreted under certain tacit premises of scientific rationality that are precisely of the kind targeted by his epistemological critique. In recent years, however, there have emerged new approaches to Bohr's idea of complementarity that place it in different, less conventional, philosophical contexts. Among the most notable of these is Arkady Plotnitsky's endeavor to connect Bohr's complementarity with Jacques Derrida's project of deconstruction. In the present article, based on my recent doctoral dissertation,1 I take up this contribution by Plotnitsky as a suitable point of reference from which to [End Page 435] explore anew Bohr's thought with its radical philosophical implications. After outlining Bohr's complementarity argument and Plotnitsky's reading thereof (in the first and second sections, respectively), I will examine a series of problems that seem to face, or to be left unsolved by, Plotnitsky's account (in the third section). This critical appraisal will finally lead me to sketch a new interpretive approach of my own (in the fourth section), which both extends and delimits the intersections between complementarity and deconstruction. As regards the historical development of Bohr's complementarity, I will largely restrict myself to the period between 1927 and 1950, in which the most crucial of his innovative ideas seem to have been presented. I. Bohr's Idea of Complementarity In his 1927 lecture delivered in Como, Italy, entitled "The Quantum Postulate and the Recent Development of Atomic Theory," Niels Bohr introduced the concept and framework of complementarity as a pivotal idea in his interpretation of quantum theory. From then on, he continually developed the idea of complementarity with regard not only to quantum theory but to other fields of knowledge as well. In what follows, I will first outline his complementarity argument in its "early" period, stretching from 1927 to the mid-thirties,—or, more precisely, until just before his 1935 debate with EPR.2 Bohr starts by noting that "our usual description of physical phenomena is based entirely on the idea that the phenomena concerned may be observed without disturbing them appreciably."3 This notion of physical phenomena as undisturbed by observation underlies all of classical physics and is still maintained in the theory of relativity. However, Bohr continues, a new situation has arisen with the development of quantum theory, specifically with "the so-called quantum postulate, which attributes to any atomic process an essential discontinuity, or rather individuality, completely foreign to the classical theories"; this "individuality" implies that "any observation of atomic phenomena will involve an interaction with the [End Page 436] agency of observation not to be neglected" (PWNB, 1: 53–54.). In more specific terms, any observation aimed at space-time coordination brings about an exchange of momentum and energy with the measuring rods and clocks. It is crucial here that this interaction between the object and the instrument of observation is not simply unavoidable, but "uncontrollable," which represents a "feature of irrationality" brought into the description of nature (PWNB, 1: 68, 91). For insofar as the measuring instruments are to fulfill their purpose, the interaction itself cannot be taken into account, and thus the magnitude of the disturbance always remains unknown. It follows, in Bohr's view, that "an independent reality in the ordinary physical sense can neither be ascribed to the phenomena nor to the agencies of observation...
[I] think I can safely say that nobody understands quantum mechanics. Richard Feynman, The Character of Physical Law Quantum mechanics [is] that mysterious, confusing discipline, which none of us really understands but which we know how to use. It works perfectly, as far as we can tell, in describing physical reality, but it is a ‘counter-intuitive discipline’… Murray Gell-Mann, Questions for the Future [The quantum] postulate implies a renunciation as regards the causal space-time co-ordination of atomic processes. Niels Bohr, Atomic Theory and the Description of Nature It should be emphasized, however, that the probability function does not in itself represent a course of events in the course of time. It represents a tendency for events and our knowledge of events. The probability function can be connected with reality only if one essential condition is fulfilled: if a new measurement is made to determine a certain property of the system. [T]he idea of an objective real world whose smallest parts exist objectively in the same sense as stones or trees exist, independently of whether or not we observe them…is impossible … Werner Heisenberg, Physics and Philosophy [In] quantum theory it is the principle of causality , or more accurately that of determinism , which must be dropped and replaced by something else.… We now have a new form of the law of causality.… It is as follows: if in a certain process the initial conditions are determined as accurately as the uncertainty relations permit, then the probabilities of all possible subsequent states are governed by exact laws. Max Born, The Restless Universe