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Epistemology & Philosophy of Science

Heisenberg’s Pythagorean Revolution

Arkady Plotnitsky

Published Jan 1, 2025• 1 citation
Publisher

Abstract

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.

DOI
10.5840/eps202562455

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Epistemology & Philosophy of Science•Jan 1, 2025•1 citation
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.
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.
This article offers a new argument concerning the relationships between mathematics and physical reality in quantum theory. While, as dedicated to the centenary of Heisenberg's invention of quantum mechanics, the article contains a historical discussion, it is not historical, but physical and philosophical. Heisenberg's thinking leading him to QM and beyond is only part of the genealogy of this argument, which also differs from that of Heisenberg and builds on the previous work of the present author. Among the contributions in the article are a new conception of the ultimate reality responsible for quantum phenomena; a new understanding, based on this conception, of the role of mathematics in physics in quantum theory; a critique of Heisenberg's and all Platonism in quantum theory and beyond; a new perspective on the role of symmetries in quantum field theory; and a new understanding of the relationships between continuity and discontinuity in quantum physics.
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.
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.
The centenary of quantum mechanics brings into focus the question of the accuracy of established terminology for describing the radical transformations that occurred. Critical analysis reveals that the term “quantum revolution” fosters a simplified perception of a single, pivotal turn in physics during the 1920s and 1930s and provides a superficial account of the actual changes over the past 100 years. This article critically re-examines the established term “quantum revolution” from the perspective of its conceptual limitations in describing the real changes of the last century. Arguments are presented for its partial replacement with the more flexible concept of “revolutionary transformations in quantum theory and its interpretations”, which emphasises the processual and multifaceted nature of these changes. The methodological foundation of this research is the distinction between two types of interpretations of quantum theory: “pragmatic” interpretations, which focus on connecting the formalism with experiment, and “explanatory” interpretations, which aim to form conceptions of quantum reality. The application of the concept of a quantum revolution is justified for the pragmatic interpretation, which was formed in 1925–1927 and later became established as the orthodox view, but not for interpretations of the explanatory type. Three initial strategies for preserving classical language in the description of quantum phenomena are identified: classical realism, quantum dualism, and instrumentalism. The analysis addresses persistent historiographical myths surrounding the Copenhagen interpretation – namely, that it is inherent in the postulates of quantum theory, and that it is inherently instrumentalist and subjectivist. A distinction is shown between the orthodox (pragmatic) and the Copenhagen (explanatory) interpretations. Particular attention is paid to the realistic turn in explanatory interpretations (1952–1958), largely associated with the later works of Heisenberg. It is concluded that the development of quantum theory is characterised not by a single revolution, but by a series of transformations of varying revolutionary intensity, many of which occurred in parallel and are still far from complete.