The quantum mechanics instituted a completely new mathematical language. This change in physics required physicists and philosophers to rethink the concepts by which reality could be represented, since classical notions were limited in the understanding of atomic phenomena. The French philosopher G. Bachelard and the German physicist W. Heisenberg are authors who have discussed the major changes that have occurred in physics and have dealt with the problem of language in quantum mechanics. In this article, the objective is to resort to the arguments of both authors to evidence relations between their ideas about the referred subject. It is noteworthy that Bachelard and Heisenberg criticize the application of the usual language and philosophical concepts of modernity in the new physics, but, through his notion of rupture, the French philosopher proposes that quantum mechanics be restricted to mathematical language. This idea runs counter to Bohr's principle of complementarity, which Heisenberg acknowledges in the understanding of quantum phenomena and an interpretation of quantum physics.
The quantum mechanics instituted a completely new mathematical language. This change in physics required physicists and philosophers to rethink the concepts by which reality could be represented, since classical notions were limited in the understanding of atomic phenomena. The French philosopher G. Bachelard and the German physicist W. Heisenberg are authors who have discussed the major changes that have occurred in physics and have dealt with the problem of language in quantum mechanics. In this article, the objective is to resort to the arguments of both authors to evidence relations between their ideas about the referred subject. It is noteworthy that Bachelard and Heisenberg criticize the application of the usual language and philosophical concepts of modernity in the new physics, but, through his notion of rupture, the French philosopher proposes that quantum mechanics be restricted to mathematical language. This idea runs counter to Bohr's principle of complementarity, which Heisenberg acknowledges in the understanding of quantum phenomena and an interpretation of quantum physics.
Gaston Bachelard (1884-1962), French philosopher, followed a period of ruptures, that is, of conceptual and methodological changes in contemporary physics. He is one of several thinkers who presented important reflections for the understanding of contemporary atomistics. This article highlights the main philosophical reflections of Gaston Bachelard about the foundations of quantum mechanics. For that, it uses important concepts of its epistemology without which its ideas become incomprehensible. Thus, this work highlights how this science breaks with traditional scientific and philosophical ideas in the first half of the 20th century by presenting a new object of knowledge, namely, the quantum corpuscles. Furthermore, in order to characterize the philosophy of bachelardian quantum physics, according to the author, the nature of atomic particles stands out, as the scientific activity of this science in the creation of new phenomena is emphasized and its rationalism applied as philosophy is emphasized best suited to the new physics. Finally, it is emphasized in this work that Bachelard's ideas are different from other interpretations of quantum mechanics.
The ideas in Heisenberg's paper on quantum mechanics in 1925 mark the beginning not only of a new phase in modern physics, but also of Heisenberg's own philosophical journey. This thesis examines that journey between 1925 and the late 1950s by situating Heisenberg's philosophy of quantum mechanics in the context of his encounters with his contemporaries as well as the context of various strands of thought in the German-speaking world at the time. Heisenberg's early philosophical critique of the 'classical' viewpoint between 1925 and 1927 bears the decisive influence of Einstein's theory of relativity, more specifically, the positivism he saw as underpinning Einstein's emancipation from Newtonian physics. The positivist influence on Heisenberg's early attitude to quantum mechanics is evident in three ways: (a) his invocation of an observability principle in 1925 to justify the renunciation of the concept of the electron orbit, (b) an instrumentalist conception of understanding, which characterised Heisenberg's response to Schrodinger's demand for classical visualisation in space and time in 1926-7, and (c) the introduction of an operational definition of concepts such as position and velocity in 1927, in an attempt to replace the concepts of classical physics. But after discussions with Bohr and Einstein in 1926-7, Heisenberg soon recognised what we might term his `empiricist' viewpoint was problematic. In 1927 Heisenberg's thought undergoes a shift away from the `empiricist' viewpoint that had underpinned his early philosophy of quantum mechanics. The nature and scope of this transformation, which forms the central theme in this thesis, has, up until now, been poorly understood and often completely neglected. Through his discussions with Bohr, Heisenberg came to the realisation that despite their limitations, classical concepts were conditions for the possibility of the description of all experience. This marked the abandonment of his earlier attempt to replace classical concepts with quantum concepts. The recognition of the primacy of classical language forms the point of departure for much of Heisenberg's later thought, which brought him into contact with the attempts in the German-speaking world in the 1920s to reconstruct Kantian epistemology. By the mid-1930s, Heisenberg advocated a 'pragmatic transformation' of Kantian philosophy, in which classical concepts were held to be a priori in the sense that they remained the conditions for the possibility of experience, but were no longer held to be necessary or universal in a strict Kantian sense. After 1940 Heisenberg saw the paradoxes of quantum mechanics under the aegis of what can be termed a 'transcendental conception of language', according to which language is not a mere tool, but actively shapes, gives form, and objectifies, our 'reality'. The limits of a classical 'description' in quantum mechanics therefore came to signify for Heisenberg, the limits of 'objective reality'. While Bohr exerted perhaps the most important philosophical influence on Heisenberg, their intellectual relationship was characterised by disagreement and misunderstanding. This is most strikingly displayed in their respective views on wave-particle duality and complementarily. While after 1927 Heisenberg accepted Bohr's basic insight that our knowledge of the quantum world is mediated through classical language, he did not share Rohr's interpretation of complementarity. While Heisenberg certainly used terms such as 'complementarity' and wave-particle duality' in his writings, a close reading reveals that these terms had very different meanings for the two physicists. This is particularly evident in the contrast between Heisenberg's notion of wave-particle equivalence and Bohr's idea of complementarity. In bringing to light these divergences between Bohr and Heisenberg, this thesis lends further weight to the view - already advocated by scholars such as John Hendry and Mara Beller - that the so-called Copenhagen interpretation of quantum mechanics should not be thought of as a unified philosophical position, but actually comprises a number of different strands.
The rupture established by quantum physics in relation to classical physics led to a redefinition of scientific objectivity, which has since relied on mathematical formalism for the knowledge of wave functions. This conception of a "weak objectivity" motivated Werner Heisenberg to resort to Plato's idealism to explain the internal constitution of the material world from geometric structures. However, faced with an idealist paradigm incompatible with modern science, Heisenberg conceived that Kant's philosophy would be the most acceptable reference for interpreting quantum phenomena within the empiricist limits of scientific research. This article presents Hegel's idealism of the absolute as a philosophical horizon for a possible overcoming of the rigidity of the Kantian limits, aiming at a metaphysical interpretation of quantum physics.
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 argument of this article is threefold. First, the article argues that from its rise in the sixteenth century to our own time, the advancement of modern physics as mathematical-experimental science has been defined by the invention of new mathematical structures. Second, the article argues that quantum theory, especially following quantum mechanics, gives this thesis a radically new meaning by virtue of the following two features: on the one hand, quantum phenomena are defined as essentially different from those found in all previous physics by purely physical features; and on the other, quantum mechanics and quantum field theory are defined by purely mathematical postulates, which connect them to quantum phenomena strictly in terms of probabilities, without, as in all previous physics, representing or otherwise relating to how these phenomena physically come about. While these two features may appear discordant, if not inconsistent, I argue that they are in accord with each other, at least in certain interpretations (including the one adopted here), designated as “reality without realism”, RWR, interpretations. This argument also allows this article to offer a new perspective on a thorny problem of the relationships between continuity and discontinuity in quantum physics. In particular, rather than being concerned only with the discreteness and continuity of quantum objects or phenomena, quantum mechanics and quantum field theory relate their continuous mathematics to the irreducibly discrete quantum phenomena in terms of probabilistic predictions while, at least in RWR interpretations, precluding a representation or even conception of how these phenomena come about. This subject is rarely, if ever, discussed apart from previous work by the present author. It is, however, given a new dimension in this article which introduces, as one of its main contributions, a new principle: the mathematical complexity principle.
The new discoveries of QM led to re-assessing, broadening the meanings of many physical concepts, and formulating a new logic that was no longer based on the classical principles of non-contradiction, identity, and causality. Heisenberg considered the classical logic and the conception of language expressed in the Tractatus Logico-Philosophicus inadequate for the understanding of the problems of language with which the physicists of the Copenhagen school had had to deal in order to define the foundations of Quantum Mechanics. On the contrary, he saw in Wittgenstein’s posthumous Philosophical Investigations the key to solving those problems. One may formulate a proportion and state that the use of language described in the Tractatus fits the use of language in Classical Mechanics, as the use of language described in PI fits the use of language in QM. I interpret the reflections of the physicists of the Copenhagen school on the limits of language relative to QM by highlighting how the epistemological revolution of quantum physics shares a conception of language similar to that expressed by late Wittgenstein in PI. I also aim to explain why Heisenberg considered it inappropriate to subsume the propositions and concepts of QM under the rules of the propositional logic of Tractatus. I explain why the philosophy of language expounded in PI, which is based on language games and resemblance families, sheds a light on how and why QM has contributed to renewing existing concepts (such as space, trajectory, observer, etc.) and to formulate a new logic (quantum logic).