Heisenberg in Göttingen, Copenhagen and Helgoland Werner Heisenberg studied under Sommerfeld in Munich and was present at the Bohr Festspiele held in Göttingen in 1922 (Sect. 8.2). Although aged only 20, he challenged Bohr's support of Kramers' analysis of the quadratic Stark effect, having studied the paper in detail for Sommerfeld's seminar in Munich. The result was a long walk with Bohr during which they discussed this topic and the more general problems of quantum physics. This encounter made a strong impression on Heisenberg. Much later Heisenberg stated: ‘That discussion, which took us back and forth over Hainberg's wooded heights, was the first thorough discussion I can remember on the fundamental physical and philosophical problems of modern atomic theory, and it has certainly had a decisive influence on my later career. For the first time, I understood that Bohr's view of his theory was much more sceptical than that of many other physicists – for example, Sommerfeld – at that time, and that his insight into the structure of the theory was not a result of mathematical analysis of the basic assumptions, but rather of an intense occupation with the actual phenomena, such that it was possible for him to sense the relationships intuitively rather than derive them formally.’ Heisenberg spent the winter of 1922–1923 working in Göttingen as Born's assistant. The astronomers had made great progress in the use of perturbations techniques within the action–angle formulation of classical dynamics to study the gravitational perturbations of planetary orbits.
Heisenberg in Göttingen, Copenhagen and Helgoland Werner Heisenberg studied under Sommerfeld in Munich and was present at the Bohr Festspiele held in Göttingen in 1922 (Sect. 8.2). Although aged only 20, he challenged Bohr's support of Kramers' analysis of the quadratic Stark effect, having studied the paper in detail for Sommerfeld's seminar in Munich. The result was a long walk with Bohr during which they discussed this topic and the more general problems of quantum physics. This encounter made a strong impression on Heisenberg. Much later Heisenberg stated: ‘That discussion, which took us back and forth over Hainberg's wooded heights, was the first thorough discussion I can remember on the fundamental physical and philosophical problems of modern atomic theory, and it has certainly had a decisive influence on my later career. For the first time, I understood that Bohr's view of his theory was much more sceptical than that of many other physicists – for example, Sommerfeld – at that time, and that his insight into the structure of the theory was not a result of mathematical analysis of the basic assumptions, but rather of an intense occupation with the actual phenomena, such that it was possible for him to sense the relationships intuitively rather than derive them formally.’ Heisenberg spent the winter of 1922–1923 working in Göttingen as Born's assistant. The astronomers had made great progress in the use of perturbations techniques within the action–angle formulation of classical dynamics to study the gravitational perturbations of planetary orbits.
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.
Abstract There is a certain similarity in the early lives of Planck and of Heisenberg [1,2]. Both had fathers who were professors at the University of Munich, both visited the Maximilians-Gymnasium in Munich, and both went to see a professor in Munich to seek advice for their studies. We have mentioned at the beginning of the Prologue how Jolly in vain tried to dissuade Planck from studying physics. Heisenberg, in his autobiographic book [3], which is devised as a series of conversations, tells us of a similar experience. In the autumn of 1920, when he was about to enter the university, his first choice was mathematics. He wanted not only to do course work but also learn about problems of current interest. This, he thought, he could do best by participating in a professor’s seminar usually reserved to advanced students and Ph.D. candidates. He asked for an interview with Lindemann , the most distinguished mathematician in Munich, who was famous for having proved that the number π is transcendental. But the old professor and the young student found no understanding, partly because Lindemann’s dog noisily interfered. The result was that Heisenberg opted for theoretical physics and went to ask Sommerfeld to be admitted to his seminar. Sommerfeld agreed. At that time Pauli, only a year older than Heisenberg, was already actively doing research under Sommerfeld. The two young men became life-long friends.
Abstract Driven by the idea that a physical theory should only deal with observable quantities, Werner Heisenberg, a young post-doc working with Max Born in Göttingen, who had earlier done his Ph.D. work under Sommerfeld in Munich, was led to introduce a new type of object which represented the transitions between Bohr-Sommerfeld orbits. Max Born realized and recognized these objects as matrices. Together with Pascual Jordan, another post-doc, they worked out a complete theory, matrix mechanics. They completed this work in a few months. We discuss the role of matrix mechanics in the development of quantum mechanics.
The difficulties of the old quantum theory were largely dispelled by the development of quantum mechanics in the 1920s. First Heisenberg (1925) developed the rather abstract matrix mechanics and soon after Schro¨dinger (1926; see also Eckart, 1926) developed the physically more appealing wave mechanics. Subsequently he showed them to be mathematically equivalent. The physicists were greatly relieved; now they had once again a mathematical formalism that enabled the results of experiments to be calculated. It was possible to move forward. It is certainly a very elegant and indeed beautiful formalism, and does enable the results of many physical measurements to be calculated with great accuracy. It is used daily by atomic and nuclear physicists; there is no other way to make calculations. From the earliest days there has been intense debate about the interpretation of quantum mechanics, and it shows no signs of being settled; if anything it is becoming more intense over the years. As Penrose has remarked, no one understands quantum mechanics. Feynman (1967; see also Sykes, 1994) also admitted that ‘nobody understands quantum mechanics’, and Einstein once remarked: ‘I have thought a hundred times as much about the quantum problems as I have about general relativity theory’ (Pais, 1994, p. 57). It should therefore be evident that the most that can be done here is to try to show where the real difficulties lie, and how the failure to recognize that quantum mechanics is an essentially statistical theory has led to a series of confusing quantum paradoxes. It is just these paradoxes that have often been used to support theological speculations. It is useful to ask what ‘understanding quantum mechanics’ actually means. Certainly it means being able to calculate the results of many measurements. The same applies to Newton’s theory of gravitation, which we understand in the sense that we can use it as a basis of calculation, although we do not really understand the gravitational force itself. Very often, especially in modern physics, the mathematical formalism does not give us the sort of intuitive physical feeling for what is going on that we often obtain from classical mechanics. Perhaps we can never achieve more than this for quantum mechanics. In classical mechanics we can assume that a property that is measured objectively exists prior to the interaction of the measuring apparatus with the observed system. Quantum mechanics, however, ‘is incompatible with the proposition that measurement discovers some unknown but pre-existing property’ (Peres, 1997, p. 14). There is an important distinction between mysteries and absurdities. We may be forced to live with mysteries, but there is no reason why we should put up with absurdities such as the wave-particle duality, tunnelling through potential barriers, acausal events and the collapse of the wave function. These are the quantum paradoxes that will be discussed later on. They arise within the Copenhagen interpretation of quantum mechanics and are solved by other interpretations. These alternative interpretations enable us to make conjectures about what is going on, even though we cannot understand it in detail. This is acceptable and a stimulus to further research. It is certainly difficult enough to understand quantum mechanics, but there is no need to try to visualize logical absurdities in the effort to do so. Quantum mechanics is a mathematical formalism that makes it possible to calculate the results of some experiments. Anything more than this, such as questions about the interpretation of what is measured and whether it tells us what is actually going on in the system being studied, belongs to philosophy. Thus we are concerned here with what is essentially a philosophical debate; if it were just a matter of physics the debate would have been settled long ago. One of the difficulties is that it invokes the results of experiments and uses the language of quantum mechanics. Inevitably this language uses philosophical terms and then it is easy to give the impression that the philosophical propositions are in some way entailed by the physical results. These in turn can influence theological thinking. In order to be quite clear which arguments are justified and which are not, it is essential to separate the three levels of discourse: physical, philosophical and theological. Our task is to relate these together, and this immediately raises the traditional problems of the philosophy of science, including the relation of experiment to theory, and of theory to explanation. We begin by discussing experiments, distinguishing between those that are real and those that are imaginary.
THE conceptual problems raised by the discovery of quantum effects have not been fully resolved after half a century. Part of the reason for this is undoubtedly to be found in the mutual ignorance which prevails between physicists and philosophers. In his book Heisenberg brings together a philosophically inclined temperament with an unrivalled knowledge of physics. The result is a book of very great interest, however much one might disagree with his conclusions. The collection of essays of which the other book is made up is intended to bring crucial conceptual problems in physics especially to the notice of philosophers. The design and intention of the collection is admirable for this is the proper way to overcome the departmentalization of interest that has left the deep conceptual problems still unresolved. Men like Heisenberg who combine philosophical temperament with scientic knowledge of great distinction are rare, and yet the difficulties can only be cleared up by the application of philosophical techniques of analysis to problems which are an intimate and difficult part of physics. A great deal of the interest of Heisenberg's book lies in the very comprehensive account he gives of the origin and growth of the Copenhagen school, and the way the new phenomena forced a largely unwelcome picture of nature upon Bohr and his friends. The most important chapter from a philosophical point of view is that in which Heisenberg defends this interpretation against the attacks to which it has been subjected. The essence of his argument for the interpretation can be summed up in two propositions. (i) The Copenhagen interpretation of physical theory, which depends upon the acceptance of the so-called Principle of Complementarity, is an inevitable and final interpretation. The reason for this is that there are only two possible general models for understanding given physical phenomena; a particle model or a wave model. These are exhaustive and exclusive because the former depends upon discontinuous and the latter upon continuous (using substance here in the traditional philosophical sense). If we find, as we do, that the two fundamental constituents of the universe, matter and radiation, each exhibit two classes of phenomena, one explainable only on a particle model and one on a wave model, then we are compelled to adopt a complementarity hypothesis and give up the idea of finding a single and uniform model for the understanding of phenomena. There are only two kinds of models; they are mutually exclusive; both are required; hence we either despair before an insoluble problem or adopt the Copenhagen interpretation. (2) Any serious criticism of this interpretation must offer an alternative
‘Sprache und Wirklichkeit in der modernen Physik’ is the title of a lecture Heisenberg gave in 1960 at the Bayerische Akademie der Schönen Künste. The polemics that had accompanied the establishment of quantum mechanics were over by then and the so-called problems of its foundations had lost much of their initial interest. Einstein had been dead for some years. Right up to the end he had expressed his profound dissatisfaction with a theory which, in his opinion, had something unreasonable about it. With the volume dedicated to him by the community of physicists and philosophers, the long debate between Bohr and Einstein had come to an end. It had been a disappointing conclusion, marked by the reaffirmation of the respective viewpoints of two scientists who by now found great difficulty even in defining a common code of communication. As though seeking to narrow the gap between them, Heisenberg took the opportunity to underline the existence of a common feature in their contributions to 20th century physics. Their discoveries had in fact made it possible to recognize that ‘even the fundamental and most elementary concepts of science, such as space, time, place, velocity, have become problematic and must be re-examined’. The conceptual and cognitive implications of relativity and of quantum mechanics were obviously different but Heisenberg maintained that both theories asked the same question: ‘Does the language we use when we speak of experiments correspond to the artificial language of mathematics which, as we know, describes real relationships correctly; or has it become separated from it so that we must be content with imprecise linguistic formulations and only return to the artificial language of mathematics when we are forced to express ourselves with precision?’.