At the 1927 Solvay conference Born and Heisenberg presented a joint report on quantum mechanics. I suggest that the significance of this report lies in that it contains a ‘final’ formulation of the statistical interpretation of quantum mechanics that goes beyond Born’s origi-nal proposal. In particular, this formulation imports elements from Heisenberg’s work as well as from the transformation theory of Dirac and Jordan. I suggest further a reading of Born and Heisenberg’s position in which the wave function is an effective notion. This can make sense of a remarkable aspect of their presentation, namely the fact that the ‘quantum mechanics’ of Born and Heisenberg apparently lacks wave function collapse.
At the 1927 Solvay conference Born and Heisenberg presented a joint report on quantum mechanics. I suggest that the significance of this report lies in that it contains a ‘final’ formulation of the statistical interpretation of quantum mechanics that goes beyond Born’s origi-nal proposal. In particular, this formulation imports elements from Heisenberg’s work as well as from the transformation theory of Dirac and Jordan. I suggest further a reading of Born and Heisenberg’s position in which the wave function is an effective notion. This can make sense of a remarkable aspect of their presentation, namely the fact that the ‘quantum mechanics’ of Born and Heisenberg apparently lacks wave function collapse.
Abstract This chapter covers the emergence of the statistical interpretation of the new quantum mechanics. After covering the earliest suggestions in this direction by Born and Pauli, it covers the statistical transformation theory of Dirac and Jordan, focusing on Jordan’s version. This version was an important part of the inspiration of Heisenberg’s uncertainty paper, which is covered next. The chapter concludes with the Como and Solvay conferences of late 1927 where Bohr revealed his complementarity principle and where the Copenhagen-Göttingen matrix-mechanics camp of Bohr, Born, Heisenberg, and Pauli squared off with Schrödinger, Einstein, De Broglie, and others in the wave-mechanics camp over the interpretation of the new quantum formalism.
The report by Born and Heisenberg on ‘quantum mechanics’ may seem surprisingly difficult to the modern reader. This is partly because Born and Heisenberg are describing various stages of development of the theory that are quite different from today's quantum mechanics. Among these, it should be noted in particular that the theory developed by Heisenberg, Born and Jordan in the years 1925–6 and known today as matrix mechanics (Heisenberg 1925b [1], Born and Jordan 1925 [2], Born, Heisenberg and Jordan 1926 [4]) a differs from standard quantum mechanics in several important respects. At the same time, the interpretation of the theory (the topic of Section II of the report) also appears to have undergone important modifications, in particular regarding the notion of the state of a system. Initially, Born and Heisenberg insist on the notion that a system is always in a stationary state (performing quantum jumps between different stationary states). Then the notion of the wave function is introduced and related to probabilities for the stationary states. At a later stage, probabilistic notions (in particular, what one now calls transition probabilities) are extended to arbitrary observables, but it remains somewhat unclear whether the wave function itself should be regarded as a fundamental entity or merely as an effective one. This may reflect the different routes followed by Born and by Heisenberg in the development of their ideas. The common position presented by Born and Heisenberg emphasises the probabilistic aspect of the theory as fundamental, and the conclusion of the report expresses strong confidence in the resulting picture.
The 1927 Solvay conference was perhaps the most important in the history of quantum theory. Contrary to popular belief, questions of interpretation were not settled at this conference. Instead, a range of sharply conflicting views were extensively discussed, including de Broglie's pilot-wave theory (which de Broglie presented for a many-body system), Born and Heisenberg's 'quantum mechanics' (which apparently lacked wave function collapse or fundamental time evolution), and Schrödinger's wave mechanics. Today, there is no longer a dominant interpretation of quantum theory, so it is important to re-evaluate the historical sources and keep the debate open. This book contains a complete translation of the original proceedings, with essays on the three main interpretations presented, and a detailed analysis of the lectures and discussions in the light of current research. This book will be of interest to graduate students and researchers in physics and in the history and philosophy of quantum theory.
We reconsider the crucial 1927 Solvay conference in the context of current research in the foundations of quantum theory. Contrary to folklore, the interpretation question was not settled at this conference and no consensus was reached; instead, a range of sharply conflicting views were presented and extensively discussed. Today, there is no longer an established or dominant interpretation of quantum theory, so it is important to re-evaluate the historical sources and keep the interpretation debate open. In this spirit, we provide a complete English translation of the original proceedings (lectures and discussions), and give background essays on the three main interpretations presented: de Broglie's pilot-wave theory, Born and Heisenberg's quantum mechanics, and Schroedinger's wave mechanics. We provide an extensive analysis of the lectures and discussions that took place, in the light of current debates about the meaning of quantum theory. The proceedings contain much unexpected material, including extensive discussions of de Broglie's pilot-wave theory (which de Broglie presented for a many-body system), and a "quantum mechanics" apparently lacking in wave function collapse or fundamental time evolution. We hope that the book will contribute to the ongoing revival of research in quantum foundations, as well as stimulate a reconsideration of the historical development of quantum physics. A more detailed description of the book may be found in the Preface. (Copyright by Cambridge University Press (ISBN: 9780521814218).)
In the 1927 Solvay conference, three apparently irreconcilable interpretations of the quantum mechanics wave function were presented: the pilot-wave interpretation by de Broglie, the soliton wave interpretation by Schrödinger and the Born statistical rule by Born and Heisenberg. In this paper, we demonstrate the complementarity of these interpretations corresponding to quantum systems that are prepared differently and we deduce a synthetic interpretation: the double-preparation theory. We first introduce in quantum mechanics the concept of semi-classical statistically prepared particles, and we show that in the Schrödinger equation these particles converge, when , to the equations of a statistical set of classical particles. These classical particles are undiscerned, and if we assume continuity between classical mechanics and quantum mechanics, we conclude the necessity of the de Broglie–Bohm interpretation for the semi-classical statistically prepared particles (statistical wave). We then introduce in quantum mechanics the concept of a semi-classical deterministically prepared particle, and we show that in the Schrödinger equation this particle converges, when , to the equations of a single classical particle. This classical particle is discerned and assuming continuity between classical mechanics and quantum mechanics, we conclude the necessity of the Schrödinger interpretation for the semi-classical deterministically prepared particle (the soliton wave). Finally we propose, in the semi-classical approximation, a new interpretation of quantum mechanics, the 'theory of the double preparation', which depends on the preparation of the particles.
Historical remarks The quantum mechanical formalism discovered by Heisenberg [Heis 25] an Schrödinger [Schrö 26] in 1925 was first interpreted in a statistical sense by Born [Born 26]. The formal expressions p (φ, a i ) = |(φ,φ ai )| 2 , i ∈ N, were interpreted as the probabilities that a quantum system S with preparation φ possesses the value a i that belongs to the state φ ai . This original Born interpretation, which was formulated for scattering processes, was, however, not tenable in the general case. The probabilities must not be related to the system S in state φ, since in the preparation φ the value a i of an observable A is in general not subjectively unknown but objectively undecided. Instead, one has to interpret the formal expressions p ( a i , a i ) as the probabilities of finding the value a i after measurement of the observable A of the system S with preparation φ. In this improved version, the statistical or Born interpretation is used in the present-day literature. On the one hand, the statistical (Born) interpretation of quantum mechanics is usually taken for granted, and the formalism of quantum mechanics is considered as a theory that provides statistical predictions referring to a sufficiently large ensemble of identically prepared systems S (φ) after the measurement of the observable in question. On the other hand, the meaning of the same formal terms p (φ, a i ) for an individual system is highly problematic.