Schrödinger's work on wave mechanics in 1926 appears to have been driven by the idea that one could give a purely wave-theoretical description of matter. Key elements in this picture were the idea of particles as wave packets (Section 4.3) and the possible implications for the problem of radiation (Section 4.4). This pure wave theory, in contrast to de Broglie's work, did away with the idea of particle trajectories altogether (Section 4.5). The main conflict, however, was between Schrödinger and the proponents of quantum mechanics (in particular Heisenberg, Section 4.6), both in its form at the time of Schrödinger's papers and in its further developments as sketched in the previous chapter.

For reference, we provide a brief chronology of Schrödinger's writings relating to wave mechanics up to the Solvay conference:

• Paper on Einstein's gas theory, submitted 15 December 1925, published 1 March 1926 (Schrödinger 1926a).

• First paper on quantisation, submitted 27 January 1926, addendum in proof 28 February 1926, published 13 March 1926 (Schrödinger 1926b).

• Second paper on quantisation, submitted 23 February 1926, published 6 April 1926 (Schrödinger 1926c).

• Paper on the relation between wave and matrix mechanics (‘equivalence paper’), submitted 18 March 1926, published 4 May 1926 (Schrödinger 1926d).

• Paper on micro- and macromechanics (coherent states for the harmonic oscillator), published 9 July 1926 (Schrödinger 1926e).

• […]

Einstein's 1927 argument for incompleteness

A huge literature arose out of the famous ‘EPR’ paper by Einstein, Podolsky and Rosen (1935), entitled ‘Can quantum-mechanical description of physical reality be considered complete?’. The EPR paper argued, on the basis of (among other things) the absence of action at a distance, that quantum theory must be incomplete. It is less well-known that a much simpler argument, leading to the same conclusion, was presented by Einstein eight years earlier in the general discussion at the fifth Solvay conference (pp. 440ff.).

Einstein compares and contrasts two views about the nature of the wave function ψ, for the specific case of a single electron. According to view I, ψ represents an ensemble (or ‘cloud’) of electrons, while according to view II, ψ is a complete description of an individual electron. Einstein argues that view II is incompatible with locality, and that to avoid this, in addition to ψ there should exist a localised particle (along the lines of de Broglie's theory). Thus, according to this reasoning, if one assumes locality, then quantum theory (as normally understood today) is incomplete.

The conclusion of Einstein's argument in 1927 is the same as that of EPR in 1935, even if the form of the argument is rather different. Einstein considers electrons striking a screen with a small hole that diffracts the electron wave, which on the far side of the screen spreads out uniformly in all directions and strikes a photographic film in the shape of a hemisphere with large radius (see Einstein's figure, p. 440).

Time in quantum theory

By 1920, the spectacular confirmation of general relativity, during the solar eclipse of 1919, had made Einstein a household name. Not only did relativity theory (both special and general) upset the long-received Newtonian ideas of space and time, it also stimulated a widespread ‘operationalist’ attitude to physical theories. Physical quantities came to be seen as inextricably interwoven with our means of measuring them, in the sense that any limits on our means of measurement were taken to imply limits on the definability, or ‘meaningfulness’, of the physical quantities themselves. In particular, Einstein's relativity paper of 1905 – with its operational analysis of simultaneity – came to be widely regarded as a model for the new operationalist approach to physics.

Not surprisingly, then, as the puzzles continued to emerge from atomic experiments, in the 1920s a number of workers suggested that the concepts of space and time would require still further revision in the atomic domain. Thus, Campbell (1921, 1926) suggested that the puzzles in atomic physics could be removed if the concept of time was given a purely statistical significance: ‘time, like temperature, is a purely statistical conception, having no meaning except as applied to statistical aggregates’ (quoted in Beller 1999, p. 97).

This appendix reproduces most of the material contained in an envelope marked ‘Solvaykongressen 1927’, held in the Bohr Archive in Copenhagen. This material concerns the discussions at the Solvay conference, in particular Bohr's contributions and the general discussion. It has not been microfilmed, and only brief extracts have been published previously, in Bohr's Collected Works (Bohr 1985, pp. 103–5), where they are published together with some brief descriptions and comments (Bohr 1985, pp. 35–7, 100 and 478–9). The material consists of the following.

(1) In J.-É. Verschaffelt's hand (ten-and-a-half densely written pages), the transcripts of Bohr's major discussion contributions (after Compton's report and during the general discussion). These transcripts were presumably prepared on the basis of the (shorthand) notes taken during the conference, and they contain a large number of gaps. They are marked (in Danish) at the top: ‘Verschaffelt – sent to Bohr’, and they are evidently the material that Verschaffelt had supplied in order for Bohr to work out a final version of his contributions. The language is mainly English, with some German and French (and the annotation in Danish at the top).

Causality, determinism, probability

Mr Lorentz. – I should like to draw attention to the difficulties one encounters in the old theories. We wish to make a representation of the phenomena, to form an image of them in our minds. Until now, we have always wanted to form these images by means of the ordinary notions of time and space. These notions are perhaps innate; in any case, they have developed from our personal experience, by our daily observations. For me, these notions are clear and I confess that I should be unable to imagine physics without these notions. The image that I wish to form of phenomena must be absolutely sharp and definite, and it seems to me that we can form such an image only in the framework of space and time.

For me, an electron is a corpuscle that, at a given instant, is present at a definite point in space, and if I had the idea that at a following moment the corpuscle is present somewhere else, I must think of its trajectory, which is a line in space. And if the electron encounters an atom and penetrates it, and after several incidents leaves the atom, I make up a theory in which the electron preserves its individuality; that is to say, I imagine a line following which the electron passes through the atom. Obviously, such a theory may be very difficult to develop, but a priori it does not seem to me impossible.

Introduction

Quantum mechanics is based on the intuition that the essential difference between atomic physics and classical physics is the occurrence of discontinuities (see in particular [1,4,58–63]). Quantum mechanics should thus be considered a direct continuation of the quantum theory founded by Planck, Einstein and Bohr. Bohr in particular stressed repeatedly, already before the birth of quantum mechanics, that the discontinuities must lead to the introduction of new kinematical and mechanical concepts, so that indeed classical mechanics and its corresponding conceptual scheme should be abandoned [1,4]. Quantum mechanics tries to introduce the new concepts through a precise analysis of what is ‘observable in principle’. In fact, this does not mean setting up the principle that a sharp division between ‘observable’ and ‘unobservable’ quantities is possible and necessary. As soon as a conceptual scheme is given, one can infer from the observations to other facts that are actually not observable directly, and the boundary between ‘observable’ and ‘unobservable’ quantities becomes altogether indeterminate. But if the conceptual scheme itself is still unknown, it will be expedient to enquire only about the observations themselves, without drawing conclusions from them, because otherwise wrong concepts and prejudices taken over from before will block the way to recognising the physical relationships [Zusammenhänge].

At the fifth Solvay conference, some questions that are closely related to the quantum measurement problem (as we would now call it) were addressed in the context of pilot-wave theory, in both the discussion following de Broglie's report and the general discussion. Most of these questions concerned the treatment of scattering (elastic and inelastic); they were raised by Born and Pauli, and replies were given by Brillouin and de Broglie. Of special interest is the famous – and widely misunderstood – objection by Pauli concerning inelastic scattering. Another question closely related to the measurement problem was raised by Kramers, concerning the recoil of a single photon on a mirror.

In this chapter, we shall first outline the pilot-wave theory of scattering, as currently understood, and examine the extensive discussions of scattering – in the context of de Broglie's theory – that took place at the conference.

We shall see that de Broglie and Brillouin correctly answered the query raised by Born concerning elastic scattering. Further, we shall see that Pauli's objection concerning the inelastic case was both more subtle and more confused than is generally thought; in particular, Pauli presented his example in terms of a misleading optical analogy (that was originally given by Fermi in a more restricted context).

Anyone who has taken part in a debate on the interpretation of quantum theory will recognise how fitting is the above quotation from the book of Genesis, according to which the builders of the Tower of Babel found that they could no longer understand one another's speech. For when it comes to the interpretation of quantum theory, even the most clear-thinking and capable physicists are often unable to understand each other.

This state of affairs dates back to the genesis of quantum theory itself. In October 1927, during the ‘general discussion’ that took place in Brussels at the end of the fifth Solvay conference, Paul Ehrenfest wrote the above lines on the blackboard. As Langevin later remarked, the Solvay meeting in 1927 was the conference where ‘the confusion of ideas reached its peak’.

Ehrenfest's perceptive gesture captured the essence of a situation that has persisted for three-quarters of a century. According to widespread historical folklore, the deep differences of opinion among the leading physicists of the day led to intense debates, which were satisfactorily resolved by Bohr and Heisenberg around the time of the 1927 Solvay meeting.