Abstract The orthodox solution to the measurement problem is often presented in terms of ‘consciousness causes collapse’. It is widely taken to have been developed and presented by the mathematician von Neumann in his classic book, Mathematical Foundations of Quantum Mechanics (1932/1955) which lays down the core theoretical framework of quantum mechanics. However, the ‘problem’ was not even presented as such until the 1950s, which is when von Neumann’s book was finally translated into English, and there is barely any mention of consciousness in it. It is partly for this reason that London and Bauer are typically regarded as having clearly articulated what von Neumann only hinted at. This chapter examines what von Neumann actually wrote about measurement in quantum mechanics. It presents his ‘psychophysical parallelism’ and the famous ‘chain’ argument which concludes that something non-physical must induce the wave-function to collapse. The chapter concludes with brief comments on von Neumann’s later thoughts concerning the comparison between computers and the human brain.
Abstract The orthodox solution to the measurement problem is often presented in terms of ‘consciousness causes collapse’. It is widely taken to have been developed and presented by the mathematician von Neumann in his classic book, Mathematical Foundations of Quantum Mechanics (1932/1955) which lays down the core theoretical framework of quantum mechanics. However, the ‘problem’ was not even presented as such until the 1950s, which is when von Neumann’s book was finally translated into English, and there is barely any mention of consciousness in it. It is partly for this reason that London and Bauer are typically regarded as having clearly articulated what von Neumann only hinted at. This chapter examines what von Neumann actually wrote about measurement in quantum mechanics. It presents his ‘psychophysical parallelism’ and the famous ‘chain’ argument which concludes that something non-physical must induce the wave-function to collapse. The chapter concludes with brief comments on von Neumann’s later thoughts concerning the comparison between computers and the human brain.
Von Neumann's theory of measurement in Quantum Mechanics was spelled out in the last chapter of his book, which was published in 1932. This book was highly mathematical for its time, and in 1939 London and Bauer provided a simplified account of the measurement theory part of it (London and Bauer, 1939). Von Neumann died in 1957. Thirty years after the publication of von Neumann's book, Wigner published a review containing his views on the shortcomings of von Neumann's theory, but omitting any discussion of its mathematical core, namely von Neumann's analysis of composite systems (Wigner, 1963). He also published a set of lecture notes entitled Interpretation of Quantum Mechanics (Wigner, 1983) in which some of his concerns were spelled out in greater detail, and an article addressed ‘to an audience of non-physicists’ (Wigner, 1964). Wigner's own contributions to measurement theory were discussed by Shimony in a talk at the Wigner centennial conference (Shimony, 2002). The English translation of von Neumann's book was published in 1955.1 The account that follows is based on these sources. We shall assume that the reader is acquainted with notions such as wave function collapse and the Heisenberg cut, but we shall not assume familiarity with the technicalities of von Neumann's theory. This chapter is organized accordingly. Section 8.1 explains what we mean by the term von Neumann's measurement theory and gives an overview of the subject. It is followed by Sections 8.2 and 8.3, in which the theory is spelled out in detail. Section 8.4 recounts Wigner's reservations.
An analysis has been performed of the theories and postulates advanced by von Neumann, London and Bauer, and Wigner, concerning the role that consciousness might play in the collapse of the wave function, which has become known as the measurement problem. This reveals that an error may have been made by them in the area of biology and its interface with quantum mechanics, when they called for the reduction of any superposition states in the brain through the mind or consciousness. Many years later Wigner changed his mind to reflect a simpler and more realistic objective position, expanded upon by Shimony, which appears to offer a way to resolve this issue. The argument is therefore made that the wave function of any superposed photon state or states is always objectively changed within the complex architecture of the eye in a continuous linear process initially for most of the superposed photons, followed by a discontinuous nonlinear collapse process later for any remaining superposed photons, thereby guaranteeing that only final, measured information is presented to the brain, mind or consciousness. An experiment to be conducted in the near future may enable us to simultaneously resolve the measurement problem and also determine if the linear nature of quantum mechanics is violated by the perceptual process.
Abstract The measurement problem remains one of the outstanding issues in the foundations of quantum theory: how do we go from the multiple options encoded in the wave-function to the definite outcome that we observe? One of the most well-known solutions to this problem maintained that it is the observer’s consciousness that somehow causes the wave-function to collapse. Now widely dismissed for introducing an irreducible element of subjectivity into science, both advocates and critics cited a ‘little book’, La Théorie de L’Observation en Mécanique Quantique, by Edmund Bauer and Fritz London (1938; English trans. 1983) as giving the clearest presentation of this solution. However, as well as being an extremely accomplished physicist, London was also trained in the phenomenological tradition that was initiated by the philosopher Edmund Husserl. This casts his work with Bauer in an entirely new and different light, and by assigning a very different and more profound role to consciousness in resolving the measurement problem, yields an understanding of quantum theory that has not hitherto been fully explored. The aim of this book is to initiate just such an exploration. It begins by setting London and Bauer’s ‘little book’ in its historical and philosophical context and then draws out the implications for not only quantum physics but our view of science and the world more generally.
Few things in physics have caused so much hand-wringing as von Neumann's collapse hypothesis. Unable to derive it mathematically, von Neumann attributed it to interaction with the observer's brain! Few physicists agreed, but tweaks of von Neumann's measurement theory did not lead to collapse, and Shimony and Brown proved theorems establishing `the insolubility of the quantum measurement problem'. Many different `interpretations' of quantum mechanics were put forward, none gained a consensus, and some scholars suggested that the foundations of quantum mechanics were flawed to begin with. Yet, in the last ninety years, no-one looked into now von Neumann had arrived at his collapse hypothesis! Von Neumann based his argument on the experiment of Compton and Simon. But, by comparing readings from von Neumann's book and the Compton-Simon paper, we find that the experiment provides no evidence for the collapse hypothesis; von Neumann had misread it completely! We suggest that von Neumann had relied on his phenomenal memory rather than the printed Compton-Simon paper, and his memory had failed him for once. Our finding has considerable implications for physics, which -- briefly sketched here -- will be discussed elsewhere in detail. An Appendix raises some questions for historians of physics.
Von Neumann’s 1932 analysis of the quantum measurement chain establishes that unitary evolution can be extended through any physical apparatus or the observer’s body, and that the formalism supplies no intrinsic criterion for locating a non-unitary cut. The later rejection of placing that terminus at subjective perception did not follow from a defect in the chain argument. It followed from a physicalist ontology that treats mind and world as ontologically distinct—an assumption the mathematics of quantum mechanics does not require. Under Phenomenological Absolutism and Mutual Exclusivity, each localized actualized field configuration is identical with the absolute is-ness of first-person phenomenology. On that ontology the endpoint is not an extra-physical intervention in a closed material chain. It is what an actualized configuration already is. We reconstruct von Neumann’s position with textual fidelity, distinguish it from later causal claims that consciousness collapses the state, and show that the dualistic objections lose their force once the extraneous metaphysical premise is withdrawn. The mathematics remains compatible with other interpretations. Our claim is that von Neumann’s conclusion fits naturally when the ontology does not smuggle in a subject–object split the theory itself never licensed.
In his book Mathematical Foundations of Quantum Mechanics von Neumann asserted that the state vector must collapse upon measurement of any self-adjoint operator. This assertion was based on his reading of the Compton-Simon experiment. However, comparing von Neumann’s account with the Compton-Simon paper itself, we find that von Neumann had completely misinterpreted the experiment. Compton and Simon measured two angles on the same photographic plate; in von Neumann’s reading it became two successive measurements which gave identical results, where the experimenter could choose which measurement to perform first. In short, von Neumann’s case for collapse simply did not exist! In quantum mechanics, superpositions of different eigenvalues of conserved observables are freely admissible, but conservation laws require successive measurements of a conserved quantity upon the same object to return the same value (if the object is isolated and moves under a Schrödinger equation). This can be guaranteed only if the first measurement has caused the state vector to collapse. Thus collapse is a consistency condition which the theory must satisfy. Consistency problems are solved by displaying examples, or models, which fulfil the conditions in question. We therefore have to construct a mathematical model of the measurement process. This requires taking a stand on whether the measuring instrument does (Bohr) or does not (von Neumann-Wigner) have a classical description. If it does not, the ‘quantum measurement problem’ is insoluble. If it does, the problem – for conserved quantities – does have a solution, given by Sewell in 2005. The model displays collapse while evolving under the Schrödinger equation with a time-dependent hamiltonian; it does not have to call upon the observer’s ‘conscious ego’. Its existence shows that additive conservation laws are consistent with the superposition principle and Schrodinger evolution. Measurement of a conserved observable returns an eigenvalue of the observable; measurement of a non-conserved observable returns a diagonal matrix element of the observable in the basis of energy eigenvectors. If ‘classical descriptions’ of the apparatus are essential for these consistency conditions to be satisfied, what does it imply about the relation between classical and quantum mechanics? If the two are on the same footing, is it not possible that ‘dark matter’ is purely classical?