Many works intended to introduce interpretive issues in quantum mechanics present John von Neumann as having a view in which measurement produces a physical collapse in the system being measured. In this paper I argue that such a reading of von Neumann is inconsistent with what von Neumann actually says. I show that much of what he says makes no sense on the physical collapse reading, but falls into place if we assume he does not have such a view. I show that the physical collapse view is based on an understanding of ‘state’ which von Neumann does not share. 1. Introduction2. The standard reading of von Neumann3. The standard reading of von Neumann and Chapter VI4. The Chapter VI argument5. The Chapter V argument6. The Chapters III and IV argument7. Conclusion
Many works intended to introduce interpretive issues in quantum mechanics present John von Neumann as having a view in which measurement produces a physical collapse in the system being measured. In this paper I argue that such a reading of von Neumann is inconsistent with what von Neumann actually says. I show that much of what he says makes no sense on the physical collapse reading, but falls into place if we assume he does not have such a view. I show that the physical collapse view is based on an understanding of ‘state’ which von Neumann does not share. 1. Introduction2. The standard reading of von Neumann3. The standard reading of von Neumann and Chapter VI4. The Chapter VI argument5. The Chapter V argument6. The Chapters III and IV argument7. Conclusion
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.
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.
Abstract The Bohr and von Neumann views on the measurement process in quantum mechanics have been interpreted for a long time in somewhat controversial terms, often leading to misconceptions. On the basis of some textual analysis, I would like to show that—contrary to a widespread opinion—their views should be taken less inconsistent, and much closer to each other, than usually thought. As a consequence, I claim that Bohr and von Neumann are conceptually on the same side on the issue of the universality of quantum mechanics: hopefully, this might contribute to a more accurate history of the measurement problem in quantum mechanics.
Abstract As Heisenberg began to promulgate his version of the new quantum philosophy as the ‘Copenhagen spirit’, John von Neumann undertook to purge quantum mechanics of its defects and make it comprehensible to Göttingen’s prince of mathematics, David Hilbert. The result is familiar to any student of physical science. Von Neumann separated the continuous, deterministic, and reversible evolution of the wavefunction from its discontinuous, indeterministic, and irreversible ‘collapse’ in an act of measurement. He saw no reason why the first process should not continue all the way up the chain to the observer’s conscious mind, where the second process occurs. Bohr had little to say about von Neumann’s theory, other than it was ‘wrongly put’. Von Neumann also closed the door that Born had left ajar. Causality could not be restored to the quantum domain by supposing the existence of ‘hidden variables’, as these, according to his reasoning, were mathematically impossible.
The notion of quantum state plays a fundamental role within the Standard account of Quantum Mechanics (SQM) as established by Dirac and von Neumann during 1930s and up to the present. In this work we expose the deep inconsistencies that exist within the multiple definitions of the notion of quantum state that are provided within this axiomatic formulation. As we will argue, these different inconsistent definitions continue to be -- even today -- uncritically confused within the mainstream physical and philosophical literature leading to self-contradictory statements and wrong conclusions. We end with a discussion regarding the untenability of this concept for any rational understanding of theoretical physics.
Chapter 4 introduces a great QM mystery: the notion of quantum measurements. Henry is in a superposition of versions localized in several places, but when Eve measures Henry’s position she (as a classical observer) either sees Henry or she does not. Physical reality is made of such measurements. Eve’s measurement projects or collapses Henry’s superposition state to a single location. The meaning of quantum-state or wavefunction “collapse” and the role of the observer have been at the heart of the historical debate concerning the interpretation of QM. Whereas Von Neumann and Wigner stressed the inseparability of the observed (measured) world from the human mind, alternative “observer-free” views were suggested, such as Everett’s many-world interpretation or Zurek’s quantum Darwinism that replaces the observer by the environment. In the appendix to this chapter the notion of probability amplitudes is elucidated, new notations for operators are introduced and projection operators are presented.