The quantum measurement is one of the key elements of quantum theory. In his book the Mathematical Foundations of Quantum Mechanics, von Neumann delved into the 问题 of measurements. He concluded that the entire physical world could be governed by a universal wave function. The collapse of the wave function is caused by the experimenter's consciousness due to the need for “something other than computation". He argued that the mathematics of quantum mechanics allows the collapse of the wave function to be located anywhere in the causal chain from the measuring device to the human observer's “subjective consciousness". Measurements lead to the inevitable collapse of the system under tests. For this reason, Aharonov et al. (1987) put forward the theory of weak measurements and the concept of weak values. In this paper, the causes of the weak value anomalies, and the uncertainty and complementarity caused by the weak measurements are analyzed from the basic level.
The quantum measurement is one of the key elements of quantum theory. In his book the Mathematical Foundations of Quantum Mechanics, von Neumann delved into the 问题 of measurements. He concluded that the entire physical world could be governed by a universal wave function. The collapse of the wave function is caused by the experimenter's consciousness due to the need for “something other than computation". He argued that the mathematics of quantum mechanics allows the collapse of the wave function to be located anywhere in the causal chain from the measuring device to the human observer's “subjective consciousness". Measurements lead to the inevitable collapse of the system under tests. For this reason, Aharonov et al. (1987) put forward the theory of weak measurements and the concept of weak values. In this paper, the causes of the weak value anomalies, and the uncertainty and complementarity caused by the weak measurements are analyzed from the basic level.
A variant of the von Neumann-Wigner Interpretation is proposed. Problems arising from the quantum Zeno effect are addressed as we have described previously. We do, however, offer some new, and perhaps unexpected observations. We are accustomed to thinking of wave function collapse as occurring consequent to laboratory measurements. We speculate that, whatever physical correlate of consciousness exists within the brain, it is quantum mechanical in the sense that a brain, left to itself, would eventually decohere into a state no longer compatible with its conscious functioning. Wave function collapse returns it to a state compatible with consciousness. Indeed, this may be its important reason for occurring. A universe without it simply could not play host to conscious brains. The fact that it also prevents us from encountering "absurd" situations in the laboratory is merely a fortunate dividend. Whenever a quantum measurement is made the universe's future history splits into a number of possibilities. This number may be very large or infinite. And we believe consciousness plays a vital role in this happening. A "conscious" universe where quantum measurements are being made allows for an enormous number of equally acceptable world-histories. An "unconscious" one, always evolving in a unitary fashion, allows for only one. If we assume that the decision as to which worldhistory is the real one (i.e. this one) is made at random we see that the universe is overwhelmingly more likely to be "conscious" than not.
A variant of the von Neumann-Wigner Interpretation is proposed. Problems arising from the quantum Zeno effect are addressed as we have described previously. We do, however, offer some new, and perhaps unexpected observations. We are accustomed to thinking of wave function collapse as occurring consequent to laboratory measurements. We speculate that, whatever physical correlate of consciousness exists within the brain, it is quantum mechanical in the sense that a brain, left to itself, would eventually decohere into a state no longer compatible with its conscious functioning. Wave function collapse returns it to a state compatible with consciousness. Indeed, this may be its important reason for occurring. A universe without it simply could not play host to conscious brains. The fact that it also prevents us from encountering "absurd" situations in the laboratory is merely a fortunate dividend. Whenever a quantum measurement is made the universe's future history splits into a number of possibilities. This number may be very large or infinite. And we believe consciousness plays a vital role in this happening. A "conscious" universe where quantum measurements are being made allows for an enormous number of equally acceptable world-histories. An "unconscious" one, always evolving in a unitary fashion, allows for only one. If we assume that the decision as to which worldhistory is the real one (i.e. this one) is made at random we see that the universe is overwhelmingly more likely to be "conscious" than not.
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.
Quantum physicists have made many attempts to solve the quantum measurement problem, but no solution seems to have received widespread acceptance. The time has come for a new approach. In Sense Perception and Reality: A Theory of Perceptual Relativity, Quantum Mechanics and the Observer Dependent Universe and in a new paper The End of Realism I suggest the quantum measurement problem is caused by a failure to understand that each species has its own sensory world and that when we say the wave function collapses and brings a particle into existence we mean the particle is bought into existence in the human sensory world by the combined operation of the human sensory apparatus, particle detectors and the experimental set up. This is similar to the Copenhagen Interpretation suggested by Niels Bohr and others, but the understanding that the collapse of the wave function brings a particle into existence in the human sensory world removes the need for a dividing line between the quantum world and the macro world. The same rules can apply to both worlds and the ideas stated in this paper considerably strengthen the Copenhagen Interpretation of quantum mechanics.
The physical meaning of the quantum weak value still remains a matter of debate. Originally introduced by Aharonov et al. [Phys. Rev. Lett. 60, 1351 (1988).] as another counterintuitive feature of quantum mechanics, it eventually evolved into a practical tool that is widely used. The theoretical framework in which weak values were introduced was given by von Neumann's model of quantum measurements. In this model, a system is submitted to measurement by coupling it to a ``pointer,'' or meter. In the weak-coupling regime, one may perform a low-order Taylor expansion for the evolution operator of the system and meter. This standard approach ties weak values with weak couplings and weak measurements. We report closed-form expressions that can be used to untie weak values from weak measurements. The regime of strong measurements thereby becomes accessible to weak values, without leaving the framework in which the latter were originally introduced. The reported results should also help us to better understand the physical meaning of weak values.
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.