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The Puzzlement of Reduction in Quantum Measurement

Shen Jie Jia

Published Jan 1, 2007• 0 citations
OpenAlex

Abstract

Quantum measurement is the most sensitive part of quantum mechanics and physics. Researching it can incite much philosophical debate. One of hot topics currently is reduction. Many people argue that it is received wisdom that quantum measurement puts an end to reductionism. Psychology, emergence and holism are their arguments against reduction. Is reduction really dead? I will not only argue that reduction in quantum measurement is still animate, but also try to put forward some effective means which can eliminate conflict between quantum measurement and reduction.

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Quantum measurement is the most sensitive part of quantum mechanics and physics. Researching it can incite much philosophical debate. One of hot topics currently is reduction. Many people argue that it is received wisdom that quantum measurement puts an end to reductionism. Psychology, emergence and holism are their arguments against reduction. Is reduction really dead? I will not only argue that reduction in quantum measurement is still animate, but also try to put forward some effective means which can eliminate conflict between quantum measurement and reduction.
This paper tries to get a grip on two seemingly conflicting intuitions about reductionism in quantum mechanics. On one hand it is received wisdom that quantum mechanics puts an end to ‘reductionism’. Quantum entanglement is responsible for such features of quantum mechanics as holism, the failure of supervenience, and emergence. While I agree with these claims, I will argue that it is only part of the story. Quantum mechanics provides us with thoroughgoing reductionist explanations. I will distinguish two kinds of microexplanation (or micro-‘reduction’). I will argue that even though quantum entanglement provides an example of the failure of one kind of microexplanation, it does not affect the other. Contrary to a recent paper by Kronz and Tiehen, I claim that the explanation of the dynamics of quantum mechanical systems is just as reductionist as it used to be in classical mechanics.
Decoherence is widely felt to have something to do with the quantum measurement problem, but getting clear on just what is made difficult by the fact that the 'measurement problem', as traditionally presented in foundational and philosophical discussions, has become somewhat disconnected from the conceptual problems posed by real physics. This, in turn, is because quantum mechanics as discussed in textbooks and in foundational discussions has become somewhat removed from scientific practice, especially where the analysis of measurement is concerned. This paper has two goals: firstly (§§1-2), to present an account of how quantum measurements are actually dealt with in modern physics (hint: it does not involve a collapse of the wave function) and to state the measurement problem from the perspective of that account; and secondly (§§3-4), to clarify what role decoherence plays in modern measurement theory and what effect it has on the various strategies that have been proposed to solve the measurement problem.
In most textbooks, measurement does not receive the full attention it deserves and sometimes is even not treated at all, apart a brief and cryptic mention of the “reduction of the wave packet.” However, in the last decades, the situation has profoundly changed and it is time to consider measurement a fundamental part of quantum mechanics, even, to a certain extent, an important generalization of the traditional theory (see also Chs. 14–15). This chapter consists of three major parts. In the first block (Secs. 9.1–9.4) we develop the main physical features of the measurement process: the heart of the argument is here represented by the aspects related to the interpretation. In the second part (Secs. 9.5–9.8) we discuss several special (and partly interdependent) topics of measurement: the heart here is represented by experimental aspects. In the third part (Secs. 9.9–9.12) we deal with the measurement process on a more formal plane, making use, in particular, of the generalization represented by the concepts of effect and positive operator valued measure (POVM). As we have said, the measurement problem is one of the most fundamental issues in the conceptual structure of quantum mechanics (as described in Sec. 9.1) and has a long history that will be examined in Sec. 9.2. In this context, the existence of apparently paradoxical quantum states comes about: the so-called Schrödinger cat states (see Sec. 9.3).
Abstract Quantum mechanics is often said to entail holism—that wholes are more than just the sum of their parts—and hence violate Humean supervenience. Certainly an entangled state cannot readily be interpreted in terms of the properties of the individual particles involved. But there is no clear general argument from quantum mechanics to holism. Still, each of the three major interpretations of quantum mechanics—Bohm, GRW, and many worlds—embodies some form of holism. One might try to rescue Humean supervenience by moving to high-dimensional representation of physical systems, or by constructing a theory with backward-in-time causation, but it is unclear if such strategies will succeed. If holism is accepted, some argue further that there are no individuals at the fundamental physical level: Either relations are fundamental, or the whole universe is fundamental. The arguments for these positions are assessed and found to be wanting.
The descriptions of the quantum realm and the macroscopic classical world differ significantly not only in their mathematical formulations but also in their foundational concepts and philosophical consequences. When and how physical systems stop to behave quantum mechanically and begin to behave classically is still heavily debated in the physics community and subject to theoretical and experimental research. This dissertation puts forward an approach to the quantum-to-classical transition fully within quantum theory and conceptually different from already existing models: It neither needs to refer to the uncontrollable environment of a system (decoherence) nor to change the quantum laws itself (collapse models), but puts the stress on the limits of observability of quantum phenomena due to the imprecision of our measurement apparatuses. For a certain class of time evolutions it is this mere restriction to coarse-grained measurements which is sufficient to see the natural emergence of macroscopic realism and even the classical Newtonian laws out of the full quantum formalism. But there also exist "non-classical" Hamiltonians for which a classical spatiotemporal description of the system's time evolution remains impossible even under fuzzy measurements or decoherence. It is argued that such Hamiltonians are unlikely to be spontaneously realized in nature because of their high complexity. The last part addresses the question of the origin of quantum randomness and proposes a link with mathematical undecidability.