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과학철학

통계적 앙상블 해석과 측정의 문제

김재영

Published Jan 1, 2014• 0 citations
OpenAlex

Abstract

I examined the Statistical Ensemble Interpretation (SEI) of quantum mechanics. Historical reappraisal of Max Born's statistical interpretation shows precisely how Born used the concept of the probability. After investigating the so-called Ensemble Interpretation proposed by Albert Einstein based on ...

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Historical remarks The quantum mechanical formalism discovered by Heisenberg [Heis 25] an Schrödinger [Schrö 26] in 1925 was first interpreted in a statistical sense by Born [Born 26]. The formal expressions p (φ, a i ) = |(φ,φ ai )| 2 , i ∈ N, were interpreted as the probabilities that a quantum system S with preparation φ possesses the value a i that belongs to the state φ ai . This original Born interpretation, which was formulated for scattering processes, was, however, not tenable in the general case. The probabilities must not be related to the system S in state φ, since in the preparation φ the value a i of an observable A is in general not subjectively unknown but objectively undecided. Instead, one has to interpret the formal expressions p ( a i , a i ) as the probabilities of finding the value a i after measurement of the observable A of the system S with preparation φ. In this improved version, the statistical or Born interpretation is used in the present-day literature. On the one hand, the statistical (Born) interpretation of quantum mechanics is usually taken for granted, and the formalism of quantum mechanics is considered as a theory that provides statistical predictions referring to a sufficiently large ensemble of identically prepared systems S (φ) after the measurement of the observable in question. On the other hand, the meaning of the same formal terms p (φ, a i ) for an individual system is highly problematic.
This chapter first discusses statistical techniques and concepts — including probability, probability distribution, average and expectation value, and uncertainty — that are relevant to quantum mechanics. The physical interpretation of probability in quantum mechanics is then discussed. It is argued that by adopting the statistical interpretation, one can think clearly about quantum mechanics without committing to any of the various physical interpretations, and without tackling the conceptual hurdles that they present. The history and substance of interpretational issues in quantum mechanics is then briefly discussed, the point being to introduce these profound, unresolved questions without taking sides in ongoing scientific debates. The chapter closes with a personal reflection on Albert Einstein, the most revered and fascinating figure in physics, and the one most famously at odds with the conventional interpretation of quantum mechanics.
양자역학의 해석에서 통계적 앙상블 해석(SEI)을 검토한다. 막스 보른의 통계적 해석을 역사적 맥락에 따라 상세하게 살펴보고, 보른이 확률의 개념을 어떻게 사용했는지 논의한다. 나아가 아인슈타인이 보른의 논의와 관련하여 제시한 앙상블 해석을 검토한 뒤, 이를 확장한 통계적 앙상블 해석을 상세하게 다룬다. 특히 상태의 준비와 측정을 상세히 논의하고, 덧붙여 통계적 해석과 ‘서울 해석’(SI)의 관계에 대한 함의를 모색한다.
A longstanding issue in the Everettian (Many-Worlds) interpretation is to justify and make sense of the Born rule that underlies the statistical predictions of standard quantum mechanics. The paper offers a reappraisal of Everett’s original account in light of the recent literature on the concept of typicality. It argues that Everett’s derivation of the Born rule is sound and, in a certain sense, even an optimal result, and defends it against the charge of circularity. The conclusion is that Everett’s typicality argument can successfully ground post-factum explanations of Born statistics, while questions remain about the predictive power of the Many-Worlds interpretation.