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Birkhäuser Basel eBooks

Measurement and Quantum States

Yorick Hardy, Willi-Hans Steeb

Published Jan 1, 2001• 0 citations
Publisher

Abstract

The interpretation of measurements in quantum mechanics is still under discussion (Healey [84], Bell [9], Redhead [136]). Besides the Copenhagen interpretation we have the many-worlds interpretations (Everett interpretations), the modal interpretations, the decoherence interpretations, the interpretations in terms of (nonlocal) hidden variables, the quantum logical interpretations. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

DOI
10.1007/978-3-0348-8366-5_18

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The interpretation of measurements in quantum mechanics is still under discussion (Healey [84], Bell [9], Redhead [136]). Besides the Copenhagen interpretation we have the many-worlds interpretations (Everett interpretations), the modal interpretations, the decoherence interpretations, the interpretations in terms of (nonlocal) hidden variables, the quantum logical interpretations. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Interpretations of quantum theory can be usefully categorised according to which moves they make to avoid the measurement problem. The chapter gives a more systematic exposition of that problem, followed by an overview of the answers that are given by the most popular interpretations. As we shall see, it is helpful to group the interpretations together according to which of the assumptions that lead to the measurement problem they reject. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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The objective of Chapter 4 is to give an overview of the basic concepts of quantum mechanics and their interpretation. Thus this chapter functions as a theoretical preparation for a better understanding of the quantum world and of the knowledge measurement process. First, the terminology of the word “quantum” and its impact on the derivation of the term “knowledge quantum” is explained in Chapter 4.1. Then, the discussion moves to the historical development of quantum mechanics. The key issues and current research field for quantum theory will be given in an overview. The following chapters show some insights into key quantum mechanical concepts such as slit-experiments, wave-particle duality, the Copenhagener interpretation, and quantum probability. Chapter 4 closes with an explanation of the Uncertainty Principle of Werner Heisenberg, especially since the Uncertainty Principle is used to derive the knowledge measurement process through the method of analogical reasoning. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Although there is a complete consensus among working physicists with respect to the practical and operational meanings of quantum states, and also a rather loosely formulated general philosophic view called the Copenhagen interpretation, a great deal of confusion and divergence of opinions exist as to the details of the measurement process and its effects upon quantum states. This paper reviews the current expositions of the measurement problem, limiting itself for lack of space primarily to the writings of physicists; it calls attention to inconsistencies and proposes resolutions. Except for a summary of the properties of statistical matrices which are needed in Part II, the first part is non-mathematical and deals largely with two kinds of probability, reducible and irreducible probabilities, which need to be distinguished for a proper understanding of the measurement act.
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