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Springer eBooks

Quantum Mechanics of Macroscopic Systems and Measurement Processes

Mikio Namiki

Published Jan 1, 1988• 1 citation
Publisher
DOI
10.1007/978-94-009-2925-8_1

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The question as to whether quantum mechanics can be applied to a macroscopic system, which has recently been raised through discussions of the problem of how to interpret the so-called “reduction of a wave packet”, is discussed. It is shown by a detailed analysis of the destruction of interference which brings about the reduction, that a supplementary assumption on the preciseness of measurements must at least be introduced in order to interpret the reduction process as an objective process, and it does not, however, necessarily imply inapplicability of quantum mechanics to a macroscopic system.
Macroscopic variables of the macroscopic system lose the quantum fluctuations in the macroscopic limit. A separate Hilbert space corresponds to each c-number value of these macroscopic variables. The measuring process in quantum mechanics consists of recording these c-number values and amounts to determination of the Hilbert space to which the system belongs. These observations provide a solution to the problem of measurement and lead to predictions concerning the c-number equations of motion of the macroscopic variables.
In this paper, we discuss the importance of measurement in quantum mechanics and the so-called measurement problem. Any quantum system can be described as a linear combination of eigenstates of an operator representing a physical quantity; this means that the system can be in a superposition of states that corresponds to different eigenvalues, i.e., different physical outcomes, each one incompatible with the others. The measurement process converts a state of superposition (not macroscopically defined) in a well-defined state. We show that, if we describe the measurement by the standard laws of quantum mechanics, the system would preserve its state of superposition even on a macroscopic scale. Since this is not the case, we assume that a measurement does not obey to standard quantum mechanics, but to a new set of laws that form a “quantum measurement theory”.