Macroscopic Quantum Systems and the Quantum Theory of Measurement

A. J. Leggett

R. Fukuda

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.

Klaus Hepp

R. Fukuda

Models are presented as examples in order to illustrate the previously proposed theory of measurement in quantum mechanics [R. Fukuda, Phys. Rev. A 35, 8 (1987)]. It is based on the specific structure of the Hilbert space of the macroscopic system. It is shown that after the interaction of an object with a detector we have to prepare the exponential of the extensive operators to recover the interference which is lost in the measuring process.

Mikio Namiki

Bernard d’Espagnat

Instruments are necessarily of macroscopic size because our sense organs—which can be considered as instruments occupying a certain rank in the von Neumann hierarchy—are of macroscopic size. It is only natural, therefore, that physicists should have attempted to make use of this property for constructing quantum measurement theories. Moreover, one of the remarkable properties possessed by most macroscopic systems, including all instruments, but lacking in microscopic systems is irreversibility. This simple observation suggests very strongly that the phenomenon of irreversibility and the phenomenon of "wave packet reduction," which is associated in some way or other with the measurement process, should somehow be correlated. The theories in the chapter show that it is in practice always possible to attribute definite macroscopic properties to the measuring instruments. The danger that the error we thus make will ever be detected has been proved to be vanishingly small.