Prog. Theor. Phys. Vol. 87 No. 2 (1992) pp. 293-305

[ Full Text PDF : FREE ACCESS (828K) ]

Theory of Measurement

— A Note on Conceptual Foundation of Quantum Mechanics —

Yutaka Toyozawa

Department of Physics, Chuo University, Tokyo 112

(Received August 28, 1991)

Abstract:

Theory of measurement is presented which is based on the statistical interpretation of quantum mechanics. The reduction of wave packet is ascribed to undue comparison of the state of an ensemble before measurement and the state of an individual system after measurement. By studying the evolution of statistical operators for subsystems and composite systems comprising an object, a measuring apparatus and an observer, one can definitely locate where the measurement is done, thus negating the principle of psycho-physical parallelism due to von Neumann. Time needed for measurement is also discussed. The Einstein-Podolsky-Rosen state is described as an eigenstate of correlation. The argument lends support to the standpoint that the physical state of a system is to be represented by the statistical operator, not by the wave function, in the conceptual foundation of quantum mechanics.

URL : http://ptp.ipap.jp/link?PTP/87/293/
DOI : 10.1143/PTP.87.293

References:

M. Jammer, The Philosophy of Quantum Mechanics (J. Wiley & Sons, New York, 1974). This book provides a comprehensive critical review of controversies on the conceptual foundation of quantum mechanics.
J. von Neumann, Mathematische Grundlagen der Quanten Mechanik (Springer, Berlin, 1932).
D. I. Blokhintsev, Osnovy Kvantovoi Mekhaniki (G. T. T. L., Moscow and Leningrad, 1949).
See also Chapter 10 of Ref. 1) for a comprehensive survey of the statistical interpretation.
Y. Toyozawa, J. Phys. Soc. Jpn. 55 (1986), 2572[JPSJ].
U. Fano, Rev. Mod. Phys. 29 (1957), 74[APS].
L. Landau, Z. Phys. 45 (1927), 430.
E. Schrödinger, Proc. Cambridge Phil. Soc. 31 (1935), 555; ibid. 32 (1936), 446.
A. J. Leggett, in Foundation of Quantum Mechanics (Phys. Soc. Jpn., 1986), p. 287.
A. Daneri, A. Loinger and G. M. Prosperi, Nucl. Phys. 33 (1962), 297[CrossRef].
W. H. Furry, in Lectures in Theoretical Physics, ed. W. E. Britten (Univ. of Colorado Press, Boulder 1966), p. 287.
J. M. Jauch, E. P. Wigner and M. M. Yanase. Nuovo Cim. 48B (1967), 144.
A. Einstein, B. Podolsky and N. Rosen, Phys. Rev. 47 (1935), 777[APS].
R. Tolman, The Principles of Statistical Mechanics (Oxford Univ. Press, 1938).
B. d'Espagnat, Conceptual Foundation of Quantum Mechanics, 2nd Ed. (Adison-Wesley, 1976).

Citing Article(s) :

Journal of the Physical Society of Japan 62 (1993) pp. 3395-3401 :
The Effect of Path Observation on Quantum Interference Pattern

Kōshi Koide and Yutaka Toyozawa