Prog. Theor. Phys. Vol. 88 No. 6 (1992) pp. 1051-1064
Cat Paradox for C*-Dynamical Systems
Department of Mathematics, College of General Education,
Nagoya University, Nagoya 464-01
(Received October 8, 1992)
In the algebraic approach to the quantum physics, the notion of a macroscopic observable has been well established. This paper examines a program for the unification of classical mechanics and quantum mechanics based on the macroscopic observable and the algebraic description of a dynamical system such as a C*-dynamical system. It is proved quite generally that in this approach we cannot describe the measuring interaction between a microscopic system and a macroscopic apparatus by a C*-dynamical system, or any similar frameworks, as long as the time reversibility of the dynamics of isolated systems is assumed.
DOI : 10.1143/PTP.88.1051
- E. Schrödinger, Naturwissenshaften 23 (1935), 807, 823, 844. [English translation by J. D. Trimmer, Proc. Am. Philos. Soc. 124 (1980), 323].
- H. Araki, Prog. Theor. Phys. 64 (1980), 719[PTP]; in Fundamental Aspects of Quantum Theory, ed. V. Gorini and A. Frigerio (Plenum, New York, 1986), p. 23.
- O. Bratteli and D. W. Robinson, Operator Algebras and Quantum Statistical Mechanics, I (Springer-Verlag, New York, 1979); II (1981).
- J. von Neumann, Mathematical Foundations of Quantum Mechanics (Princeton UP, Princeton, NJ, 1955).
- M. Takesaki, Theory of Operator Algebras, I (Springer-Verlag, New York, 1979).
- E. B. Davies, Quantum Theory of Open Systems (Academic Press, London, 1976).
C. W. Helstrom, Quantum Detection and Estimation Theory (Academic Press, New York, 1976).
A. S. Holevo, Probabilistic and Statistical Aspects of Quantum Theory (North-Holland, Amsterdam, 1982).
M. Ozawa, J. Math. Phys. 25 (1984), 79[CrossRef]; 26 (1985), 1948; 27 (1986), 759; Publ. RIMS, Kyoto Univ. 21 (1985), 279.
P. J. Lahti, Busch and P. Mittelstaedt, The Quantum Theory of Measurement, Lecture Notes in Physics, Vol. m2 (Springer-Verlag, Berlin, 1991).
- H. P. Yuen and J. H. Shapiro, IEEE Trans. Inf. Theory, IT-26 (1984), 78.
C. M. Caves, K. S. Throne, R. W. P. Drever, V. D. Sandberg and M. Zimmermann, Rev. Mod. Phys. 52 (1980), 341[APS].
H. P. Yuen, Phys. Rev. Lett. 51 (1983), 719[APS].
M. Ozawa, Phys. Rev. Lett. 60 (1988), 385[APS]; 67 (1991), 1956.
- H. P. Yuen and M. Lax, IEEE Trans. Inf. Theory, IT-19 (1973), 740.
E. Arthurs and M. S. Goodman, Phys. Rev. Lett. 60 (1988), 2447[APS].
H. P. Yuen and M. Ozawa, “The Ultimate lnformation Carrying Limit of Quantum Systems", Phys. Rev. Lett. (to appear).
- R. J. Glauber, in Group Theoretical Methods in Physics (Harwood Academic Publishers, 1985); in Frontiers of Quantum Optics, ed. E. R. Pike and S. Sarker (Adam Hilger, Bristol, 1986).
- H. Umegaki, Tôhoku Math. J. (2) 6 (1954), 177; 8 (1956), 86; Kodai Math. Sem. Rep. 11 (1959), 51; 14 (1962), 59.
- S. Machida and M. Namiki, Prog. Theor. Phys. 63 (1980), 1457, [PTP]1833.
- M. Ozawa, in Current Topics in Operator Algebras, ed. H. Araki (World Scientific, Singapore, 1991), p. 52; “Phase Operator Problem and Macroscopic Extension of Quantum Mechanics", Preprint series No. 11, Department of Mathematics, College of General Education, Nagoya University (1992).
Citing Article(s) :
Progress of Theoretical Physics Vol. 93 No. 3 (1995) pp. 631-646
Particle Tracks, Events and Quantum Theory