Abstract
It is shown that the physics and semantics of quantum measurement provide a natural interpretation of the weak neighborhoods of the states on observable algebras without invoking any idea of “a reading error” or “a measured range.” Then the state preparation process in quantum measurement theory is shown to give the normal (or locally normal) states on the observable algebra. Some remarks are made concerning the physical implications of normal states for systems with an infinite number of degrees of freedom, including questions on open and closed algebraic theories.
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References
E. T. Whittaker and G. N. Watson,A Course in Modern Analysis, 4th ed., Cambridge University Press, Cambridge, England (1927).
E. Hewitt and K. Stromberg,Real and Abstract Analysis, Springer-Verlag, Berlin (1963).
G. G. Emch,Algebraic Methods in Statistical Mechanics and Quantum Field Theory, Wiley, New York (1972).
Ruelle,Statistical Mechanics, W. A. Benjamin, New York (1969).
H. Araki, inLocal Quantum Theory, R. Jost, ed., Academic Press, New York (1969).
J. Dixmier, inLocal Quantum Theory, R. Jost, ed., Academic Press, New York (1969).
M. Guenin, in1966 Boulder Lectures in Physics, Volume IXA, W. Brittinet al., eds., Gordon and Breach, New York (1967).
M. Guenin, in1969 Boulder Lectures in Physics, Volume XIC, W. Brittinet al., eds., Gordon and Breach, New York (1970).
W. Wyss, in1968 Boulder Lectures in Physics, Volume XID, W. Brittinet al., eds., Gordon and Breach, New York (1969).
J. Dixmier,Les C*-algèbras et leurs représentations, 2nd ed., Gauthier-Villars, Paris (1969).
J. Dixmier,Les algèbras d'opérateurs dans l'espace hilbertien, 2nd ed., Gauthier-Villars, Paris (1969).
I. E. Segal,Mathematical Problems in Relativistic Physics, American Mathematical Society, Providence, Rhode Island (1963).
R. Haag and D. Kastler,J. Math. Phys. 4, 848 (1964).
H. Ekstein,Phys. Rev. 184, 1315 (1969); (E)D 1, 1851 (1970).
Y. Avashai and H. Ekstein,Found. Phys. 2, 257 (1972).
B. DeFacio and D. C. Taylor,Phys. Rev. D 8, 2729 (1973).
B. DeFacio,Found. Phys. 5, 229 (1975).
W. Band and J. L. Park,Found. Phys. 1, 133 (1970).
W. Band and J. L. Park,Found. Phys. 1, 339 (1971).
H. Margenau and J. L. Park,Found. Phys. 3, 19 (1973).
J. L. Park and H. Margenau,Int. J. Theoret. Phys. 1, 211 (1968).
E. Prugovečki,Found. Phys. 3, 3 (1973).
E. Prugovečki, “Measurement in Quantum Mechanics as a Stochastic Process on Spaces of Fuzzy Events,” University of Toronto Preprint (February 1974).
J. M. G. Fell,Trans. Amer. Math. Soc. 94, 365 (1960).
W. Band and J. L. Park,J. Math. Phys. 14, 551 (1973).
J. L. Park and W. Band,J. Math. Phys. 14, 688 (1973).
D. W. Robinson,Commun. Math. Phys. 19, 219 (1970).
P. Havas,Syntheses 18, 75 (1968).
P. Havas, inProceedings of the 1964 International Congress for Logic, Methodology and Philosophy of Science, North-Holland, Amsterdam (1965).
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Work supported in part by the U. S. Atomic Energy Commission.
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DeFacio, B. Quantum measurement and algebraic quantum field theories. Found Phys 6, 185–192 (1976). https://doi.org/10.1007/BF00708959
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DOI: https://doi.org/10.1007/BF00708959