Abstract
We present a new approach to measurement theory. Our definition of measurement is motivated by direct laboratory procedures as they are carried out in practice. The theory is developed within the quantum logic framework. This work clarifies an important problem in the quantum logic approach; namely, where the Hilbert space comes from. We consider the relationship between measurements and observables, and present a Hilbert space embedding theorem. We conclude with a discussion of charge systems.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
H. A. Araki and M. M. Yanase, “Measurement of quantum mechanical operators,”Phys. Rev. 120, 622–626, (1960).
E. G. Beltrametti and G. Cassinelli,The Logic of Quantum Mechanics (Addison-Wesley, Reading, Mass., 1981).
V. Cantoni, “Generalized transition probability,”Commun. Math. Phys. 44, 125–128 (1975).
V. Cantoni, “The Riemannian structure on the states of quantum-like systems,”Commun. Math. Phys. 56, 189–193 (1977).
A. Daneri, A. Loinger, and G. M. Prosperi, “Quantum theory of measurement and ergodicity conditions,”Nucl. Phys. 33, 297–319 (1962).
A. I. Fine, “On the general theory of measurement,”Proc. Cambr. Philos. Soc. 65, 111–122 (1969).
S. Gudder, “Statistical inference in quantum mechanics,”Rep. Math. Phys. 17, 265–274 (1980).
S. Gudder,Stochastic Methods in Quantum Mechanics (North Holland, New York, 1979).
S. Gudder, “A logical explanation for quarks,”Found. Phys. 12, 419–431 (1982).
S. Gudder, G. Ruttimann, and G. Greechie, “Measurements, Hilbert Space and Quantum Logics,”J. Math. Phys. (to appear).
F. Haake and W. Weidlick, “A model for the measuing process in quantum theory,”Z. Phys. 213, 451–465 (1968).
J. Jauch,Foundations of Quantum Mechanics (Addison-Wesley, Reading, Mass., 1968).
J. M. Jauch, E. P. Wigner, and M. M. Yanase, “Some comments concerning measurement in quantum mechanics,”Nuovo Cimento 48B, 144–151 (1967).
P. Jordan, “On the process of measurement in quantum mechanics,”Philos. Sci. 16, 269–278 (1949).
G. Ludwig, “Der Messprozess,”Z. Phys. 135, 483–511 (1953).
J.-P. Marchand, “Relative coarse-graining,”Found. Phys. 7, 35–49 (1977).
J.-P. Marchand and W. Wyss, “Statistical inference and entropy,”J. Stat. Phys. 16, 349–355 (1977).
C. Piron,Foundations of Quantum Mechanics (Benjamin, New York, 1976).
V. S. Varadarajan,Geometry of Quantum Theory, Vols. 1 and 2 (Van Nostrand Reinhold, Princeton, N.J., 1968, 1971).
J. von Neumann,Mathematical Foundations of Quantum Mechanics (Princeton Univ. Press, Princeton, N.J., 1955).
W. Weidlich, “Problems of the quantum theory of measurement,”Z. Phys. 205, 199–220 (1967).
E. P. Wigner, “Die Messung quantenmechanischer Operatoren,”Z. Phys. 133, 101–108 (1952).
E. P. Wigner, Theorie der quantenmechanischer Messung, inPhysikertagung (Physik Verlag, Mosbach, 1962).
E. P. Wigner, “The problem of measurement,”Amer. J. Phys. 31, 6–15 (1963).
E. P. Wigner, “Two kinds of reality,”The Monist 48, 248–264 (1964).
M. M. Yanase, “Optimal measuring apparatus,”Phys. Rev. 122, 666–668 (1961).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Gudder, S.P. An approach to measurement. Found Phys 13, 35–49 (1983). https://doi.org/10.1007/BF01889409
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01889409