Abstract
We present a model system that behaves as a measurement apparatus for quantum systems should. The device is macroscopic, it interacts with the microscopic system to be measured, and the results of that interaction affect the macroscopic device in a macroscopic, irreversible way. Everything is treated quantum mechanically: the apparatus is defined in terms of its (many) coordinates, the Hamiltonian is given, and time evolution follows Schrödinger's equation. It is proposed that this model be itself used as a laboratory for testing ideas on the measurement process.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
L. S. Schulman,Phys. Lett. A 102:396 (1984).
L. S. Schulman,J. Stat. Phys. 42:689 (1986).
L. S. Schulman,Phys. Lett. A 130:194 (1988);Ann. Phys. 183:320 (1988); Remote twotime boundary conditions and special states in quantum mechanics,Found. Phys. Lett., to appear; Semiclassical two-time localization and the consequences of restrictions on wave packet spreading, preprint.
F. Benatti, G. C. Ghirardi, A. Rimini, and T. Weber,Nuovo Cimento B 100:27 (1987); P. Pearle,Phys. Rev. D 13:857 (1976); P. Pearle,Phys. Rev. A 39:2277 (1989); D. Bohm and J. Bub,Rev. Mod. Phys. 38:453 (1966).
K. Hepp,Helv. Phys. Acta 45:237 (1972).
J. S. Bell,Helv. Phys. Acta 48:93 (1975).
K. Gottfried,Quantum Mechanics (Benjamin, New York, 1966), Section 20.3.
H. S. Green,Nuovo Cimento 9:880 (1958).
N. G. van Kampen,Physica A 153:97 (1988).
G. T. Zimanyi and K. Vladar,Phys. Rev. A 34:3496 (1986); G. T. Zimanyi and K. Vladar, Symmetry breaking and measurement theory,Found. Phys. Lett. 1:175 (1988).
P. W. Anderson, Measurement in quantum theory and the problem of complex systems, inThe Lesson of Quantum Theory, J. de Boer, E. Dal, and O. Ulfbeck, eds. (Elsevier, 1986).
A. O. Caldeira and A. J. Leggett,Phys. Rev. Lett. 46:211 (1981);Ann. Phys. 149:374 (1983).
M. Aizenman, J. T. Chayes, L. Chayes, and C. M. Newman,J. Stat. Phys. 50:1 (1988); C. M. Newman and L. S. Schulman,Commun. Math. Phys. 104:547 (1986).
P. W. Milonni, J. R. Ackerhalt, H. W. Galbraith, and M.-L. Shih,Phys. Rev. A 28:32 (1983).
J. Ford,J. Math. Phys. 2:387 (1961).
P. Bocchieri and A. Loinger,Phys. Rev. 107:337 (1957).
L. S. Schulman,Phys. Rev. A 18:2379 (1978).
E. P. Wigner, Interpretation of quantum mechanics, inQuantum Theory and Measurement, J. A. Wheeler and W. H. Zurek, eds. (Princeton University Press, Princeton, New Jersey, 1983).
J. A. Wheeler and W. H. Zurek, eds.,Quantum Theory and Measurement (Princeton University Press, Princeton, New Jersey, 1983).
A. Daneri, A. Loinger, and G. M. Prosperi,Nucl. Phys. 33:297 (1962).
W. H. Zurek,Phys. Rev. D 26:1862 (1982).
R. J. Glauber, Amplifiers, attenuators, and Schrödinger's cat, inNew Techniques and Ideas in Quantum Measurement Theory, D. M. Greenberger, ed. (New York Academy of Science, New York, 1986).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Gaveau, B., Schulman, L.S. Model apparatus for quantum measurements. J Stat Phys 58, 1209–1230 (1990). https://doi.org/10.1007/BF01026572
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01026572