Abstract
It is shown that the rule for obtaining probabilities by squaring amplitudes is deducible from ideal experiments in a mechanics of unitary motion in a complex-linear space, with tensor product for making compound systems. Difficulty with tensor product in undoctored quaternionic quantum mechanics makes the argument inapplicable there. Except for the replacement by ideal experiments of a more formal unitary equivalence, the discussion is similar to that of Everett (1957). Diagonal expression of a general vector in the tensor product of two spaces is related to polar form of a matrix, in the Appendix.
Similar content being viewed by others
References
Birkhoff, G., and von Neumann, J. (1936).Annals of Mathematics,37, 823.
Descartes, R. (1637).Discours de la Methode, 2e partie.
de Witt, B. C., and Graham, R. N. (1973).The Many Worlds Interpretation of Quantum Mechanics, Princeton University Press, Princeton, New Jersey.
Dicke, R. H., and Wittke, J. P. (1960).Introduction to Quantum Mechanics, Addison-Wesley, Reading, Massachusetts.
Dirac, P. A. M. (1938–1939).Proceedings of the Royal Society of Edinburgh,59, 2, 122.
Einstein, A., Podolsky, B., and Rosen, N. (1935).Physical Review,47, 777.
Everett, H., III. (1957).Reviews of Modern Physics,29, 454.
Finkelstein, D., Jauch, J. M., Schiminovich, S., and Speiser, D. (1962).Journal of Mathematical Physics,3, 207.
Finkelstein, D. (1963).Transactions of the New York Academy of Sciences,25, 621–637.
Hartle, J. B. (1968).American Journal of Physics,36, 704.
Jauch, J. M. (1968).Foundations of Quantum Mechanics, Addison-Wesley, Reading, Massachusetts.
Landau, L. D. (1927).Zeitschrift für Physik,45, 430.
Latham, R. E. (1951).On the Nature of the Universe, p. 66, a translation of Lucretius (∼55 B.C.), Penguin, Toronto.
Lubkin, E. (1974),Journal of Mathematical Physics,15, 673–674.
Lubkin, E. (1978).Journal of Mathematical Physics,19, 1028–1031.
Titus Lucretius Carus (∼55 B.C.).De Rerum Natura. See Latham (1951).
Ludwig, G. (1961). InWerner Heisenberg und die Physik unserer Zeit, Vieweg u. Sohn, Braunschweig.
Mielnick, B. (1977 or 1978).Mobility, preprint.
Schrödinger, E. (1935).Naturwissenschaften,48, 52.
Thomas, L. H. (1958).Physical Reviews,112, 2129.
von Neumann, J. (1932, 1955).Mathematical Foundations of Quantum Mechanics, tr. Beyer, R. T., Princeton, 1955.
Wheeler, J. A. (1957).Reviews of Modern Physics,29, 454.
Wigner, E. P. (1952).Zeitschrift für Physik,133, 101, footnote 2, p. 102.
Wigner, E. P. (1963).American Journal of Physics,31, 6.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Lubkin, E. An application of ideal experiments to quantum mechanical measurement theory. Int J Theor Phys 18, 165–177 (1979). https://doi.org/10.1007/BF00670393
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00670393