Abstract
First steps are taken toward a formulation of quantum mechanics which avoids the use of probability amplitudes and is expressed entirely in terms of observable probabilities. Quantum states are represented not by state vectors or density matrices but by “probability tables,” which contain only the probabilities of the outcomes of certain special measurements. The rule for computing transition probabilities, normally given by the squared modulus of the inner product of two state vectors, is re-expressed in terms of probability tables. The new version of the rule is surprisingly simple, especially when one considers that the notion of complex phases, so crucial in the evaluation of inner products, is entirely absent from the representation of states used here.
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References
John A. Wheeler, “Genesis and Observership,” inFoundational Problems in the Special Sciences, R. E. Butts and J. Hintikka, eds. (Reidel, Dordrecht, Holland, 1987); “Frontiers of Time,” inProblems in the Foundations of Physics (Proceedings of the International School of Physics “Enrico Fermi”: course 72) (Italian Physical Society, 1979); “Beyond the Black Hole,” inSome Strangeness in the Proportion, Harry Woolf, ed. (Addison-Wesley, Reading, Massachusetts, 1980);Am. J. Phys. 51, 398 (1983).
W. Gale, C. Guth, and G. T. Trammell,Phys. Rev. 165, 1434 (1968); W. Band and J. L. Park,Found. Phys. 1, 133 (1970); J. L. Park and W. Band,Found. Phys. 1, 211 (1971); W. Band and J. L. Park,Found. Phys. 1, 339 (1971);Am. J. Phys. 47, 188 (1979); I. D. Ivanovic,J. Math. Phys. 24, 1199 (1983).
I. D. Ivanovic,J. Phys. A: Mat. Gen. 14, 3241 (1981).
John S. Bell,Physics 1, 195 (1964); John F. Clauser, Michael A. Horne, Abner Shimony, and Richard A. Holt,Phys. Rev. Lett. 23, 880 (1969); Stuart J. Freedman and John F. Clauser,Phys. Rev. Lett. 28, 938 (1972); P. J. Bussey,Phys. Lett. A 90, 9 (1982).
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Wootters, W.K. Quantum mechanics without probability amplitudes. Found Phys 16, 391–405 (1986). https://doi.org/10.1007/BF01882696
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DOI: https://doi.org/10.1007/BF01882696