Abstract
The quantum mechanical formalism which was discovered by Heisenberg [1] and Schrödinger [2] in 1925 was first interpreted by Born [3] in a statistical sense. The formal expressions p(φ, a i ) = ׀(φ, φ ai)׀2, i ∊ N were interpreted as the probabilities that a quantum system S with preparation φ possesses the value a i which belongs to the state φ αi. This original Bom interpretation which was formulated for scattering processes was, however, not tenable in the general case. The probabilities must not be related to the system S in state φ since in the preparation φ the value α i of an observable A is in general not subjectively unknown but objectively undecided. Instead one has to interpret the formal terms p(φ, α i ) as the probabilities to find the value at after the measurement of the observable A of the system S with preparation φ. In this improved version the statistical or “Born interpretation” is used in the present day literature.
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References
Heisenberg, W. (1925), “Über quantentheoretische Umdeutung kinematischer und mechanischer Beziehungen”, Z Phys. 33, 879–893.
Schrödinger, E. (1926), “Quantisierung als Eigenwertproblem’’, Annal. Phys 79, 361–376.
Born, M. (1926), “Zur Quantenmechanik der Sto/Wgänge”, Z. Phys 37, 863–867.
Heisenberg, W. (1959), “Die Plancksche Entdeckung und die physikalischen Probleme der Atomphysik’’, Universitas 14, 135–148.
Busch, P., P. Lahti and P. Mittelstaedt (1991), The Quantum Theory of Measurement, Springer, Heidelberg (2nd ed., 1996 ).
Mittelstaedt, P. (1993), “The Measuring Process and the Interpretation of Quantum Mechanics”, Int. J. Theor. Phys 32, 1763–1775.
Einstein, A., B. Podolsky and N. Rosen (1935), “Can Quantum-Mechanical Description of Physical Reality be considered complete?”, Phys. Rev 32, 777–780.
Popper, R.K. (1957), “The Propensity Interpretation of the Calculus of Probability and the Quantum Theory”, in Observation and Interpretation in the Philosophy of Physics, S. Körner, ed., Butterworth, London.
Sklar, L. (1970), “Is Probability a Dispositional Property?”, J. Phil 67, 355–366.
Giere, R. (1973), “Objective Single-Case Probabilities”, in Logic, Methodology and Philosophy of Science, P. Suppes et al, eds. pp. 457–483.
Schneider, C. (1994), “Two Interpretations of Objective Probabilities”, Philosoph. Naturalis 31, 107–131.
Popper, R.K. (1982), “Quantum Theory and the Schism of Physics”, in Postscript III to the Logic of Scientific Discovery, W.W.Bartley, HI, ed., Hutchinson, London Melbourne, 1988.
Everett, H. (1957), “The Theory of the Universal Wave Function”, theses, Princeton University; reprinted in The Many Worlds Interpretation of Quantum Mechanics, B.S. DeWitt and N. Graham, eds., Princeton University Press, Princeton N.J., 1973, pp. 1–140.
Finkelstein, D. (1962), “The Logic of Quantum Physics”, Trans. NY Acad. Sei 25, 621–637.
Hartle, J.B. (1968), “Quantum Mechanics of Individual Systems”, Am. J. Phys 36, 704–712.
Graham, N. (1973), “The Measurement of Relative Frequency”, in The Many-Worlds Interpretation of Quantum Mechanics, B.S. DeWitt and N. Graham, eds., Princeton University Press, Princeton, N.J., pp. 229–252.
DeWitt, B.S. (1971), “The Many-Universes Interpretation of Quantum Mechanics”, in Foundations of Quantum Mechanics, Academic Press, New York, pp. 167–218.
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Mittelstaedt, P. (1997). Is Quantum Mechanics a Probabilistic Theory?. In: Cohen, R.S., Horne, M., Stachel, J. (eds) Potentiality, Entanglement and Passion-at-a-Distance. Boston Studies in the Philosophy of Science, vol 194. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-2732-7_12
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DOI: https://doi.org/10.1007/978-94-017-2732-7_12
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