Abstract
A theory describing the dynamics of the reduction of the statevector is presented. A nonlinear term is added to the Schrödinger equation which causes an interaction between the superposed vectors making up the statevector. The indeterminism in quantum theory is ascribed to randomly fluctuating coefficients governing the nonlinear term. Three further investigations into the antecedents and consequences of this theory are reported. First, it is argued that there exists a relation between the nonlinear term and an antilinear operator analogous to the relation between the usual linear term and the linear Hamiltonian operator. Second, a possible mechanism for producing the randomly fluctuating coefficients is presented: it is ascribed to the complicated fluctuations of the statevector describing an apparatus. Third, the predictions of this theory are discussed for rapidly repeated experiments: remarkably, it is shown that they are identical to those of quantum theory, even when the time between experiments is comparable to the reduction time. Some experiments which can test this theory are mentioned.
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References
Bohr, N.: 1966, Essays 1958–1962 on Atomic Physics and Human Knowledge (Random House, New York); Schilpp, P.A., ed.: 1959, Albert Einstein, Philosopher Scientist (Harper and Row, New York). There are a number of versions of this so-called “Copenhagen interpretation”: see e.g. Heisenberg, W.: 1958, Physics and Philosophy, The Revolution tn Modern Science (world perspectives. New York); Born, M.: 1964, The Natural Philosophy of Cause and Chance (New York). A historical and critical discussion appears in jammer, M.: 1974, The Philosophy of Quantum Mechanics (Wiley, New York).
Einstein, A.: 1959 in Schilpp, P.A., ed. Ibid; Pearle, P.: 1967, Am. J. Phys 35, p. 742; Ballentine, L.E.: 1970, Revs. Mod. Phys. 42, p. 358; Belinfante, F.: 1975, MeasurementS and Time Reversal In Objective, Quantum Theory (Pergamon, Oxford).
This was the original idea of Born, though he later disavowed it: see Jammer, M., Ibid, and Einstein’s letter to Schrödinger in 1939 in Klein, M.: 1968, Letters on Wave Mechanics (Vision, London). A modern version of this position appears in Hartle, J.B.: 1968, Am. J. Phys. 36, p. 704.
Everett, H.: 1957, Revs. Mod. Phys. 29, p. 454; Wheeler, J.A.: 1957, Revs. Mod. Phys. 29, p. 463; Dewitt, B.S., and Graham, R.N.: 1973, The Many-Worlds Interpretation of Quantum Mechanics (Princeton University Press, Princeton, New Jersey); Deutsch, D.: 1981, “Quantum Theory as a Universal Physical Theory,” preprint.
Wigner, E.: 197O. Symmetries and Reflections (M.I.T. press, Cambridge, Massachusetts) argues that consciousness may be responsible for the reduction of the statevector. If that is so, then perhaps something which is not physical also belongs in the quantum description!
Schrödinger, E.: 1935, Naturwissenschaften 23, p. 807; Dewitt, B.S.: 1970, Physics Today 23, #9, p. 30; 1971, Ibid 24, #4, p. 36.
Pearle, P.: 1981, “Reduction of the Statevector, Continuous Measurements, and the Rules of Quantum Theory,” preprint.
Bloch, I. and Burba, D.A.: 1974, Phys. Rev D. 10, p. 3206; Misra, B. and Sudarshan, E.C.G.: 1977, Journ. Math. Phys. 18, p. 756; Chiu, C.B., Sudarshan, E.C.G. and Misra, B.: 1977, Phys, Rev. D 16, p. 520; Allcock, G.R.: 1969, Ann. Phys. 53, p. 253; Ibid, p. 286; Ibid, p. 311; Aharanov, Y. and vardi, M.: 1980, Phys. Rev. D 21, p. 2235; Simonius, M.: 1978, Phys. Rev. Lett. 40, p. 980; Peres, A.: 1980, Am. Journ. Phys. 48, p. 931.
Kubler, O. and Zen, H.: 1973, Ann. Phys. 76, p. 405.
Pearle, P.: 1979, Int’l Journ. of Theor. Phys. 18, p. 489.
Deutsch, D., (4).
Zurek, W.H.: 1981, Phys. Rev. D 24, p. 1516.
Feller, W.: 1950, An Introduction to “Probability Theory and Its Applications (Wiley, New York), Chapter 14.
Pearle, P.: 1982, Found, of Phys. 12, p. 249.
Pearle, P.: 1976, Phys. Rev. D 13, p. 857.
Chandrasekhar, S.: 1943, Rev. Mod. Phys. 15, p. 1 [also in Wax, N., ed.: 1954, Selected Vapehs on Holse and Stochastic Processes (Dover, New York).
Wong, E.: 1971, Stochastic Processes In Information and Dynamical Systems (McGraw Hill, New York).
Penrose, R. in Isham, C.J., Penrose, R. and Sciama, D.W., eds.: 1981, Quantum Gravity 2, A Second Oxford Symposium (Clarendon, Oxford).
Takesaki, M.: 1970, Tomita’s Theory of Modular Hilbert Algebras and its Applications (Springer-Verlag, Berlin).
Huang, K.: 1963, Statistical Mechanics (Wiley, New York).
Bohm, D. and Bub, J.: 1966, Rev. Mod. Phys. 38, p. 453.
Bohm, D., private communication.
Leggett, A.J.: 1980, Suppl. Prog. Theor. Phys. 69, p. 80.
den Boer, W. and de Bruyn Ouboter, R.: 1980, Physica 98 B+C, p. 185; Prance, R.J. et al.: 1981, Nature 289, p. 543.
Zeilinger, A., Gaehler, R., Shull, C.G. and Treimer, W.: 1981, “Experimental Status and Recent Results of Neutron Interference Optics,” in the proceedings of the Symposium on Neutron Scattering, to be published.
Pearle, P. and Zeilinger, A.: 1982, “Experimental Tests of Dynamical Statevector Reduction,” preprint.
Pipkin, F.M.: 1979, Advances in Atomic and Molecular Physics 14 (Academic Press, New York), p. 281.
Papaliolios, C.: 1967), Phys. Rev. Lett. 18, p. 622; Belinfante, F.: 1975, A Survey of Hidden Variable Theories (Pergamon, Oxford).
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Pearle, P. (1984). Dynamics of the Reduction of the Statevector. In: Diner, S., Fargue, D., Lochak, G., Selleri, F. (eds) The Wave-Particle Dualism. Fundamental Theories of Physics, vol 3. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-6286-6_26
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DOI: https://doi.org/10.1007/978-94-009-6286-6_26
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