Abstract
We apply the distinction between parameter independence and outcome independence to the linear and nonlinear models of a recent nonrelativistic theory of continuous statevector reduction. We show that in the nonlinear model there is a set of realizations of the stochastic process that drives the statevector reduction for which parameter independence is violated for parallel spin components in the EPR-Bohm setup. Such a set has an appreciable probability of occurrence (≈ 1/2). On the other hand, the linear model exhibits only extremely small parameter dependence effects. The final section discusses the difficulties of finding a relativistic generalization of a parameter-dependent nonrelativistic theory. We identify this difficulty precisely and show how the weak parameter dependence of the linear model avoids it, provided one uses an appropriate criterion for the existence of definite outcomes.
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References
Aharonov, Y., and Albert, D. (1980). States and observables in relativistic quantum field theories,Physical Review D,21, 3316–3324.
Bell, J. S. (1971). Introduction to the hidden variable question, inFoundations of Quantum Mechanics, B. d'Espagnat, ed., Academic Press, New York, pp. 171–181 [reprinted in Bell (1987b), pp. 29–39].
Bell, J. S. (1987). Are there quantum jumps?, inSchrödinger-Centenary Celebration of a Polymath, C. E. W. Kilmister, ed., Cambridge University Press, Cambridge [reprinted in Bell (1987b), pp. 201–212].
Bell, J. S. (1987b).Speakable and Unspeakable in Quantum Mechanics, Cambridge University Press, Cambridge.
Bell, J. S. (1989). Towards an exact quantum mechanics, inThemes in Contemporary Physics II, Essays in Honor of Julian Schwinger's 70th Birthday, S. Deser and R. J. Finkelstein, eds., World Scientific, Singapore, pp. 1–26.
Bell, J. S., Shimony, A., Horne, M., and Clauser, J. (1985). An exchange on local beables,Dialeclica,39, 85–110.
Benatti, F., Ghirardi, G. C., Rimini, A., and Weber, T. (1987). Quantum mechanics with spontaneous localization and the quantum theory of measurement,Nuovo Cimento,100B, 27–41.
Bloch, I. (1967). Some relativistic oddities in the quantum theory of observation,Physical Review,156, 1377–1384.
Bohm, D. (1952). A suggested interpretation of quantum theory in terms of“hidden”variables,Physical Review,85, 166–193.
Butterfield, J. (1992). Bell's theorem: What it takes,British Journal for the Philosophy of Science,43, 41–83.
Eberhard, P. (1978). Bell's theorem and the different concepts of locality,Nuovo Cimento,46B, 392–419.
Ghirardi, G. C., and Rimini, A. (1990). Old and new ideas in quantum theory of measurement, inSixty-Two Years of Uncertainty: Historical, Philosophical and Physical Inquiries into the Foundations of Quantum Physics. A. I. Miller, ed., Plenum Press, New York, pp. 167–191.
Ghirardi, G. C., Rimini, A., and Weber, T. (1980). A general argument against superluminal transmission through the quantum mechanical measurement process,Lettere al Nuovo Cimento,27, 293–298.
Ghirardi, G. C., Rimini, A., and Weber, T. (1986). Unified dynamics for microscopic and macroscopic systems,Physical Review D,34, 470–491.
Ghirardi, G. C., Grassi, R., Rimini, A., and Weber, T. (1988). Experiments of EPR-type involving CP-violation do not allow faster-than-light communication,Europhysics Letters,6, 95–100.
Ghirardi, G. C., Pearle, P., and Rimini, A. (1990a). Markov processes in Hilbert space and continuous spontaneous localization of identical particles,Physical Review A,42, 78–89.
Ghirardi, G. C., Grassi, R., and Pearle, P. (1990b). Relativistic dynamical reduction models: General framework and examples.Foundations of Physics,20, 1271–1316.
Ghirardi, G. C., Grassi, R., and Pearle, P. (1990c). Relativistic dynamical reduction models, inSymposium on the Foundations of Modern Physics 1990, P. Lahti and P. Mittelstaedt, eds., World Scientific, Singapore, pp. 109–123.
Ghirardi, G. C., Grassi, R., Butterfield, J., and Fleming, G. (1993). Parameter dependence and outcome dependence in dynamical models of state vector reduction,Foundations of Physics,23, 341–364.
Hellwig, K., and Kraus, K. (1970). Formal description of measurements in local quantum field theory,Physical Review D,1, 566–571.
Holland, P., and Vigier, J. (1988). The quantum potential and signalling in the EPR experiment,Foundations of Physics,18, 741–750.
Jarrett, J. (1984). On the physical significance of the locality conditions in the Bell arguments,Nous,18, 569–589.
Pearle, P. (1989). Combining stochastic dynamical statevector reduction with spontaneous localization,Physical Review A,39, 2277–2289.
Pearle, P. (1990). Towards a relativistic theory of state reduction, inSixty-Two Years of Uncertainty: Historical, Philosophical and Physical Inquiries into the Foundations of Quantum Physics, A. I. Miller, ed., Plenum Press, New York, pp. 193–213.
Shimony, A. (1984). Controllable and uncontrollable nonlocality, inProceedings of the International Symposium on the Foundations of Quantum Mechanics, S. Kamefuchiet al., eds., Physical Society of Japan, Tokyo, pp. 225–230.
Suppes, P., and Zanotti, M. (1976).On the determinism of hidden variable theories with strict correlation and conditional statistical independence of observables, Reidel, Dordrecht, pp. 445–455.
Van Fraassen, B. (1982). The Charybdis of realism,Synthese,52, 25–38.
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Butterfield, J., Fleming, G.N., Ghirardi, G.C. et al. Parameter dependence in dynamical models for statevector reduction. Int J Theor Phys 32, 2287–2304 (1993). https://doi.org/10.1007/BF00673000
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DOI: https://doi.org/10.1007/BF00673000