Abstract
Counting outcomes is the obvious algorithm for generating probabilities in quantum mechanics without state-vector reduction (i.e., many-worlds). This procedure has usually been rejected because for purely linear dynamics it gives results in disagreement with experiment. Here it is shown that if non-linear decoherence effects (previously proposed by other authors) are combined with an exponential time dependence of the scale for the non-linear effects, the correct measure-dependent probabilities can emerge via outcome counting, without the addition of any stochastic fields or metaphysical hypotheses.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
W. H. Zurek, Phys. Today 44 (1991) 36.
L. E. Ballentine, Found. Phys. 3 (1973) 229.
N. Graham, in The Many-Worlds Interpretation of Quantum Mechanics (Princeton University Press, Princeton, 1973), pp. 229-553.
J. Ellis, N. E. Mavromatos, and D. V. Nanopoulos, Mod. Phys. Lett. A 10 (1995) 425.
J. Ellis, N. E. Mavromatos, and D. V. Nanopoulos, J. Chaos, Solitons and Fractals, 10 (1999) 345.
P. Pearle, Phys. Rev. A 48 (1993) 913.
P. Pearle, in Perspectives on Quantum Reality, R. Clifton, ed. (Kluwer Academic, Dordrecht, 1996), pp. 93-109.
P. Pearle and E. Squires, Found. Phys. 26 (1996) 291.
P. Pearle, J. Ring, J. I. Collar, and F. T. Avignone, Found. Phys. 29 (1999) 465.
P. Pearle, in Open Systems and Measurement in Relativistic Quantum Mechanics, F. Petruccione and H. P. Breuer, eds. (Springer, New York, in press).
H. Everett, Rev. Mod. Phys. 29 (1957) 141.
B. DeWitt and N. Graham, The Many-Worlds Interpretation of Quantum Mechanics (Princeton University Press, Princeton, 1973).
M. Gell-Mann and J. B. Hartle, Phys. Rev. D 47 (1993) 3345.
F. Dowker and A. Kent, J. Stat. Phys. 82 (1996) 1575.
W. H. Zurek, Phil. Trans. R. Soc. Lond. A 356 (1998) 1793.
S. Saunders, in Perspectives on Quantum Reality R. Clifton, ed. (Kluwer Academic, Dordrecht, 1996), pp. 125-142.
D. Deutsch, Int. J. Theor. Phys. 24 (1985) 1.
D. Albert and B. Loewer, Synthese 77 (1988) 195.
G. C. Ghirardi, A. Rimini, and T. Weber, Phys. Rev. D 34 (1986) 4701.
A. J. Leggett, Found. Phys. 18 (1988) 939.
J. Butterfield, G. N. Fleming, G. C. Ghirardi, and R. Grassi, Int. J. Theor. Phys. 32 (1993) 2287.
E. Squires, The Mystery of the Quantum World (Institute of Physics, Bristol, 1994).
N. D. Mermin, Am. J. Phys. 66 (1998) 753.
D. Bohm and B. J. Hiley, The Undivided Universe (Routledge, London, 1993).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Weissman, M.B. Emergent Measure-Dependent Probabilities from Modified Quantum Dynamics Without State-Vector Reduction. Found Phys Lett 12, 407–426 (1999). https://doi.org/10.1023/A:1021625209799
Published:
Issue Date:
DOI: https://doi.org/10.1023/A:1021625209799