Abstract
A modified Beltrametti-Cassinelli-Lahti model of the measurement apparatus that satisfies both the probability reproducibility condition and the objectification requirement is constructed. Only measurements on microsystems are considered. The cluster separability forms a basis for the first working hypothesis: the current version of quantum mechanics leaves open what happens to systems when they change their separation status. New rules that close this gap can therefore be added without disturbing the logic of quantum mechanics. The second working hypothesis is that registration apparatuses for microsystems must contain detectors and that their readings are signals from detectors. This implies that the separation status of a microsystem changes during both preparation and registration. A new rule that specifies what happens when these changes occur and that guarantees the objectification is formulated and discussed. A part of our result has certain similarities with ‘collapse of the wave function’.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Ludwig, G.: Foundations of Quantum Mechanics I. Springer, New York (1983)
Ludwig, G.: Foundations of Quantum Mechanics II. Springer, New York (1985)
Ludwig, G.: An Axiomatic Basis for Quantum Mechanics 1. Springer, Berlin (1985)
Ludwig, G.: An Axiomatic Basis for Quantum Mechanics 2. Springer, Berlin (1987)
Giulini, D., Joos, E., Kiefer, C., Kupsch, J., Stamatescu, I.-O., Zeh, H.D.: Decoherence and the Appearance of Classical World in Quantum Theory. Springer, Berlin (1996)
Zurek, W.H.: Rev. Mod. Phys. 75, 715 (2003)
Hepp, K.: Helv. Phys. Acta 45, 237 (1972)
Primas, H.: Chemistry, Quantum Mechanics and Reductionism. Springer, Berlin (1983)
Bub, J.: Interpreting the Quantum World. Cambridge University Press, Cabridge (1999)
Bush, P., Lahti, P.J., Mittelstaed, P.: The Quantum Theory of Measurement. Springer, Heidelberg (1996)
d’Espagnat, B.: Veiled Reality. Addison-Wesley, Reading (1995)
Hájíček, P., Tolar, J.: Found. Phys. 39, 411 (2009)
Hájíček, P.: Found. Phys. 39, 1072 (2009)
Beltrametti, E.G., Cassinelli, G., Lahti, P.J.: J. Math. Phys. 31, 91 (1990)
Peres, A.: Quantum Theory: Concepts and Methods. Kluwer, Dordrecht (1995)
von Neumann, J.: Mathematical Foundation of Quantum Mechanics. Princeton University Press, Princeton (1983)
Bohm, D.: Quantum Theory. Prentice-Hall, Englewood Cliffs (1951)
Leo, W.R.: Techniques for Nuclear and Particle Physics Experiments. Springer, Berlin (1987)
Twerenbold, D.: Rep. Progr. Phys. 59, 239 (1996)
Weinberg, S.: The Quantum Theory of Fields, vol. I, p. 177. Cambridge University Press, Cambridge (1995)
Haag, R.: Local Quantum Physics. Fields, Particles, Algebras. Springer, Berlin (1992)
Keiser, B.D., Polyzou, W.N.: In: Negele, J.W., Vogt, E. (eds.) Advances in Nuclear Physics, vol. 20. Plenum, New York (2002)
Coester, F.: Int. J. Mod. Phys. 17, 5328 (2003)
Mott, N.F.: Proc. R. Soc. Lond. A 126, 79 (1929)
Davisson, C., Germer, L.: Phys. Rev. 30 (1927)
Mandel, L., Wolf, E.: Optical Coherence and Quantum Optics. Cambridge University Press, Cambridge (1995)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Hájíček, P. The Quantum Measurement Problem and Cluster Separability. Found Phys 41, 640–666 (2011). https://doi.org/10.1007/s10701-010-9506-3
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10701-010-9506-3