Abstract
When a quantum system is macroscopic and becomes entangled with a microscopic one, entanglement is not immediately total, but gradual and local. A study of this locality is the starting point of the present work and shows unexpected and detailed properties in the generation and propagation of entanglement between a measuring apparatus and a microscopic measured system. Of special importance is the propagation of entanglement in nonlinear waves with a finite velocity. When applied to the entanglement between a macroscopic system and its environment, this study yields also new results about the resulting disordered state. Finally, a mechanism of wave function collapse is proposed as an effect of perturbation in the growth of local entanglement between a measuring system and the measured one by waves of entanglement with the environment.
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References
Schrödinger, E.: Die gegenwärtige Situation in der Quantenmechanik. Naturwissenschaften 23, 807 (1935). 823, 844, reprinted with English translation in J.A Wheeler and W.H. Zurek, Quantum mechanics and measurement. Princeton University Press, Princeton (1983)
Schrödinger, E.: Discussion of probability relations in separated systems. Proc. Camb. Philol. Soc. 31, 555 (1935). 32, 446 (1936)
Haroche, S., Raimond, J.M.: Exploring the Quantum. Oxford University Press, Oxford (2006)
Von Neumann, J.: Mathematische Grundlagen der Quantenmechanik. Springer, Berlin (1932). English translation by R.T. Beyer, Mathematical Foundations of Quantum Mechanics. Princeton University Press, Princeton (1955)
Ghirardi, G.C., Rimini, A., Weber, T.: Unified dynamics for microscopic and macroscopic systems. Phys. Rev. D 34, 470 (1986)
Joos, E., Zeh, H.D., Kiefer, C., Giulini, D., Kupsch, K., Stamatescu, I.O.: Decoherence and the Appearance of a Classical World in Quantum Theory. Springer, Berlin (2003)
Hugenholtz, N.M.: Physica 23, 481 (1957)
Kubo, R.: J. Math. Phys. 4, 174 (1963)
Wichmann, E.H., Crichton, J.H.: Phys. Rev. 132, 2788 (1983)
Weinberg, S.: The Quantum Theory of Fields I. Cambridge University Press, Cambridge (2011). Chap. 4
Faddeev, L.D., Merkuriev, S.P.: Quantum Scattering Theory for Several Particle Systems. Springer, Berlin (1993)
Brown, L.S.: Quantum Field Theory. Cambridge University Press, Cambridge (1992), Chap. 2
Hörmander, L.: The Analysis of Linear Partial Differential Operators. Springer, Berlin (1985)
Godement, R.: Topologie Algébrique et Théorie des Faisceaux. Hermann, Paris (1981)
Dautray, R., Lions, J.-L.: Mathematical Analysis and Numerical Methods for Science and Technology. Evolution Problems, I, II. Springer, Berlin (2000)
Balian, R.: From Microphysics to Macrophysics. Springer, Berlin (2006)
Mehta, M.L.: Random Matrices. Elsevier/Academic Press, Amsterdam (2004)
Omnès, R.: Decoherence and wave function collapse. Found. Phys. 41, 1857 (2011)
d’Espagnat, B.: On Physics and Philosophy. Princeton University Press, Princeton (2006)
Pearle, P.: Reduction of the state vector by a nonlinear Schrödinger equation. Phys. Rev. D 13, 857 (1976)
Zurek, W.H.: Quantum Darwinism. Nat. Phys. 5, 181 (2009)
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Omnès, R. Local Properties of Entanglement and Application to Collapse. Found Phys 43, 1339–1368 (2013). https://doi.org/10.1007/s10701-013-9750-4
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DOI: https://doi.org/10.1007/s10701-013-9750-4