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How can this loss of information modelled? An essential step towards a better understanding was accomplished by the theory of quantum decoherence, originating with the work by Zeh (1970). Decoherence can explain how, in an approximate way, a quantum object acquires classical properties. There is a recent and detailed book (Schlosshauer, 2007) to which the reader is referred to for technical details. The central point is that for the composite system of the object, the measuring device, and the environment, the non-diagonal elements in the partial density matrix of the object become exponentially small in a short time.

ArXiv:quant-ph/9803052v1 19 Mar Zeh, H. D. (1996), in Editors D. Giulini, E. Joos, C. Kiefer, J. -O. Stamatescu, and H. D. Zeh, Decoherence and Appearance of a Classical World in Quantum Theory, Springer, Berlin, Heidelberg 0 2 Effects on Quantum Physics of the Local Availability of Mathematics and Space Time Dependent Scaling Factors for Number Systems Paul Benioff Physics division, Argonne National Laboratory, Argonne, IL USA 1. Introduction The relation of mathematics to physics and its influence on physics have been a topic of much interest for some time.

For a point x with C¯ x , H¯ x , the integrand factors are parallel transformed to obtain (ψ1,2 ) x = Here x (dz1 ) x (dz2 ) x ( (eiz1 p ) x ψ1 ( p) x | p x 1 (e−iz2 p ) x ψ2 (− p) x | − p x 2 dp x ). (55) (eiz1 p ) x = Fx,z1 (eiz1 p ) (56) (e−iz2 p ) x = Fx,z2 (e−iz2 p ) Also p x is the same value in C¯ x as p is in C¯ z1 in the z1 integral, Eq. 54, and − p x is the same value in C¯ x as − p is in C¯ z2 in the z2 integral. 2 Inclusion of number system scale factors The above shows that the imposition of "mathematics is local" on quantum theory is more complex than the usual treatment with just one scalar field and one Hilbert space for all space points.

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