Decoherence, basic concepts and interpretation by Zeh.

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This confusion of the concepts of causes and reasons seems to have a long tradition in philosophy, while even in mathematics the truth of logical theorems is often inappropriately defined by means of logical operations that have to be performed in time (thus mimicking a causal relationship). In the theory of decoherence, apparent events in the detector are described dynamically by a universal Schr¨ odinger equation, using certain initial conditions for the environment, as a very fast but smooth formation of entanglement.

18) m and valid in the time direction defined by decoherence, as was shown by Joos (1984). 18) describes an ensemble of stochastic evolutions n(t), it defines probabilities for coarse-grained “histories”, corresponding to timeordered sequences of projections Pn1 (t1 ) . . Pnk (tk ). Probabilities for such histories in discrete time steps can be written as p(n1 , . . , nk ) = tr{Pnk (tk ) . . 19) (using the property P 2 = P of projection operators). States nk dynamically arising according to a stochastic equation may contain “consistent memories” (or “time capsules” in Barbour’s terminology – Barbour 1999).

Nk ) = tr{Pnk (tk ) . . 19) (using the property P 2 = P of projection operators). States nk dynamically arising according to a stochastic equation may contain “consistent memories” (or “time capsules” in Barbour’s terminology – Barbour 1999). Individual stochastic histories obey a quantum Langevin equation (an indeterministic generalization of the Schr¨ odinger equation). Models have been proposed by Di´ osi (1986), Belavkin (1989a), Gisin and Percival (1992), and others – see also Di´ osi and Kiefer (2001).

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