Quantum Physics

Advanced Quantum Theory by Paul Roman

By Paul Roman

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Similar to the motion of a shadow that merely reflects the regular motion of a physical object, the reduced information content of the subsystem density matrix by itself is insufficient to determine its own change. Likewise, Boltzmann had to introduce his Stoßzahlansatz, based on statistical assumptions, when neglecting statistical correlations between particles (instead of quantum entanglement). The exact dynamics of any local “system” would in general require the whole Universe to be taken into account; no effective time-dependent Hamiltonian would suffice.

Dieks 1995). 38 H. D. Zeh declare the program of decoherence a failure. As explained in Sect. 3, both claims miss the point. However, decoherence represents a crucial dynamical step in the measurement process. The rest may remain a pure epistemological problem (requiring only a reformulation of the psycho-physical parallelism in consistent quantum mechanical terms). If the Schr¨odinger equation is exact, the observed quantum indeterminism can only reflect that of the observer’s identity – not one to be found in objective dynamics.

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).

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