Can the Quantum Measurement Problem Be Resolved within the Framework of Schroedinger Dynamics?

G. Sewell

2007, v.13, №2, 425-440

ABSTRACT

We formulate the dynamics of the generic quantum system $S_{c}$ comprising a microsystem $S$ and a macroscopic measuring instrument ${\cal I}$, whose pointer positions are represented by orthogonal subspaces of the Hilbert space of its pure states. These subspaces are the simultaneous eigenspaces of a set of coarse grained intercommuting macroscopic observables and, most crucially, their dimensionalities are astronomically large, increasing exponentially with the number, $N$, of particles comprising ${\cal I}$. We formulate conditions under which the conservative dynamics of $S_{c}$ yields both a reduction of the wave packet describing the state of $S$ and a one-to-one correspondence, following a measurement, between the pointer position of ${\cal I}$ and the resultant eigenstate of $S$; and we show that these conditions are fulfilled, up to utterly negligible corrections that decrease exponentially with $N$, by the finite version of the Coleman-Hepp model.

Keywords: Schroedinger dynamics of microsystem-cum-measuringinstrument,macroscopic phase cells as pointer positions,macroscopic decoherence,reduction of wave-packet of microsystem

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