Physics – Quantum Physics
Scientific paper
2005-12-13
Physics
Quantum Physics
15 pages, based on a lecture at the J. T. Lewis Memorial Conference held in Dublin, June 14-17, 2005. To be published in "Mark
Scientific paper
We formulate the dynamics of the generic quantum system S_{c} comprising a microsystem S and a macroscopic measuring instrument I, whose pointer positions are represented by orthogonal subspaces of the Hilbert space of its pure states. These subspaces are 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 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 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.
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