dorsal/arxiv
View SchemaCan the Quantum Measurement Problem be resolved within the framework of Schroedinger Dynamics?
| Authors | Geoffrey Sewell |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0512098 |
| URL | https://arxiv.org/abs/quant-ph/0512098 |
Abstract
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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"abstract": "We formulate the dynamics of the generic quantum system S_{c} comprising a\nmicrosystem S and a macroscopic measuring instrument I, whose pointer positions\nare represented by orthogonal subspaces of the Hilbert space of its pure\nstates. These subspaces are simultaneous eigenspaces of a set of coarse grained\nintercommuting macroscopic observables and, most crucially, their\ndimensionalities are astronomically large, increasing exponentially with the\nnumber, N, of particles comprising I. We formulate conditions under which the\nconservative dynamics of S_{c} yields both a reduction of the wave packet\ndescribing the state of S and a one-to-one correspondence, following a\nmeasurement, between the pointer position of I and the resultant eigenstate of\nS; and we show that these conditions are fulfilled, up to utterly negligible\ncorrections that decrease exponentially with N, by the finite version of the\nColeman-Hepp model.",
"arxiv_id": "quant-ph/0512098",
"authors": [
"Geoffrey Sewell"
],
"categories": [
"quant-ph",
"math-ph",
"math.MP"
],
"title": "Can the Quantum Measurement Problem be resolved within the framework of Schroedinger Dynamics?",
"url": "https://arxiv.org/abs/quant-ph/0512098"
},
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