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Completely Quantized Collapse and Consequences
Philip Pearle
abstract: Promotion of quantum theory from a theory of measurement to a theory of
reality requires an unambiguous specification of the ensemble of realizable
states (and each state's probability of realization). Although not yet achieved
within the framework of standard quantum theory, it has been achieved within
the framework of the Continuous Spontaneous Localization (CSL) wave function
collapse model. In this paper, I consider a previously presented model, which
is predictively equivalent to CSL. In this Completely Quantized Collapse (CQC)
model, the classical random field which causes collapse in CSL is quantized.
The ensemble of realizable states is described by a single state vector, the
"ensemble vector," the sum of the direct product of an eigenstate of the
quantized field and the CSL state corresponding to that eigenstate. Using this
description, a long standing problem is resolved: it is shown how to define
energy of the random field and its energy of interaction with particles so that
total energy is conserved for the ensemble of realizable states. As a
byproduct, since the random field energy spectrum is unbounded, its canonical
conjugate, a self-adjoint time operator, is discussed. Finally, CSL is a
phenomenological description, whose connection to, or derivation from, more
conventional physics has not yet appeared. We suggest that, because CQC is
fully quantized, it is a natural framework for replacement of the classical
field of CSL by a quantized physical entity. Two illustrative examples are
given.
- oai_identifier:
- oai:arXiv.org:quant-ph/0506177
- categories:
- quant-ph
- comments:
- 18 pages
- doi:
- 10.1103/PhysRevA.72.022112
- arxiv_id:
- quant-ph/0506177
- created:
- 2005-06-21
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