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Completely Quantized Collapse and Consequences

Philip Pearle
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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.

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Philip Pearle. 2005-06-21. Completely Quantized Collapse and Consequences. https://doi.org/10.1103/physreva.72.022112

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