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arXiv:quant-ph/0411050 · Foundations of Physics Letters

The Status of the Wave Function in Dynamical Collapse Models

Fay Dowker B, Isabelle Herbauts

Published Nov 1, 2005• 31 citations
arXivHTMLPDF
DOI
10.1007/s10702-005-1125-4

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The notion of a physical collapse of the wave function is embodied in dynamical collapse models. These involve a modification of the unitary evolution of the wave function so as to give a dynamical account of collapse. The resulting dynamics is at first sight time asymmetric for the simple reason that the wave function depends on those collapse events in the past but not those in the future. Here we show that dynamical wave-function collapse models admit a general description that has no built-in direction of time. Given some simple constraints, we show that there exist empirically equivalent pictures of collapsing wave functions in both time directions, each satisfying the same dynamical rules. A preferred direction is singled out only by the asymmetric initial and final time constraints on the state of the universe.
Namiki and Pascazio [Phys. Rev. A 44, 39 (1991)] propose a model of wave-function collapse associated with the nonfiring of a detector in one of two paths for which a particle is known to be present, and argue that the collapse has the same status as the collapse associated with a measurement involving an actual detection. I question this proposal on the following grounds: (i) it is based on a shift in detection probabilities in the two paths while there is no shift in wave-function amplitudes, and (ii) Namiki and Pascazio use an insufficient measure, loss of interference, as an indicator of collapse.
Gravitational decoherence and gravitational wave function collapse are presented as two related but conceptually distinct ideas. Gravitational decoherence measures the effect of gravitational perturbations on the evolution of quantum systems, in particular their progressive lack of coherence. Gravitational wave function collapse starts with the assumption that the Schr¨odinger equation is not entirely right, and must be supplemented with extra terms, which cause the (random) collapse of the wave function; the collapse is then linked to gravity. Some of the most popular models are reviewed, with an emphasis on their conceptual status, stage of development, and open questions.