Consistent histories , quantum truth functionals , and hidden variables
نویسنده
چکیده
A central principle of consistent histories quantum theory, the requirement that quantum descriptions be based upon a single framework (or family), is employed to show that there is no conflict between consistent histories and a no-hidden-variables theorem of Bell, and Kochen and Specker, contrary to a recent claim by Bassi and Ghirardi. The argument makes use of “truth functionals” defined on a Boolean algebra of classical or quantum properties.
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ua nt - p h / 99 12 06 5 v 1 1 3 D ec 1 99 9 About the Notion of Truth in the Decoherent Histories Approach : a Reply to Griffiths
Griffiths claims that the “single family rule”, a basic postulate of the decoherent histories approach, rules out our requirement that any decoherent history has a unique truth value, independently from the decoherent family to which it may belong. Here we analyze the reasons which make our requirement indispensable and we discuss the consequences of rejecting it. This short letter is a reply t...
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The basic ingredients of the consistent histories approach to quantum mechanics are the space of histories and the space of decoherence functionals. In this work we extend the classification theorem for decoherence functionals proven by Isham, Linden and Schreckenberg to the case where the space of histories is the lattice of projection operators on an arbitrary separable or non-separable compl...
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The geometry of decoherence in generalized “consistent histories” quantum theory is explored, revealing properties of the theory that are independent of any particular application of it. Attention is focussed on the case of quantum mechanics in a finite dimensional Hilbert space H. It is shown how the domain of definition of a general decoherence functional naturally extends to the entire space...
متن کاملThe Consistent Histories Interpretation of Quantum Mechanics
The consistent histories (CH) reformulation of quantum mechanics (QM) was developed by Robert Griffiths, given a formal logical systematization by Roland Omnès, and under the label ‘decoherent histories’, was independently developed by Murray Gell-Mann and James Hartle and extended to quantum cosmology. Criticisms of CH involve issues of meaning, truth, objectivity, and coherence, a mixture of ...
متن کاملUniversity of Southampton,
Using a reformulation of conventional results in decoherence theory, a condition is proposed for singling out a distinguished class of histories which includes those which use the " pointer basis " of Zurek. 1. What's good and bad about consistent histories The basic problem faced by any extension of quantum theory outside the laboratory realm of Bohr's interpretation can be expressed by the sl...
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