Branch Dependence in the “Consistent Histories” Approach to Quantum Mechanics
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In the consistent histories formalism one specifies a family of histories as an exhaustive set of pairwise exclusive descriptions of the dynamics of a quantum system. We define branching families of histories, which strike a middle ground between the two available mathematically precise definitions of families of histories, viz., product families and Isham’s history projector operator formalism. The former are too narrow for applications, and the latter’s generality comes at a certain cost, barring an intuitive reading of the “histories”. Branching families retain the intuitiveness of product families, they allow for the interpretation of a history’s weight as a probability, and they allow one to distinguish two kinds of coarse-graining, leading to reconsidering the motivation for the consistency condition.
Keywordsquantum histories branching time probability coarse graining
PACS Numbers03.65.Ca 03.65.Ta 05.30.-d
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- Belnap N., Perloff M., Xu M., (2001). Facing the Future. Oxford University Press, OxfordGoogle Scholar
- M. Gell-Mann and Hartle J., “Quantum mechanics in the light of quantum cosmology,” in Complexity, Entropy and the Physics of Information, W.H. Zurek, ed. 425–458 (Addison-Wesley, Reading, MA, 1990).Google Scholar
- Griffiths R.B., (2003). Consistent Quantum Theory. Cambridge University Press, CambridgeGoogle Scholar
- Kent A., “Quantum histories and their implications,” In Relativistic Quantum Measurement and Decoherence, Springer Lecture Notes in Physics, 559, F. Petruccione ed. 93–115. (Springer, Heidelberg, 2000).Google Scholar
- T. Müller, “Relativistic quantum histories in branching space-times,” in preparation (2007).Google Scholar