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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Aspect A., Dalibard J., Roger G., (1982). “Experimental test of Bell’s inequalities using time-varying analyzers”. Phys. Rev. Lett. 49: 1804–1807
Belnap N., (1992). “Branching space-time”. Synthese 92, 385–434
Belnap N., (2005). “A theory of causation: Causae causantes (originating causes) as inus conditions in branching space-times”. Brit. J. Phil. Sci. 56, 221–253
Belnap N., Perloff M., Xu M., (2001). Facing the Future. Oxford University Press, Oxford
Dowker F., Kent A., (1996). “On the consistent histories approach to quantum mechanics”. J. Stat. Phys. 82: 1575–1646
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).
Gell-Mann M., Hartle J., (1993). “Classical equations for quantum systems”. Phys. Rev. D 47: 3345–3382
Griffiths R.B., (1984). “Consistent histories and the interpretation of quantum mechanics”. J. Stat. Phys. 36, 219–272
Griffiths R.B., (1998). “Choice of consistent family, and quantum incompatibility”. Phys. Rev. A 57: 1604–1618
Griffiths R.B., (2003). Consistent Quantum Theory. Cambridge University Press, Cambridge
Isham C.J., (1994). “Quantum logic and the histories approach to quantum theory”. J. Math. Phys. 35: 2157–2185
Isham C.J., Linden N., (1994). “Quantum temporal logic and decoherence functionals in the histories approach to generalized quantum theory”. J. Math. Phys. 35: 5452–5476
Isham C.J., Linden N., Savvidou K., Schreckenberg S., (1998). “Continuous time and consistent histories”. J. Math. Phys. 39, 1818–1834
Kent A., (1998). “Quantum histories”. Physica Scripta T76: 78–84
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).
Müller T., (2005). “Probability and causation. A branching space-times analysis”. Brit. J. Phil. Sci. 56, 487–520
T. Müller, “Relativistic quantum histories in branching space-times,” in preparation (2007).
Nisticò G., (1999). “Consistency conditions for probabilities of quantum histories”. Found. Phys. 29, 221–229
Omnès R., (1994). The Interpretation of Quantum Mechanics. Princeton University Press, Princeton
Peres A., (2000). “Classical interventions in quantum systems I: The measuring process”. Phys. Rev. A 61: 022116
Prior A.N., (1967). Past, Present and Future. Oxford University Press, Oxford
Xu M., (1997). “Causation in branching time (I): Transitions, events and causes”. Synthese 112, 137–192
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Müller, T. Branch Dependence in the “Consistent Histories” Approach to Quantum Mechanics. Found Phys 37, 253–276 (2007). https://doi.org/10.1007/s10701-006-9100-x
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10701-006-9100-x