On the Consistent Histories Approach to Quantum Mechanics

Details On the Consistent Histories Approach to Quantum Mechanics On the Consistent Histories Approach to Quantum Mechanics

1994-12-22

arxiv.org/abs/gr-qc/9412067v2

J.Statist.Phys. 82 (1996) 1575-1646

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

Published version, to appear in J. Stat. Phys. in early 1996. The main arguments and conclusions remain unaltered, but there a

Scientific paper

10.1007/BF02183396

We review the consistent histories formulations of quantum mechanics developed by Griffiths, Omn\`es and Gell-Mann and Hartle, and describe the classification of consistent sets. We illustrate some general features of consistent sets by a few simple lemmas and examples. We consider various interpretations of the formalism, and examine the new problems which arise in reconstructing the past and predicting the future. It is shown that Omn\`es' characterisation of true statements --- statements which can be deduced unconditionally in his interpretation --- is incorrect. We examine critically Gell-Mann and Hartle's interpretation of the formalism, and in particular their discussions of communication, prediction and retrodiction, and conclude that their explanation of the apparent persistence of quasiclassicality relies on assumptions about an as yet unknown theory of experience. Our overall conclusion is that the consistent histories approach illustrates the need to supplement quantum mechanics by some selection principle in order to produce a fundamental theory capable of unconditional predictions.

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