On the Consistent Histories Approach to Quantum Mechanics

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.Comment: Published version, to appear in J. Stat. Phys. in early 1996. The main arguments and conclusions remain unaltered, but there are significant revisions from the earlier archive version. These include a new subsection on interpretations of the formalism, other additions clarifying various arguments in response to comments, and some minor corrections. (87 pages, TeX with harvmac.

Quasiclassical Dynamics in a Closed Quantum System

We consider Gell-Mann and Hartle's consistent histories formulation of quantum cosmology in the interpretation in which one history, chosen randomly according to the decoherence functional probabilities, is realised from each consistent set. We show that in this interpretation, if one assumes that an observed quasiclassical structure will continue to be quasiclassical, one cannot infer that it will obey the predictions of classical or Copenhagen quantum mechanics.Comment: Published version, to appear in Phys. Rev. A. Clarificatory remarks added on interpretations outside the scope of the paper. (TeX with harvmac, 13 pages.

Modelling Private Wealth Accumulation and Spend-down in the Italian Microsimulation Model CAPP_DYN: A Life-Cycle Approach

In microsimulation literature a limited number of models include a module aimed at analyzing and projecting the evolution of privat e wealth over time. However, this issue appears crucial in order to comprehensively evaluate the li kely distributional effects of institutional reforms adopted to cope with population ageing. In this work we describe the implementation in the Italian dynamic micro simulation model CAPP_DYN of a new module in which households\u2019 savings and asset allocation are modelled. In parti cular, we aim to account for possible behavioural responses to pension reforms in househo ld savings. To this end, we rely on an approximate life cycle structural framework for est imating saving behaviour, while adopting a traditional stochastic micro simulation approach fo r asset allocation. In line with Ando and Nicoletti Altimari (2004), we emphasize the role of lifetime economic resources in households\u2019 consumption decisions, yet we further account for i nternal habit formation and subjective expectations on pension outcomes in the econometric stage. In addition, we model intergenerational transfers of private wealth in a probabilistic fashio