Critique of weakly decohering and linearly positive histories

TL;DR

This paper critically examines the assumptions and limitations of weakly decohering and linearly positive histories in quantum mechanics, highlighting the need for medium decoherence and identifying missing classical features.

Contribution

It provides a critique of the composition rules and classical features assumed in weakly decohering and linearly positive histories, emphasizing the importance of medium decoherence.

Findings

Medium decoherence is necessary for composition rules.

Linearly positive histories require additional constraints.

Certain classical features are absent in linear positive histories.

Abstract

The usual composition rule of independent systems, as applied to decoherent histories or to linearly positive histories, requires (at least) medium decoherence and, consequently, a second constraint for the linearly positive histories of Goldstein and Page. Other plausible classical features, valid for medium decoherence, seem anyhow to be missed by linear positive histories.