An insider's guide to quantum causal histories

TL;DR

This paper reviews the development of quantum causal histories, a framework for quantum cosmology where observables are observer-dependent and related to horizons and topology, using a many-Hilbert space formalism.

Contribution

It introduces the quantum causal histories formalism, incorporating observer-dependent observables and a non-Boolean algebra structure for quantum cosmology.

Findings

Observer-dependent algebra of observables is a Heyting algebra.

Representation requires a many-Hilbert space formalism.

Examples include causally evolving spin networks and quantum computers.

Abstract

A review is given of recent work aimed at constructing a quantum theory of cosmology in which all observables refer to information measurable by observers inside the universe. At the classical level the algebra of observables should be modified to take into account the fact that observers can only give truth values to observables that have to do with their backwards light cone. The resulting algebra is a Heyting rather than a Boolean algebra. The complement is non-trivial and contains information about horizons and topology change. Representation of such observables quantum mechanically requires a many-Hilbert space formalism, in which different observers make measurements in different Hilbert spaces. I describe such a formalism, called "quantum causal histories"; examples include causally evolving spin networks and quantum computers.