Riders on the storm

 Finally, it has been suggested that decoherence should be a useful ingredient in a theory of quantum gravity (see the entry on quantum gravity), as discussed e.g. by Kiefer (1994). First, because a suitable generalisation of decoherence theory to a full theory of quantum gravity should yield suppression of interference between different classical spacetimes (see e.g. also Giulini et al. 1996, Section 4.2). Second, it is speculated that decoherence might solve the so-called problem of time, which arises as a prominent puzzle in (the ‘canonical’ approach to) quantum gravity. 

This is the problem that the candidate fundamental equation (in this approach) – the Wheeler–DeWitt equation – is an analogue of a time-independent Schrödinger equation, and does not contain time at all, so that time needs somehow to emerge. In the context of decoherence theory, one can for instance construct toy models in which the analogue of the Wheeler–DeWitt wave function decomposes into non-interfering components (for a suitable sub-system) each satisfying a time-dependent Schrödinger equation, so that decoherence appears in fact as the source of time. An accessible introduction to and philosophical discussion of such models is given by Ridderbos (1999), with references to the original papers. See also the more recent model by Halliwell and Thorwart (2002).[40]