Machian classical and semiclassical emergent time

Abstract

Classical and semiclassical schemes are presented that are timeless at the primary level and recover time from Mach’s ‘time is to be abstracted from change’ principle at the emergent secondary level. The semiclassical scheme is a Machian variant of the semiclassical approach to the problem of time in quantum gravity. The classical scheme is Barbour’s, cast here explicitly as the classical precursor of the semiclassical approach. Thus the two schemes have been married up, as equally-Machian and necessarily distinct, since the latter’s timestandard is abstracted in part from quantum change. I provide perturbative schemes for these in which the timefunction is to be determined rather than assumed. This paper is useful modelling as regards the Halliwell–Hawking arena for the quantum origin of the inhomogeneous cosmological fluctuations.