  We compare two temporal properties of classical double radio sources: i)
radiative lifetimes of synchrotron-emitting particles and ii) dynamical source
ages. We discuss how these can be quite discrepant from one another, rendering
use of the traditional spectral ageing method inappropriate: we contend that
spectral ages give meaningful estimates of dynamical ages only when these ages
are << 10^7 years. In juxtaposing the fleeting radiative lifetimes with source
ages which are significantly longer, a refinement of the paradigm for radio
source evolution is required. The changing spectra along lobes are explained,
not predominantly by synchrotron ageing but, by gentle gradients in a magnetic
field mediated by a low-gamma matrix which illuminates an energy-distribution
of particles, controlled largely by classical synchrotron loss in the high
magnetic field of the hotspot. The energy in the particles is an order of
magnitude higher than that inferred from the minimum-energy estimate, implying
that the jet-power is of the same order as the accretion luminosity produced by
the quasar central engine. This refined paradigm points to a resolution of the
findings of Rudnick et al (1994) and Katz-Stone & Rudnick (1994) that both the
Jaffe-Perola and Kardashev-Pacholczyk model spectra are invariably poor
descriptions of the curved spectral shape of lobe emission, and indeed that for
Cygnus A all regions of the lobes are characterised by a `universal spectrum'.
[abridged]
