  A common belief about big-bang cosmology is that the cosmological redshift
cannot be properly viewed as a Doppler shift (that is, as evidence for a
recession velocity), but must be viewed in terms of the stretching of space. We
argue that, contrary to this view, the most natural interpretation of the
redshift is as a Doppler shift, or rather as the accumulation of many
infinitesimal Doppler shifts. The stretching-of-space interpretation obscures a
central idea of relativity, namely that it is always valid to choose a
coordinate system that is locally Minkowskian. We show that an observed
frequency shift in any spacetime can be interpreted either as a kinematic
(Doppler) shift or a gravitational shift by imagining a suitable family of
observers along the photon's path. In the context of the expanding universe the
kinematic interpretation corresponds to a family of comoving observers and
hence is more natural.
