Reinventing the slide rule for redshifts: the case for logarithmic
  wavelength shift
  Redshift is not a shift, it is defined as a fractional change in wavelength.
Nevertheless, it is a fairly common misconception that Delta-z c represents a
velocity where Delta-z is the redshift separation between two galaxies. When
evaluating large changes in a quantity, it is often more useful to consider
logarithmic differences. Defining zeta = ln lambda_obs - ln lambda_em results
in a more accurate approximation for line-of-sight velocity and, more
importantly, this means that the cosmological and peculiar velocity terms
become additive: Delta-zeta c can represent a velocity at any cosmological
distance. Logarithmic shift zeta, or equivalently ln(1+z), should arguably be
used for photometric redshift evaluation. For a comparative non-accelerating
universe, used in cosmology, comoving distance is proportional to zeta. This
means that galaxy population distributions in zeta, rather than z, are close to
being evenly distributed in comoving distance, and they have a more aesthetic
spacing when considering galaxy evolution. Some pedagogic notes on these
quantities are presented.
