  The generation of primordial magnetic fields from cosmological phase
transitions is discussed, paying particular attention to the electroweak
transition and to the various definitions of the `average' field that have been
put forward. It is emphasised that only the volume average has dynamical
significance as a seed for galactic dynamos. On rather general grounds of
causality and energy conservation, it is shown that, in the absence of MHD
effects that transfer power in the magnetic field from small to large scales,
processes occurring at the electroweak transition cannot generate fields
stronger than $10^{-20}$ Gauss on a scale of 0.5 Mpc. However, it is
implausible that this upper bound could ever be reached, as it would require
all the energy in the Universe to be turned into a magnetic field coherent at
the horizon scale. Non-linear MHD effects seem therefore to be necessary if the
electroweak transition is to create a primordial seed field.
