  Correlations between the intrinsic shapes of galaxy pairs, and between the
intrinsic shapes of galaxies and the large-scale density field, may be induced
by tidal fields. These correlations, which have been detected at low redshifts
(z<0.35) for bright red galaxies in the Sloan Digital Sky Survey (SDSS), and
for which upper limits exist for blue galaxies at z~0.1, provide a window into
galaxy formation and evolution, and are also an important contaminant for
current and future weak lensing surveys. Measurements of these alignments at
intermediate redshifts (z~0.6) that are more relevant for cosmic shear
observations are very important for understanding the origin and redshift
evolution of these alignments, and for minimising their impact on weak lensing
measurements. We present the first such intermediate-redshift measurement for
blue galaxies, using galaxy shape measurements from SDSS and spectroscopic
redshifts from the WiggleZ Dark Energy Survey. Our null detection allows us to
place upper limits on the contamination of weak lensing measurements by blue
galaxy intrinsic alignments that, for the first time, do not require
significant model-dependent extrapolation from the z~0.1 SDSS observations.
Also, combining the SDSS and WiggleZ constraints gives us a long redshift
baseline with which to constrain intrinsic alignment models and contamination
of the cosmic shear power spectrum. Assuming that the alignments can be
explained by linear alignment with the smoothed local density field, we find
that a measurement of \sigma_8 in a blue-galaxy dominated, CFHTLS-like survey
would be contaminated by at most +/-0.02 (95% confidence level, SDSS and
WiggleZ) or +/-0.03 (WiggleZ alone) due to intrinsic alignments. [Abridged]
