  We investigate the correlation between far-infrared (FIR) and radio
luminosities in distant galaxies, a lynchpin of modern astronomy. We use data
from the Balloon-borne Large Aperture Submillimetre Telescope (BLAST), Spitzer,
the Large Apex BOlometer CamerA (LABOCA), the Very Large Array (VLA) and the
Giant Metre-wave Radio Telescope (GMRT) in the Extended Chandra Deep Field
South (ECDFS). For a catalogue of BLAST 250-micron-selected galaxies, we
re-measure the 70--870-micron flux densities at the positions of their most
likely 24-micron counterparts, which have a median [interquartile] redshift of
0.74 [0.25, 1.57]. From these, we determine the monochromatic flux density
ratio, q_250 = log_10 (S_250micron / S_1400MHz), and the bolometric equivalent,
q_IR. At z ~= 0.6, where our 250-micron filter probes rest-frame 160-micron
emission, we find no evolution relative to q_160 for local galaxies. We also
stack the FIR and submm images at the positions of 24-micron- and
radio-selected galaxies. The difference between q_IR seen for 250-micron- and
radio-selected galaxies suggests star formation provides most of the IR
luminosity in ~< 100-uJy radio galaxies, but rather less for those in the mJy
regime. For the 24-micron sample, the radio spectral index is constant across 0
< z < 3, but q_IR exhibits tentative evidence of a steady decline such that
q_IR is proportional to (1+z)^(-0.15 +/- 0.03) - significant evolution,
spanning the epoch of galaxy formation, with major implications for techniques
that rely on the FIR/radio correlation. We compare with model predictions and
speculate that we may be seeing the increase in radio activity that gives rise
to the radio background.
