  We present an investigation into the possible relationship between
side-to-side asymmetries of powerful radio galaxies at high redshift, with the
goal of understanding the geometry, orientation and gas dynamics of these
sources. Our sample consists of 11 radio galaxies at 2.3<z<3.6 previously known
to have giant, kinematically quiescent nebulae. We identify several correlated
asymmetries: on the side of the brightest radio jet and hotspot (i) the
redshift of the kinematically quiescent nebula is highest, (ii) Ly-alpha is
brighter relative to the other lines and continuum, (iii) the radio spectrum is
flattest and (iv) the radio structure has its highest polarization. These
asymmetries are not found to be correlated with either the radio arm length
asymmetry or the brightness asymmetry of the UV-optical emitting material. The
correlation between the radio brightness asymmetry and the radial velocity of
the quiescent gas also appears to be present in powerful radio galaxies with
0<z<1.
  Collectively, these asymmetries are most naturally explained as an effect of
orientation, with the quiescent nebulae in infall: this is the first study to
distinguish between the rotation, infall, outflow and chaotic motion scenarios
for the kinematically quiescent emission line nebulae around powerful active
galactic nuclei.
