  The LaAlO$_3$/SrTiO$_3$ system exhibits unusual magnetic and superconducting
behavior arising from electron-electron interactions whose physical origin is
not well understood. Quantum transport techniques, especially those involving
mesoscopic geometries, can offer insight into these interactions. Here we
report evidence for long-range electron-electron interactions in
LaAlO$_3$/SrTiO$_3$ nanowires, measured through the phenomenon of frictional
drag, in which current passing through one nanowire induces a voltage across a
nearby electrically isolated nanowire. Frictional drag mediated by the Coulomb
interaction is predicted to decay exponentially with interwire separation, but
with the LaAlO$_3$/SrTiO$_3$ nanowire system it is found to be nearly
independent of separation. Frictional drag experiments performed with three
parallel wires demonstrates long-range frictional coupling even in the presence
of an electrically grounded central wire. Collectively, these results provides
evidence for a new long-range non-Coulombic electron-electron interaction
unlike anything previously reported for semiconducting systems.
