  We have measured the collective excitation spectrum of interacting electrons
in one-dimension. The experiment consists of controlling the energy and
momentum of electrons tunneling between two clean and closely situated,
parallel quantum wires in a GaAs/AlGaAs heterostructure while measuring the
resulting conductance. We measure excitation spectra that clearly deviate from
the non-interacting spectrum, attesting to the importance of Coulomb
interactions. Notable is an observed 30% enhancement of the velocity of the
main excitation branch relative to non-interacting electrons with the same
density. In short wires, finite size effects resulting from broken
translational invariance are observed. Spin - charge separation is manifested
through moire patterns, reflecting different spin and charge excitation
velocities.
