  Determining the (bare) electron mass $m_0$ in crystals is often hindered by
many-body effects since Fermi-liquid physics renormalises the band mass, making
the observed effective mass $m^*$ depend on density. Here, we use a
one-dimensional (1D) geometry to amplify the effect of interactions, forcing
the electrons to form a nonlinear Luttinger liquid with separate holon and
spinon bands, therefore separating the interaction effects from $m_0$.
Measuring the spectral function of gated quantum wires formed in GaAs by means
of magnetotunnelling spectroscopy and interpreting them using the 1D
Fermi-Hubbard model, we obtain $m_0=(0.0525\pm0.0015)m_\textrm{e}$ in this
material, where $m_\textrm{e}$ is the free-electron mass. By varying the
density in the wires, we change the interaction parameter $r_\textrm{s}$ in the
range from $\sim$1-4 and show that $m_0$ remains constant. The determined value
of $m_0$ is $\sim 22$% lighter than observed in GaAs in geometries of higher
dimensionality $D$ ($D>1$), consistent with the quasi-particle picture of a
Fermi liquid that makes electrons heavier in the presence of interactions.
