  We suggest an experiment to investigate the linear superposition of two
spatially separated Bose-Einstein condensates. Due to the coherent combination
of the two wave functions, the dynamic structure factor, measurable through
inelastic photon scattering at high momentum transfer $q$, is predicted to
exhibit interference fringes with frequency period $\Delta\nu = q/md$ where $d$
is the distance between the condensates. We show that the coherent
configuration corresponds to an eigenstate of the physical observable measured
in the experiment and that the relative phase of the condensates is hence
created through the measurement process.
