  One of the most fundamental properties of an interacting electron system is
its frequency- and wave-vector-dependent density response function, $\chi({\bf
q},\omega)$. The imaginary part, $\chi''({\bf q},\omega)$, defines the
fundamental bosonic charge excitations of the system, exhibiting peaks wherever
collective modes are present. $\chi$ quantifies the electronic compressibility
of a material, its response to external fields, its ability to screen charge,
and its tendency to form charge density waves. Unfortunately, there has never
been a fully momentum-resolved means to measure $\chi({\bf q},\omega)$ at the
meV energy scale relevant to modern elecronic materials. Here, we demonstrate a
way to measure $\chi$ with quantitative momentum resolution by applying
alignment techniques from x-ray and neutron scattering to surface
high-resolution electron energy-loss spectroscopy (HR-EELS). This approach,
which we refer to here as "M-EELS," allows direct measurement of $\chi''({\bf
q},\omega)$ with meV resolution while controlling the momentum with an accuracy
better than a percent of a typical Brillouin zone. We apply this technique to
finite-q excitations in the optimally-doped high temperature superconductor,
Bi$_2$Sr$_2$CaCu$_2$O$_{8+x}$ (Bi2212), which exhibits several phonons
potentially relevant to dispersion anomalies observed in ARPES and STM
experiments. Our study defines a path to studying the long-sought collective
charge modes in quantum materials at the meV scale and with full momentum
control.
