  The density fluctuation spectrum captures many fundamental properties of
strange metals. Using momentum-resolved electron energy-loss spectroscopy
(M-EELS), we recently showed that the density response of the strange metal
Bi$_2$Sr$_2$CaCu$_2$O$_{8+x}$ (Bi-2212) at large momentum, $q$, exhibits a
constant-in-frequency continuum [Mitrano, PNAS $\textbf{115}$, 5392 (2018);
Husain, PRX $\textbf{9}$, 041062 (2019)] reminiscent of the marginal Fermi
liquid (MFL) hypothesis of the late 1980s [Varma, PRL $\textbf{63}$, 1996
(1989)]. However, reconciling this observation with infrared (IR) optics
experiments, which show a well-defined plasmon excitation at $q \sim 0$, has
been challenging. Here we report M-EELS measurements of Bi-2212 using 4$\times$
improved momentum resolution, allowing us to reach the optical limit. For
momenta $q<0.04$ r.l.u., the M-EELS data show a plasmon feature that is
quantitatively consistent with IR optics. For $q>0.04$ r.l.u., the spectra
become incoherent with an MFL-like, constant-in-frequency form. We speculate
that, at finite frequency, $\omega$, and nonzero $q$, some attribute of this
Planckian metal randomizes the probe electron, causing it to lose information
about its own momentum.
