  The occurrence of charge-density-wave (CDW) order in underdoped cuprates is
now well established, although the precise nature of the CDW and its
relationship with superconductivity is not. Theoretical proposals include
contrasting ideas such as that pairing may be driven by CDW fluctuations or
that static CDWs may intertwine with a spatially-modulated superconducting wave
function. We test the dynamics of CDW order in La$_{1.825}$Ba$_{0.125}$CuO$_4$
by using x-ray photon correlation spectroscopy (XPCS) at the CDW wave vector,
detected resonantly at the Cu $L_3$-edge. We find that the CDW domains are
strikingly static, with no evidence of significant fluctuations up to
2\,\nicefrac{3}{4} hours. We discuss the implications of these results for some
of the competing theories.
