  We discuss the density fluctuations of a fluid due to zero point motion.
These can be regarded as density fluctuations in the phonon vacuum state. We
assume a linear dispersion relation with a fixed speed of sound and calculate
the density correlation function. We note that this function has the same form
as the correlation function for the time derivative of a relativistic massless
scalar field, but with the speed of light replaced by the speed of sound. As a
result, the study of density fluctuations in a fluid can be a useful analog
model for better understanding fluctuations in relativistic quantum field
theory. We next calculate the differential cross section for light scattering
by the zero point density fluctuations, and find a result proportional to the
fifth power of the light frequency. This can be understood as the product of
fourth power dependence of the usual Rayleigh cross section with the linear
frequency dependence of the spectrum of zero point density fluctuations. We
give some estimates of the relative magnitude of this effect compared to the
scattering by thermal density fluctuations, and find that it can be of order
0.5% for water at room temperature and optical frequencies. This relative
magnitude is proportional to frequency and inversely proportional to
temperature. Although the scattering by zero point density fluctuation is
small, it may be observable.
