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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. Weassume a linear dispersion relation with a fixed speed of sound and calculatethe density correlation function. We note that this function has the same formas the correlation function for the time derivative of a relativistic masslessscalar field, but with the speed of light replaced by the speed of sound. As aresult, the study of density fluctuations in a fluid can be a useful analogmodel for better understanding fluctuations in relativistic quantum fieldtheory. We next calculate the differential cross section for light scatteringby the zero point density fluctuations, and find a result proportional to thefifth power of the light frequency. This can be understood as the product offourth power dependence of the usual Rayleigh cross section with the linearfrequency dependence of the spectrum of zero point density fluctuations. Wegive some estimates of the relative magnitude of this effect compared to thescattering by thermal density fluctuations, and find that it can be of order0.5% for water at room temperature and optical frequencies. This relativemagnitude is proportional to frequency and inversely proportional totemperature. Although the scattering by zero point density fluctuation issmall, it may be observable.

Quantum Density Fluctuations in Classical Liquids