We treat the effects of compactified spatial dimensions on the propagation of light in the uncompactified directions in the context of linearized quantum gravity. We find that the flight times of pulses can fluctuate due to modification of the gravit
on vacuum by the compactification. In the case of a five dimensional Kaluza-Klein theory, the mean variation in flight time can grow logarithmically with the flight distance. This effect is in principle observable, but too small to serve as a realistic probe of the existence of extra dimensions. We also examine the effect of the compactification on the widths of spectral lines, and find that there is a small line narrowing effect. This effect is also small for compactification well above the Planck scale, but might serve as a test of the existence of extra dimensions.
Quantum fluctuations in the density of a fluid with a linear phonon dispersion relation are studied. In particular, we treat the changes in these fluctuations due to non-classical states of phonons and to the presence of boundaries. These effects are
analogous to similar effects in relativistic quantum field theory, and we argue that the case of the fluid is a useful analog model for effects in field theory. We further argue that the changes in the mean squared density are in principle observable by light scattering experiments.
We discuss the quantization of sound waves in a fluid with a linear dispersion relation and calculate the quantum density fluctuations of the fluid in several cases. These include a fluid in its ground state. In this case, we discuss the scattering c
ross section of light by the density fluctuations, and find that in many situations it is small compared to the thermal fluctuations, but not negligibly small and might be observable at room temperature. We also consider a fluid in a squeezed state of phonons and fluids containing boundaries. We suggest that the latter may be a useful analog model for better understanding boundary effects in quantum field theory. In all cases involving boundaries which we consider, the mean squared density fluctuations are reduced by the presence of the boundary. This implies a reduction in the light scattering cross section, which is potentially an observable effect.
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 correlatio
n 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.
