Quasielastic light scattering (QLS) in the frequency interval 100-1000 GHz is measured in some polymers : polycarbonate, polybutadiene, polystyrene, and poly(methyl methacrylate). To describe the spectra, a model of the fast picosecond relaxation processes responsible for the QLS, which is based on the damping of the boson peak vibrations by the dynamic hole volume fluctuations, is used. Within the frame of the model, the intensity of the fast relaxation process is proportional to the fractional dynamic hole volume (which above the glass transition temperature Tg is known as the fractional free volume). The hole volumes can be measured using the positron annihilation lifetime spectroscopy (PALS). The comparison of the literature PALS data in the four polymers with the QLS shows an apparent correlation between the relaxation strength and the fractional dynamic hole volume in good agreement with the predictions of the model.