We have made a series of isotropic pressure-densified atactic poly(methyl methacrylate) (PMMA) glasses with densities ranging from 1.1823 g/cm(3) to 1.1963 g/cm(3), in order to investigate how the glassy dynamics, measured by Raman scattering in the frequency range of 0.1-10 THz, depends on the thermomechanical history of the glasses. In particular, we investigate whether there is a correlation between the strength of the fast relaxation dynamics and the free-volume characteristics, such as the average free-volume size and the free-volume fraction. The fast relaxation strength is deduced from the quasielastic light scattering (QES) intensity; the free-volume size is measured with positron annihilation lifetime spectroscopy (PALS); and the free-volume fraction is determined from pressure-volume-temperature (PVT) data and the Simha-Somcynsky equation-of-state (EOS) theory. Our temperature-dependent Raman and PALS measurements show that both the QES intensity and the ortho-positronium (o-Ps) lifetime increase smoothly with the temperature. On the other hand, the relaxation strength of the densified glasses at room temperature is, within experimental error, independent of the density, whereas both the o-Ps lifetime from PALS and the free volume fraction from the PVT data decrease significantly with pressure densification. We therefore conclude that the fast relaxation intensity cannot be explained on the basis of free-volume quantities, contrary to a recently suggested correlation between the QES intensity and the free volume [V. N. Novikov , J. Chem. Phys. 107, 1057 (1997)]. On the other hand, the observed behavior is consistent with another recently suggested model [V. N. Novikov, Phys. Rev. B 58, 8367 (1998)] which attributes the fast relaxations to vibration anharmonicity. Moreover, we show that the measured increase in the refractive index of the pressure-densified glasses fits the Lorentz-Lorenz equation and compares well to predictions of the relative change in refractive index with formation pressure from our own as well as published PVT data.