Dielectric spectra were obtained on a low molecular weight poly(methyl methacrylate) (PMMA) over a range of temperatures (331 < T (K) < 386) at pressures approaching 0.8 GPa. The alpha relaxation times, tau(alpha), superpose when plotted versus T/rho(gamma), where rho is density and gamma a material constant, in accord with results for many other van der Waals liquids and polymers. However, the Johari-Goldstein (JG) relaxation times, tau(JG), do not conform to this density scaling for the same value of the exponent gamma. Likewise, the frequency separation of the alpha and JG loss peaks in the spectrum increases with pressure for constant tau(alpha); that is, state points having the same alpha relaxation time and same peak breadth have different tau(JG). Similar results were obtained on a lower molecular weight PMMA, for which there was less overlap of the two peaks. The implication is that density scaling of the segmental relaxation times originates in the glass transition dynamics, not, as recently suggested, in higher frequency secondary processes.