Quasielastic neutron scattering, dielectric spectroscopy, and mechanical relaxation have been employed to study the dynamics of Bisphenol A polycarbonate (BPA-PC) in the glassy and rubbery state. The neutron scattering measurements were made in the temperature range (DELTAT) 296-586 K and over the Q-range 0.31-1.54 angstrom-1, for the dielectric measurements in DELTAT = 200-467 K and for the mechanical measurements in DELTAT = 113-443 K. Using these techniques we obtain the dynamics associated with the primary (alpha-) relaxation and of the gamma-relaxation in a frequency interval spanning 13 decades. The temperature dependence of the primary relaxation times conforms to the Vogel-Fulcher-Tammann equation, whereas the gamma-relaxation times display an Arrhenius temperature dependence with an apparent activation energy of 10.8 kcal/mol. From the neutron scattering measurements, made in the gigahertz to terahertz frequency range, we obtain direct evidence that phenylene pi-flips are not of paramount importance to the gamma-relaxation. This is confirmed by the mechanical and neutron scattering measurements on the polycarbonate of 3,3'-dihydroxy-6,6'-dimethylbiphenyl (BPPC), which displays a similar gamma-relaxation in which pi-flips cannot participate.