Microfabricated monolithic shock target arrays with embedded thin layers of dye-doped polymer films, termed optical nanogauges, are used to measure the velocity and pressure (U-s=3.5 km/s; P = 2.1 GPa) of picosecond-laser-driven shock waves in polymers. The 60 (+/-20) ps rise time of absorbance changes of the dye in the nanogauge appears to be limited by the transit time of the shock across the 300 nm thick gauge. The intrinsic rise time of the 2 GPa shock front in poly-methyl methacrylate must therefore be <60 ps. These measurements are the first to obtain picosecond resolution of molecular dynamics induced by the passage of a shock front through a solid. Good agreement was obtained between the nanosecond time scale shock-induced adsorption redshift of the dye behind the P = 2 GPa shock front, and the redshift of a nanogauge, under conditions of static high pressure loading in a diamond anvil cell at P = 2 GPa. Transient effects on the approximate to 100 ps time scale are observed in the dye spectrum, primarily on the red absorption edge where hot-band transitions are most significant. These effects are interpreted as arising from transient overheating and subsequent fast cooling of the dye molecules behind the shock front.