  Quantum electrodynamic effects have been systematically tested in the
progression of rotational quantum states in the $X ^{1}\Sigma_{g}^{+}, v=0$
vibronic ground state of molecular hydrogen. High-precision Doppler-free
spectroscopy of the $EF ^{1}\Sigma_{g}^{+} - X ^{1}\Sigma_{g}^{+}$ (0,0) band
was performed with 0.005 cm$^{-1}$ accuracy on rotationally-hot H$_2$ (with
rotational quantum states J up to 16). QED and relativistic contributions to
rotational level energies as high as 0.13 cm$^{-1}$ are extracted, and are in
perfect agreement with recent calculations of QED and high-order relativistic
effects for the H$_2$ ground state.
