We use the technique of terahertz time-domain spectroscopy to experimentally and theoretically study the absorption and the dispersion of ammonia vapor. Our measurements show small deviations from the rotation-inversion spectrum which originate from transitions in the v(2) hot band and from the (NH3)(2) dimer. We investigate the molecular tunneling in ammonia and apply our new molecular response theory to analyze the inversion spectrum of this molecule. The theory includes the molecular response of polar molecules to an external electric field over the duration of a collision with the molecular response time as a control parameter. and it unifies the basic collision theories of Lorentz, van Vleck-Weisskopf, and Dc bye. The calculated absorption and dispersion based on this theory fits the measurements over the full spectral range of the THz spectrum and allows to determine a response time of the order of 100 fs.