Tunneling time experiments with quantum particles like electrons are extremely difficult, not only because of the timescales (attoseconds) and length scales (sub-nanometre) involved, but also because of possible confounding interactions with the environment that have nothing to do with the actual tunneling process itself. As a result, the only experimental observations of the Hartman effect have been based on electromagnetic analogs to quantum tunneling. The first experimental verification of the Hartman effect was by Enders and Nimtz, who used a microwave waveguide with a narrowed region that served as a barrier to waves with frequencies below the cutoff frequency in that region. They measured the frequency-dependent phase shift of continuous wave (cw) microwaves transmitted by the structure. They found that the frequency-dependent phase shift was independent of the length of the barrier region. Since the group delay (phase time) is the derivative of the phase shift with respect to frequency, this independence of the phase shift means that the group delay is independent of barrier length, a confirmation of the Hartman effect. They also found that the measured group delay was shorter than the transit time L / c for a pulse travelling at the speed of light c over the same barrier distance L in vacuum. From this, it was inferred that the tunneling of evanescent waves is superluminal, despite it is now known on rigorous mathematical grounds that the relativistic quantum tunneling (modeled using the Dirac equation) is a subluminal process.