  A multi-time probing of density fluctuations is introduced to investigate
hidden time scales of heterogeneous dynamics in glass-forming liquids.
Molecular dynamics simulations for simple glass-forming liquids are performed,
and a three-time correlation function is numerically calculated for general
time intervals. It is demonstrated that the three-time correlation function is
sensitive to the heterogeneous dynamics and that it reveals couplings of
correlated motions over a wide range of time scales. Furthermore, the time
scale of the heterogeneous dynamics $\tau_{\rm hetero}$ is determined by the
change in the second time interval in the three-time correlation function. The
present results show that the time scale of the heterogeneous dynamics
$\tau_{\rm hetero}$ becomes larger than the $\alpha$-relaxation time at low
temperatures and large wavelengths. We also find a dynamical scaling relation
between the time scale $\tau_{\rm hetero}$ and the length scale $\xi$ of
dynamical heterogeneity as $\tau_{\rm hetero} \sim \xi^{z}$ with $z=3$.
