  Activity-driven glassy dynamics, while ubiquitous in collective cell
migration, intracellular transport, dynamics in bacterial and ant colonies,
etc., also extend the scope and extent of the as-yet mysterious physics of
glass transition. Active glasses are hitherto assumed to be qualitatively
similar to their equilibrium counterparts at an effective temperature,
$T_{eff}$. Here we combine large-scale simulations and an analytical
mode-coupling theory (MCT) for such systems and show that, in fact, an active
glass is inherently different from an equilibrium glass. Although the
relaxation dynamics can be equilibrium-like at a $T_{eff}$, the effects of
activity on the dynamical heterogeneity (DH), which has emerged as a
cornerstone of glassy dynamics, are quite nontrivial and complex. With no
preexisting data, we employ four distinct methods for reliable estimates of the
DH length scales. Our work shows active glasses exhibit dramatic growth of DH
and systems with similar relaxation times, and $T_{eff}$ can have widely
varying DH. To theoretically study DH, we extend active MCT and find excellent
agreement between the theory and simulation results. Our results question the
supposedly central role of DH in glassy dynamics and can have fundamental
significance even in equilibrium.
