  A dispersionless shock wave in a fluid without friction develops an acoustic
spacetime singularity which is naked (not hidden by a horizon). We show that
this naked nondispersive shock-wave singularity is prohibited to form in a
Bose-Einstein condensate, due to the microscopic structure of the underlying
${\rm a}\!{\rm e}$ther and the resulting effective trans-Planckian dispersion.
Approaching the instant of shock $t_{\rm shock}$, rapid spatial oscillations of
density and velocity develop around the shock location, which begin to emerge
already slightly before $t_{\rm shock}$, due to the quantum pressure in the
condensate. These oscillations render the acoustic spacetime structure
completely regular, and therefore lead to a removal (censoring) of the
spacetime singularity. Thus, distinct from the cosmic censorship hypothesis of
Penrose formulated within Einsteinian gravity, the quantum pressure in
Bose-Einstein condensates censors (prohibits) the formation of a naked
shock-wave singularity, instead of hiding it behind a horizon.
