  The anti self-adjoint operators of coordinate and momentum are introduced and
applied in discussion of tunneling through the potential barrier where
imaginary value of momentum unavoidably appears. Tunneling through temporal
barrier is proceeded in a similar way and it is shown that the quantum system
can tunnel, while the classical systems are destroyed by such barrier. The
imaginary observables of coordinate and momentum are used in a novel treatment
of passage through the event horizon. By considering the event horizon as the
border of the finite potential barrier, it is found that there is no
singularity at the center of a black hole. The imaginary variables of
coordinate and momentum are used for the construction of a toy model of the
universe. It is shown that the acceleration of the expansion of the universe
does not need dark energies to be explained since negative energies are present
and characteristic for the imaginary world.
