  We consider branching of baby universes off parent one in (1+1)-dimensional
dilaton gravity with 24 types of conformal matter fields. This theory is
equivalent to string theory in a certain background in D=26-dimensional target
space, so this process may be also viewed as the emission of a light string
state by a heavy string. We find that bare energy is not conserved in (1+1)
dimensions due to the emission of baby universes, and that the probability of
this process is finite even for local distribution of matter in the parent
universe. We present a scenario suggesting that the non-conservation of bare
energy may be consistent with the locality of the baby universe emission
process in (1+1) dimensions and the existence of the long ranged dilaton field
whose source is bare energy. This scenario involves the generation of
longitudinal gravitational waves in the parent universe.
