  In string theories, interactions are exponentially suppressed for
trans-Planckian space-like external momenta. We study a class of quantum field
theories that exhibit this feature modeled after Witten's bosonic open string
field theory, and discover a Lorentz-invariant UV/IR relation that leads to the
spacetime uncertainty principle proposed by Yoneya. Application to a dynamical
black hole background suggests that Hawking radiation is turned off around the
scrambling time.
