  Within the twistorial parametrization of Loop Quantum Gravity we investigate
the consequences of choosing a spacelike normal vector in the linear simplicity
constraints. The amplitudes for the $SU(2)$ boundary states of Loop Quantum
Gravity, given by most of the current spinfoam models, are constructed in such
a way that even in the bulk only spacelike building blocks occur. Using a
spacelike normal vector in the linear simplicity constraints allows us to
distinguish spacelike from timelike 2-surfaces. We propose in this paper a
quantum theory that includes both spatial and temporal building blocks and
hence a more complete picture of quantum spacetime. At the classical level we
show how we can describe $T^{\ast}SU(1,1)$ as a symplectic quotient of
2-twistor space $\mathbb{T}^2$ by area matching and simplicity constraints.
This provides us with the underlying classical phase space for $SU(1,1)$ spin
networks describing timelike boundaries and their extension into the bulk.
Applying a Dirac quantization we show that the reduced Hilbert space is spanned
by $SU(1,1)$ spin networks and hence are able to give a quantum description of
both spacelike and timelike faces. We discuss in particular the spectrum of the
area operator and argue that for spacelike and timelike 2-surfaces it is
discrete.
