  It is shown that physical signals and space-time intervals modeled on
split-octonion geometry naturally exhibit properties from conventional
(3+1)-theory (e.g. number of dimensions, existence of maximal velocities,
Heisenberg uncertainty, particle generations, etc.). This paper demonstrates
these properties using an explicit representation of the automorphisms on
split-octonions, the noncompact form of the exceptional Lie group G2. This
group generates specific rotations of (3+4)-vector parts of split octonions
with three extra time-like coordinates and in infinitesimal limit imitate
standard Poincare transformations. In this picture translations are represented
by non-compact Lorentz-type rotations towards the extra time-like coordinates.
It is shown how the G2 algebra's chirality yields an intrinsic left-right
asymmetry of a certain 3-vector (spin), as well as a parity violating effect on
light emitted by a moving quantum system. Elementary particles are connected
with the special elements of the algebra which nullify octonionic intervals.
Then the zero-norm conditions lead to free particle Lagrangians, which allow
virtual trajectories also and exhibit the appearance of spatial horizons
governing by mass parameters.
