  Among $T^7/\Gamma$ orbifold compactifications of $M$-theory, we examine
models containing the particle physics Standard Model in four-dimensional
spacetimes, which appear as fixed subspaces of the ten-dimensional spacetimes
at each end of the interval, $I^1\simeq S^1/Z_2$, spanning the $11^\text{th}$
dimension. Using the $Z_7$ projection to break the $E_8$ gauge symmetry in each
of the four-planes and a limiting relation to corresponding heterotic string
compactifications, we discuss the restrictions on the possible resulting gauge
field and matter spectra. In particular, some of the states are non-local: they
connect two four-dimensional Worlds across the $11^\text{th}$ dimension.
  We illustrate our programmable calculations of the matter field spectrum,
including the anomalous U(1) factor which satisfies a universal Green-Schwarz
relation, discuss a Dynkin diagram technique to showcase a model with
$SU(3)\times SU(2)\times U(1)^5$ gauge symmetry, and discuss generalizations to
higher order orbifolds.
