The Earth spins.
It is possible to determine that the Earth spins by
observing the handedness of tornadoes.
The universe spins.
It is possible to determine that the universe spins by
observing the handedness of neutrinos, sugars and
other such stuff.
The universe does not spin in spacetime.
The universe spins in its natural frame of reference.
The universe spins with respect to itself.
One possible geometry that supports self referential
spin is that of a torus that turns itself inside out.
The universe is a single background free dynamic
spin structure.