  Physical states in quantum mechanics are rays in a Hilbert space. Projective
representations of a relativity group transform between the quantum physical
states that are in the admissible class. The physical observables of position,
time, energy and momentum are the Hermitian representation of the
Weyl-Heisenberg algebra. We show that there is a consistency condition that
requires the relativity group to be a subgroup of the group of automorphisms of
the Weyl-Heisenberg algebra. This, together with the requirement of the
invariance of classical time, results in the inhomogeneous Hamilton group that
is the relativity group for noninertial frames in classical Hamilton's
mechanics. The projective representation of a group is equivalent to unitary
representations of its central extension. The central extension of the
inhomogeneous Hamilton group and its corresponding Casimir invariants are
computed. One of the Casimir invariants is a generalized spin that is invariant
for noninertial states. It is the familiar inertial Galilean spin with
additional terms that may be compared to noninertial experimental results.
