Does the spin of a particle change if observed from an accelerating reference frame? If we consider a spin-$\frac12$ particle at rest in the absence of any potentials, we can use the Pauli spin operators and an associated basis to describe the observable.
Let's arbitrarily choose the $Z$ basis and consider the particle to initially be in state $\newcommand{\k}[1]{\left|\;#1\;\right\rangle}$ $\k{\downarrow}$. 
If we then move into an accelerating reference frame, do we require a new spin operator? Secondly, what is the spin state of the particle in this new reference frame?
To make this somewhat more intuitive, this question arose from considering a particle in free fall in a uniform gravitational field. Does the spin state change depending on whether we measure the particle in the laboratory frame or the particle own frame of reference?
EDIT:
The particle and its measurement apparatus are at rest in a laboratory. They are technically in an accelerating reference frame subject to gravitational forces. The spin is measured and found to be in the $\k{\downarrow}$ eigenstate. If we then release both the particle and the apparatus, they will be in an inertial (freely falling) frame. Is there a way to quantify the state of the particle now? Will it still be in the $\k{\downarrow}$ eigenstate or do the eigenstate have to be redefined altogether?
 A: A series of lorentz boosts can generate a rotation therefore an observer in a reference frame that is moving with respect to the rest reference frame where the particle is at rest will measure a value of spin that depends on the momentum of the particle in the transformed frame and the lorentz transformation needed to relate the two reference frames. This is all true in special relativity. It is hard for me to imagine that things would be simpler in accelerating reference frame i.e GR. So yes, the spin of the particle should change since it can change in special relativity.
A: I think such experimental evidence of spin-flips due to frame velocity or intense gravitational field  have not been seen or reported in literature;
however looking at nature of spin states of particles which are devoid of any mechanical rotations as such should not be affected by gravity  generated by space time curvature  or such forces generated by motion of the frames (mechanical in nature); the spin/color and other quantum mechanical attributes are distinguishing  labels and has nothing in common with usual spinning tops....
