  It was argued by Mashhoon that a spin-rotation coupling term should add to
the Hamiltonian operator in a rotating frame, as compared with the one in an
inertial frame. For a Dirac particle, the Hamiltonian and energy operators H
and E were recently proved to depend on the tetrad field. We argue that this
non-uniqueness of H and E really is a physical problem. We compute the energy
operator in the inertial and the rotating frame, using three tetrad fields: one
for each of two frameworks proposed to select the tetrad field so as to solve
this non-uniqueness problem, and one proposed by Ryder. We find that Mashhoon's
term is there if the tetrad rotates as does the reference frame --- but then it
is also there in the energy operator for the inertial frame. In fact, the Dirac
Hamiltonian operators in two reference frames in relative rotation, but
corresponding to the same tetrad field, differ only by the angular momentum
term. If the Mashhoon effect is to exist for a Dirac particle, the tetrad field
must be selected in a specific way for each reference frame.
