  In a general spacetime, the possible choices for the field of orthonormal
tetrads lead (in standard conditions) to equivalent Dirac equations. However,
the Hamiltonian operator is got from rewriting the Dirac equation in a form
adapted to a particular reference frame, or class of coordinate systems. That
rewriting does not commute with changing the tetrad field $(u_\alpha)$. The
data of a reference frame F fixes a four-velocity field $v$, and also fixes a
rotation-rate field $\Mat{\Omega}$. It is natural to impose that $u_0=v$. We
show that then the spatial triad $(u_p)$ can only be rotating w.r.t. F, and
that the title problem is solved if one imposes that the corresponding rotation
rate $\Mat{\Xi}$ be equal to $\Mat{\Omega}$ - or also, if one imposes that
$\Mat{\Xi}=\Mat{0}$. We also analyze other proposals which aimed at solving the
title problem.
