Laboratory spin in rectilinear Fermi-Walker transport ($s_{\parallel }=\mathrm{const},\gamma {\mathbf{s}}_{\perp }=\mathrm{const}$)

For the orthogonal parametrization $s^{\mu }=\gamma (\mathbf{s}\cdot \mathbf{v}/c,\mathbf{s})$, torque-free acceleration along a fixed direction keeps the longitudinal laboratory component constant and the transverse component proportional to $1/\gamma$. The invariant proper-spin length remains constant; these changing three-components are not a torque-induced loss of spin.