Proper force
= Proper force
{title2=$\mathbf f_0=d\mathbf p/dt\ \text{in the instantaneous rest frame}$}
The three-force measured in a particle's instantaneous <rest frame>. For a <pure force>, $\mathbf f_0=m_0\mathbf a_0$, where $\mathbf a_0$ is the rest-frame <acceleration>. In that frame the <four-force> has zero temporal component and spatial part $\mathbf f_0$; the <four-force> itself is a different object.