# Tag Info

Use: $$u_{\alpha}= g_{\alpha\beta}u^{\beta}$$ where $g_{\alpha\beta}$ is the metric tensor.
You can always transform to the coordinates of the traveler which experiences no motion in space but only in time (with proper time!). That way $d\tau=dt$ and $dx=dy=dz=0$ . $|u|^2 = \eta_{\alpha \beta} u^{\alpha} u^{\beta}=-1$ - which is a scalar. Scalars are invariant under any coordinate transformation, so even after you return to your original ...