= Solution
The upper index identifies $P^\alpha$ as a contravariant <Lorentz four-vector>, obeying the rank-one <contravariant tensor> transformation law. Its components transform with the coordinate Jacobian,
$$
\boxed{P'^\alpha=\frac{\partial x'^\alpha}{\partial x^\beta}P^\beta.}
$$
It is not invariant component by component. Its contracted square $P_\alpha P^\alpha=m^2c^2$, for metric signature $(+,-,-,-)$, is a <Lorentz invariant>. This distinguishes a contravariant transformation law from an invariant scalar.
Back to article page
