Physical content of a passive Lorentz transformation

A passive Lorentz transformation changes the components used to describe the same events and fields while preserving the standard Minkowski metric matrix: ${\Lambda }^T\eta \Lambda =\eta$. This expresses the relation between standard clock-normalized inertial frames. An arbitrary coordinate relabeling remains possible, but generally changes that metric matrix. Active boost invariance of a physical system additionally requires the relevant dynamical symmetry; a preferred physical background can obstruct it even when every equation is written in tensor notation.