Solution (source code)

= Solution

A <coordinate transformation> considered solely as a relabeling of events has no independent observable outcome: changing labels changes neither a detector record nor a <clock> comparison. But the <Lorentz transformation>[Lorentz transformations] also express substantive relations between operationally realized inertial coordinates. With clocks and rulers specified, their velocity-dependent <time dilation>, length relations and <velocity> composition make testable claims about how material systems and electromagnetic signals behave.

The distinction matters for <synchronization (computing)>[synchronization]. One-way coordinate light <speed> depends on how distant clocks are synchronized; a conventional alteration changes the displayed transformation law while leaving two-way timing observations unchanged. It would therefore be incorrect to regard every coefficient in an unspecified coordinate formula as a separately measurable physical fact. Testable content comes from the transformation together with the protocol and dynamical behavior of the systems implementing the coordinates.

Tests can compare <clock> <Proper time>[proper times], decay lifetimes or <resonance (chemistry)>[resonance] behavior across <relative motion> and orientation. Agreement supports <Lorentz invariance>[Lorentz-invariant] kinematics and the associated matter dynamics over the range tested; it does not prove exact invariance at every possible scale. A rival theory with an undetectable preferred frame can reproduce the same observations by changing its explanatory commitments. <Empirical equivalence> of that rival does not make the observable <clock> relations untestable.

Thus the answer is qualified: transformations as passive mathematical changes are not experiments, while Lorentzian relations among specified measuring procedures have substantial empirical consequences. Separating these roles avoids both treating coordinate convention as a measured <force> and declaring the entire relativistic structure immune to evidence.