Symmetry in relativistic measurements
The covarying scale effect in the observational relativistic measurement has been found a few years ago that the Lorentz factor is a scale conversion ratio between the virtual covarying scale of measurement in relative motion and the real invariant scale at rest with respect to the observer.
We find this scale conversion ratio is the bridge between two relative frames, and is a logical symmetry for the measurement of the spatial distance and the measurement of time interval by using the same scale conversion. Hence the two relative frames are not only reciprocal to each other, but also symmetric with respect to the scale conversion to each other.
See paper in HTML format here.