Above we have shown that there is a problem with Einstein's
idea that simultaneity is not absolute across inertial frames.

Here, we add one more demonstration, based on insisting
on use of the generalized cartesian coordinate form in
our transformed equations, as a means of avoiding data
degradation from ratio scale to interval scale.

Using analytic geometry's obvious (x-x0) form, where
x0 is an important 'anchor' or 'centroid' such as a
circle center, we apply the SR transforms, x'=gx-gvt,
and t'=gt-gxv/cc.


(a) (x'-x0')=[ g(x-vt) - g(x0-vt) ] = g(x-x0);
    this shows (1) that the transform is thus
    a rescaled invariant, and (2) one x transforms
    to only one x', regardless of t.

(b) (t'-t0')=[ g(t-vx/cc) - g(t0-vx/cc) ] = g(t-t0);
    this shows (1) that the transform is thus
    a rescaled invariant, and (2) one t transforms
    to only one t', regardless of x.

(c) therefore any pair of points (xa,tc), (xb,tc)
    transform to one and only one (xa',tc') and
    (xb',tc') pair, which shows that time transformed
    intervals do not depend on location and therefore
    absolute simultaneity holds.

(d) therefore any pair of points (xc,ta), (xc,tb)
    transform to one and only one (xc',ta') and
    (xc',tb') pair, which shows that spatial transformed
    intervals do not depend on time, and therefore absolute
    spatial congruence holds.