ABSTRACT
The basic equations for the coordinate transformations are the same as the equations (11.1) through (11.5) for the general time-invariant nonuniform transformations,
ti = μit, μi = const. ∈ R+. (12.1)
ti = α i j
tj +
rP (tj)
, αij ∈ R+, (12.2)
tj = α j i
ti −
rP (ti)
, αji ∈ R+, (12.3)
rP (ti) = λ i j
8 rP (tj) + v
9 , λij ∈ R+, (12.4)
rP (tj) = λ j i
rP (ti)− vijitiu
, λji ∈ R+, (12.5)
where
q(.), w(.) ∈ R+, v(.)ji ∈ R+,
q(.)w(.) ∈ 8 c (.) (.)
92 , 8 v (.) P
92 , 8 v (.) SU
92 is permitted but not required. (12.6)
We will change only the spatial reference point. It will not be the light signal
it is by the subscript SU (for: Spatial Uniformity). This spatial uniformity is general because any point with any constant speed can be chosen and fixed for the reference point PSU . The choice of a light signal L for PSU , hence v
c (.) (.), represents a singular case. The selection of the reference point PSU to be
different from the light signal L, i.e. v(.)SU = c (.) (.), makes what follows to be
beyond Einsteinian relativity theory. The temporal transformations (12.2) and (12.3) are nonuniform due to their
dependence on the position rP t(.) of the arbitrary point P .
