The document presents new relational transformations called the Lorentz's Transformations which directly transform spacetime coordinates from one reference frame to another. The transformations relate the time and spatial coordinates between two reference frames in motion relative to each other, and include terms for the relative velocity between the frames. A local relational metric is also defined which depends on the relative velocity between reference frames.

1. THE NEW LORENTZ’S TRANSFORMATIONS
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The new “Lorentz’s Transformations” are the new relational transformations:
Direct transformations A → B for C :
1  v 
dtCB =  dtCA − BA dxCA 
2
v BAvCA  c 
1−
c2
dxCB =
1
v BAvCA
(dxCA − v BAdtCA )
1−
c2
v 2 BA
1−
dyCB = c 2 dy
CA
v v
1 − BA 2 CA
c
v 2 BA
1−
dzCB = c 2 dz
CA
v v
1 − BA 2 CA
c
Relational local metric associated:
 − k CA 
 
 k CA 
g CA = 
k CA

 
 k CA 

where k CA :
1
k CA =
v 2 CA
1− 2
c