*Coordinate Transformations with t*

*x* = space coordinate, *t* = time coordinate, *v* = velocity, *u* = pace

Galileian transformation

speed: *x´* = *x* – *vt* and *t**´* = *t*, pace: *x´* = *x* – *t/u* and *t**´* = *t*.

Co-Galileian transformation

speed: *t´* = *t* – *x/v* and *x**´* = *x*, pace: *t´* = *t* – *ux* and *x**´* = *x*.

Light: *c* := speed of light, *c´* := pace of light.

speed: *x* = *ct* or* x/c = t* and *x´* = *ct´*, or *x´/c* = *t´*,

pace: *c´x* = *t* or *x* = *t/c´* and *c´r′ *= *t´* or *x´ *= *t´/c´*.

Lorentz transformation

speed: *γ* = (1 – *v*^{2}/*c*^{2})^{–1/2} with *x**´* = *γ* (*x − vt*) and *t´* = *γ* (*t* – *xv/c²*),

pace: *γ* = (1 – *c´*^{2}/*u*^{2})^{–1/2} with *x´* = *γ* (*x* – *t/u*) and *t**´* = *γ* (*t* – *xc´²/u*),

which applies only if |*v*| < |*c*| or |*u*| > |*c´*|.

Co-Lorentz transformation

speed: *λ* = (1 − *c*^{2}/*v*^{2})^{–1/2} with *t´* = *λ* (*t − x/v*) and *x´* = *λ* (*x* − *t* (*c*^{2}*/v*)),

pace: *λ* = (1 – *u*^{2}/*c´*^{2})^{–1/2} with *t´* = *λ* (*t* – *ux*) and *x´ *= *λ* (*x* – *t* (*u/c´²*)),

which applies only if |*v*| > |*c*| or |*u*| < |*c´*|.