  We review the Inertial transformation and Lorentz transformation under a new
context, by using Clifford Algebra or Geometric Algebra. The apparent
contradiction between theses two approach is simply stems from different
procedures for clock synchronization associated with different choices of the
coordinates used to describe the physical world. We find the physical and
coordinates components of both transformations. A important result is that in
the case of Inertial transformation the physical components are exactly the
Galilean transformations, but the speed of light is not c. Another interesting
result is due to the fact the Lorentz transformations lead directly to physical
components, and this case the speed of light is c. Finally e show that both
scenarios, de-synchronization Einstein theory and synchronized theory, are all
mathematically equivalent by means of Clifford Algebra Transformations.
