We review the Inertial transformation and Lorentz transformation under a newcontext, by using Clifford Algebra or Geometric Algebra. The apparentcontradiction between theses two approach is simply stems from differentprocedures for clock synchronization associated with different choices of thecoordinates used to describe the physical world. We find the physical andcoordinates components of both transformations. A important result is that inthe case of Inertial transformation the physical components are exactly theGalilean transformations, but the speed of light is not c. Another interestingresult is due to the fact the Lorentz transformations lead directly to physicalcomponents, and this case the speed of light is c. Finally e show that bothscenarios, de-synchronization Einstein theory and synchronized theory, are allmathematically equivalent by means of Clifford Algebra Transformations.
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