The Witte Effect, that was first observed by R. D. Witte in 1991, and consist of a phase error between two synchronized atomic clocks, due to rotation of the earth, that can be connected to the earth “absolute” movement in the space. The Witte Effect was explained in context of General Relativity, by R. T. Chaill, based on the Michelson-Morley Interferometer. Dr. Chaill demonstrates that, if the light speed in the medium (that forms the interferometer arms) is smaller than in vacuum (for example, using optical fibers) “absolute” velocities can be obtained. On this way, Chaill proposed that Witte experiments, in fact were measured “absolute” velocities of earth displacement in space, which maybe associated to the large gravitational fields references frames. In this paper the author explains the Witte Effect, using only the Especial Relativity models, more specifically, rotating the Einstein’s light clock and demonstrate that this Effect not is really connect to the Michelson-Morley Interferometer experiment. If this is true the Witte Effect can be used to update the gravitational wave detector, like the LIGO (Laser Interferometer Gravitational Wave Observatory), and make it work.