In this paper we introduced the fundamental elements of a new relativistic physics for the lower transversal spaces. The classical Einstein’s theory (physics) of the upper transversal spaces is linear via Lorentz’s transformations. On the other hand, the physics of the lower transversal spaces is nonlinear via the nonlinear transformations. Also, for the upper transversal spaces, as and Einstein’s physics, is essential that the ”live” is finite , but in the lower transversal spaces the ”live” is infinite. This is a result (fact) of the deepest connection between new nonlinear physics and the geometry of the lower transversal spaces. The relativistic physics and the new nonlinear physics are essential different, but the equation for Energy in the form $E = mc^{2}$ is in the same in both physics!