Discrete mechanics postulates the conservation of acceleration; it establishes a law of conservation where the proper acceleration of the material medium or of the particle is equal to the sum of the accelerations which are applied to it. The abandonment of the mass of Newton's second law is not in contradiction with the principle of equivalence of Galileo; it leads to acceleration being considered as an absolute quantity, independent of the local reference frame chosen. The immediate consequence is that the fundamental quantities necessary for the description of any mechanical problem are limited to two and only two, a length and a time. These two intrinsic quantities are independent of all the others which result from it. The theory of relativity, like classical mechanics, gives mass a primordial role by setting as a principle the conservation of momentum; in special relativity, mass is a function of velocity through a Lorentz transformation. The discrete mechanics formulated without mass within the equation of motion is directly confronted with the indisputable results of the theory of relativity verified by experience. The solutions of two cases of relativity are found: the movement of a uniformly accelerated isolated particle and the deflection of light by the sun. An application to the interference produced by two sources of coherent light in direct simulation makes it possible to show the robustness of the discrete equation at very small time scales.