The proposal for an alternative to the theory of special and general relativity is based on the transformation of the Weak Equivalence Principle into a law of conservation of acceleration. This states that the intrinsic acceleration of a particle with or without mass is equal to the sum of the accelerations imposed on it by the exterior; the fundamental law of dynamics is therefore expressed exclusively in terms of accelerations. To establish it, a number of general concepts were revisited: (i) the principle of inertia, extended to uniform expansion and rotation motions; (ii) the compatibility of the Galilean and Lorentz transformations; (iii) the abandonment of the concept of space-time; (iv) the substitution of the notion of gravitational deformation of space-time by that of gravitational potentials. Maxwell's major idea of the unification of electrodynamics and magnetism, where direct and induced currents flow on the same support, is taken up to form intrinsic acceleration, an energy per unit of mass and length. The law of motion is a naturally relativistic wave equation obtained without recourse to the Lorentz transformation. Three emblematic examples taken up by the proposed formulation enable us to recover the results of observations, even though it is strictly disjoined from the theory of relativity.