  The attempt to unify the laws of physics is approached from a discrete vision
of space and time, abandoning the continuous medium paradigm that presided over
the derivation of certain equations of physics-Navier-Stokes., Navier-Lam{\'e},
Maxwell, etc. Acceleration considered as an absolute quantity is expressed as a
Hodge-Helmholtz decomposition, the sum of a solenoidal component and an
irrotational component. Discrete mechanics, which has already unified mechanics
in a relativistic formulation, is extended to electromagnetism with the same
equation of motion expressed in terms of scalar and vector potentials. All the
variables and parameters of this equation are described with only two
fundamental units, those of length and time. The discrete equation makes it
possible to account for persistent phenomena in the absence of any excitation,
permanent magnetization, pressure, shear stress and purely unsteady effects
such as magnetic induction, longitudinal and transversal wave propagation,
differential rotation.
