  If the systems of quantum theory are thought of as elementary information
carriers in the first place, rather than elementary constituents of matter, and
their connections are logical connections within a given algorithm, rather than
space-time relations, then we need to find the origin of mechanical
concepts---that characterise quantum mechanics as a theory of physical systems.
To this end, we will illustrate how physical laws can be viewed as algorithms
for the update of memory registers that make a physical system. Imposing the
characteristic properties of physical laws to such an algorithm, i.e.
homogeneity, reversibility and isotropy, we will show that the physical laws
thus selected are particular algorithms known as cellular automata. Further
assumptions regarding maximal simplicity of the algorithm lead to two cellular
automata only, that in a suitable regime can be described by Weyl's
differential equations, lying at the basis of the dynamics of relativistic
quantum fields. We will finally discuss how the same cellular automaton can
give rise to both Fermionic field dynamics and to Maxwell's equations, that
rule the dynamics of the electromagnetic field. We will conclude reviewing the
discussion of the relativity principle, that must be suitably adapted to the
scenario where space-time is not an elementary notion, through the definition
of a change of inertial reference frame, and whose formulation leads to the
recovery of the symmetry of Minkowski space-time, identified with Poincar\'e's
group. Space-time thus emerges as one of the manifestations of physical laws,
rather than the background where they occur, and its features are determined by
the dynamics of systems, necessarily equipped with differential equations that
express it. In brief, there is no space-time unless an evolution rule requires
it.
