“…Lorentz-breaking observable effects appear in Grand-Unification Theories [4], in String Theories [5], in Quantum Gravity [6], in foam-like quantum spacetimes [7]; in spacetimes endowed with a nontrivial topology or with a discrete structure at the Planck length [8,9], or with a (canonical or noncanonical) noncommutative geometry [10,11,12]; in the so-called "extensions" of the Standard Model incorporating breaking of Lorentz and CPT symmetries [13]; in theories with a variable speed of light or variable physical constants. In particular, the M-Theory [5], the Loop Quantum Gravity [8,9,14] and the Causal Dynamical Triangulation [15] lead to postulate an essentially discrete and quantized spacetime, where a fundamental mass-energy scale naturally arises, in addition to and c. An intrinsic length is directly correlated to the existence of a "cut-off" in the transferred momentum necessary to avoid the occurrence of "UV catastrophes" in Quantum Field Theories. Moreover, some authors suspect that the Lorentz symmetry breaking may play a role in extreme astrophysical phenomena as, e.g., the observation of ultra-high energy cosmic rays with energies [16] beyond the GreisenZatsepin-Kuzmin [17] cut-off, and of gamma rays bursts with energies beyond 20 TeV originated in distant galactic sources [18].…”