I review, on an advanced level, some of the algebraic and geometric structures that underlie the theory of Special Relativity. This includes a discussion of relativity as a symmetry principle, derivations of the Lorentz group, its composition law, its Lie algebra, comparison with the Galilei group, Einstein synchronization, the lattice of causally and chronologically complete regions in Minkows...

This paper describes a rational reconstruction of Einstein’s discovery of special relativity, validated through an implementation: the Erlanger program. Einstein’s discovery of special relativity revolutionized both the content of physics and the research strategy used by theoretical physicists. This research strategy entails a mutual bootstrapping process between a hypothesis space for biases....

Recently, [10,11], the Heisenberg Uncertainty relation and the NoCloning property in Quantum Mechanics and Quantum Computation, respectively, have been extended to versions of Quantum Mechanics and Quantum Computation which are re-formulated using scalars in reduced power algebras, [2-9], instead of the usual real or complex scalars. Here, the Lorentz coordinate transformations, fundamental in ...

In this paper we have studied the nature of kinematical and dynamical laws in κ-Minkowski spacetime from a new perspective: the canonical phase space approach. We have introduced a new form of κ-Minkowski phase space algebra from which we recover the κ-extended finite Lorentz transformations derived in [13]. This is a particular form of a Deformed Special Relativity model that admits a modified...

We suggest the reexamination of the validity of the Lorentz invariance at the small distance of the order of 10-16 cm in the light of high energy available at CERN and NAL. Using the modified weak interaction Lagrangian with a noncausal form factor we evaluate the muon decay lifetime including the effect of the radiative corrections as a function of the particle energy and characteristic length...