The Lorentz transformation is derived from invariance of an information quantity related to statistical hypothesis testing on single particle system identification parameters. Invariance results from recognition of an equivalent observer as one who reaches the same conclusions as another when the same statistical methods are used. System identity is maintained by parameter values which minimize...

Q. Does the Lorentz transformation reduce to the Galilean transformation when the ratio v /c is small? A. No. At least two routes are available to substantiate the negative response. I will first give a direct, algebraic route and then a more sophisticated indirect route. Consider the usual pair of inertial reference frames, the primed frame moving with speed v along the x axis of the unprimed ...

the decomposition $gamma=bh$ of a group $gamma$ into a subset $b$ and a subgroup $h$ of $gamma$ induces, under general conditions, a group-like structure for $b$, known as a gyrogroup. the famous concrete realization of a gyrogroup, which motivated the emergence of gyrogroups into the mainstream, is the space of all relativistically admissible velocities along with a binary operation given by t...

Space-like and time-like invariant space-time intervals are used to analyse measurements of spatial and temporal distances. The former are found to be Lorentz invariant –there is no 'relativistic length contraction', whereas the latter exhibit the experimentally confirmed 'time dilatation' effect, without, however, 'relativity of simultaneity'. It is shown how the spurious predictions of length...

We give an overview on the problem of finding isometry as Lorentz transformation between given vectors of 4-velocity and its solutions. These Lorentz transformations are usually referenced as Lorentz links. We show that the links by boost, obtained independently by different authors in different forms, are identical. Finally, we discuss briefly some implications of the non-uniqueness of boost l...

We show that the hadron vector resonances are described by fields transforming according to different inequivalent representations of the Lorentz group: (1/2, 1/2) and (1, 0) + (0, 1). The vector representation (1/2, 1/2) is well studied and corresponds to the gauge fields. On the other hand, the chiral representations (1, 0) and (0, 1) are described by the second rank antisymmetric tensor fiel...

The Stokes parameters form a Minkowskian four-vector under various optical transformations. As a consequence, the resulting two-by-two density matrix constitutes a representation of the Lorentz group. The associated Poincaré sphere is a geometric representation of the Lorentz group. Since the Lorentz group preserves the determinant of the density matrix, it cannot accommodate the decoherence pr...