Tomislav Ivezić Ruder Bošković Institute, P.O.B. 180, 10002 Zagreb, Croatia [email protected] It is shown in this paper that the difference between the two forms of relativity the ”true transformation (TT) relativity” and the ”apparent transformation (AT) relativity” is essentially caused by the difference in the concept of sameness of a physical system, i.e., of a physical quantity, for dif...

We outline a new and simple development of special and general relativity based on the physical meaning of the spacetime interval. The Lorentz transformation is not used.

It is demonstrated how the right hand sides of the Lorentz Transformation equations may be written, in a Lorentz invariant manner, as 4–vector scalar products. This implies the existence of invariant length intervals analogous to invariant proper time intervals. The formalism is shown to provide a short derivation of the Lorentz force law of classical electrodynamics, and the conventional defin...

We present a pedagogical approach to the Lorentz group. We start by introducing a compact notation to express the elements of the fundamental representation of the rotations group. Lorentz coordinate transformations are derived in a novel and compact form. We show how to make a Lorentz transformation on the electromagnetic fields as well. A covariant time-derivative is introduced in order to de...

For a 1s electron, whose velocity is equal to Z in atomic units, the relativistic effect leading to heavier mass, for heavy elements (Z high), thus cannot be ignored. The result is a relativistic contraction of the orbitals, causing lowering of Zeff on orbitals of higher angular momentum. This calls for a relativistic treatment of quantum dynamics. For an equation of motion to hold in a relativ...

The spin degrees of freedom for the relativistic particle are described by either Lorentz group variables (classically) or Grassmann variables (pseudo-classically). The relationship between those two descriptions are given. In doing that, appropriate constraints are constructed to put into the lagrangian. Especially a natural relation of Lorentz group variables and Grassmann variables is obtain...

In this note, we construct Noether charges for the chiral supergravity, which contains the Lorentz Chern–Simons term, by applying Wald’s prescription to the vielbein formalism. We investigate the AdS3/CFT2 correspondence by using the vielbein formalism. The asymptotic symmetry group is carefully examined by taking into account the local Lorentz transformation, and we construct super Virasoro al...

‎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 ‎mbox{...