the only justification for the einstein velocity addition law appeared to be its empirical adequacy, so that the intrinsic beauty and harmony in einstein addition remained for a long timea mystery to be conquered. accordingly, the aim of this expository article is to present(i) the einstein relativistic vector addition,(ii) the resulting einstein scalar multiplication,(iii) the einstein relativ...

We present some basic facts concerning simultaneity in both special and general relativity. We discuss Weyl’s proof of the consistence of Einstein’s synchronization convention and consider the general relativistic problem of assigning a time function to a congruence of timelike curves. 1 Simultaneity in special relativity In special relativity the possibility of synchronizing distant clocks so ...

In this brief paper we justify observations made in El Naschie's paper " On the Unification of the Fundamental Forces... " , on the Planck scale, fractal space time and the unification of interactions, from different standpoints. In a recent paper El Naschie[1] has emphasized the intimate connection between the Planck length, the Compton wavelength and a unification of the fundamental interacti...

In a new theory, local Lorentz invariance is a low-energy symmetry which no longer holds when a fermion energy E is well above 1 TeV. Here we find that the modified E(p) relation is consistent with observation, and is in fact nearly the same as in Einstein relativity. On the other hand, there is a strong modification of the fermion equation of motion and propagator at ultrahigh energy, which sh...