Is the Special Relativity Compatible With Einstein’s Static Universe?Proposal for New “Generic” Transformations. The Twin Paradox

Abstract

Albert Einstein, shortly after publishing his General Relativity Theory (GRT) applied it to the entire universe in a paper [1] of 1917. Einstein assumed that such a universe was static in time and possessed a uniform distribution of matter on the largest scales, obtaining a static and finite universe of spherical spatial curvature of radius _R_. Although this model was refuted by Edwin Hubble's discovery of the expansion of the universe, it is still often studied as a theoretical framework for some problems, such as the twin paradox. This paper will show that Einstein's static universe model leads to a privileged frame of reference, so that any observer moving at the speed _v_ will be able to measure speeds of light other than _c_ depending on the direction of beam transmission. The above will refute the validity of the application to this closed and static universe of the Special Relativity Theory (SRT) proposed by Einstein in 1905 in his article [2]. In addition, a new synchronization convention and new coordinate transformations will be deduced, THE "GENERIC" TRANSFORMATIONS, which will replace those of Lorentz. Finally, the twin paradox in this universe will be solved by making use of them.