Reformulating Special Relativity on a Two-World Background

Abstract

A new spacetime is isolated and added to the existing spacetime, yielding a pair of co-existing spacetimes, which are four-dimensional inversions of each other. The separation of the spacetimes by the special-relativistic event horizon, compels an interpretation of a pair of symmetrical worlds (or universes) in nature. Furthermore, a two-dimensional intrinsic spacetime that underlies the four-dimensional spacetime in each universe is introduced. The four-dimensional spacetime is the outward manifestation of the two-dimensional intrinsic spacetime, just as the special theory of relativity (SR) on flat four-dimensional spacetime is the outward manifestation of the intrinsic special theory of relativity (∅SR) on flat two-dimensional intrinsic spacetime in each universe. A new set of spacetime/intrinsic spacetime diagrams in the two-world picture is developed, from which intrinsic Lorentz transformation in ∅SR and Lorentz transformation in SR are derived and intrinsic Lorentz invariance and Lorentz invariance are validated in each universe. The SR remains unchanged, but the exposition of its two-world background, the isolated parallel new theory ∅SR and other isolated new features in this article, allow a broader view of SR. This article includes a new addition to the conceptions of many worlds (or universes) in physics and it is effectively a review (in the two-world picture) of the existing geometrical representations of the Lorentz transformation (in a one-world picture).