Authors: Akindele O. J. Adekugbe
A new sheet of spacetime is isolated and added to the existing sheet, thereby yielding a pair of co-existing sheets of spacetimes, which are four-dimensional inversions of each other. The separation of the spacetimes by the special-relativistic event horizon compels an interpretation of the existence of a pair of symmetrical worlds (or universes) in nature. Further more, a flat two-dimensional intrinsic spacetime that underlies the flat four-dimensional spacetime in each universe is introduced. The four-dimensional spacetime is outward manifestation of the two-dimensional intrinsic spacetime, just as the Special Theory of Relativity (SR) on four-dimensional spacetime is mere outward manifestation of the intrinsic Special Theory of Relativity (φSR) on two-dimensional intrinsic spacetime. A new set of diagrams in the two-world picture that involves relative rotation of the coordinates of the two-dimensional intrinsic spacetime is drawn and intrinsic Lorentz transformation derived from it. The Lorentz transformation in SR is then written directly from intrinsic Lorentz transformation in φSR without any need to draw diagrams involving relative rotation of the coordinates of four-dimensional spacetime, as usually done until now. Indeed every result of SR can be written directly from the corresponding result of φSR. The non-existence of the light cone concept in the two-world picture is shown and good prospect for making the Lorentz group SO(3,1) compact in the two-world picture is highlighted.
Comments: 19 pages, published in Progress in Physics, 2010, vol.1 30-48
[v1] 19 Feb 2010
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