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Towards a new Relativity: How to Travel Faster than Light

Abstract

The main purpose of this paper lies in the attempt to identify a different meaning concerning equations usually classified as relativistic, such as the well known Lorentz Transformations. On the one hand, we can no longer deny that several phenomena can be effectively described by the above-mentioned equations; on the other hand, generally speaking, we should acknowledge that, although some mathematical relations have proved to be evidently suitable for describing the phenomenological reality, their meaning could be deeply different from the one we are used to ascribing to them. The current cosmological theories contemplate the possibility that our Universe could be characterized by a positive curvature. In this case, with the usual hypothesis of homogeneity and isotropy, our Universe is commonly imagined as evenly spread on the surface of a four dimensional ball. In this paper, the existence of at least a further spatial dimension is at least contemplated: in other terms, from a topological point of view, the Universe is no longer assimilated to a three dimensional spherical shell, but rather to a closed 4 - ball. As a consequence, the concept of material point should be replaced by the one of material segment. The angular distance between two points is equal to the angle formed by their radial extensions; the geodesic distance depends on the value of the speed. Naturally, the speed of light is still to be considered constant and independent of the motion of the source. Time is considered absolute. Among the various results, the possibility of travelling apparently faster than light stands out.

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