Reciprocity Principle and Extended Special Relativity

Abstract

Extended Lorentz transformations (ELT) based on spatial anisotropy and time isotropy of a particular inertial frame together with the reciprocity principle are derived. The isolated pair of two inertial frames is proposed to satisfy the condition of frame-independent relative velocities mapping. The relations of sub-superluminal spaces are discussed via continuous bijective mappings and the Einstein velocities addition formula. By using a relative velocity of two inertial frames as a parameter, which is similar to Hill-Cox [2] derivations, the consistent form of ELT is obtained. We then propose the transformation of the inertial frames’ configuration by utilizing the three velocity mappings. By focusing on the issue of inconsistency with special relativity of the derived ELT, we further review the six-dimensional structure of spacetime which is suggested previously by an author [1]. In addition, we suggest a particular mathematical structure of spacetime, i.e., an ultra-hyperbolic (3, n)- structure for any finite n ∈Z+ , n ≥2 , under the assumption that only when an observation of light is made in either frame (of reference), an observer in that frame can access all n-degrees of freedom of time coordinates to maintain the spherical propagation of light in spatial dimensions (3D).