A new ?Projective relativity? based on the De Sitter universe

The principle of relativity and the special relativity triple

“…Thus, this confirms that on the dS/AdS spacetime of possitive/negative constant curvature of radius l, there are indeed other two kinds of the Beltrami inertial frames with inertial motions for the dS/AdS special relativity, respectively [8][9][10][11][12][13][14][15][16][17][18][19][20][21].…”

“…Later, the dS/anti-de Sitter (AdS) special relativity has been proposed [8][9][10][11][12][13][14][15][16][17][18][19][20][21], based on the principle of relativity [8,9] and the postulate on two universal constants (c and l) [12]. The dS/AdS special relativity is invariant under the LF T s of dS/AdS-group SO(1, 4)/SO(2, 3) among the inertial motions in the Beltrami model [22] of dS/AdS-spacetime [12,21] with curvature radius l, respectively.…”

“…Actually, the inertial motion (1) may be viewed as a straight line and the most general transformations among straight lines may form a group, which may be referred to the real projective transformations of the real projective group RP (4)(see, e.g. [10,11]). But, care should be taken for the orientation [12].…”

On a Time–Space Operator (and other Non-Self-Adjoint Operators) for Observables in QM and QFT

“…More specifically, the "archaic universe" theories go back to the group theoretical approaches proposed in the mentioned, classical works of Arcidiacono and Fantappié [121][122][123][124][125][126] wherein the Projective Relativity" was introduced. Let us recall some basic concepts.…”

Lie Group of Spacetime

“…Due to these facts alternative theories have been considered as, for example, Extended Theories of Gravity which have become a sort of paradigm in the study of gravitational interaction based on the enlargement and the correction of the traditional Einstein scheme [6,7] role in the development of GR, as, for example, the Brans-Dicke theory in which the gravitational interaction is mediated by a scalar field as well as the tensor field of GR, and the gravitational constant G is not presumed to be constant but instead 1/G is replaced by a scalar field which can vary from place to place and with time [8]. Another theory in accord with Mach's Principle is de Sitter-Fantappiè relativity initially proposed by Fantappiè and subsequently developed by Arcidiacono and other authors [9][10][11][12][13][14][15][16][17][18][19][20][21][22]. At present, both Brans-Dicke theory and de Sitter-Fantappiè relativity are generally held to be in agreement with observation.…”