Lorentz violation with a universal minimum speed as foundation of de Sitter relativity

Abstract

We aim to investigate the theory of Lorentz violation with an invariant minimum speed called Symmetrical Special Relativity (SSR) from the viewpoint of its metric. Thus, we should explore the nature of SSR-metric in order to understand the origin of the conformal factor that appears in the metric by deforming Minkowski metric by means of an invariant minimum speed that breaks down Lorentz symmetry. So, we are able to realize that there is a similarity between SSR and a new space with variable negative curvature (−∞ < R < 0) connected to a set of infinite cosmological constants (0 < Λ < ∞), working like an extended de Sitter (dS) relativity, so that such extended dS-relativity has curvature and cosmological "constant" varying in time. We obtain a scenario that is more similar to dS-relativity given in the approximation of a slightly negative curvature for representing the current universe having a tiny cosmological constant. Finally, we show that the invariant minimum speed provides the foundation for understanding the kinematics origin of the extra dimension considered in dS-relativity in order to represent the dS-length.

On how Bohr model of hydrogen atom is connected to nuclear physics

“…Now, one hundred years after the solar eclipse in 1919, a new experiment can prove that Einstein's theory is being superseded by the Symmetric Special Relativity (SSR) developed by Cláudio Nassif da Cruz. He proposes the existence of an invariant minimum speed connected to the fundamental vacuum state, i.e., a new aether that leads us to understand the origin of the cosmological constant or the cosmological anti-gravity in a de Sitter scenario (Cruz, dos Santos, & Amaro de Faria, 2018). Nassif has also proposed an experimental route for testing the existence of such a minimum speed (aether) that breaks down the Lorentz symmetry in the infrared (IR) regime by considering a ultra-cold Sodium Potassium dipolar gas ( 23 − 40 ) thermalized with the radioactive isotope single atom ( 25 ) working like an atomic clock close to a minimum temperature (~10 −12 ) (Nassif, 2017).…”

Modified Lorentz transformations and quantum mechanics

“…The space-time geometry has been one of the main topics of the physics research. This research includes the special and general relativities, quantum mechanics, manifold mathematical physics, cosmology and standard model [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. The Lorentz transformations have been derived in the special relativity [1,2].…”

“…Because of this definition, the space-time geometry has been very complicated as seen in the special and general relativities. In this case, the space-time geometry has been expressed as the coordinates of (x1,x2,x3,ctl) with the metric signature of (+ ---) [1][2][3]10,14]. In this case, the space-time distance is s 2 = (ctl) 2 -x1 2 -x2 2 -x3 2 .…”