Symmetrical special relativity: quantum and cosmological implications

Abstract

This work presents a literature review of the Symmetrical Special Relativity (SSR) theory, which extends special relativity by introducing a minimum invariant speed 𝑉 in spacetime, thereby breaking Lorentz symmetry at low energies. The study synthesizes and clarifies the most relevant results of the theory. The lower speed limit 𝑉 is associated with a background ultra-referential frame 𝑆𝑉 , which remains covariant under all inertial frames. The work analyzes the new coordinate and velocity transformations proposed by SSR, as well as their fundamental consequences: a deformed invariant interval 𝑑𝑠*, the dilation of proper time, and a deformed metric given by 𝐺𝜇𝜈 = 𝜃−2𝜂𝜇𝜈. The theory leads to a modified relativistic dynamics, with a new expression for energy and an altered dispersion relation, in addition to facilitating the understanding of mass anisotropy. Furthermore, an energy barrier emerges in the limit 𝑣 → 𝑉 , which renders absolute rest unattainable. The study also explores the nature of non-Galilean reference frames, which introduce an intrinsic uncertainty in the position of particles and establish an uncertainty principle associated with the structure of the modified spacetime. Subsequently, the work investigates the cosmological implications of the theory. It is obtained, from the energy-momentum, the equation of state of the cosmological constant, 𝑝 = −𝜖. A simplified toy cosmological model is then proposed, predicting an antigravitational regime, yielding values of Λ0 ∼ 10−35 s−2 and 𝜌Λ𝑃 ∼ 1093 g/cm3, consistent with observational data. The theory also establishes significant correlations between the deformed SSR metric and a de Sitter metric with a conformal factor. The study concludes with considerations on the possible implications of SSR in quantum field theory (QFT) and in the description of magnetic fields arising from a modified electromagnetism.