Relativity and Cosmology

   

The Relational Dynamics of Space-Time

Authors: Daniel Marques Rodrigues

This article proposes a theoretical framework for an emergent model of spacetime, conceptualized as a relational structure built from fundamental discrete interactions. The formulation is guided by the central postulate: "Nothing is empty, nothing is solitary; interactions define reality", alongside the Dual Stability Principle and the Triple Existence Principle. In the proposed model:u2022 Binary interactions (EAB) establish local equilibrium and static structure.u2022 Triple interactions (EABC) introduce dynamical complexity and emergentnon-linearity.u2022 Higher-order interactions (EA...N ) describe quantum-scale fluctuations,endowing space-time with intrinsic granularity.A mathematical formalism is developed to sum these contributions into an emergent metric tensor, which smoothly transitions between discrete (microscopic) and continuous (macroscopic) scales. Notably, the model recovers classical General Relativity (GR) solutions, including the Schwarzschild, Kerr, and FLRW metrics, in the macroscopic limit.At extreme regimes—such as black holes and the primordial universe—the model regularizes classical singularities via quantum-induced oscillations and fluctuations, ensuring finite curvature and physical consistency.Testable predictions are presented, including quantum corrections to gravitational waves near horizons (detectable by LIGO, Virgo, and LISA) and nonGaussian signatures in the cosmic microwave background (CMB), observablethrough Planck and future CMB-S4 missions. These results pave the way toward a unified gravitational description across all physical scales.

Comments: 18 Pages.

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[v1] 2024-12-19 02:28:27

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