Adaptive Constraint Cascade (ACC): A Unified Framework for Gravity – Case Study ACC_2: Newton → Special Relativity → General Relativity
Year: 2026
Type: article
Abstract: We extend the Adaptive Constraint Cascade (ACC) framework to gravity. Three major theories of gravity – Newtonian gravity (NM), special relativity (SR), and general relativity (GR) – are usually treated as discrete, disjoint domains. Here we show that they can be connected by a two-parameter family of constraint algebras A(β, ε), where β = v/c governs the transition from NM to SR (Galilei → Poincaré), and ε = GM/(c²r) governs the transition from SR to GR (flat Minkowski → curved spacetime). The ACC_2 framework equation is presented as a deformed constraint algebra that reduces to the three classical theories in appropriate limits. Using the precession of Mercury's perihelion, we illustrate how the cascade smoothly interpolates between Newtonian, special-relativistic, and general-relativistic predictions. This work is the second in a three-part series on ACC, following ACC_1 (quantum–classical transition) and preceding ACC_3 (quantum field theory).
Author: Nguyen, Thanh Minh
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7160692023
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