Systemic Relativity & Adaptive Gravity: A Conceptual Scale-Dependent Framework for Unifying Quantum & Cosmic Phenomena
Creators: name: Sosna, Lukas
name: Sosna, Lukas
Publisher: name: Zenodo
Year: 2025
Subjects: subject: Modified gravity
subject: SPARC
subject: Apative Gravity
subject: Non-local gravity
subject: Galactic rotation curves
subject: Astrophysical anomalies
subject: Gravitational waves
subject: System Boundaries
subject: Gravitation
subject: Physical cosmology
subject: Cosmology
subject: Gravity
subject: Specific Gravity
subject: cosmos
subject: Physics
subject: Physics
subject: Mathematical physics
subject: Physics/methods
subject: Physics/standards
subject: Quantum physics
subject: Solar physics
subject: Theoretical physics

description: This paper introduces Systemic Relativity & Adaptive Gravity (SRAG), a conceptual framework exploring gravity as an adaptive process that systematically evolves across scales. SRAG proposes that gravitational interaction responds dynamically to energy density and spatial configuration, potentially offering new perspectives on both quantum-classical reconciliation and astrophysical phenomena currently attributed to dark matter.

The framework is constructed around the dimensionless parameter λ, defined as the logarithmic derivative of gravitational binding energy relative to Planck energy. Through a coherence function C(λ), SRAG provides a mathematical structure enabling continuous transitions between different gravitational regimes without imposing artificial boundaries between quantum and classical domains.

Our analysis of 175 galaxies from the SPARC database demonstrates encouraging results: SRAG reduces rotation curve prediction errors by approximately 50% compared to standard Newtonian models without dark matter. The framework achieves this with a consistent value of λ ≈ 0.08 across diverse galaxy types, suggesting it captures fundamental aspects of gravitational scaling.

The wave-based interpretation developed in this paper yields specific, testable predictions for gravitational wave propagation, including frequency-dependent phase shifts following δΦ = λ·ln(ω₀/ω)/C(λ) and amplitude modulation that might be detectable with next-generation observatories. These predictions provide concrete ways to evaluate whether gravity exhibits the adaptive characteristics proposed by this framework (also refer to my paper: Wave-Based Adaptive Gravity: Coherence-Mediated Gravitational Scaling https://zenodo.org/records/15164559) 

SRAG represents a contribution to ongoing explorations of gravity's fundamental nature, offering a structured approach that connects mathematical formalism with observable phenomena. While much work remains to fully validate or refine this perspective, it provides a coherent stepping stone toward understanding how gravitational effects might systematically transform across the vast range of scales in our universe.

Note: This paper represents a substantial revision and refinement of concepts previously introduced under the name "Scale-Relativistic Logarithmic Gravity (SRLG).
description: SRAG Framework: Core Structure

SRAG proposes a novel perspective on gravitational phenomena through three fundamental postulates that characterize gravity as an adaptive process varying with scale:

Core Postulates



Postulate 1: System-Specific Coherence establishes that gravitational manifestation depends on system scale, with boundaries defined by informational coherence and causal connectivity rather than mere binding energy.

Postulate 2: Observation Dependence recognizes that no physical component remains constant across system transitions, with observational consistency maintained within, but not between - systems of differing λ values.

Postulate 3: Decoupled Observations addresses how system rules require adjustment during coherence loss, with entanglement across gravitational regimes producing observable effects governed by λ changes.


Mathematical Implementation

These postulates are expressed through two complementary approaches:



Energy Transformation: Characterized by the dimensionless parameter λ = (d/d ln(r))(E_bind/E_Planck) = -GM²/(r·E_Planck), representing the logarithmic derivative of gravitational binding energy relative to Planck energy.

Coherence Modulation: Represented by the function C(λ) = 1 - exp(-κ·λ^β), which modulates gravitational behavior across scales.


The framework's unified mathematical formalism describes gravitational acceleration as:

g(r) = (GM/r²) × [C(λ)/(1 + λ^γ ln(1+r/r₀))]

Distinctive Elements

SRAG differs from traditional modified gravity theories by treating gravity not as fundamentally changed, but as adaptively expressed through system-specific coherence. This approach maintains core General Relativity principles while extending applicability to scales exhibiting gravitational anomalies.

The coherence-based definition of system size - where L_system = max{r | IC(λ,r) × CC(λ,r) > ε} ,provides a natural explanation for why gravitational phenomena appear different across cosmic scales without requiring separate theoretical frameworks for each regime.

The wave-based interpretation yields specific, testable predictions for gravitational wave propagation, including frequency-dependent phase shifts described by δΦ = λ·ln(ω₀/ω)/C(λ), offering distinctive signatures that could validate or falsify the framework through future observations.
description: Physics: Gravitation, Astrophysics, Theoretical Physics, General Relativity, Quantum Cosmology

Mathematics: Mathematical Physics, Applied Mathematics

Astronomy: Galactic Dynamics, Observational Cosmology

Interdisciplinary: Philosophy of Science, Computational Physics 


Keywords:



Apative Gravity

Modified gravity

Scale-dependent physics

Logarithmic gravity

Astrophysical anomalies

Galaxy rotation curves

Gravitational lensing

Gravitational waves

Emergent gravity

Dark matter alternatives

Quantum gravity

Radial acceleration relation

Extended theories of gravity

Cosmological tests of gravity

Non-local gravity

Fundamental physics

Scale-dependent gravity

Logarithmic gravitational modification

Coherence function

System boundaries

Energy transformation

Gravitational wave dispersion

Adaptive gravitational coupling

Galactic rotation curves

λ parameter

Quantum-classical transition

Gravitational coherence

Systemic relativity

Subject Classifications



Physics > Gravitation and Cosmology

Physics > Alternative Theories of Gravity

Physics > Astrophysics > Galactic Dynamics

Physics > Quantum Gravity > Phenomenological Models

Physics > Mathematical Physics > Scale-Dependent Phenomena

Astronomy > Dark Matter Alternatives

Physics > Gravitational Waves > Theoretical Models

Physics > General Relativity Extensions

Physics > Theoretical Physics > System Boundaries

Physics > Scale Relativity