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The Simple Framework of the Extended Entropy-Driven Gravitation Effect (EDGE)

William Cawley
Independent Researcher
@William54656169 | GitHub: willstar777
October 28, 2025

Abstract

We present the Simple Framework of the Extended Entropy-Driven Gravitation Effect (EDGE), a theoretical model in which gravity emerges from entropy gradients in quantum fields. Gravity is not a fundamental force but a statistical consequence of the universe’s drive to maximize disorder. The core principle is: entropy drives gravity that drives entropy, with gravity as a form of entropy. We modify Einstein’s field equations with a single entropic term ( S_{\mu\nu} ), constructed from thermodynamic and holographic entropy. This framework unifies local gravitational attraction and cosmic expansion (dark energy) under one mechanism. Dark energy arises from holographic entropy gradients at the cosmological horizon. The model is designed for clarity and testability, avoiding complex quantum entropy measures. Speculative extensions (e.g., primordial gravitational waves) are noted but not included. Testable predictions include a dynamic dark energy equation of state and CMB power spectrum anomalies.

1. Introduction

Physics seeks a unified description of reality. Current theories treat gravity as fundamental (general relativity) or emergent from quantum geometry (string theory, loop quantum gravity). We propose a different path: entropy is the fundamental principle.

The Simple Framework of EDGE asserts:

A theory of everything is a theory of entropy.

Gravity does not curve space-time directly. Instead, entropy gradients in quantum fields induce curvature, producing the effects we observe as gravity. This occurs in a change-driven reality—a universe in constant flux, where quantum fluctuations, particle interactions, and cosmic evolution generate dynamic entropy flows.

The central idea is:

Entropy drives gravity that drives entropy. Gravity is a form of entropy.

This paper presents the minimal, publishable version of EDGE—clean, mathematically transparent, and focused on two entropy types: thermodynamic and holographic. No von Neumann entropy, no quasiparticle Lagrangians, no complex computational schemes. Just the core mechanism and its cosmological implications.

2. The Simple Framework

2.1 Modified Field Equations

We begin with Einstein’s equations and add one new term:

[ \boxed{ R_{\mu\nu} - \frac{1}{2} R g_{\mu\nu} + \Lambda g_{\mu\nu} + S_{\mu\nu} = \frac{8\pi G}{c^4} T_{\mu\nu} } ]

( R_{\mu\nu}, R, g_{\mu\nu} ): standard geometry,
( \Lambda g_{\mu\nu} ): cosmological term (to be reinterpreted),
( T_{\mu\nu} ): matter and energy,
( S_{\mu\nu} ): entropic stress-energy tensor.

2.2 The Entropic Tensor ( S_{\mu\nu} )

We define:

[ \boxed{ S_{\mu\nu} = \alpha (\nabla_\mu S \nabla_\nu S - \frac{1}{2} g_{\mu\nu} (\nabla S)^2) } ]

where:

( S = S_{\text{therm}} + S_{\text{hol}} ): total entropy density,
( \alpha ): coupling constant with units of inverse energy,
( \nabla_\mu S ): entropy gradient four-vector.

This form is inspired by the stress-energy tensor of a perfect fluid but driven by entropy flow, not pressure or velocity.

3. Entropy Components

3.1 Thermodynamic Entropy

[ S_{\text{therm}} = k \ln W ]

( k ): Boltzmann constant,
( W ): number of microstates.

Drives local collapse: gas clouds, stars, galaxies. Higher temperature → higher ( S_{\text{therm}} ) → stronger gradient → stronger pull.

3.2 Holographic Entropy

[ S_{\text{hol}} = \frac{k A}{4 l_p^2} ]

( A ): surface area of a region,
( l_p = \sqrt{\frac{\hbar G}{c^3}} ): Planck length.

Drives cosmic expansion: the universe’s horizon grows → ( S_{\text{hol}} ) increases → outward gradient → repulsion.

4. The Feedback Loop

[ \boxed{ \text{Entropy} \xrightarrow{\text{gradient}} \text{Gravity} \xrightarrow{\text{clustering}} \text{More Entropy} \rightarrow \cdots } ]

Entropy → Gravity:
( \nabla S > 0 ) → ( S_{\mu\nu} ) curves space-time → matter falls in.
Gravity → Entropy:
Collapse increases ( W ) (fusion) or ( A ) (black holes) → ( S ) rises.
Loop Closure:
New ( \nabla S ) reinforces gravity.

Gravity is the macroscopic expression of this loop—a form of entropy in motion.

5. Dark Energy from Holographic Entropy

5.1 The Cosmic Horizon

The affectable universe has a cosmological event horizon with radius ( R_h \approx 16 ) billion light-years.

Area: [ A \approx 4\pi R_h^2 \approx 10^{61} , l_p^2 ]

Entropy: [ S_{\text{hol}} \approx 10^{61} k ]

5.2 Expansion Increases Entropy

As the universe expands: [ \frac{dA}{dt} > 0 \quad \Rightarrow \quad \frac{dS_{\text{hol}}}{dt} > 0 ]

This creates an outward entropy gradient ( \nabla S \parallel \hat{r} ).

5.3 Repulsive Entropic Force

In ( S_{\mu\nu} ), the term ( \nabla_\mu S \nabla_\nu S ) produces negative pressure:

[ p_{\text{entropic}} \propto -(\nabla S)^2 < 0 ]

This accelerates expansion—the observed effect of dark energy.

5.4 Dynamic ( \Lambda )

EDGE predicts:

[ \boxed{ \Lambda_{\text{eff}}(t) = \beta \frac{dS_{\text{hol}}/dt}{V} } ]

( \beta ): constant,
( V ): comoving volume.

Not fixed. Evolves with cosmic growth.

6. Predictions

Observable	EDGE Prediction	Current Data
Dark Energy ( w )	( w = -1 + \epsilon(z) ), small deviation	( w = -1.03 \pm 0.03 ) (Planck)
CMB Low-( \ell ) Power	Suppression from entropy smoothing	Observed anomaly
Hubble Tension	Resolved via ( \Lambda_{\text{eff}}(t) )	( H_0 = 67 ) vs ( 74 ) km/s/Mpc

7. Speculative Note: Primordial Gravitational Waves

Not part of the simple framework.

Primordial GW may carry entropy across the cosmos.
Could amplify ( \nabla S ) on large scales.
May contribute to expansion if entropy coupling is strong.

Left for future work.

8. Conclusion

The Simple Framework of EDGE is:

Minimal: One new term ( S_{\mu\nu} ),
Unified: Gravity and dark energy from the same principle,
Testable: Predicts evolving ( \Lambda ), CMB anomalies,
Philosophical: Gravity is entropy.

We do not fall. We flow toward maximum entropy.

This is the foundation. The complex framework—von Neumann entropy, quasiparticles, simulations—awaits.

Acknowledgments

Developed openly on X (@William54656169) and GitHub (willstar777). Community feedback welcome.

References

Cawley, W. (2024). EDGE Drafts. GitHub: willstar777.

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