Phase 5: Falsifiable Galactic Weak-Field Predictions from Entropic Gravity
Authors/Creators
Description
This dataset and notebook accompany Phase 5 of the Entropic Gravity project. Phase 5 extends the previously developed conserved total entropy S_tot framework to weak-field, linearized relativistic regimes, producing testable predictions for galaxies without invoking full General Relativity or dark matter.
Contents:
Python Notebook (Phase5_Figure1.ipynb)
Computes the entropic acceleration fraction f_ent for different galaxy types: dwarf, Milky Way bulge, and large spiral.
Computes corresponding PPN gamma values:
gamma_PPN = 1 - 0.5 * f_ent (weak-field linearized metric)
Figure 1 (Figure1_gent_fraction_final.png) for inclusion in publications.
Figure 1
Bar chart of f_ent per galaxy
Line overlay of gamma_PPN
Visualizes contribution of entropic gravity to galactic rotation curves.
Methodology
Linearized expansion of the entropic scalar action:
ln(1 - g / a0) ≈ -g / a0 - 0.5 * (g / a0)^2 + higher order terms
First-order entropic acceleration:
g_ent ≈ - (a0 / rho_Q) * gradient(rho_Q)
Weak-field Einstein equations extended with entropic energy-momentum tensor:
box(h_bar_mu_nu) = -16 * pi * G * (T_mu_nu_matter + tau_mu_nu_ent),
with tau_mu_nu_ent ~ rho_Q * g / a0.
Falsifiability and Limits
Linear approximation valid for galactic accelerations g << a0 ≈ 1.2e-10 m/s^2
Predicts weak lensing PPN gamma deviations: gamma ≈ 0.95 for dwarfs
Approximation fails in cluster cores, neutron stars, and black hole horizons, where the full nonlinear entropic action is needed.
Zenodo Contribution
Includes reproducible Python notebook for galaxy calculations
Figure ready for LaTeX/Zenodo inclusion
Demonstrates Phase 5 derivations and testable predictions
Supports open reproducibility of entropic gravity results.
Author and ORCID:
Mat Ward, ORCID: 0009-0007-3500-2240
Keywords:
Entropic gravity, emergent gravity, dark matter alternative, galactic rotation curves, PPN gamma, weak-field limit, linearized GR, holographic entropy, Phase 5
Files
Phase5EntropicGravity.pdf
Files
(192.6 kB)
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Additional details
References
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