05-07-2026, 09:00 PM
(This post was last modified: 05-07-2026, 10:12 PM by Buzzie mcnugget.)
I've had to update it after math gave me some disapproving maths....
# THE RELATIONAL INFORMATION MODEL OF GRAVITY (RIMG)
**Emergent Spacetime via Fisher Information on a Statistical Manifold**
**Abstract**
We propose a relational framework where spacetime geometry is not a fundamental background but an emergent property of quantum informational distinguishability. By identifying the spacetime metric g_{\mu\nu} with the Fisher information metric associated with quantum probability amplitudes, we show that gravitational curvature arises naturally from informational gradients. We derive the Schwarzschild geometry and a Lorentzian signature from the extremization of informational entropy and state update rates, respectively. The resulting model provides a unitary, singularity-regularized description of gravity that remains consistent with the Standard Model.
### I. INTRODUCTION
The search for a consistent theory of quantum gravity often assumes a pre-existing manifold upon which fields evolve. In this work, we reverse this priority, treating the statistical properties of quantum states as the primary ontology. We define the Relational Information Model of Gravity (RIMG), which constructs spacetime geometry as a representation of the distinguishability between local quantum states. Within this framework, "mass" is understood as a concentration of informational density, and "gravity" is the resulting refraction of probability flows through these high-density regions.
### II. FOUNDATIONAL POSTULATES
**Postulate I.** The physical vacuum is fundamentally described by a set of quantum probability amplitudes \Psi(x). Spacetime coordinates x^\mu serve as parameters for a statistical manifold of these states.
**Postulate II.** The spacetime metric g_{\mu\nu} is defined as the pullback of the Fisher Information Metric (FIM) onto the parameter space. For a probability density p(x|\theta), the metric coefficients are:
where p(x|\theta) = |\Psi(x;\theta)|^2.
**Postulate III.** Geometric stability and localization emerge from decoherence. The interaction between quantum systems localizes probability spreads ("mutual pinning"), generating the informational gradients perceived as gravitational curvature.
### III. MATHEMATICAL DERIVATIONS
**A. Emergence of Schwarzschild Geometry**
In a spherically symmetric vacuum, we define a radial probability spread \sigma®. The radial metric component is g_{rr} = 1/\sigma^2®. By extremizing the total Fisher information functional I[\sigma] subject to a mass-energy constraint, we employ the variational principle:
Solving the associated Euler-Lagrange equations under the boundary condition \sigma® \to r as r \to \infty yields the stabilization:
Substituting this into g_{rr} recovers the standard Schwarzschild metric:
**B. Lorentzian Signature from Update Rates**
A signature of (- + + +) is required for a metric to represent spacetime. In RIMG, time t is the parameter governing the divergence rate of information states. Utilizing the De Bruijn Identity, we link the Shannon entropy flux \frac{dH}{dt} to the Fisher Information I:
The temporal dimension emerges as a measure of information divergence (Kullback-Leibler divergence). Within a symplectic phase-space structure, this divergence naturally yields a negative eigenvalue relative to the spatial Fisher densities, establishing the Lorentzian manifold.
### IV. INFORMATIONAL REGULARIZATION AND \alpha
To address the r \to 0 singularity, we introduce a Planck-scale regulator \epsilon. The Fisher scalar density is regularized as:
This prevents the information density from diverging, suggesting a maximum saturation state at the Planck scale.
Furthermore, we identify the fine-structure constant (\alpha \approx 1/137) as a dimensionless ratio of the informational surface tension of the vacuum. In this 3+1 dimensional statistical manifold, \alpha represents the geometric scaling required for stable informational flow, preventing spontaneous field collapse.
### V. EMPIRICAL PREDICTIONS
RIMG offers several distinct avenues for experimental verification:
1. **Coherence-Dependent Gravity:** Macroscopic quantum coherent states, such as Bose-Einstein Condensates, should exhibit a measurable deviation \delta g in their local gravitational field compared to decohered matter of equal mass, as their Fisher gradients differ fundamentally.
2. **Entropic Lensing:** High-order corrections to gravitational lensing should be observable near high-energy sources, proportional to the local informational update rate (entropy flux).
### VI. CONCLUSION
RIMG provides a unitary, information-geometric framework that suggests gravity is a derivative, not a fundamental, force. By grounding geometry in the distinguishability of quantum states, it resolves the singularity problem and provides a natural bridge between the Standard Model and General Relativity. Future work will focus on the cosmological implications of informational saturation in the early universe.
# THE RELATIONAL INFORMATION MODEL OF GRAVITY (RIMG)
**Emergent Spacetime via Fisher Information on a Statistical Manifold**
**Abstract**
We propose a relational framework where spacetime geometry is not a fundamental background but an emergent property of quantum informational distinguishability. By identifying the spacetime metric g_{\mu\nu} with the Fisher information metric associated with quantum probability amplitudes, we show that gravitational curvature arises naturally from informational gradients. We derive the Schwarzschild geometry and a Lorentzian signature from the extremization of informational entropy and state update rates, respectively. The resulting model provides a unitary, singularity-regularized description of gravity that remains consistent with the Standard Model.
### I. INTRODUCTION
The search for a consistent theory of quantum gravity often assumes a pre-existing manifold upon which fields evolve. In this work, we reverse this priority, treating the statistical properties of quantum states as the primary ontology. We define the Relational Information Model of Gravity (RIMG), which constructs spacetime geometry as a representation of the distinguishability between local quantum states. Within this framework, "mass" is understood as a concentration of informational density, and "gravity" is the resulting refraction of probability flows through these high-density regions.
### II. FOUNDATIONAL POSTULATES
**Postulate I.** The physical vacuum is fundamentally described by a set of quantum probability amplitudes \Psi(x). Spacetime coordinates x^\mu serve as parameters for a statistical manifold of these states.
**Postulate II.** The spacetime metric g_{\mu\nu} is defined as the pullback of the Fisher Information Metric (FIM) onto the parameter space. For a probability density p(x|\theta), the metric coefficients are:
where p(x|\theta) = |\Psi(x;\theta)|^2.
**Postulate III.** Geometric stability and localization emerge from decoherence. The interaction between quantum systems localizes probability spreads ("mutual pinning"), generating the informational gradients perceived as gravitational curvature.
### III. MATHEMATICAL DERIVATIONS
**A. Emergence of Schwarzschild Geometry**
In a spherically symmetric vacuum, we define a radial probability spread \sigma®. The radial metric component is g_{rr} = 1/\sigma^2®. By extremizing the total Fisher information functional I[\sigma] subject to a mass-energy constraint, we employ the variational principle:
Solving the associated Euler-Lagrange equations under the boundary condition \sigma® \to r as r \to \infty yields the stabilization:
Substituting this into g_{rr} recovers the standard Schwarzschild metric:
**B. Lorentzian Signature from Update Rates**
A signature of (- + + +) is required for a metric to represent spacetime. In RIMG, time t is the parameter governing the divergence rate of information states. Utilizing the De Bruijn Identity, we link the Shannon entropy flux \frac{dH}{dt} to the Fisher Information I:
The temporal dimension emerges as a measure of information divergence (Kullback-Leibler divergence). Within a symplectic phase-space structure, this divergence naturally yields a negative eigenvalue relative to the spatial Fisher densities, establishing the Lorentzian manifold.
### IV. INFORMATIONAL REGULARIZATION AND \alpha
To address the r \to 0 singularity, we introduce a Planck-scale regulator \epsilon. The Fisher scalar density is regularized as:
This prevents the information density from diverging, suggesting a maximum saturation state at the Planck scale.
Furthermore, we identify the fine-structure constant (\alpha \approx 1/137) as a dimensionless ratio of the informational surface tension of the vacuum. In this 3+1 dimensional statistical manifold, \alpha represents the geometric scaling required for stable informational flow, preventing spontaneous field collapse.
### V. EMPIRICAL PREDICTIONS
RIMG offers several distinct avenues for experimental verification:
1. **Coherence-Dependent Gravity:** Macroscopic quantum coherent states, such as Bose-Einstein Condensates, should exhibit a measurable deviation \delta g in their local gravitational field compared to decohered matter of equal mass, as their Fisher gradients differ fundamentally.
2. **Entropic Lensing:** High-order corrections to gravitational lensing should be observable near high-energy sources, proportional to the local informational update rate (entropy flux).
### VI. CONCLUSION
RIMG provides a unitary, information-geometric framework that suggests gravity is a derivative, not a fundamental, force. By grounding geometry in the distinguishability of quantum states, it resolves the singularity problem and provides a natural bridge between the Standard Model and General Relativity. Future work will focus on the cosmological implications of informational saturation in the early universe.