The Obidi Transformation and the Obidi Metric in Modern Theoretical Physics from Innovations of the Theory of Entropicity (ToE)

In theoretical physics, the Obidi metric and Obidi transformation are central mathematical components of the Theory of Entropicity (ToE), an emerging framework proposed by researcher John Onimisi Obidi. The theory posits that entropy is not just a secondary measurement of thermodynamic disorder, but rather the fundamental, continuous physical field ($S(x)$) from which spacetime, gravity, and physical matter emerge. [1, 2, 3, 4, 5]

Here is how the metric and the transformation function within this framework:

The Obidi Metric (Entropic Metric)

In standard information geometry, statistical manifolds use frameworks like the Fisher–Rao metric to measure the "distance" or distinguishability between different probability states. [6, 7]

The Obidi metric modifies this purely mathematical concept into a physical, dynamic geometry: [8]

• Deformation by Entropy: Under the governing principle of the theory (the Obidi Action), the abstract Fisher–Rao metric undergoes an entropy-dependent deformation—traditionally scaled by an exponential factor like $e^{S/k_B}$. [8, 9]
• Physical Curvature: This mathematical scaling transforms abstract statistical data into a dynamic "metric-affine geometry". In this geometry, distances and curves are defined strictly by how entropy gradients are distributed. [1, 8, 10, 11]

The Obidi Transformation

The Obidi transformation refers to the overarching mechanism and variational process that translates this deeper, informational substrate into the physical universe we experience. [6, 7]

It relies on a few core mathematical steps:

• The Obidi Action Principle: A central variational principle that drives and optimizes the flow of the entropic field across a manifold. [7]
• The Curvature Transfer Theorem (CTT): This theorem mathematically proves that the physical Riemann curvature tensor of spacetime ($R_S$) is a thermodynamic projection (or pushforward) of the deeper informational Riemann tensor ($R_I$). [12, 13]
• Spacetime Coarse-Graining: Through macroscopic coarse-graining, the multidimensional entropic metric ($g_{IJ}^{\text{entropic}}$) is projected down to manifest as our traditional 4D spacetime metric ($g_{\mu\nu}$). [9]

The Core Result

Through this metric and transformation, Einstein's field equations of General Relativity are recovered as an emergent thermodynamic identity rather than an fundamental axiom of nature. Gravity is stripped of its status as a primary force and is instead reinterpreted as a macro-level "shadow" cast by underlying entropic gradients rearranging themselves. [9, 12, 13]

If you are trying to parse the mathematics behind this theory, let us know:

• Do you want to look closer at the Master Entropic Equation (MEE)?
• Are you interested in the Obidi Curvature Invariant (OCI) and the role of $\ln 2$?
• Do you need a breakdown of how it attempts to bridge quantum mechanics and general relativity? [2, 14, 15, 16, 17]

 

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The Obidi metric and Obidi transformation are core mathematical and conceptual constructs within the Theory of Entropicity (ToE), a theoretical framework developed by John Onimisi Obidi. The theory proposes that entropy is not merely a derived measure of disorder, but rather the fundamental dynamic field of the universe from which all physical reality (space, time, matter, and gravity) emerges. [1, 2, 3, 4, 5]

 

1. The Obidi Transformation (Information Geometry to Spacetime)

In traditional mathematics and statistics, information geometry provides ways to measure how distinguishable probability distributions are from one another (using concepts like the Fisher–Rao metric). [1]

The Obidi transformation refers to the mathematical and ontological shift where these abstract, statistical information-geometric manifolds are deformed and translated into physical spacetime. [1]

• Instead of particles moving on a pre-existing spacetime grid, the Obidi transformation derives physical reality directly from informational distinguishability. [1]
• Information about different states of the entropic field (\(S(x)\)) translates into geometric curvature. [1]
• Using principles like the Curvature Transfer Theorem, the theory dictates that physical spacetime metrics (like those in Einstein's General Relativity) are the macroscopic projections of underlying information geometry. [1, 2]

 

2. The Obidi Metric

In this framework, distances are not computed based on spatial coordinates or mass-energy, but rather on the information-geometric metric of the entropy field. [1, 2]

• The Obidi metric relies on combining classical and quantum metrics (such as the Fisher-Rao metric for classical systems and the Fubini-Study metric for quantum states) into a single "Hybrid Metric-Affine Space". [1]
• This metric allows physicists to mathematically measure the distance, or "distinguishability," between two different configurations of the universe's entropic field. [1, 2]

 

Core Concepts Related to these Transformations

• The Obidi Action: A universal variational principle that drives the evolution and flow of the entropic field. Minimizing this action yields equations that mirror Einstein's field equations of relativity, but on an informational basis. [1, 2, 3]
• The Obidi Curvature Invariant (OCI): A theoretical foundation within the metric proposing that the smallest stable distinction between two entropic configurations is equivalent to a curvature ratio of 2:1, which mathematically corresponds to \(\ln(2)\). [1]

(Note: The Theory of Entropicity and its accompanying mathematics represent a highly theoretical framework in modern physics that seeks to approach quantum gravity through informational principles). [1]

If you are interested in exploring this further, we can:

• Detail how the Obidi Equivalence Principle works
• Explain how the Master Entropic Equation is derived [1, 2]

Let us know if you would like to narrow down the focus.

 

 

 

🌌 On the Cross‑Domain Mathematical and Conceptual Complexity of the Theory of Entropicity (ToE): Foundations of a New Physics for the 21st Century (Scholium)

The Theory of Entropicity (ToE)—first formulated and developed by John Onimisi Obidi in early 2025—begins from a bold and transformative insight:

Entropy is not disorder. Entropy is the fundamental measure of distinguishability between physical states.

In this view, the universe is not fundamentally built from particles, fields, or even spacetime. Instead, it is built from entropic information—the deep structural content that allows one physical state to be told apart from another. Everything else we observe—geometry, matter, energy, motion—emerges from the structure and flow of this entropic information.

🧭 Rethinking the Foundations of Physics

From “Information as Data” to “Information as a Physical Field”

The mathematics of ToE is challenging not because of its symbols, but because it forces us to reinterpret what those symbols represent. In ToE, information is not something stored in computers or transmitted in messages. It is a physical field that:

• lives on a manifold,

• interacts with itself,

• shapes geometry,

• and drives the evolution of the universe.

This shift begins with information geometry, pioneered by Fisher, Rao, Čencov, and Amari. In this framework, the “distance” between two probability distributions is measured not in meters or seconds, but in how distinguishable they are.

Two distributions that are easy to tell apart are “far apart.” Two that are nearly identical are “close.”

This distance is encoded in the information metric, which becomes the seed of spacetime in ToE.

Explore more: Information Geometry

⏳ The Entropy Field and the Arrow of Time

How ToE Introduces Causality into Information Geometry

Traditional information geometry is timeless—it has no causal structure, no light cones, no past or future. ToE introduces a new ingredient: the entropy field, defined at every point of spacetime.

Its gradient—the direction in which entropy increases most rapidly—creates a natural arrow of time.

Using this gradient, ToE performs the Lorentzian Lift (via the Obidi Transformation), converting the timeless geometry of information into the time‑oriented geometry of spacetime.

This is the moment where information becomes gravity.

Learn more: Lorentzian Lift

🌐 When Information Becomes Matter

The Deepest Innovation: The Stress–Energy Tensor from Information Flow

Einstein’s theory requires not only geometry but also a source of curvature: the stress–energy tensor, which encodes mass, pressure, radiation, momentum, and stress.

ToE shows that these physical quantities arise from the flow of information.

Information is represented as a distribution on the cotangent bundle—a mathematical space pairing each point in spacetime with every possible momentum at that point. In ordinary physics, this is the home of particles and radiation. In ToE, it becomes the home of information itself.

Once information is represented this way, the universal mathematics of kinetic theory takes over. The second moment of the information distribution produces a symmetric tensor with exactly the structure of the stress–energy tensor.

This is not metaphor. It is a mathematical identity.

Explore: Information Distribution

🧩 A Unified Entropic Framework

How the Pieces Fit Together

The elegance of ToE lies in how its components interlock:

• The entropy field shapes the geometry of the information manifold.

• This manifold becomes spacetime through the Lorentzian lift.

• The flow of information through this geometry produces the stress–energy tensor.

• The curvature of spacetime responds to this tensor through Einstein’s equations.

• The entropy field evolves according to the Obidi Action, unifying geometric, kinetic, and constraint sectors.

The complexity of ToE arises not from equations, but from the interdependence of its structures:

Information geometry shapes spacetime geometry. Spacetime geometry shapes information flow. Information flow shapes the stress–energy tensor. The stress–energy tensor shapes curvature. Curvature shapes the entropy field. The entropy field shapes information geometry.

This closed loop is the hallmark of a self‑consistent entropic universe.

🔭 A New Ontology for Physics

From Particles and Fields to Entropy and Information

ToE is not merely a new theory. It is a new way of thinking about what physics is made of.

It replaces the ontology of particles and fields with an ontology of entropy and information. It replaces the geometry of spacetime with the geometry of distinguishability. It replaces the traditional division between matter and geometry with a unified entropic structure from which both emerge.

This is the conceptual heart of the Theory of Entropicity:

The universe is the geometry of entropic information, and gravity is the curvature of that geometry.

Learn more: ToE Overview Obidi Transformation Information Gravity

📚 References & Canonical Sources

1. https://doi.org/10.13140/RG.2.2.14211.26405

2. https://doi.org/10.17605/OSF.IO/PT9U8

3. https://entropicity.github.io/Theory-of-Entropicity-ToE/docs/ToE-Living-Review-Letters-Series-Letter-III-From-Information-Geometry-to-Information-Gravity-Origin-of-Einstein's-Gravity-in-ToE_U1.pdf

4. Canonical Archive: https://entropicity.github.io/Theory-of-Entropicity-ToE/

On the Cross-Domain Mathematical and Conceptual Complexity of the Theory of Entropicity (ToE): Foundations of a New Physics for the 21st Century 

The Theory of Entropicity (ToE), first formulated and further developed by John Onimisi Obidi in early 2025, begins from a simple but radical premise: 

That the most fundamental ingredient of physical reality is entropy, understood not as disorder or randomness, but as the deep measure of distinguishability between physical states. 

In this view, the universe is not built from particles, fields, or spacetime itself, but from the entropic information that allows one state of the world to be told apart from another. Everything else—geometry, matter, energy, motion—emerges from the structure and flow of this entropic information [and the associated gradients].To make such a claim scientifically meaningful, ToE must translate the abstract idea of “entropic information” into a precise mathematical object capable of generating the familiar structures of physics. This is where the theory becomes subtle and conceptually rich. 

The mathematics [and concepts] of the Theory of Entropicity (ToE) is not difficult because it is filled with symbols; it is difficult because it asks us to rethink what the symbols mean. It asks us to see information not as something stored in computers or communicated in messages, but as a physical field that lives on a manifold, interacts with itself, and shapes the geometry of the universe. The first step in this translation is the recognition that information, itself constructed from entropy, has a geometry. This is the insight of information geometry, a field pioneered by Fisher, Rao, Čencov, and Amari. In information geometry, the “distance” between two probability distributions is not measured in meters or seconds, but in how distinguishable they are. 

Two distributions that are easy to tell apart are “far apart”; two that are nearly identical are “close.” This distance is encoded in a geometric object called the information metric, which measures how sensitive a distribution is to changes in its parameters. In the Theory of Entropicity (ToE), Obidi employs this metric to become the seed of spacetime itself. But information geometry is originally Riemannian—it has no notion of time, no causal structure, no light cones, no distinction between past and future. ToE introduces a new ingredient: the entropy field, a scalar field defined at every point of spacetime. The gradient of this field—the direction in which entropy increases most rapidly—provides a natural arrow of time. 

By using this gradient to deform the information metric, Obidi is able to construct ToE to perform what is known as the Lorentzian lift (via what is known as the Obidi Transformation): a transformation that converts the timeless geometry of information into the time‑oriented geometry of spacetime. This is the moment where information becomes gravity, because the curvature of this Lorentzian geometry is what we recognize as gravitational curvature.Yet geometry is only half of Einstein’s theory of General Relativity (GR). The other half is the stress–energy tensor (SET), the object that encodes mass, pressure, radiation, momentum, and stress. ToE must show not only how information curves spacetime, but also how information becomes the source of that curvature. 

This is where Obidi's theory reaches its deepest conceptual innovation in modern theoretical physics. In physics, the stress–energy tensor always arises from the flow of momentum. Whether we are describing a gas, a beam of light, a fluid, or a scalar field, the structure is the same: the energy density, pressure, and stresses are all determined by how momentum is distributed and how it moves. The Theory of Entropicity (ToE) adopts this universal structure, but with a twist: instead of describing particles or radiation, it describes the flow of information.To do this, ToE represents information as a distribution on the cotangent bundle of spacetime. The cotangent bundle is a mathematical space that pairs every point in spacetime with every possible momentum at that point. In ordinary physics, this is the natural home of particles and radiation. In the Theory of Entropicity (ToE), Obidi reconstructs it to become the natural home of information. 

The information distribution tells us how much information is present at each point, and how it is moving—its direction, intensity, and flow. Once information is represented this way, the rest follows from the universal mathematics of kinetic theory. The second moment of the distribution—the average of the product of momentum with itself—produces a symmetric tensor with exactly the structure of the stress–energy tensor. This is not an analogy or a metaphor; it is a mathematical identity. The components of this tensor correspond to energy density, pressure, momentum flux, and shear stress because that is what the second moment of any momentum distribution must represent. In this way, information becomes mass, pressure, radiation, and stress not by assumption, but by the intrinsic geometry of momentum space.

The elegance of Obidi's Theory of Entropicity (ToE) lies in how these jigsaw pieces all fit together. The entropy field shapes the geometry of the information manifold, which becomes spacetime through the Lorentzian lift. The flow of information through this geometry produces the stress–energy tensor through the second moment of its distribution. The curvature of spacetime responds to this tensor through the Einstein equations. And the entropy field itself evolves according to the dynamics encoded in the Obidi Action of the Theory of Entropicity (ToE), which unifies the geometric, kinetic, and constraint sectors into a single entropic framework.

What makes the mathematics of ToE complex is not the presence of equations, but the interdependence of its structures: 

Information geometry shapes spacetime geometry; spacetime geometry shapes information flow; information flow shapes the stress–energy tensor; the stress–energy tensor shapes curvature; curvature shapes the entropy field; and the entropy field shapes information geometry. 

Thus, Obidi shows that Lorentzian spacetime geometry emerges from information geometry via a controlled entropy‑gradient disformal transformation, and that the curvature of this emergent metric reproduces the Einstein gravity of General Relativity (GR).

The theory is thus a closed loop, a self‑consistent system in which entropic information and geometry continually generate and constrain one another. The Theory of Entropicity (ToE) is therefore not a theory about information; it is a theory of information emergent from entropy itself. It does not treat information as a property of matter, but as the substrate from which matter and geometry emerge. It does not treat entropy as a measure of ignorance, but as the fundamental field that gives rise to that information [and its distribution] componented [projected] into time, causality, and gravitational dynamics. It does not treat spacetime as a stage on which physics happens, but as a projection of a deeper entropic informational manifold.

This is why the mathematics of ToE feels both familiar and foreign. It uses the tools of differential geometry, kinetic theory, and statistical mechanics, but it uses them in a radically new way, with new meanings and new connections. Obidi asks us to see information not as something abstract, but as something physical—something that moves, flows, curves, and interacts. Something that can be measured, integrated, and transformed. Something that can become mass, pressure, radiation, and gravity.

In this sense, Obidi's Theory of Entropicity (ToE) is not merely a new theory; it is a new way of thinking about what physics is made of. It replaces the ontology of particles and fields with an ontology of entropy and information. It replaces the geometry of spacetime with the geometry of distinguishability. And it replaces the traditional division between matter and geometry with a unified entropic structure from which both emerge.This is the conceptual heart of the Theory of Entropicity (ToE): the universe is the geometry of entropic information, and gravity is the curvature of that geometry.

References

1) https://doi.org/10.13140/RG.2.2.14211.26405

2) https://doi.org/10.17605/OSF.IO/PT9U8

3) https://entropicity.github.io/Theory-of-Entropicity-ToE/docs/ToE-Living-Review-Letters-Series-Letter-III-From-Information-Geometry-to-Information-Gravity-Origin-of-Einstein's-Gravity-in-ToE_U1.pdf

4) Canonical Archive: https://entropicity.github.io/Theory-of-Entropicity-ToE/

On the Broad Span and Multiple Domain Complexity of the Theory of Entropicity (ToE)

 

The Theory of Entropicity (ToE) is highly complex, both mathematically and conceptually. Proposed by researcher John Onimisi Obidi, it is a radical framework in theoretical physics that elevates entropy from a mere statistical measure of disorder into the primary, fundamental field of the universe. [1, 2, 3, 4, 5]

The complexity of the theory spans across multiple layers:

🧠 Mathematical Complexity

• Nonlinear and Nonlocal Equations: The theory relies on the Master Entropic Equation (MEE), which acts as its core field equation. Unlike standard linear physics formulas, it must be solved through highly intensive iterative computations. [6, 7, 8]
• The Obidi Action: ToE uses a complicated variational principle known as the Obidi Action to dictate the dynamics of the universal entropic field. [9, 10]
• Information Geometry: It heavily merges advanced information theory, thermodynamics, and differential geometry to model how the universe "computes" its own existence. [7, 8]

🌌 Conceptual Complexity

• Emergent Spacetime: In ToE, space, time, and gravity are not fundamental constants. They are emergent properties that materialize from the flow and curvature of the underlying entropic field. [10, 11]
• Redefining the Speed of Light ($c$): Rather than accepting $c$ as an arbitrary postulate, ToE argues that the speed of light is the maximum possible rate of entropic rearrangement and information distribution in the universe. [12]
• Grand Unification Intent: The theory is inherently complex because it attempts to unify fields of physics that are traditionally deeply incompatible: general relativity, quantum mechanics, and thermodynamics. [13]

⚖️ Current Scientific Status

Because it is an emerging, radical framework, ToE is still being mathematically refined and stress-tested by the wider theoretical physics community. It is currently undergoing rigorous and vigorous research to build it into an established mainstream scientific theory. [14, 15, 16]

Would you like to explore the mathematical equations behind the Obidi Action, or should we look at how the theory attempts to explain quantum mechanics and gravity? [10, 11]

 

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The Theory of Entropicity (ToE) is considered highly complex. Originated by John Onimisi Obidi in 2025, it is an audacious theoretical framework that attempts to unify thermodynamics, relativity, and quantum mechanics by positioning entropy as the fundamental field underlying reality. [1, 2]

The mathematical and conceptual architecture is complex for a few key reasons:

• Information & Iteration: Instead of using classical differential calculus to map space and time, ToE's field equations—like the Master Entropic Equation (MEE)—are nonlinear, nonlocal, and iterative. The framework models the universe as a self-correcting computation where geometry and space continuously evolve through entropic feedback. [1, 2]
• Vast Scope: Rather than tackling one isolated problem, ToE attempts to simultaneously derive the speed of light, quantum coherence, and spacetime curvature as direct consequences of entropic dynamics. [1, 2]
• Post-Einsteinian Physics: It frames the famous Einstein field equations as merely a low-entropy macroscopic approximation, replacing them with entirely new mathematical constructs rooted in the "Obidi Action". [1, 2]

Because it is an emerging framework, its mathematical and empirical validation is actively being stress-tested by the scientific community. [1, 2]

If you are interested in exploring this topic further, we can:

• Provide a breakdown of the Master Entropic Equation in simpler terms.
• Explain how ToE interprets the speed of light.
• Compare it to traditional entropic gravity models. [1, 2, 3]

Let us know which of these you'd like to dive into next.

 

 

 

From Information Geometry to Information Gravity,  
Information Geometry as the Origin of Einstein’s Gravity:  
Correspondence of the Obidi Action and the Einstein–Hilbert Action in the Theory of Entropicity (ToE), Theory of Entropicity (ToE) Living Review Letters Series (ToE LRLS) — Letter III

Obidi shows that Lorentzian spacetime geometry emerges from information geometry via a controlled entropy‑gradient disformal transformation, and that the curvature of this emergent metric reproduces the Einstein gravity of General Relativity (GR).

From Information Geometry to Information Gravity: Information Geometry as the Origin of Einstein's Gravity in General Relativity (GR)

https://doi.org/10.13140/RG.2.2.14211.26405

https://doi.org/10.17605/OSF.IO/PT9U8

── ⬡ ──  

John Onimisi Obidi  

Research Lab, The Aether  

Email: jonimisiobidi@gmail.com  

Canonical Archive: https://entropicity.github.io/Theory-of-Entropicity-ToE/  

May 31, 2026  

── ⬡ ──

Keywords:

Theory of Entropicity (ToE); Obidi Action; Obidi Transformation; Obidi Metric; Obidi Relativistic Reduction Theorem; Einstein–Hilbert Action; Information Gravity; Information Geometry; Fisher–Rao metric; Fubini–Study metric; Bures metric; Amari–Čencov α-connections; Rényi–Tsallis entropy; Master Entropic Equation; Vuli–Ndlela Integral; Emergent Gravity; Entropic Field; General Relativity; Levi–Civita connection; Hybrid Metric-Affine Space (HMAS); Entropic Cosmological Constant.

John Onimisi Obidi’s framework, titled "From Information Geometry to Information Gravity," outlines the core mathematical and philosophical foundation of his Theory of Entropicity (ToE). The core thesis is that physical spacetime, gravity, and matter are not fundamental, but rather emergent macroscopic properties generated by a deeper, underlying statistical manifold governed by information geometry. [1, 2, 3, 4, 5]

Instead of viewing information geometry as a mere mathematical tool for data analysis, Obidi introduces an ontological shift that treats statistical distinguishability as the primary engine of reality. [3, 6]

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🧠 The Ontological Shift: Distinguishability to Distance [6]

In classical information geometry, metrics like the Fisher–Rao metric (for classical systems) and the Fubini–Study metric (for quantum states) are used to measure the statistical "distinguishability" between probability distributions. Obidi maps these abstract properties directly onto physical reality: [3, 6, 7]

• The Entropic Field $S(x)$: Entropy is redefined as a fundamental, continuous scalar field whose gradients and dynamics generate all physical phenomena. [3]
• Distance from Distinguishability: Physical distance in spacetime is a macro-projection of how distinguishable two underlying informational states are. [4, 6]
• The Arrow of Time: By isolating the Amari–Čencov $\alpha$-connections (specifically where $\alpha=0$), the theory derives a naturally time-asymmetric, irreversible flow that defines the classical Levi-Civita connection used in General Relativity. [3, 8, 9]

📐 The Obidi Action Principle

To bridge abstract mathematical information and dynamic physical force, the framework introduces the Obidi Action (featuring both Local and Spectral variations). [10, 11]

• The Variational Principle: Minimizing or stationarizing the Obidi Action describes the continuous, irreversible rearrangement of underlying informational degrees of freedom. [6, 8]
• Haller–Obidi Correspondence (HOC): This correspondence establishes an identity between thermodynamic entropy and classical action ($H \propto \int L \, dt$). Under this rule, the Principle of Least Action becomes a principle of extremal entropy—meaning physical trajectories naturally maximize or extremize entropic flow. [1, 12]

🌌 Information Gravity: Emergent Spacetime

Under the Obidi Equivalence Principle (OEP), spacetime geometry is an isomorphic, coarse-grained projection of the underlying information-geometric manifold. Gravity is stripped of its status as a fundamental attractive force: [4, 12]

1. Entropic Gradients: Gravity emerges naturally from the tendency of the entropic field to redistribute itself. [12]
2. Curvature Generation: The curvature coupling term within the Obidi Action ensures that variations and gradients in entropy generate physical spacetime curvature ($R$). [12]
3. General Relativity as a Limit: When the entropic field is perfectly uniform, the field equations reduce exactly to the standard Einstein–Hilbert action of General Relativity. When $S(x)$ varies, it introduces non-linear corrections that offer testable deviations from classical gravity (e.g., modified gravitational lensing). [12, 13]

🧪 Physical & Quantum Consequences

Rather than relying on holographic boundaries or virtual particles, ToE attempts a top-down unification that impacts several physics anomalies: [11, 14]

• Entropic Speed Limit (ESL): The cosmic speed of light ($c$) is reinterpreted as the maximum allowable rate for entropic redistribution.
• The No-Rush Theorem: This places a universal bound on quantum reconfigurations, successfully predicting a finite, non-zero duration for the formation of quantum entanglement ($\approx 232$ attoseconds).
• Universal Constants: The framework bridges the quantum, thermodynamic, and geometric worlds through a core constraint equation: $\hbar c = k_B T_S \ell_S$. [12, 14, 15]

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Would you like to take a deeper look at the mathematical structure of the Obidi Action, explore its specific non-linear corrections to General Relativity, or compare how it differs from Erik Verlinde’s Entropic Gravity?

 

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John Onimisi Obidi’s Theory of Entropicity (ToE) redefines gravity. Moving from Information Geometry (the geometry of statistical distinguishability) to Information Gravity, Obidi argues that entropy and information form the foundation of physical reality. In this framework, spacetime and gravity are not fundamental; rather, gravity emerges naturally from the gradients of an informational/entropic manifold. [1, 2, 3, 4]

 

1. Information Geometry as the Substrate

In conventional statistics, information geometry measures how distinguishable two probability distributions are, using tools like the Fisher–Rao metric. Obidi makes an ontological shift: he asserts that this abstract statistical manifold is the underlying, actual substrate of physical reality before spacetime emerges. [1, 2, 3]

 

2. The Obidi Action and Emergent Spacetime

At the core of the theory lies the Obidi Action, a foundational variational principle. Through a process of coarse-graining, the fundamental information geometry (which contains the Fisher–Rao metric and the Fubini–Study metric for quantum states) undergoes an informational phase transition. This projection forms the macroscopic four-dimensional spacetime we observe, with the Einstein-Hilbert action arising as a natural consequence of this entropic rearrangement. [1, 2, 3, 4, 5]

 

3. Gravity as an Entropic Gradient

Instead of the classical understanding—where matter curves spacetime—the Theory of Entropicity proposes that entropy curves existence. Key mechanics include: [1]

• The Obidi Equivalence Principle (OEP): Spacetime curvature and geodesics are directly isomorphic to the curvature and geodesics of the underlying information-geometric manifold. [1]
• Information Gravity: Gravity is not a pulling force, but rather the macro-projection of entropic gradients. Mass is interpreted as an information-curvature density. [1]
• No-Rush Theorem & Arrow of Time: The theory relies on the \(\alpha \)-connections (representing irreversibility), placing a finite time constraint on entropic reconfiguration, which naturally dictates the arrow of time and quantum entanglement limits. [1, 2]

You can read more about the mathematical and philosophical frameworks directly on the Medium Publication by Obidi or via the Authorea Pre-Print.

If you want to dive deeper into this, let us know:

• Would you like to compare Obidi’s Information Gravity to older frameworks like Erik Verlinde's Entropic Gravity?
• Are you interested in the mathematical formulation of the Obidi Action or how it accounts for dark matter? [1, 2]