On the Ontological Cost of Bianconi’s Paradox and Dualism in Her Theory of Gravity from Entropy — A Conceptual and Philosophical Encounter with the Theory of Entropicity (ToE): A ToE Series

On the Ontological Cost of Bianconi’s Paradox and Dualism in Her Theory of Gravity from Entropy — A Conceptual and Philosophical Encounter with the Theory of Entropicity (ToE): A ToE Series — Introduction

Introduction: Entropy as Measure, Entropy as Field

Entropy has long been the language of disorder, uncertainty, and information. In physics, it has served as a measure — a way of comparing states, quantifying differences, and tracking the arrow of time. Yet in recent years, entropy has begun to be reimagined not merely as a tool but as a possible foundation of reality itself.

Two striking approaches exemplify this turn. Ginestra Bianconi’s Gravity from Entropy (2025) proposes that gravity emerges from the quantum relative entropy between spacetime and matter metrics. John Onimisi Obidi’s Theory of Entropicity (ToE) goes further, arguing that entropy is not a comparison but the field of reality itself.

The encounter between these two visions reveals a paradox and a dualism at the heart of Bianconi’s framework, and a radical ontological inversion in Obidi’s Theory of Entropicity (ToE). The cost of this paradox is philosophical as much as physical.

Bianconi’s Paradox: Dual Metrics, Dual Realities, One Gravity

Bianconi’s formulation begins with two metrics:

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Bianconi’s Metric of Spacetime

the metric of spacetime; and

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Bianconi’s Metric Induced by Matter Fields

the metric induced by matter fields.

The Bianconi Action is therefore expressed as:

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Bianconi Action

This is elegant: gravity is derived from the entropic mismatch between geometry and matter. Yet it introduces a dualism — two metrics, two realities, whose difference defines the action — one gravity.

The paradox is ontological. If gravity arises from the entropy between two metrics, then reality is defined not by a single continuum but by a comparison. Spacetime is not self-sufficient; it is meaningful only in relation to matter-induced geometry — in which case, matter is equally also not self-sufficient: because it requires an extraneous spacetime [metric] for it to possess meaning in [our] experience. Entropy here is a measure of difference, not a substance in itself.

The Ontological Cost

This dualism carries a cost. It implies that reality is fundamentally relational, that spacetime and matter are co‑defined only through their mismatch. But if entropy is only a measure of difference, then it lacks ontological independence. It cannot generate reality; it can only compare realities.

The cost is that entropy remains secondary. It is a tool, not a field. Gravity becomes emergent from comparison, but comparison itself requires two pre‑existing structures. Entropy here is parasitic: it feeds on dualism, but it does not ground being.

ToE’s Encounter: Entropy as Field, the Observer Dethroned

The Theory of Entropicity (ToE) confronts this paradox head‑on. It argues that entropy is not a measure of reality — it is reality.

In the Theory of Entropicity (ToE):

The Spectral Obidi Action (SOA) reframes Araki relative entropy as a dynamical action principle, not a static measure.

The No‑Rush Theorem enforces finite‑rate bounds on entropy redistribution, making causality and relativistic effects physical consequences of entropy.

Length contraction and time dilation are not kinematic artifacts but field‑driven realities, enforced by entropy’s constraints.

Observers are secondary (Observer Dethroned): what they see has already been computed by the entropic field. Relativity itself is emergent.

Where Bianconi compares metrics, ToE generates them. Where Bianconi’s entropy is relational, ToE’s entropy is ontological. The observer is dethroned; reality precedes perception.

Philosophical Implications: From Dualism to Monism

The philosophical encounter between Bianconi and ToE is stark.

Bianconi’s dualism: Reality is defined by the difference between two metrics. Entropy is comparative, parasitic, secondary.

ToE’s monism: Reality is entropy. Metrics, motion, and observation emerge from the entropic field. Entropy is generative, primary, ontological.

The cost of Bianconi’s paradox is that it cannot escape dualism. It cannot explain why spacetime and matter metrics exist to be compared. ToE avoids this cost by collapsing dualism into monism: there is only entropy, and everything else is emergent.

Relativity Reconsidered

This encounter reframes relativity itself. In Einstein’s theory, length contraction and time dilation are kinematic effects, perspectival artifacts of observer frames. In Bianconi’s entropy, they remain comparative, defined by mismatches. In ToE, they become physical, enforced by entropy’s finite‑rate dynamics.

Relativity is dethroned. It is no longer fundamental but emergent. The observer is no longer central but constrained. Reality is not shaped by perception but by entropy.

Conclusion: The Ontological Revolution of ToE

The paradox of Bianconi’s dualism is profound. It shows the power of entropy as a comparative tool but reveals its ontological weakness. Entropy as difference cannot ground reality.

The Theory of Entropicity offers a way out. By treating entropy as the field itself, it collapses dualism into monism, dethrones the observer, and reframes relativity as emergent. The cost of Bianconi’s paradox is paid in ontological dependence. The originality of ToE is its refusal to pay that cost.

In this encounter, entropy ceases to be a measure. It becomes the fabric of reality. And that is the philosophical revolution at stake.