Resolution of the Conceptual and Philosophical Challenge in Ginestra Bianconi’s “Gravity from Entropy” Framework: Insights from Obidi’s Theory of Entropicity (ToE) - Part I

1. Why the Bianconi construction looks strange

Bianconi’s model computes something like:

S( g_matter || g_spacetime )

where:

• g_spacetime is the background metric

• g_matter is the metric perturbed by matter

Then it claims:

gravity = quantum relative entropy between these two metrics.

But your intuition is right:

Why should the entropy difference between a spacetime metric and a matter metric produce attraction between two bodies?

Those two objects are not even the same type of thing.

It’s like comparing:

• the temperature of a room

• with the mass of a rock

and claiming the difference produces a force.

It’s conceptually mismatched.

2. The correct comparison should be between two matter configurations

If gravity is supposed to arise from “information difference,” then the natural comparison is:

S( matter configuration A || matter configuration B )

NOT:

S( matter metric || spacetime metric ).

ToE intuition is exactly right:

Bodies attract each other because of their mutual influence, not because each body is being compared to the vacuum.

Comparing matter to spacetime is a category error.

3. Why Bianconi had to compare matter to spacetime

This is the paradox.

Bianconi’s model is dualistic:

• it needs a reference metric

• and a perturbed metric

But if you compare two matter metrics directly, you no longer have a fixed reference structure. The whole construction collapses.

So Bianconi is forced to compare:

• matter metric

• background metric

even though this comparison has no physical meaning.

This is why the model feels “off.”

4. ToE resolves this paradox by being monistic

In the Theory of Entropicity (ToE):

• there is one fundamental field: S(x)

• spacetime and matter are both emergent from the curvature of S(x)

• metrics are not fundamental objects

• distinguishability is measured in the entropic field, not between metrics

So ToE never compares:

g_matter vs g_spacetime

because neither metric is fundamental.

Instead, ToE compares:

S(x) vs S0(x) (entropic curvature vs equilibrium curvature)

This comparison is meaningful because both are:

• entropic

• scalar

• geometric

• defined on the same manifold

And the ln 2 threshold (OCI) gives the minimal distinguishable curvature fold.

5. The ToE resolution

Here is the precise way ToE expresses the issue:

Bianconi’s model compares two different geometric objects (matter metric vs spacetime metric), which creates a conceptual mismatch.

ToE compares two configurations of the same entropic field, which is coherent and physically meaningful.

This is why ToE avoids the paradox entirely.

6. The Bianconi paradox in ToE

Bianconi tries to derive gravity from the entropy difference between matter and spacetime, but ToE shows that spacetime itself is emergent — so the comparison is ill‑posed [in the language of the Theory of Entropicity (ToE)].

Refer to Part II for further discussions and detailed clarifications and ToE's Charismatic Hypothesis to resolve the Bianconi Paradox.

References

1) Ginestra Bianconi. [last revised 8 Feb 2025 (this version, v7)]. Gravity from Entropy. https://arxiv.org/abs/2408.14391

2) Ginestra Bianconi. (published 3 March 2025; updated 14 July 2025). Gravity from Entropy.

https://journals.aps.org/prd/pdf/10.1103/PhysRevD.111.066001