🚀 Creation and Generation of Mass and Matter from the Fiber Integrals of the Obidi Action on the Entropic Field of the Theory of Entropicity (ToE)

🔷 Obidi generates mass from the fiber integral of the Entropic Action

In the Theory of Entropicity (ToE), John Onimisi Obidi shows that mass and matter are not fundamental inputs. They are outputs of the fiber integrals of the Obidi Action applied to the Entropic Field. 

Mass is “frozen” or stabilized internal entropic content emerging from a deeper entropic geometry.

🔶 The Mechanism: Mass as Frozen Entropy

🔹 1️⃣ The Entropic Action (Local Obidi Action, LOA)

The LOA couples the entropy field S(x) to geometry through an exponential weight exp(S/k_B). 

Varying this action with respect to the emergent metric produces the entropic stress-energy tensor Tᵤᵥ^(S).

🔹 2️⃣ Fiber Integration → Creation of Mass

Obidi defines the tensor as the second fiber moment of the entropic distribution:

Tᵤᵥ^(S)(x) = ∫ pᵤ pᵥ · f_ent(x, Ω) · dΩ

This integral coarse-grains microscopic entropic fluctuations into:
• mass
• energy density 
• pressure 
• momentum flux 
• stress 

Matter becomes the macroscopic condensation of entropic microstructure.

🔷 Why This Reverses Standard Physics

🧭 Standard View

Mass-energy curves spacetime.

🌀 Obidi’s View

The Entropy Field generates mass-energy via fiber integrals, and that mass-energy curves spacetime. 
• Spacetime is created, not an independent background

• Matter is generated, not assumed. 

• Gravity is projected, not fundamental. 

• Mass is entropic inertia, not intrinsic.

🔶 Why It’s Not a Tautology

Obidi does not assume matter. 
He begins with:

• the Entropic Field S(x) 
• the entropic manifold 
• the Obidi Probability Law 

The distribution f_ent describes informational configurations, not particles. 

The fiber integral creates the stress-energy tensor:

Tᵤᵥ = ∫ pᵤ pᵥ · f_ent · dΩ

This is a generative transformation, not a circular definition.

🔷 How Specific Mass Values Arise

🔹 1️⃣ Entropy Density → Mass
m ∝ s (mass proportional to entropy density)

🔹 2️⃣ Spectral Obidi Action (SOA)
I_SOA = –Tr(ln Δ) 

Mass values correspond to eigenvalues of the Entropic Modular Operator.

🔹 3️⃣ Relativistic Mass
m(v) = γₑ · m₀ 

where:
γₑ is the entropic Lorentz factor, derived from entropy budgets of ToE rather than relativistic geometry.

🔶 The Big Picture

Obidi shows that:

> Mass and matter are emergent fiber-integral projections of the Entropic Field.

In this ToE framework:

• entropy generates mass 
• information geometry generates matter 
• fiber integrals generate stress-energy 
• geometry emerges from entropy 
• Einstein gravity appears as the infrared limit 

The Theory of Entropicity (ToE) is not a modification of physics — it is a reconstruction of physics from first principles, with the Entropic Field as its Foundation.

For Details:

📚Reference(s):

The Canonical Archives: https://lnkd.in/gnwMP-Py