Deriving Einstein’s Special Relativity from the Theory of Entropicity (ToE)

A complete entropic reformulation of time dilation, length contraction, mass increase, and the speed of light from the Theory of Entropicity (ToE)

1. Introduction: Relativity Without Geometry

In Einstein’s theory, the phenomena of relativistic kinematics—time dilation, length contraction, mass increase, and the invariance of the speed of light—arise from coordinate transformations on a fixed geometric manifold. They are presented as geometric necessities of Minkowski spacetime.

In the Theory of Entropicity (ToE), these same phenomena arise not from geometry but from the finite-speed dynamics of the entropic field, the fundamental field that generates all physical structures and processes.

In ToE:

Spacetime is not the cause of physical effects.
Observers are not responsible for measurement distortions.
Geometry is not fundamental.

Instead:

Time dilation, length contraction, mass increase, and the speed of light emerge as consequences of the finite rate at which the entropic field can redistribute information.

2. The Entropic Field and the Entropic Speed Limit (ESL)

ToE begins with the entropic field S(x), whose redistribution governs all motion, change, and interaction. This field obeys a universal constraint:

The entropic field cannot update reality faster than a finite maximum rate.

This maximum rate—called the Entropic Speed Limit (ESL)—is denoted by ccc.
Einstein called the same constant “speed of light,” but that was only the projection of the deeper entropic limit.

Thus:

c is not a geometric postulate.
c is not a property of photons.
c is the maximum rate of entropy flow in nature.

Photons simply saturate that limit.

3. The Entropic Accounting Principle (EAP)

The Entropic Accounting Principle (EAP) is the core insight of the Theory of Entropicity (ToE) that replaces Minkowski geometry:

When an object is in motion “relative” to the surrounding entropic field (actually, an object does not have any motion independent of the entropic field, because the entropic field is in and of itself what is responsible for the object and its motion), it must be continually “recomputed” by the field. This re-computation consumes part of the field’s entropic capacity.

Now, let the following hold:

Φ₀ be the total entropic update capacity available to the system
Φᵥ be the entropic cost of motion at velocity v; entropic capacity required to maintain motion at speed v
Φᵢₙₜ be the remaining entropic capacity for internal processes

Then ToE imposes the conservation law:

The faster an object moves, the more of the entropic field’s capacity is consumed by motion, leaving less available for internal processes such as the passage of time or spatial stability.

That is: Φ₀ = Φᵥ + Φᵢₙₜ + … (where the “… “denote other entropic components constrained by the entropic field).

The “internal processes” term (Φᵢₙₜ) includes both time passage and the entropic cost of sustaining rest mass. As velocity grows, the recomputation load increases, so the effective mass grows naturally.

This is the EAP (Entropic Accounting Principle) of the Theory of Entropicity (ToE).

From the EAP alone, all of [Einstein’s special] relativity emerges, and the following immediately follows:

3.1 Reformulating Relativity

Time Dilation: Internal processes slow down when more entropic capacity is used for motion. In Einstein’s relativity, faster motion reduces the rate of internal processes (clocks tick slower). In EAP, this emerges because Φᵥ grows with velocity, reducing Φᵢₙₜ.
Length Contraction: Spatial coherence collapses along direction of motion to preserve entropic conservation. Spatial stability requires entropic capacity. As velocity consumes more, less remains for maintaining spatial extension, leading to contraction.
Relativistic Mass/Energy: More entropic capacity must be allocated to maintain internal order [primary entropy] as speed increases. The “cost” of motion in entropic terms parallels the increase in kinetic energy. The field must allocate more capacity to sustain higher speeds.
Invariant Speed of Light: As v→c, Φᵢₙₜ→0, so no object can reach or exceed the entropic speed limit. If Φ₀ is finite, then there’s a maximum allocation to motion. Once Φᵥ = Φ₀, no capacity remains for internal processes—this corresponds to the speed of light limit.

Einstein assumed:

The speed of light is constant
Physics is the same in all inertial frames

ToE derives:

The speed of light is the maximum entropic update rate
Relativistic transformations follow from entropic conservation

This is a bold and elegant reframing: ToE essentially proposes that Einstein’s kinematics can be derived not from geometry (Minkowski spacetime), but from entropic bookkeeping. We consider this as the core breakthrough of the Theory of Entropicity (ToE).

🔑 Core Idea

Entropic Field as Fundamental: Instead of spacetime being the stage, the entropic field is the substrate. Objects don’t “move” independently; their motion is a continual re-computation by the field.
Capacity Accounting: The field has a finite update capacity Φ_0 (Phi_0). Motion consumes part of it (Φ_v [Phi_v]), leaving less for internal processes (Φ_int [Phi_{int}]).

3.2 The foundation of ToE’s derivation of Special Relativity

In the Theory of Entropicity (ToE), an object has no motion independent of the entropic field.
The entropic field creates the object and drives its motion.

Thus:

Motion is nothing but the entropic field continuously recomputing the object’s configuration in spacetime.

This re-computation requires a finite entropic capacity.

4. Time Dilation as Entropic Delay (CDP + No-Rush)

Time runs slow because entropy cannot update all degrees of freedom simultaneously

When motion consumes entropic capacity, the internal entropic updates (which define “time”) must slow down.

This is the Cumulative Delay Principle (CDP):

“When the entropic field is burdened by motion, all internal processes experience cumulative delay.”

Thus:

A fast-moving clock ticks slower
A fast-moving biological system ages slower
A fast-moving particle decays slower

Time dilation is not relative.
It is physically caused by entropic delay.

[The Theory of Entropicity (ToE) declares that] No observer interpretation is [inherently] needed.

5. Length Contraction as Entropic Compression

Space shrinks because the field reallocates degrees of freedom

Keeping a moving object stable (coherent) requires more entropic effort as velocity increases. The entropic field responds by reducing the number of spatial degrees of freedom available to the object.

This yields entropic contraction:

“To preserve coherence at high velocity, the entropic field compresses the object along the direction of motion.”

This is not a coordinate illusion.
It is a physical reorganization of entropic energy.

6. Mass Increase Through Obidi’s Loop

Acceleration becomes harder because the field is reaching its update limit

In ToE, “mass increase” is simply:

“The extra entropic cost of preserving internal order as the field approaches its update capacity.”

When velocity increases:

More entropic capacity must be used for motion
Less is available to maintain internal structure
The field must allocate even more capacity to preserve coherence
This additional entropic effort appears as an increase in inertial resistance

This process is governed by Obidi’s Loop:

The more you accelerate, the more entropy the field must allocate to maintain consistency, which increases effective mass, which demands even more entropic effort.

Thus, mass increase is a feedback loop, not a geometric artifact.

6.1 How Mass Increases in ToE

Mass as entropic inertia In ToE, mass is not a separate “bucket” of entropic cost. It is the manifestation of the field’s entropic re-computation load required to sustain an object’s persistence. The more the field must recompute an object’s state, the greater its effective inertia — which we perceive as mass.
Velocity dependence As velocity increases, the entropic field allocates more of its finite capacity to motion (Φv). This increases the re-computation burden. That burden shows up as an increase in effective mass — exactly what Einstein’s relativity encodes as relativistic mass.

7. Why No Object Can Reach the Entropic Speed Limit (ESL)

As the object’s velocity v approaches the ESL of c:

All entropic capacity is consumed by motion
Zero capacity remains for maintaining structure
The object would dissolve informationally
Nature therefore forbids reaching c

This mirrors Einstein’s “speed limit,” but with far deeper ontological meaning.

In ToE:

You cannot exceed c because the universe cannot recompute you faster than its fundamental entropic clock allows.

8. Reconstructing the Lorentz Factor from Entropic Principles

From the conservation of entropic capacity, ToE recovers the Lorentz factor:

Thus:

Time dilation
Length contraction
Mass increase

all follow the familiar Lorentz relations—
but this time derived from entropy, not geometry.

9. Why This Is Superior to Einstein’s Interpretation

Einstein’s postulates:

Speed of light is constant
Laws of physics are the same in inertial frames

ToE replaces them with a single principle:

Entropy flows through the universe at a finite maximum rate.
Everything else is a consequence.

Thus ToE:

derives relativity rather than assuming it
explains why the speed of light is constant
makes no reference to “observers”
requires no geometric interpretation
provides a physical mechanism for mass increase
predicts entropic breakdown near ccc
connects relativity to information theory and thermodynamics

This is a unification Einstein never achieved.

10. Philosophical Shift

From Geometry to Process: Minkowski spacetime treats relativity as geometry. EAP treats relativity as a consequence of finite computational/entropic resources.
Observer Dethroned: Instead of relativity being about frames of reference, it’s about the entropic field’s allocation of capacity. The observer is no longer fundamental—entropy is.
Mass is entropy made persistent. It is the field’s ongoing re-computation cost of keeping an object “real.”
Relativistic mass increase is simply the field’s entropic burden rising as velocity drains capacity. This keeps ToE aligned with relativity while offering a deeper explanation: mass is not a primitive property, but an emergent entropic phenomenon.

11. Why This Is Revolutionary

No known theory before ToE [at least in the author’s knowledge] has ever:

replaced Minkowski geometry with an entropic field
derived the Lorentz factor from thermodynamic constraints
interpreted ccc as a structural limitation of entropy flow
explained mass increase through an entropic feedback loop
connected all kinematic effects to a single accounting principle

Einstein used geometry as input.
ToE shows geometry is an output.

Einstein’s postulates were axioms.
ToE shows they are emergent thermodynamic laws.

This is perhaps the most radical reinterpretation of Special Relativity since 1905.

12. Closure Highlight

All relativistic effects (time dilation, length contraction, mass increase, speed limit) are caused by entropic field dynamics—not geometry and not observer measurement.

In the Theory of Entropicity:

Motion is entropic consumption
Time is entropic updating
Mass is entropic stabilization
Space is entropic allocation
ccc is entropic saturation

Thus, Special Relativity is not fundamental.
It is the shadow of a deeper entropic law.

This is a genuinely novel reframing: relativity as entropic resource management rather than spacetime geometry, which constitutes the cornerstone of the Theory of Entropicity’s claim to originality.

References

Obidi, John Onimisi. (12th November, 2025). On the Theory of Entropicity (ToE) and Ginestra Bianconi’s Gravity from Entropy: A Rigorous Derivation of Bianconi’s Results from the Entropic Obidi Actions of the Theory of Entropicity (ToE). Cambridge University. https//doi.org/10.33774/coe-2025-g7ztq
John Onimisi Obidi. (6th November, 2025). Comparative analysis between john onimisi obidi’s theory of entropicity (toe) and waldemar marek feldt’s feldt–higgs universal bridge (f–hub) theory. International Journal of Current Science Research and Review, 8(11), pp. 5642–5657, 19th November 2025. URL: https: //doi.org/10.47191/ijcsrr/V8-i11–21.
Obidi, John Onimisi. 2025. On the Conceptual and Mathematical Foundations of the Theory of Entropicity (ToE): An Alternative Path toward Quantum Gravity and the Unification of Physics. Cambridge University. Published October 17, 2025. https://doi.org/10.33774/coe-2025-1dsrv
Obidi, John Onimisi (17th October 2025). On the Conceptual and Mathematical Foundations of the Theory of Entropicity (ToE): An Alternative Path toward Quantum Gravity and the Unification of Physics. Figshare. https://doi.org/10.6084/m9.figshare.30337396.v2
Obidi, John Onimisi. 2025. A Simple Explanation of the Unifying Mathematical Architecture of the Theory of Entropicity (ToE): Crucial Elements of ToE as a Field Theory. Cambridge University. Published October 20, 2025. https://doi.org/10.33774/coe-2025-bpvf3
Obidi, John Onimisi (15 November 2025). The Theory of Entropicity (ToE) Goes Beyond Holographic Pseudo-Entropy: From Boundary Diagnostics to a Universal Entropic Field Theory. Figshare. https://doi.org/10.6084/m9.figshare.30627200.v1
Obidi, John Onimisi. Unified Field Architecture of Theory of Entropicity (ToE). Encyclopedia. Available online: https://encyclopedia.pub/entry/59276 (accessed on 19 November 2025).
Obidi, John Onimisi. (4 November, 2025). The Theory of Entropicity (ToE) Derives Einstein’s Relativistic Speed of Light (c) as a Function of the Entropic Field: ToE Applies Logical Entropic Concepts and Principles to Derive Einstein’s Second Postulate. Cambridge University. https://doi.org/10.33774/coe-2025-f5qw8-v2
Obidi, John Onimisi. (28 October, 2025). The Theory of Entropicity (ToE) Derives and Explains Mass Increase, Time Dilation and Length Contraction in Einstein’s Theory of Relativity (ToR): ToE Applies Logical Entropic Concepts and Principles to Verify Einstein’s Relativity. Cambridge University. https://doi.org/10.33774/coe-2025-6wrkm

Further Resources on the Theory of Entropicity (ToE):

Website: Theory of Entropicity ToE — https://theoryofentropicity.blogspot.com
LinkedIn: Theory of Entropicity ToE — https://www.linkedin.com/company/theory-of-entropicity-toe/about/?viewAsMember=true
Notion-1: Theory of Entropicity (ToE)
Notion-2: Theory of Entropicity (ToE)
Notion-3: Theory of Entropicity (ToE)
Notion-4: Theory of Entropicity (ToE)
Substack: Theory of Entropicity (ToE) — John Onimisi Obidi | Substack
Medium: Theory of Entropicity (ToE) — John Onimisi Obidi — Medium
SciProfiles: Theory of Entropicity (ToE) — John Onimisi Obidi | Author
Encyclopedia.pub: Theory of Entropicity (ToE) — John Onimisi Obidi | Author
HandWiki contributors, “Biography: John Onimisi Obidi,” HandWiki, https://handwiki.org/wiki/index.php?title=Biography:John_Onimisi_Obidi&oldid=2743427 (accessed October 31, 2025).
HandWiki Contributions: Theory of Entropicity (ToE) — John Onimisi Obidi | HandWiki
HandWiki Home: Theory of Entropicity (ToE) — John Onimisi Obidi | HandWiki
HandWiki Homepage-User Page: Theory of Entropicity (ToE) — John Onimisi Obidi | HandWiki
Academia: Theory of Entropicity (ToE) — John Onimisi Obidi | Academia
ResearchGate: Theory of Entropicity (ToE) — John Onimisi Obidi | ResearchGate
Figshare: Theory of Entropicity (ToE) — John Onimisi Obidi | Figshare
Authoria: Theory of Entropicity (ToE) — John Onimisi Obidi | Authorea
Social Science Research Network (SSRN): Theory of Entropicity (ToE) — John Onimisi Obidi | SSRN
Wikidata contributors, Biography: John Onimisi Obidi “Q136673971,” Wikidata, https://www.wikidata.org/w/index.php?title=Q136673971&oldid=2423782576 (accessed November 13, 2025).
Google Scholar: ‪John Onimisi Obidi — ‪Google Scholar
Cambridge University Open Engage (CoE): Collected Papers on the Theory of Entropicity (ToE)

Theory of Entropicity (ToE) by John Onimisi Obidi

Deriving Einstein’s Special Relativity from the Theory of Entropicity (ToE): A complete entropic reformulation of time dilation, length contraction, mass increase, and the speed of light from the Theory of Entropicity (ToE)