A Unified Paradigm of Cosmic Manifestation: Bridging Extended Classical Mechanics, Sen’s Conjecture, and Conformal Cyclic Cosmology

The fundamental architecture of modern theoretical physics is currently undergoing a period of profound re-evaluation. While the dual pillars of General Relativity and Quantum Field Theory have provided remarkably accurate descriptions of the macroscopic and microscopic worlds respectively, the persistent inability to reconcile these frameworks—particularly at the singularity of the Big Bang and the event horizons of black holes—suggests a missing ontological layer. The standard cosmological model, ΛCDM, relies on the existence of dark energy and dark matter, components that constitute the vast majority of the universe's mass-energy budget yet lack a definitive physical carrier or structural explanation. Simultaneously, string theory, in its quest for a theory of everything, has uncovered deep truths about the nature of vacuum stability and the decay of material structures, most notably through the conjectures of Ashoke Sen. Roger Penrose’s Conformal Cyclic Cosmology (CCC) offers a complementary geometric perspective, positing that the universe does not begin or end but iterates through infinite aeons. Extended Classical Mechanics (ECM), as formulated by Soumendra Nath Thakur, provides the necessary physical bridge between these diverse perspectives. By reinterpreting mass not as a static scalar but as a dynamic, redistributable energy reservoir governed by frequency and phase, ECM offers a mechanistic explanation for the transition from non-eventful potential to manifested existence, thereby unifying Sen’s microscopic dissolution with Penrose’s macroscopic cycles.

Extended Classical Mechanics (ECM) Insight: Why Vacuum Isn’t Empty

Soumendra Nath Thakur 

January 05, 2026

In Extended Classical Mechanics (ECM), mass is not a fixed substance. It is a dynamic quantity that changes when energy is released from gravitational or motional potential. Existence in the universe is distributed across different frequency bands rather than being confined to visible matter alone.

When a system converts stored potential energy into manifested energy, part of its material mass is reduced by what ECM calls Negative Apparent Mass (NAM). When this reduction becomes equal to the matter mass itself, the effective mass of the system becomes zero. At this point, matter does not continue moving as a particle — it transitions into a vacuum-mode state of the Phase Kernel.

This vacuum-mode is called f0.

This state does not mean “nothing exists.” It means the system no longer exists as matter. Instead, it exists as a pure energy-frequency state within the Phase Kernel. In this form it has no inertia, no gravitational mass, and no classical visibility — yet it still exists physically as a field excitation.

In ECM, ordinary matter occupies the lower, perceptible frequency band of existence. Dark matter and dark energy occupy a higher frequency band that lies above ordinary matter but below the Planck limit. They are not separate substances — they are the same underlying existence expressed in different frequency states.

Dark matter arises when matter is partially shifted into this higher-frequency vacuum-mode. Its mass is reduced and it becomes invisible, but it still interacts gravitationally with visible matter. Dark energy arises when this shift is complete, producing a fully vacuum-mode state that no longer attracts matter but instead generates a repulsive, anti-gravitational background.

Crucially, f0 is not just the beginning of the universe. It is not a historical moment. It is a physical state that can occur anywhere in space and at any time whenever matter is fully converted into Phase-Kernel excitation. The universe is continuously transforming matter into vacuum-mode energy and, under suitable conditions, back again.

This means vacuum is not empty.

Vacuum is the deepest energetic form of existence — the hidden frequency band of the universe.

ECM therefore connects gravity, motion, dark matter, and dark energy through a single physical process: matter transforming into higher-frequency vacuum-mode energy within the Phase Kernel.

This is not an addition to classical physics — it is what classical physics was missing.

From Uneventful Energy to Manifested Universes: An ECM Bridge Between Sen's Conjecture and Penrose's Conformal Cyclic Cosmology: Conclusion

The paper titled, "From Uneventful Energy to Manifested Universes: An ECM Bridge Between Sen's Conjecture and Penrose's Conformal Cyclic Cosmology:" DOI: 10.13140/RG.2.2.30930.00966 concludes that:

Extended Classical Mechanics (ECM) provides a vital theoretical framework for linking Ashoke Sen's work on vacuum dissolution with Roger Penrose's Conformal Cyclic Cosmology. By identifying the non-eventful energetic reservoir PEᴇᴄᴍ as the fundamental substrate of reality, ECM allows for a consistent description of both the emergence of the universe from frequency instability and its eventual return to a scale-free potential state through the decay of mass. The "Closed Cosmic Circle" ensures that energy is conserved across aeons, while the reabsorption of manifested structure into the latent potential state offers a novel solution to the problem of entropy accumulation. The resulting picture is one of a universe that is perpetually renewed, where the end of existence is merely the energetic preparation for its next manifestation. Physical time, space, and matter are shown to be secondary outcomes of a deeper, phase-governed energy cycle—a discovery that bridges the gap between classical intuition, string theoretic complexity, and cosmological geometry.

Google Link: https://share.google/aimode/6wv5jdKrwSNfpxyEW

Methodology: A Pre-Relativistic Mass–Energy Equivalence from Newtonian Gravity in Extended Classical Mechanics

Soumendra Nath Thakur | ORCiD: 0000-0003-1871-7803 | Tagore's Electronic Lab, India.| postmasterenator@gmail.com | January 02, 2026

Extended Classical Mechanics' Pre-relativistic mass-energy equivalence Principle.

Soumendra Nath Thakur

ORCiD: 0000-0003-1871-7803

December 31, 2025

Extended Classical Mechanics' Pre-relativistic mass-energy equivalence Principle.

1. Classical Force Laws:

Newton’s Second Law

F = m a

Force is the cause of acceleration of inertial mass.

2. Newton’s Law of Gravitation:

Fɢ = G (M m/r²)

This gives the force acting on a mass (m) due to a source mass (M).

3. Dynamical Equivalence:

Set gravitational force equal to inertial force:

m a = G (M m/r²)

Cancel (m):

a = GM/r²

This shows that gravitational acceleration is independent of the test mass.

4. Gravitational Field:

g(r) = GM/r²

So the gravitational force becomes

Fɢ = mg(r)

5. Physical Causal Chain:

M → g(r) → a → F

This is exactly what Newtonian gravity means physically:

Mass produces a field, the field produces acceleration, and acceleration produces force.

6. Classical Total Mechanical Energy:

Eₜₒₜₐₗ = PE + KE

This states that the energy of a classical system is the sum of its stored (potential) and motion (kinetic) energy.

For motion in a gravitational field,

Eₜₒₜₐₗ = mgh + ½mv²

This provides the exact classical baseline, against which the ECM generalization is being built.

7. Equivalence of Inertial and Gravitational Mass — ECM Formulation:

In classical mechanics, inertial mass and gravitational mass are empirically identical:

mɪₙₑᵣₜᵢₐₗ = mɢᵣₐᵥᵢₜₐₜᵢₒₙₐₗ

mɪ = mɢ

This Weak Equivalence Principle states that the mass that resists acceleration is the same mass that produces and experiences gravity.

Classical physics treats this equality as fundamental, without explaining why it holds.

8. The ECM Conceptual Breakthrough:

Classical mechanics assumes mass is a single primitive quantity:

mɪ = mɢ = m

This works because classical theory does not resolve how energy, inertia, and gravity are stored or generated within mass.

Extended Classical Mechanics (ECM) rejects this assumption.

In ECM, mass has internal structure.

9. Mass Structure in ECM:

In ECM, gravitational and inertial behaviour arises from the effective mass:

Mᵉᶠᶠ = Mᴍ + (−Mᵃᵖᵖ) = Mɢ

where

• Mᴍ is matter mass (existence field)

• −Mᵃᵖᵖ is Negative Apparent Mass (NAM) generated by manifested potential energy

−Mᵃᵖᵖ ≡ −ΔPEᴇᴄᴍ

Thus, gravitational mass is not just matter mass — it is matter plus manifested energy field.

10. Classical Mechanics as a Special Case of ECM:

When no manifestation occurs,

−ΔPEᴇᴄᴍ = 0 → −Mᵃᵖᵖ = 0

so ECM collapses to

Mᵉᶠᶠ = Mᴍ

which gives

mɪ = mɢ

Therefore, the equivalence principle is not fundamental — it is the zero-manifestation limit of ECM.

11. What Classical Physics Cannot See:

Classical mechanics unknowingly treats

m = Mᴍ + (−Mᵃᵖᵖ)

as a single undifferentiated constant.

ECM reveals that:

• gravity

• inertia

• kinetic energy

• dark mass effects

all arise from the hidden NAM field, generated by −ΔPEᴇᴄᴍ.

Classical physics contains:

• no −Mᵃᵖᵖ

• no ΔMᴍ

• no mass–energy exchange

• no internal mass structure

So it reduces to:

Mɢ → m, Mᴍ → m, −Mᵃᵖᵖ → 0

which automatically yields

mɪ = mɢ

12. Physical Meaning:

Classical mechanics treats the entire ECM mass–energy structure as if it were already collapsed into a single constant (m).

That is why Newtonian gravity works — but it does not know why.

ECM provides the missing physics:

Classical mass = matter mass + hidden NAM field

but classical theory cannot separate them.

13. Final ECM Statement:

Mɢ = Mᵉᶠᶠ = Mᴍ + (−Mᵃᵖᵖ), −Mᵃᵖᵖ ≡ −ΔPEᴇᴄᴍ

In classical mechanics:

−ΔPEᴇᴄᴍ → 0 → Mɢ = Mᴍ

hence

mɪ = mɢ

ECM shows that this equality hides a deeper mass-energy structure that becomes visible only when motion, gravity, and manifestation occur.

14. Physical interpretation:

Classical mechanics treats the entire mass–energy structure of ECM as if it were already “pre-collapsed” into a single constant (m).

That is why classical gravity works — but it does not know why.

ECM tells the missing physics:

Classical mass matter mass + hidden NAM field

but classical theory cannot separate them.

15. Conclusion:

In classical mechanics, mɪ = mɢ because classical physics assumes −Mᵃᵖᵖ.

ECM reveals that this equality hides a deeper structure:

m = Mᴍ + (−Mᵃᵖᵖ),

which becomes visible only when motion and gravity exist.

16. ECM Extension of the Classical Force Law:

Extended Classical Mechanics (ECM) is built on the principle that kinetic energy is not independent of mass. Instead, kinetic energy arises from the redistribution of mass through the entropic release of stored potential energy,

−ΔPEᴇᴄᴍ.

In ECM, motion is powered when a portion of the system’s stored potential energy PEᴇᴄᴍ is converted into a manifested mass component,

−ΔPEᴇᴄᴍ ≡ −Mᵃᵖᵖ

which generates effective mass

Mᵉᶠᶠ = Mᴍ + (−Mᵃᵖᵖ)

and it is this effective mass that participates in inertia, gravity, and acceleration.

Thus, what appears in classical physics as “kinetic energy” is, in ECM, the dynamic manifestation of mass created by potential-energy release.

17. Classical Force Law (Newtonian Interface)

F = M a

This equation remains exactly valid in ECM — but ECM now reveals what the symbol (M) really contains.

In classical mechanics, (M) is treated as a single primitive quantity.

In ECM, that same (M) is the collapsed form of

Mᵉᶠᶠ = Mᴍ + (−Mᵃᵖᵖ)

where

• Mᴍ is matter mass (existence field),

• −Mᵃᵖᵖ is Negative Apparent Mass (NAM) generated by −ΔPEᴇᴄᴍ.

Therefore, the classical force law becomes, in ECM meaning:

F = Mᵉᶠᶠ a = (Mᴍ + (−Mᵃᵖᵖ)a,

showing that force acts on the combined matter-mass plus manifested energy-mass.

18. The ECM Bridge Behind Newton’s Law:

The Newtonian equation

F = M a

corresponds in ECM to the causal chain

F ⟶ −ΔPEᴇᴄᴍ ⟶ −Mᵃᵖᵖ ⟶ Mᵉᶠᶠ ⟶ a.

Thus, force does not directly produce acceleration. It first releases potential energy, which generates NAM, which modifies effective mass, and only then produces motion.

This is the hidden physics behind Newton’s law.

19. Newtonian Limits (Recovered Exactly)

For classical fixed mass (M):

a ∝ F

For fixed force (F):

a ∝ 1/M

These relations are not altered in ECM.

They are simply the collapsed limit where

−Mᵃᵖᵖ ⟶ 0, Mᵉᶠᶠ ⟶ Mᴍ,

so that ECM reduces to

F = Mᴍ a,

which is ordinary Newtonian mechanics.

What ECM adds?

Newton gives the result.

ECM provides the engine.

Newton sees:

F ⟶ a.

ECM reveals:

F ⟶ −ΔPEᴇᴄᴍ ⟶ −Mᵃᵖᵖ ⟶ Mᵉᶠᶠ ⟶ a.

This is why ECM can generate gravity, inertia, dark mass, and cosmic dynamics from a single physical process — the manifestation of mass from potential energy.

20. ECM Insight: Mass is Not Static in Motion

In Extended Classical Mechanics (ECM), motion is powered by mass–energy conversion, governed by the manifestation identity

−ΔPEᴇᴄᴍ ↔ ΔKEᴇᴄᴍ ↔ ΔMᴍ

This means that when potential energy is released, it does not disappear into abstract “energy”; it manifests as matter-mass.

Therefore, a moving body possesses more mass than its rest matter mass:

Mᴍₘₒₜᵢₒₙ = Mᴍᵣₑₛₜ + ΔMᴍ

where ΔMᴍ is the kinetic mass created from the released potential energy −ΔPEᴇᴄᴍ.

21. Total Energy in ECM

Classically,

Eₜₒₜₐₗ = PE + KE = mgh + ½mv².

In ECM,

Eᴇᴄᴍ,ₜₒₜₐₗ = PEᴇᴄᴍ + KEᴇᴄᴍ

But ECM resolves how this sum is formed:

PEᴇᴄᴍ + KEᴇᴄᴍ = (PEᴇᴄᴍ - ΔPEᴇᴄᴍ) + KEᴇᴄᴍ

Since

KEᴇᴄᴍ ≡ −ΔPEᴇᴄᴍ ≡ −Mᵃᵖᵖ ≡ ΔMᴍ,

we obtain

Eᴇᴄᴍ,ₜₒₜₐₗ = PEᴇᴄᴍᵉᶠᶠ + KEᴇᴄᴍ,

where:

PEᴇᴄᴍᵉᶠᶠ = PEᴇᴄᴍ − ΔPEᴇᴄᴍ = Mᵉᶠᶠgᵉᶠᶠh

This expresses that motion reduces stored potential energy and creates kinetic mass.

22. Potential Energy of the Effective Mass

The released energy modifies the gravitationally active mass.

The system now carries effective mass

Mᵉᶠᶠ = Mᴍ + (−Mᵃᵖᵖ),

so the effective potential energy becomes

PEᴇᴄᴍᵉᶠᶠ = Mᵉᶠᶠgᵉᶠᶠh

Thus gravity in ECM acts on matter mass plus manifested NAM.

23. Kinetic Energy as Frequency-Generated Mass

In ECM, kinetic energy is not an abstract term — it is mass oscillating at frequency.

The inherent (de Broglie) component is

KEᴇᴄᴍ,ᵢₙₕₑᵣₑₙₜ = ½(−Mᵃᵖᵖ,ᵢₙₕₑᵣₑₙₜ)c² = ½(ΔMᴍ,ᵢₙₕₑᵣₑₙₜ)c² = ½(fᵈᴮ)c².

When this inherent oscillation interacts with the gravitational source field Mɢ, a Planck-type interactional component appears. The total kinetic energy becomes

KEᴇᴄᴍ↑ = ½(−Mᵃᵖᵖ,ᵢₙₕₑᵣₑₙₜ −Mᵃᵖᵖ,ᵢₙₜₑᵣₐᴄₜᵢₒₙₐₗ)c² = ½(fᵈᴮ + fᴾ)c² = ΔMᴍc² = hf

Thus,

KEᴇᴄᴍ = ΔMᴍc² = hf.

For photons (pure oscillatory systems),

KEᴇᴄᴍ = ΔMᴍc² = hf.

24. Frequency-Governed Kinetic Energy Law

KEᴇᴄᴍ = (ΔMᴍᵈᴮ + ΔMᴍᴾ)c² = (αΔMᴍᵈᴮ + (1 − α)ΔMᴍᴾ)c² = h(fᵈᴮ + fᴾ) = hf

This shows that

• de Broglie frequency governs inertial motion

• Planck frequency governs field-coupled motion

• their sum governs total kinetic mass and energy

Final ECM Meaning

Classical mechanics writes

KE = ½mv².

ECM reveals the hidden structure:

KEᴇᴄᴍ = ΔMᴍc² = hf,

where the mass ΔMᴍ is created by

−ΔPEᴇᴄᴍ

Motion is therefore the physical manifestation of mass released from potential energy.

This is the engine beneath Newton’s equations.

25. Alphabetical List of ECM Terms and Denotations

α (alpha)

Weighting coefficient that determines how much of the total manifested kinetic mass comes from de Broglie (inertial) versus Planck (field-coupled) frequency contributions.

aᵉᶠᶠ

Effective acceleration produced by the action of force on the effective mass Mᵉᶠᶠ.

c

Speed of light. In ECM it acts as the mass-to-frequency conversion constant via KEᴇᴄᴍ = ΔMᴍc² .

ΔKEᴇᴄᴍ

Change in kinetic energy in ECM, generated by the manifestation of mass from released potential energy.

ΔMᴍ

Manifested matter-mass produced from released potential energy.This is the physical carrier of kinetic energy.

ΔPEᴇᴄᴍ

Change in ECM potential energy. A negative change −ΔPEᴇᴄᴍ generates NAM and kinetic mass.

f

Total effective frequency associated with manifested mass:

f = fᵈᴮ + fᴾ

fᵈᴮ (de Broglie frequency). Frequency associated with inertial motion of manifested mass.

fᴾ (Planck frequency). Frequency associated with field-coupled (gravitational) interaction of manifested mass.

gᵉᶠᶠ

Effective gravitational field acting on the effective mass Mᵉᶠᶠ.

h

Planck constant, relating frequency to manifested energy-mass via

KEᴇᴄᴍ = hf = ΔMᴍc²,

KEᴇᴄᴍ

Kinetic energy in ECM. It is not abstract motion energy but mass created from released potential energy:

KEᴇᴄᴍ = hf = ΔMᴍc²

Mᵃᵖᵖ (Negative Apparent Mass, NAM). Mass equivalent of released potential energy:

−Mᵃᵖᵖ ≡ −ΔPEᴇᴄᴍ

It is the field-like mass that drives gravity, inertia, and kinetic energy.

Mᵉᶠᶠ (Effective Mass)

Total gravitational and inertial mass of a moving system:

Mᵉᶠᶠ = Mᴍ + (−Mᵃᵖᵖ).

Mɢ (Gravitational Mass)

In ECM: Mᵉᶠᶠ = Mɢ

Gravity responds to both matter mass and NAM.

Mᴍ (Matter Mass)

The rest-existence mass of matter — the static mass stored in the potential field PEᴇᴄᴍ.

Mᴍ,ₘₒₜᵢₒₙ

Total mass of a moving body:

Mᴍ,ₘₒₜᵢₒₙ = Mᴍ,ᵣₑₛₜ + ΔMᴍ

PEᴇᴄᴍ

Stored ECM potential energy — the existence field carried by matter mass Mᴍ.

PEᴇᴄᴍᵉᶠᶠ

Effective potential energy after manifestation:

PEᴇᴄᴍᵉᶠᶠ = PEᴇᴄᴍ − ΔPEᴇᴄᴍ = Mᵉᶠᶠgᵉᶠᶠh

−ΔPEᴇᴄᴍ

Released ECM potential energy that creates NAM and kinetic mass.

−Mᵃᵖᵖ

Negative Apparent Mass created by −ΔPEᴇᴄᴍ.

It is the engine of gravity, inertia, and kinetic energy.

ΔMᴍᵈᴮ

Portion of manifested mass generated by de Broglie (inertial) oscillations.

ΔMᴍᴾ

Portion of manifested mass generated by Planck (field-coupled) oscillations.

ΔMᴍc²

Energy equivalent of manifested mass:

ΔMᴍc² = hf

Phase-Kernel

The 0-D ECM source where frequency-driven mass manifestation occurs, generating NAM, gravity, and kinetic energy.

NAM (Negative Apparent Mass)

The mass-equivalent of released potential energy.

It produces gravitational attraction, inertial resistance, and kinetic energy.

Weak Equivalence Principle (Classical Limit)

In ECM collapse limit −Mᵃᵖᵖ → 0,

Mᵉᶠᶠ → Mᴍ

so inertial mass equals gravitational mass.