Soumendra Nath Thakur | ORCiD: 0000-0003-1871-7803 | Tagore's Electronic Lab, India.| postmasterenator@gmail.com | January 02, 2026
2. Methodology
2.1 Strategy of the Analysis
The objective of this work is to extract a mass–energy equivalence directly from Newtonian gravity by reinterpreting its force laws within the framework of Extended Classical Mechanics (ECM). The methodology is therefore not experimental but structural: classical equations are retained, but their physical interpretation is replaced by a mass-manifestation model. No relativistic postulates, spacetime geometry, or Lorentz transformations are introduced.
The procedure follows four steps:
1. Identify where Newtonian mechanics hides energy-to-mass conversion.
2. Reformulate gravitational force as a manifestation process.
3. Introduce Negative Apparent Mass (NAM) as the mass equivalent of released potential energy.
4. Demonstrate that inertial and gravitational mass are both manifestations of the same effective mass.
2.2 Decomposition of Classical Mass in ECM
Classical mechanics uses a single scalar mass (m). ECM replaces this with a physically structured quantity:
Mᵉᶠᶠ = Mᴍ + (-Mᵃᵖᵖ),
where
(Mᴍ) is matter mass, and
(-Mᵃᵖᵖ) is the Negative Apparent Mass generated when potential energy is released.
This decomposition is not assumed arbitrarily. It is derived from the ECM manifestation principle:
-ΔPEᴇᴄᴍ ↔ ΔKEᴇᴄᴍ ↔ ΔMᴍ.
Potential energy is therefore a stored mass reservoir, and kinetic energy is the manifestation of that mass into motion.
2.3 Reformulation of Newton’s Second Law in ECM
Newton’s classical law
F = m a
is rewritten in ECM as
Fᴇᴄᴍ = Mᵉᶠᶠ aᵉᶠᶠ = (Mᴍ + (−Mᵃᵖᵖ)) aᵉᶠᶠ
In ECM, force does not act directly on matter mass Mᴍ. It acts on the effective mass field Mᵉᶠᶠ, which includes the manifested mass generated from released potential energy.
A force therefore first induces the conversion
-ΔPEᴇᴄᴍ ⟶ -Mᵃᵖᵖ,
thereby increasing or modifying Mᵉᶠᶠ. The resulting effective acceleration
aᵉᶠᶠ
is the kinematic response of this dynamically generated mass field.
Motion does not arise because force “pushes” matter, but because force creates mass that must move.
Effective acceleration is therefore a manifestation effect: it is the kinematic expression of mass being generated from potential energy.
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2.4 Reformulation of Newtonian Gravity in ECM
The Newtonian gravitational force
F = G m M / r²
is reinterpreted as a manifestation coupling between two effective masses:
Fɢ = G M₁ᵉᶠᶠ M₂ᵉᶠᶠ/ r².
Here, the gravitational field is not a geometric or action-at-a-distance entity; it is a mass-manifestation field that continuously converts gravitational potential energy into NAM. This produces both attraction and inertial resistance using the same mass source.
2.5 Identification of Gravitational and Inertial Mass in ECM
Because both inertia and gravitation depend on the same effective mass,
Mɪ = Mɢ = Mᵉᶠᶠ = Mᴍ + (-Mᵃᵖᵖ),
the equivalence principle emerges as a dynamical identity rather than a postulate.
Classical mechanics assumes
mɪ = mɢ = m
because it does not resolve the internal structure of (m). ECM reveals that this single mass is actually a continuously regenerated quantity.
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2.6 Extraction of Mass–Energy Equivalence in ECM
In Extended Classical Mechanics (ECM), kinetic energy does not arise from the motion of matter mass. Instead, it arises from the decomposition of matter mass through the release of stored potential energy.
Matter mass Mᴍ stores ECM potential energy:
PEᴇᴄᴍ ≡ Mᴍ
When force acts, a portion of this stored mass is released in energy form:
-ΔPEᴇᴄᴍ,ᵢₙₕ ≡ ΔMᴍ,ᵢₙₕ c².
The corresponding manifested mass appears as Negative Apparent Mass (NAM)
-Mᵃᵖᵖ,ᵢₙₕ ≡ ΔMᴍ,ᵢₙₕ
This released mass is not bound matter but a dynamic, repulsive, frequency-based field mass. This is the same physical process by which an electron releases a photon:
(Mₑ - Mᵃᵖᵖ) → ΔMᴍ = hf
Thus kinetic energy in ECM is carried only by the decomposed mass, not by the remaining matter mass.
Inherent kinetic mass:
The inherent kinetic manifestation corresponds to a Newtonian-type form
KEᴇᴄᴍ,ᵢₙₕ = ½(-Mᵃᵖᵖ,ᵢₙₕ)c² = ½ ΔMᴍ,ᵢₙₕ c²,
where c is the mass-to-frequency conversion scale, not a spacetime velocity.
This is the ECM translation of ½mv², with v replaced by the universal oscillatory scale c.
Gravitational-field-modulated amplification:
The inherent NAM does not remain isolated. It couples to the gravitational source mass (Mɢ), producing an interactional NAM component
-Mᵃᵖᵖ,ᵢₙₜ ≡ -ΔMᴍ,ᵢₙₜ ≡ -ΔPEᴇᴄᴍ,ᵢₙₜ / c²
This field-coupled manifestation adds to the inherent NAM, yielding
-Mᵃᵖᵖ,ₜₒₜₐₗ = -Mᵃᵖᵖ,ᵢₙₕ + (-Mᵃᵖᵖ,ᵢₙₜ) = -2Mᵃᵖᵖ
Physically, this is the same mechanism by which oscillatory mass acquires an interactional Planck-frequency component (fᴾ,ᵢₙₜ) in addition to its inherent de Broglie frequency (fᵈᴮ,ᵢₙₕ).
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Completion of mass–energy equivalence:
The total kinetic energy becomes
KEᴇᴄᴍ = ½(-Mᵃᵖᵖ,ᵢₙₕ -Mᵃᵖᵖ,ᵢₙₜ)c²
= ½(-2Mᵃᵖᵖ)c²
= ΔMᴍc²
Thus
[KEᴇᴄᴍ = ΔMᴍ c²]
is not a postulate but the field-completed form of Newtonian kinetic energy, produced by gravitationally amplified mass manifestation.
Physical meaning:
Classical mechanics writes
KE = ½mv²
as if matter mass itself moves.
ECM reveals that motion occurs because matter mass decomposes, releasing a frequency-governed mass ΔMᴍ that oscillates and interacts gravitationally.
Therefore:
• Kinetic energy is not stored in matter
• It is stored in manifested mass (NAM)
• It is frequency-based, not velocity-based
• It obeys a pre-relativistic mass–energy equivalence
[KEᴇᴄᴍ = ΔMᴍ c²]
This is the true engine beneath Newtonian motion - and the origin of mass–energy equivalence without relativity.
2.7 Frequency Governance
The manifested mass is further linked to frequency through
ΔMᴍc² = h f,
showing that Planck and de Broglie frequencies measure the rate of mass generation from energy. Motion, radiation, and gravitation are therefore different frequency-regulated expressions of the same mass-manifestation process.
2.8 Recovery of Classical Mechanics
In the limit
-Mᵃᵖᵖ → 0
ECM collapses back to classical Newtonian mechanics:
Mᵉᶠᶠ → Mᴍ = m.
Thus classical physics is recovered exactly as the zero-manifestation approximation of a deeper mass-energy theory.
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