Phase-indexed velocity stabilization lens of extended classical mechanics (ECM) through the Planck era

Soumendra Nath Thakur

This paper concludes that the beginning of the universe was a transition from an unmanifested, latent potential state to a structured metric entity. 

It frames the Planck era as the “birth of law-governed structure” rather than a breakdown of physics. 

By replacing “singular breakdown” with “phase change,” the ECM provides a deterministic path for how physical laws—and the metric itself—crystallized from a pre-geometric state. 

Using this phase-indexed approach, the ECM provides a consistent analytical path that explains how the “chaotic” superluminal origin stabilized into the law-governed universe we measure today. 

By deriving gravity from spatial variations in the NAM gradient, the ECM explains why gravity appears to be "breaking up" at the Planck scale in the Standard Models - it has not yet finished "organizing". 

In the ECM framework, the end of the Planck era is not an end but a crystallization. When the phase evolution is complete, the negative apparent mass (NAM) is redistributed into sufficiently released matter (ΔMM) and kinetic energy (ΔKEECM) so that the laws of physics - such as gravity and time - can operate consistently across a stable spacetime metric. 

From this perspective, the "beginning" was not a moment in time, but rather the process by which time itself became a stable, measurable dimension. 

As seen in the given data (Figure 1), the 360° point is the boundary where the "super-Planck regime" ends. This transforms a pre-geometric manifestation into a structured metric entity, effectively "starting" the universe not through an explosion, but through the stability of physical laws.

Figure 1

Extended Classical Mechanics (ECM) resolves the universe during Planck epoch.

Soumendra Nath Thakur
February 19, 2026

Its presentation is in the attached figure.

Figure 1. ECM Planck-Epoch Frequency-Velocity Stabilization and Emergent Light-Speed Convergence

Physical Interpretation of the Curves During the Planck Epoch (ECM View)

This figure represents the frequency–mass restructuring process during the Planck Epoch in Extended Classical Mechanics (ECM). It does not describe an explosion, but a progressive stabilization of a frequency-dominated pre-manifest state into a physically measurable regime where v → c.

Below is the physical meaning of each panel.

(A) Velocity Stabilization Curve - Super-Planck to Planck Transition

v ÷ c = 360 ÷ x

(where x ∈ (0°, 360°))

Physical meaning:

• At very small phase angles (x° → 0°),

• frequency is extremely high and spatial manifestation is negligible.

• In this regime, the model predicts (v ÷ c) ≫ 1.

This is not physical superluminal motion through space, because:

• Space is not yet fully manifested.

• Motion represents a frequency-propagation rate, not classical spatial velocity.

As phase increases:

• Manifestation strengthens,

• Frequency decreases,

• Velocity stabilizes.

At:

x = 360° → v = c

This represents the completion of Planck stabilization, where propagation becomes constrained by the emergent constant (c).

Physical phenomenon:

Emergence of the invariant light-speed boundary from a pre-geometric frequency domain.

(B) Frequency Evolution Curve - Super-Planck Frequency Decay

f₀ → fᴘ

Physical meaning:

• At early phase: ultra-high super-Planck frequency.

• As phase increases: frequency monotonically decreases.

• At (360°):

f₀ → fᴘ

This represents:

• Conversion of excess frequency into:

• Manifested mass (Mᴍ),

• Structured wavelength (λ₀),

• Stabilized propagation speed.

Physical phenomenon:

Entropic frequency relaxation into Planck-scale physicality.

(C) Wavelength Evolution - Emergence of Spatial Extension

λ₀ → λᴘ

At early phase:

• Spatial scale is extremely compressed (sub-Planck).

• Wavelength grows as frequency decreases.

At stabilization:

λ₀ → λᴘ

Physical phenomenon:

Emergence of measurable space from frequency condensation.

In ECM language:

• Space is not fundamental.

• It arises as the geometric imprint of frequency stabilization.

(D) Product Convergence - Light Speed Emergence

f₀ λ₀ = c

The shaded super-Planck region indicates:

• f₀ λ₀ > c

• Pre-geometric propagation regime

At (360°):

f₀ λ₀ = c

This is the critical stabilization condition.

Physical phenomenon:

The universal light-speed constant emerges as a boundary condition of frequency–wavelength equilibrium.

Unified Physical Narrative of the Planck Epoch (ECM)

During the Planck Epoch:

1. The universe begins in a frequency-dominant, unstructured state.

2. Frequency decreases through entropic redistribution.

3. Wavelength increases (space emerges).

4. Velocity converges to a stable invariant value (c).

5. The product (f₀ λ₀) locks to (c).

Thus:

• The Planck Epoch is a stabilization phase,

• Not a singular explosion,

• But a frequency-mass phase transition.

Extended Classical Mechanics (ECM): A Sub-Planck Phase-Transition Framework for Cosmogenesis

The Core Ontological Inversion

Extended Classical Mechanics (ECM) proposes a radical reconceptualization of physical origins by operating in the sub-Planck regime — a domain where conventional physics, including general relativity and quantum field theory, is fundamentally inapplicable. Rather than treating spacetime as a pre-existing stage for physical dynamics, ECM posits that space, time, energy, and the speed of light itself emerge as stabilized endpoints of a deeper phase-transition process.

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The Phase-Angle Mechanism

At the heart of ECM lies a compactified phase coordinate spanning 0° → 360°, where each degree represents a sub-Planck scale of temporal and dynamic resolution.

The total frequency excess Δf₀ = 1 Hz is distributed across the full cycle, yielding per-degree increments of:

Δf = 1⁄360 Hz

applied to a Planck-frequency base of ~10⁴³ Hz.

This generates an ultra-fine hierarchical structure:

Phase	Temporal Resolution	Dynamic Regime
1°	tₚ⁄360 ≈ 1.5 × 10⁻⁴⁶ s	Latent, superluminal, pre-metric
180°	Intermediate	Transitional, emerging geometry
360°	tₚ ≈ 5.4 × 10⁻⁴⁴ s	Stabilized, relativistic, manifested

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Velocity as Fundamental - c as Emergent

ECM inverts the standard physics hierarchy.

Velocity v is the primitive quantity, beginning at normalization factors of ~10³ or higher at small phase angles and decreasing monotonically through phase progression.

The speed of light c is not fundamental, but the asymptotic stabilized value reached at 360°.

Thus:

• superluminal phase velocities (v ≫ c) occur naturally at early angles

• c emerges numerically, not axiomatically

This does not violate relativity, because relativity does not apply in the sub-Planck pre-geometric regime.

There is:

• no spacetime metric

• no light-cone structure

• no causal ordering

“Velocity” here denotes intrinsic phase-progression rate, not motion through space.

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Time as Emergent from Phase Accumulation

ECM shows that time is not fundamental, but arises from cumulative phase evolution:

Δt(x°) = x°/360°, tₚ

Temporal flow emerges from the progressive manifestation of latent energy — tracked by phase angle rather than an independent time dimension.

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Energetic Transformation Chain (ECM Core Law)

The universal ECM conversion pathway:

-ΔPEᴇᴄᴍ ↔ ΔMᴍ ↔ KEᴇᴄᴍ

• At 0° → pure latent potential

• At 360° → fully manifested kinetic energy

Total manifested energy:

E = h·Δf₀ ≈ 6.6 × 10⁻³⁴ J

Conservation holds continuously — only the partition between −ΔPEᴇᴄᴍ and KEᴇᴄᴍ changes with phase.

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Sub-Planck Domain as Computable Phase Space

ECM’s key methodological breakthrough is treating the sub-Planck regime not as a singularity but as a traversable phase domain.

The 360° cycle compactifies:

• λ₀ < ℓᴘ

• Δt < tₚ

into a continuous computable coordinate system.

This enables quantitative modeling of how physical law itself emerges from pre-geometric dynamics.

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Cosmological Implications

ECM replaces Big Bang explosion models with a:

frequency → energy → mass manifestation transition

The Planck scale becomes a stabilization boundary, not a creation event.

The universe does not originate from a singularity — it unfolds through entropic phase progression from sub-Planck latency into relativistic reality.

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Status and Predictive Program

ECM provides an ontologically distinct foundation for cosmogenesis, with testable consequences including:

• Emergence of Lorentz symmetry at 360°

• CMB statistical anisotropy signatures

• Modified primordial power spectrum

• Distinct dark-energy equation-of-state behavior

Formal mathematical development, simulations, and observational confrontation are detailed in the forthcoming publications and datasets.

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Developed by Soumendra Nath Thakur

Tagore’s Electronic Lab, India

Extended Classical Mechanics (ECM) — A Phase-Emergent Cosmology

ECM — A Phase-Emergent Cosmology

Phase-emergent cosmology in Extended Classical Mechanics (ECM) is a framework in which the universe is not created through a singular explosive origin, nor sustained as an eternally existing physical system, but instead repeatedly manifests as physical reality through frequency-governed mass–energy transformation processes.

In ECM, physical existence is not fundamental or permanent. It emerges when high-frequency energetic states undergo stabilization and redistribution governed by entropic transformation, producing the mass, gravitation, and kinetic structure of the revealed universe. This emergence occurs through distinct phase cycles (aeons), each representing a transition from an unmanifested energetic domain into measurable physical form.

Unlike singularity-based cosmologies, ECM replaces infinite density boundaries with continuous normalization dynamics. Unlike eternal cyclic models, ECM does not rely on perpetual material recycling of stars, matter, or black holes. Instead, the physical universe itself is a temporary manifestation within a deeper transformation process.

Key characteristics of ECM phase-emergent cosmology include:

• Origin through frequency-mass normalization rather than spatial explosion

• Gravitation and kinetic energy as emergent entropic consequences

• Successive aeons of physical manifestation

• Absence of singularities

• No requirement for eternal physical matter conservation

• Time and structure arising from transformation dynamics

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In essence:

ECM describes the universe as a dynamically revealed phase of energy — not a one-time creation, not an eternal machine, but a repeatedly emerging physical reality governed by transformation laws.

Extended Classical Mechanics (ECM) and the Classification of Cosmological Models Beyond Singular and Eternal Universe Frameworks

February 10, 2026
Soumendra Nath Thakur, 
Extended Classical Mechanics (ECM)Research & Development Framework.

Conventional cosmological models are commonly classified into two broad categories:

(1) eternal cyclic universes that persist indefinitely through mechanical recycling of matter and energy, and

(2) finite-duration universes that evolve between singular boundary events such as Big Bangs or Big Crunches.

Extended Classical Mechanics (ECM) does not belong to either category.

ECM replaces both singular origin assumptions and perpetual material recycling with a transformation-governed emergence framework. In this model, the universe is not an eternally existing physical object, nor a system evolving from one singularity to another. Instead, physical reality repeatedly manifests through frequency-governed normalization of mass–energy from prior unmanifested energetic states.

In ECM, gravitation, kinetic emergence, and mass redistribution arise intrinsically from entropic-frequency transformations rather than from conserved mechanical circulation of matter. Physical existence itself is phase-emergent, occurring in successive aeons governed by stabilization processes rather than by infinite continuity.

Because ECM does not assume eternally persistent physical matter, it does not require auxiliary mechanisms such as perpetual stellar fuel recycling or black hole disintegration to preserve cosmological eternity. These requirements arise only within models that presuppose uninterrupted material existence.

Conclusion

Extended Classical Mechanics introduces a third cosmological class: phase-emergent universes, where physical reality repeatedly arises through continuous transformation rather than singular creation or eternal mechanical recycling.

By replacing singularities with normalization processes and replacing eternal physicality with governed emergence, ECM provides a structurally consistent alternative framework for understanding cosmic origin, evolution, and manifestation.