13 February 2026

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.


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:

PhaseTemporal ResolutionDynamic Regime
tₚ⁄360 ≈ 1.5 × 10⁻⁴⁶ sLatent, superluminal, pre-metric
180°IntermediateTransitional, emerging geometry
360°tₚ ≈ 5.4 × 10⁻⁴⁴ sStabilized, relativistic, manifested

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.


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.


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.


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.


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.


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.


Developed by Soumendra Nath Thakur
Tagore’s Electronic Lab, India


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