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.
