The Planck Epoch: Phase Progression from t₀ to Planck Time tₚ and the Canonical Definition of Gravity in Extended Classical Mechanics (ECM)

Soumendra Nath Thakur

March 08, 2026

Canonical ECM Definition of Gravity:

Gravity in Extended Classical Mechanics (ECM) is the reversible mass-binding condition arising from the spatial gradient of residual potential energy (−ΔPEᴇᴄᴍ) generated during frequency-driven mass manifestation.

During the primordial frequency transition (f₀ ⇒ fₚ) through the fundamental phase cycle (Δf₀ = 1 Hz = 360°), this residual potential energy appears as negative apparent mass (−Mᵃᵖᵖ), whose interaction with matter mass (Mᴍ) produces the effective gravitational field (gᵉᶠᶠ).

Unlike General Relativity, where gravity is interpreted as spacetime curvature, ECM describes gravity as a measurable energy-mass redistribution process governed by frequency transformation.

Equation 1 — ECM gravity structure

Fᴇᴄᴍ = gᵉᶠᶠ = ∇(−PEᴇᴄᴍ) ≡ ∇(Mᵃᵖᵖ) ↔ Mᴍ + (-Mᵃᵖᵖ)

Equation 2 — ECM gravity identity

gᵉᶠᶠ ≡ ∇(Mᵃᵖᵖ) ≡ ∇(−ΔPEᴇᴄᴍ) ⟺ KEᴇᴄᴍ = −ΔPEᴇᴄᴍ = −ΔMᴍ c²

Interpretation

• (Mᵃᵖᵖ ≡ −ΔPEᴇᴄᴍ)

• (gᵉᶠᶠ) arises from the spatial gradient of residual potential energy

• Gravity therefore emerges from the interaction between matter mass (Mᴍ) and negative apparent mass (−Mᵃᵖᵖ)

• This makes gravity a direct manifestation of potential-energy redistribution

I would like to clarify that Planck time (tₚ) should not be interpreted merely as a single isolated numerical value. A duration is always defined by the difference between two states, not by a number alone. For example, a duration of 10 minutes does not arise simply from the number 10; rather, it is the difference between 0 minutes and 10 minutes that constitutes the interval.

Similarly, Planck time (tₚ) may be understood as the difference between an initial reference state (t₀) and the terminal state (tₚ).

While (tₚ) is regarded as the smallest physically meaningful unit of time, the reference point (t₀) represents an abstract boundary condition, since any time smaller than (tₚ) lies outside the domain of physically measurable time.

Conceptually, the progression from (t₀) to (tₚ) may be illustrated as a phase progression, analogous to a circular scale:

t₀°, t₁°, t₂°, … , t₃₅₉°

which represents the frequency progression

f₀ ⇒ fₚ 

When the cycle completes at

t₃₆₀°

the full progression corresponds to one Planck time interval (tₚ).

Thus, the domain between (t₀°) and (t₃₆₀°)—that is, the completion of a full phase cycle (Δf₀ = 1 Hz = 360°) represents the Planck epoch in this interpretation.

In this sense, the Planck epoch represents the primordial phase domain in which frequency-governed energy transformation progressively establishes the first physically meaningful temporal interval, culminating in the emergence of Planck time (tₚ).

Within this framework, the Planck epoch is described through the energy-equivalence principle together with the frequency–energy equivalence relation, where (tₚ) emerges as the completion of a fundamental phase cycle, rather than as a single isolated constant.