Soumendra Nath Thakur | ORCiD: 0000-0003-1871-7803 | August 01, 2025

This work presents time as an emergent dimension arising from the unified progression of physical changes within spatial extensions. Unlike the three spatial coordinates—length (x), height (y), and depth (z)—which represent independent variations along measurable directions, time does not evolve separately for each. Instead, it is referenced to a common mean point that reflects the collective spatial transformations. In this view, the single dimension of time does not conflict with three variable points in space but represents their continuous, unified advancement from the origin. Time is thus not the measure of independent displacements in space but the emergent progression underlying them all.

Presentation:

For time (t) to be meaningful, it must have an origin (t = 0). That origin coincides with the origin of length (x = 0), height (y = 0), and depth (z = 0)—the three measurable extensions of space. These spatial extensions represent physical changes along their respective directions, each identifiable by a variable point (x(t), y(t), z(t)).

Yet, alongside these spatial variations, there exists a temporal progression Δt that relates to the transformations occurring within them. In Extended Classical Mechanics (ECM), such transformations are inseparable from changes in effective mass:

Δt ∝ Mᵉᶠᶠ/ΔMᴍ,

where ΔMᴍ denotes the mass–energy transition governing frequency and Mᵉᶠᶠ the effective mass associated with the system.

Time is not measured individually for each of the three spatial dimensions. Instead, it is referenced to a common mean point (r̄(t)) that represents the collective spatial variation:

r̄(t) = (1/3) (x(t) + y(t) + z(t))

Thus, the unified temporal progression emerges as:

t ∝ f (r̄(t), ΔMᴍ, Mᵉᶠᶠ).

The single dimension of time therefore does not conflict with three variable points in spatial extensions. Rather, it is the continuous advancement from the origin (t = 0, x = y = z = 0) to the common mean point of these physical variations, expressed through the equivalence:

Δt ∼ Δr̄ = (Δx + Δy + Δz)/3

and

Δt ∼ (ΔMᴍ/Mᵉᶠᶠ)

Hence, time does not merely represent the independent spatial displacements (Δx, Δy, Δz), but the emergent, unified progression governed by effective mass transitions. This links geometric variations directly with mass–energy changes, where temporal evolution is an inevitable manifestation of:

KEᴇᴄᴍ = ΔMᴍc² = hf,

and the cyclical mapping of energy into frequency ensures that temporal advancement is the universal metric of all physical change.