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In Extended Classical Mechanics (ECM), time dynamics describes how the flow of time varies in direct proportion to changes in energy, motion, and mass distribution. Rather than being an external coordinate, time in ECM is a frequency-governed parameter that evolves with every oscillation and energy transition.
Each physical system possesses its characteristic oscillation frequency f, defining its intrinsic temporal rate. The interval Δt corresponding to one cycle is given by Δt = 1 / f. When energy or effective mass changes by ΔMᴍ, the corresponding frequency and local time structure adjust according to:
KEᴇᴄᴍ = ΔMᴍc² = hf.
This establishes a direct equivalence between time rate and energy state.
In a varying gravitational potential or during acceleration, the apparent time difference (Δt) between two frames reflects the difference in effective mass Mᵉᶠᶠ and energy density gᵉᶠᶠ. The ECM formulation expresses this as:
Δt₂ / Δt₁ = (Mᵉᶠᶠ₁ / Mᵉᶠᶠ₂) = (f₂ / f₁)⁻¹,
linking gravitational time dilation directly to frequency variation rather than geometric curvature.
When −ΔMᵃᵖᵖ occurs, representing apparent energy loss or dispersion, the local oscillation frequency decreases, elongating Δt. This explains cosmological time distortion and redshift as consequences of mass–energy redistribution, not spacetime deformation.
Consequently, time dynamics in ECM reveals that every energetic interaction carries a temporal signature. The local flow of time expands or contracts in step with the oscillation frequency and effective mass. As ΔMᴍ approaches zero, time symmetry is restored; as −ΔMᵃᵖᵖ increases, time distortion grows.
This approach unifies temporal, energetic, and gravitational phenomena into one framework:
Δt = (z / f) = x° / (360°f),
showing that time difference, redshift, and frequency are co-expressions of the same underlying transition. Thus, in ECM, time is not an independent variable but a measurable outcome of energy–mass evolution.
When two repeating or oscillating signals are compared, the phase shift represents how far one signal is ahead or behind the other in its cycle. Imagine two identical waves — if one wave starts a little later than the other, the delay between their peaks is the phase difference.
A complete wave cycle corresponds to 360 degrees of phase. Therefore, any phase shift can be thought of as a fraction of this full cycle. If the shift equals half the cycle, it is 180 degrees; if it equals one-quarter, it is 90 degrees, and so on.
The phase shift is closely linked to frequency and time difference. Frequency tells us how many cycles occur each second, while the time difference shows how much one signal lags behind another. Together, these determine the observed phase shift.
When the frequency increases, a small delay in time results in a larger phase shift because the cycles repeat more rapidly. When the frequency decreases, the same time delay gives a smaller phase shift.
The time delay can therefore be found by dividing the phase shift by the frequency — it is how long one wave takes to “catch up” with another.
The fraction of the cycle that has shifted, often called the redshift factor or simply z, expresses how much the wave has stretched or shifted in proportion to its full cycle.
In simple terms: the phase shift, frequency, and time delay are three views of the same relationship. A change in one always means a change in the others.
Thus, in both phase-shift and redshift interpretations: the phase difference reflects how much one oscillation is displaced from another. The redshift expresses the same displacement as a fractional or proportional change in wavelength or frequency. The time delay is the direct temporal expression of that displacement.