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In Extended Classical Mechanics (ECM), both phase shift and redshift are viewed as measurable manifestations of the same underlying physical interaction — the temporal and energetic displacement between oscillatory systems. These effects describe how the frequency (f), time difference (Δt), and phase displacement (x°) interrelate within an energy-exchange process governed by the transformation ΔMᴍc² = hf.
The phase shift represents the angular difference between two waveforms or periodic oscillations. When one signal lags or leads another, it indicates a difference in the time of occurrence of corresponding points in their cycles. A full cycle corresponds to 360°, making the phase shift directly proportional to the frequency and the time difference:
x° = 360° · f · Δt.
The redshift (z) expresses this displacement as a fractional quantity of a complete cycle:
z = x° / 360° = f · Δt.
In cosmological and energy-transition contexts, redshift signifies a stretching of the oscillation — a frequency decrease accompanied by a proportional elongation of wavelength or temporal spacing. Within ECM, this proportional change also corresponds to a mass–energy redistribution represented as:
ΔMᴍ = −ΔMᵃᵖᵖ,
showing that the apparent redshift arises from an effective loss in oscillatory energy density.
When frequency increases, the same time delay produces a larger phase difference because the oscillations occur more rapidly. Conversely, a lower frequency yields a smaller phase difference for the same delay. The relationship can be inverted to express time difference as:
Δt = z / f = x° / (360° · f).
This frequency–time–phase relationship forms one of ECM’s fundamental equivalence bridges, connecting observable redshift phenomena with underlying mass–energy transitions:
KEᴇᴄᴍ = ΔMᴍc² = hf.
Thus, what is conventionally described as a “shift in wavelength” is reinterpreted as a frequency-governed kinetic–mass variation, demonstrating the continuous convertibility between time distortion, oscillation frequency, and mass-energy state.
The measurable redshift z therefore not only quantifies how far light has been displaced spectrally, but also indicates the temporal expansion Δt associated with each photon’s energy transition. This unifies cosmological redshift and mechanical phase shift under a single ECM relation where energy, mass, and time remain inseparably connected.
In Extended Classical Mechanics (ECM), the use of the term time-dilation (Δt) requires careful distinction. The parameter Δt denotes the standard clock-time interval, representing the invariant reference of frequency cycles in a constant-phase system. The relativistic construct of time-dilation, however, refers to an elongated interval Δt′, such that Δt′ > Δt, representing a non-standard, entropically stretched time scale.
Therefore, ECM recognizes that Δt′ is not identical to Δt, but rather:
Δt′ = Δt + Δ(Δt)
where Δ(Δt) represents the entropic deviation from the standard clock interval. Accordingly, the ECM interpretation of redshift does not equate to time-dilation but to a phase-dilation or phase-distortion phenomenon, expressed as a fractional change in temporal phase per frequency cycle:
z = (Δt′ − Δt) ⁄ Δt = Δ(Δt) ⁄ Δt = x° ⁄ 360°
This represents the fractional phase shift per oscillation cycle, where the apparent elongation of time emerges as an entropic transformation of the local field-frequency structure, rather than as a relativistic expansion of Δt itself.
This version of ECM Interpretation of Phase Shift and Redshift includes a formal clarification replacing the earlier reference to time-dilation (Δt) with the corrected ECM distinction between Δt (standard clock-time) and Δt′ (entropically expanded time-scale), where Δt′ > Δt. The redshift relation is thus interpreted not merely as a temporal dilation but as a phase-dilation phenomenon expressed as z = x° ⁄ 360° representing a fractional phase-shift per frequency cycle. This update aligns both the temporal and phase perspectives of redshift within the unified framework of Extended Classical Mechanics (ECM).
- Soumendra Nath Thakur, November 2025
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.