ECM Interpretation of Phase Shift and Redshift
In the framework of Extended Classical Mechanics (ECM), both redshift and phase shift are interpreted as manifestations of the same fundamental process —
a measurable displacement between oscillatory systems due to energy exchange.
ECM reframes traditional interpretations of redshift, viewing it not as a result of spacetime expansion but as a frequency-based effect,
where a change in frequency is equivalent to a phase shift.
This approach employs the generalized phase-time equation:
T(°) = x° / (360° × f) = Δt,
which connects the phase shift in degrees (x°), frequency (f), and time difference (Δt).
This forms the foundational link between ECM’s interpretation of frequency variation, time distortion, and redshift phenomena.
Clarification on Δt and Δt′ in ECM Interpretation
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.
ECM Frequency–Phase–Time–Redshift Relation Equations
1. f = x° / (360° Δt) = z / Δt
Defines frequency (f) as the number of phase cycles (z) or angular rotations (x°) completed per unit time (Δt).
It expresses frequency as the rate of cumulative phase rotation over a time interval.
2. x° = 360° f Δt = 360° z
Gives the total angular phase displacement (x°) for a given frequency (f) during the time interval (Δt).
One complete oscillation equals 360°, so x° represents the accumulated phase, or equivalently, 360° multiplied by the number of cycles (z).
3. Δt = x° / (360° f) = z / f
Expresses the time interval (Δt) required for a system to complete a phase rotation (x°) or a fractional number of cycles (z) at frequency (f).
It represents the inverse relation between frequency and phase progression.
4. z = f Δt = x° / 360°
Defines (z) as the phase ratio — the number of cycles completed during the interval (Δt).
It is the product of frequency and time or equivalently, the normalized phase rotation (x°) to a full cycle (360°).
Mathematical Terms and Notations
| Symbol | Definition |
|---|
| f | Frequency — number of phase cycles or oscillations per unit time (Hz). |
| x° | Angular phase displacement — total phase rotation over time (degrees). |
| Δt | Time interval corresponding to the observed phase change. |
| z | Normalized phase ratio — number of cycles completed during Δt (where 1 cycle = 360°). |
| 360° | Full angular phase of one complete oscillation or rotation; normalization constant. |
Interpretation of Phase Shift and Redshift in ECM
- Unified phenomenon: ECM treats redshift and phase shift as equivalent expressions of energy exchange, where frequency displacement leads to a measurable phase difference between a source and an observer.
- Frequency as the origin: Unlike spacetime-based models, ECM considers frequency as the fundamental variable, with time emerging as a derivative property of frequency modulation.
- Phase shift: The angular difference between two oscillations, representing how much one signal leads or lags another due to field-induced distortion.
- Redshift: A fractional change in frequency or wavelength (z) resulting from energy displacement or interaction with gravitational fields.
- Interrelation: Phase shift, frequency, and time distortion are intrinsically coupled — a change in one implies proportional change in the others. Greater phase lag corresponds to longer time delay or reduced frequency.
- Application: ECM applies these relationships to phenomena such as cosmological redshift, gravitational redshift, and time delay (Shapiro effect), showing that they emerge from cumulative phase evolution rather than spacetime expansion.
Connection with ECM Phase Kernel Formalism
The ECM Phase Kernel Formalism extends these relational equations into a full dynamic framework by quantifying how cumulative phase variations across energy domains produce observable effects such as time distortion, redshift, and frequency shifts.
It aligns with these core relations by expressing gravitational and cosmological effects as outcomes of coherent phase modulation rather than spacetime curvature.
The same mathematical relations used here form the basis of ECM’s explanation of the Shapiro delay, lensing, and gravitational time dilation, establishing a unified wave–phase interpretation of gravity and redshift.
Related ECM Phase Kernel Resources
-
ECM Phase Kernel Main Index
- Overview of ECM Phase Kernel concepts, mathematical framework, and its applications to gravitational and wave phenomena.
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ECM Phase Kernel - Detailed Phase Equations
- In-depth derivation of phase-based formulations, including frequency-time-phase relations used in ECM’s gravitational analysis.
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ECM Phase Shift, Kernel-Redshift
- Detailed ECM interpretation of frequency, phase, time, and redshift relations, linking the Phase Kernel Formalism with ECM’s phase-time-frequency framework.
