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In Extended Classical Mechanics (ECM), photon dynamics extends far beyond the classical notion of massless light quanta. Each photon is treated as a frequency-governed energy packet with an associated effective mass Mᵉᶠᶠ that arises during motion and interaction. Its behaviour reflects continuous transitions of energy and time, governed by the equivalence KEᴇᴄᴍ = ΔMᴍc² = hf.
A photon’s frequency (f) directly determines its intrinsic energy and effective mass:
Eₚₕₒₜₒₙ = hf = ΔMᴍc².
When a photon experiences a change in its frequency or energy state due to gravitational interaction, motion, or medium variation, it effectively undergoes a mass–energy adjustment expressed as:
ΔMᴍ = −ΔMᵃᵖᵖ.
The term −ΔMᵃᵖᵖ in ECM describes the apparent or effective reduction in energy density associated with photon propagation over distance or through gravitational fields. This explains redshift effects and energy attenuation as natural outcomes of photon dynamics rather than mere observational artifacts.
As photons interact with gravitational potentials, their frequency adjusts according to local energy density gᵉᶠᶠ and time distortion Δt. This interplay yields the observed gravitational redshift and blueshift:
f₂ / f₁ = (1 − gᵉᶠᶠΔt / c²).
Such relationships illustrate that photon energy is a continuously modulated function of its propagation environment.
Within ECM, photons are therefore not isolated packets of invariant energy but dynamic participants in local energy fields. Their interactions define the observable energy–time fabric, where:
Eₜₒₜₐₗ = KEᴇᴄᴍ + PEᴇᴄᴍ = (ΔMᴍ + Mᵃᵖᵖ)c².
This establishes the photon’s motion as a direct outcome of the surrounding field’s effective mass–energy structure.
In essence, photon dynamics within ECM unifies wave, particle, and field behaviours under one framework. A photon’s frequency and apparent mass reflect reciprocal forms of the same energy state, where changes in frequency correspond to equivalent mass and time distortions. This redefines light not as a passive signal but as an active energy carrier within the mass–time continuum.
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.