Formulations and Interpretations:
Redshift and Phase Shift through Extended Classical Mechanics' Lens

Abstract:
Redshift, central to astrophysics and cosmology, is reframed in Extended Classical Mechanics (ECM) as a frequency displacement effect-rather than as relativistic time dilation or geometric expansion. The ECM approach reinterprets traditional redshift equations using frequency, energy, and phase shift as primary variables, grounding them in Planck's law (E = hf) and introducing generalized phase-time relationships.

Key Equations

• Redshift by wavelength: z = Δλ / λ
• Redshift by frequency: z = f / Δf
• Redshift by energy: z = ΔE / E
• Planck relation: E = hf   →   ΔE = hΔf
• Generalized phase-time: T_deg = x / 360f = Δt
• Phase shift-redshift link: z = 360 x T_deg x ΔE / h

These formulations unify redshift phenomena at both microscopic (oscillator-based phase drift) and cosmological (wavefront propagation) scales. ECM shows that frequency is the generator of energy and that time is its emergent consequence-thus, all redshift is interpreted as a shift in frequency rather than a stretching of spacetime.

Insights from ECM Interpretation

• Phase displacement causes time distortion: Δt arises from x-degrees shift at frequency f
• Oscillator drift and cosmic propagation are both manifestations of frequency shift
• Redshift = cumulative phase distortion, not relativistic time alteration
• Blueshift = inverse phase compression or frequency elevation
• Energy change (ΔE) is inseparably tied to Δf by E = hf

ECM redefines redshift-blueshift relationships through energetics and oscillator phase distortion, enabling a non-relativistic yet fully dynamic explanation of wave behavior. This approach also informs signal transmission, photon sourcing, and cosmic evolution studies within ECM.

Reference Appendix

Title: Redshift and its Equations in Electromagnetic Waves - Version 2
Author: Soumendra Nath Thakur
DOI: https://doi.org/10.13140/RG.2.2.33004.54403
Date: July 23, 2025