Unified formula for Time-Varying Doppler effect, Cosmological redshift and Cherenkov radiation: Explaining Hubble Tension

<p dir="ltr">Doppler effect is well-known, but different formulas are required to describe Doppler effect in different scenarios, while all formulas do not include the timing of velocity which implies they only work for constant velocities. Cosmological red-shift and Cherenkov radiation are traditionally regarded as totally different phenomena from Doppler effect. This paper will unify these electromagnetic phenomena with a single mathematically derived formula which also applies to time-varying velocities. As part of a comprehensive theoretical framework mathematically derived from the principle of constant light speed, “Asymmetry Theory”, this formula is mathematically derived, supported by existing experiments and theoretically proved by Maxwell’s wave equations. It provides a straightforward mathematical explanation of the fundamental nature of Doppler effect, Cosmological red-shift, and Cherenkov radiation, and reveals the intrinsic connection between them: a common time scaling factor arising from relative motion between light source and observer. Tailored for optical and electromagnetic applications, it offers a novel tool for astrophysics, notably providing a plausible explanation for the “Hubble tension” by incorporating time-varying recessional velocities into redshift observations.</p>