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# A mathematically-derived unified formula for Time-Varying Doppler effect, Cosmological red-shift and Cherenkov radiation

preprint

posted on 2024-04-17, 12:05 authored by Qian ChenAlthough Doppler effect is a well-known phenomenon, its nature was not fully clear. Currently, many different formulas are required to describe Doppler effect in different cases, and all formulas don’t include the timing of velocity which implies they only work for constant velocities. In this paper, a general formula is mathematically derived purely from the principle of constant light speed without any other assumption. This unified formula provides a straightforward mathematical explanation of the fundamental nature of Doppler effect, Cosmological red-shift, and Cherenkov radiation. It is also supported by existing experiments and theoretically proved by Maxwell’s wave equations. This formula covers both the classical and transverse Doppler effects and applies to time-varying velocities. Furthermore, it also provides a straightforward mathematical explanation of Cherenkov radiation and Cosmological red shift. The fact that all these physical phenomena can be mathematically explained by a unified formula is interesting. Our findings reveal the intrinsic connection between these phenomena, attributing them to a common time scaling factor arising from relative motion between light source and observer. These results are just part of a new theoretical framework mathematically derived from the principle of constant light speed, named as “Asymmetry Theory”, which is comprehensive, self-consistent, and in harmony with all existing experiments. Moreover, our results suggest potential applications, including the discussion of time-varying recessional velocities in Hubble's law, which may shed new light to puzzles like “Hubble tension”.