Exact classical Doppler effect derived from the photon emission process

TL;DR

This paper demonstrates that the exact classical Doppler effect can be derived from photon emission processes using conservation laws, aligning with wave theory results, thus challenging the notion that classical Doppler effect derivations are only approximate.

Contribution

It introduces a novel derivation of the classical Doppler effect from photon emission processes, providing an exact treatment based on conservation laws.

Findings

Exact classical Doppler effect matches wave theory results.

Photon emission process can derive classical Doppler effect without approximation.

Reveals classical Doppler effect is consistent with relativistic derivations.

Abstract

The concept of photon is not necessary only applied to the relativistic Doppler theory. It may also work well for classical theory. As conservation of momentum and energy are physical laws, if applying these laws gives the exact relativistic Doppler effect, it should also give the exact classical Doppler effect. So far the classical Doppler effect is only obtained by using some approximation, as derived by Fermi in 1932. We show that the exact classical Doppler effect can be derived from the photon emission process in the exact treatment and reveal that these results are the same as those derived from the wave theory of light.