The mass-energy relation and the Doppler shift of a relativistic light source

TL;DR

This paper explores how the mass-energy relation influences the Doppler shift of light emitted by moving sources, emphasizing proper mass conservation and discussing scenarios with velocity changes post-emission.

Contribution

It presents an alternative perspective on the role of proper mass and the mass-energy relation in relativistic Doppler effects of emitted light.

Findings

Proper mass is conserved during emission.

Kinematic and dynamical Doppler shifts are interconnected.

Implications for sources changing velocity after emission.

Abstract

This work considers the cospectral and arbitrary light emission of a moving source. The observed wavelengths of the emitted photons are described in term of kinematic and dynamical Doppler shifts in which the mass-energy relation plays a fundamental role. The presentation is an alternative way of emphasizing the importance of the concept of proper mass as a conserved quantity and the implications of the mass-energy relation when a source emits radiation. The physical contexts in which the source changes velocity after emission are discussed and a set of additional problems is presented.