The relativistic Doppler effect: when a zero frequency shift or a red shift exists for sources approaching the observer

TL;DR

This paper demonstrates a relativistic zero-frequency shift phenomenon in Doppler effect without Lorentz transformations, revealing that approaching sources can cause red shifts and zero shifts do not imply stationary sources, with implications for relativity and astrophysics.

Contribution

It introduces a Lorentz-free analysis of relativistic Doppler effects, uncovering zero-frequency shifts and unconventional red shifts for approaching sources, challenging traditional interpretations.

Findings

Existence of relativistic zero-frequency shift at maximum aberration.

Approaching sources can produce red shifts under relativistic conditions.

Zero frequency shift does not necessarily mean the source is stationary.

Abstract

It is shown without making use of Lorentz transformation that there exists a phenomenon of relativistic zero-frequency shift in Doppler effect for a plane wave in free space, observed in two inertial frames of relative motion, and the zero shift takes place at a maximum aberration of light. When it is applied to analysis of a moving point light source, two unconventional physical implications result: (1) a light source, when it is approaching (moving closer to) the observer, may cause a red shift; (2) a zero-frequency-shift observation does not necessarily mean that the light source is not moving closer, and in contrast, the light source may be moving closer to the observer at a high speed. This fundamental result of special relativity may provide an alternative way to experimentally examine the principle of relativity, and might have a significant application in astrophysics.