A physical interpretation of Hubble's law and the cosmological redshift from the perspective of a static observer

TL;DR

This paper provides explicit formulas for the velocity and redshift observed in an expanding universe, clarifying that interpreting cosmological redshift as a Doppler effect is only valid at zero distance.

Contribution

It offers exact expressions for velocities and redshifts from a static observer's perspective, clarifying the physical interpretation of Hubble's law and cosmological redshift.

Findings

Redshift interpretation as Doppler effect is only valid at zero distance.

Explicit formulas for velocities and redshifts in Hubble flow.

Clarifies the physical meaning of Hubble's law.

Abstract

We derive explicit and exact expressions for the physical velocity of a free particle comoving with the Hubble flow as measured by a static observer, and for the frequency shift of light emitted by a comoving source and received, again, by a static observer. The expressions make it clear that an interpretation of the redshift as a kind of Doppler effect only makes sense when the distance between the observer and the source vanishes exactly.