This document contains comments about the article Comoving and proper distances in Wikipedia
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In the last paragraph I explain my own opinion.

Introduction

The article starts with the following sentence.
Proper distance roughly corresponds to where a distant object would be at a specific moment of cosmological time, which can change over time due to the expansion of the universe.
Comoving distance factors out the expansion of the universe, giving a distance that does not change in time due to the expansion of space (though this may change due to other, local factors, such as the motion of a galaxy within a cluster).
This means (if I understand this correct) that the proper distance includes space expansion and the comoving distance not.
This raises the practical question: What is the purpose of this distinction?
Comoving distance and proper distance are defined to be equal at the present time; therefore, the ratio of proper distance to comoving distance now is 1.
Okay.
At other times, the scale factor differs from 1.
How is this scale factor calculated?
The Universe's expansion results in the proper distance changing, while the comoving distance is unchanged by this expansion because it is the proper distance divided by that scale factor.
Comoving = proper / scale factor or scale factor = proper / comoving. This means scale factor > 1. This again results in the question: How is this scale factor calculated

1. Comoving coordinates

The comoving time coordinate is the elapsed time since the Big Bang according to a clock of a comoving observer and is a measure of cosmological time.

2 Comoving distance and proper distance

Comoving distance is the distance between two points measured along a path defined at the present cosmological time.
This implies that you have to know the coordinates of both points involved, simultaneous, at present. That is tricky.

2.1 Uses of the proper distance

All of these observers must have the same cosmological time.
How do you synchronise all the clocks that they all show the cosmological time?
Each observer measures their distance to the nearest observer in the chain, and the length of the chain, the sum of distances between nearby observers, is the total proper distance.
How do you measure the distance between two observers, which each have a clock which runs synchroneous?
I think the only solution is to have a grid, consisting of identical rods.
It is important to the definition of both comoving distance and proper distance in the cosmological sense (as opposed to proper length in special relativity) that all observers have the same cosmological age.
How can it be possible that proper distance (in cosmological sense) and proper length (in SR) are not the same?
The only thing that is important is how a length is measured.

Reflection 1 - proper distance versus comoving distances.

Accordingly to the definition the proper distance includes space expansion and the proper distance not.

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Created: 2 February 2017

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