We see a quasar 13 billion light years away. What does this mean?

[Skiessa]

TL;DR

If the furthest quasars we can see are lets say 13 billion light years away from us, then does this mean that the distance between us and that quasar was 13 billion light years at 13 billion years ago?

Summary: If the furthest quasars we can see are let's say 13 billion light years away from us, then does this mean that the distance between us and that quasar was 13 billion light years at 13 billion years ago?

To anyone educated in physics this might be a silly question but to me this is quite confusing, since the interpretations of the light speed constant and of what it says about the data we receive from the distant objects vary so much among non-educated people.

one common conception is that 13 billion years ago we were merged with the quasar, and that should at least be wrong, right? that would mean that we would have seen the light radiated by the quasar already 13 billion years ago, right?

some say that 13 billion years ago both we and the quasar were in completely different positions and that neither of our positions cannot be defined from the light we see from the quasar today, but that's also wrong, right?

but if our universe was 13 billion years ago at least big enough for us to be 13 billion LY away from the quasar already, and the universe has been expanding past-light speed ever since, it means that it must be freaking colossal today, right? if so, is there any way that we can measure of how big the universe was 13 billion years ago?

 

[Bandersnatch]

If the furthest quasars we can see are let's say 13 billion light years away from us, then does this mean that the distance between us and that quasar was 13 billion light years at 13 billion years ago?

Depending on the source that quotes such distance, it could mean either the distance now - where you'd find it if you freezed the expansion today and took a measuring stick - or the so-called 'light travel distance', which is what you take the time since emission and multiply it by the speed of light, and which doesn't have any direct physical meaning. It tends to be specified which is which, if you know what to look for. IIRC Wikipedia likes to used the latter in articles about distant objects.
The distance at emission is rarely quoted, and in any case it couldn't be 13 billion light years, since 13 billion years ago that was beyond our cosmological event horizon (beyond the maximum distance from which light can ever reach us).
The distances at emission to the farthest observable objects were much closer than today, but non-zero.

The various distances can be obtained by plugging in the redshift data into a model of expansion. The calculator in the link below uses the concordance LCDM model, and can give you information on e.g. how far something was and is now depending on when the signal was emitted:
http://www.einsteins-theory-of-relativity-4engineers.com/LightCone7-2017-02-08/LightCone_Ho7.html
E.g.:
The output table below is for the cosmic microwave background radiation:

With z being its redshift, T being time at emission, and the two distances representing distance at reception and at emission respectively.

 

[Skiessa]

Depending on the source that quotes such distance, it could mean either the distance now - where you'd find it if you freezed the expansion today and took a measuring stick - or the so-called 'light travel distance', which is what you take the time since emission and multiply it by the speed of light, and which doesn't have any direct physical meaning. It tends to be specified which is which, if you know what to look for. IIRC Wikipedia likes to used the latter in articles about distant objects.
The distance at emission is rarely quoted, and in any case it couldn't be 13 billion light years, since 13 billion years ago that was beyond our cosmological event horizon (beyond the maximum distance from which light can ever reach us).
The distances at emission to the farthest observable objects were much closer than today, but non-zero.

The various distances can be obtained by plugging in the redshift data into a model of expansion. The calculator in the link below uses the concordance LCDM model, and can give you information on e.g. how far something was and is now depending on when the signal was emitted:
http://www.einsteins-theory-of-relativity-4engineers.com/LightCone7-2017-02-08/LightCone_Ho7.html
E.g.:
The output table below is for the cosmic microwave background radiation:
View attachment 252334
With z being its redshift, T being time at emission, and the two distances representing distance at reception and at emission respectively.

If i understood it correct, while discovering 13 billion years old light from a quasar wouldn't mean physically anything other than the light itself being 13 billion years old and that the actual quasar has to be much further away today, discovering anything that's 13 billion LY away today would require us to discover much younger light from an object and then calculating from it's departure speed that it has to be 13 billion LY from us today. and it should be stated on the study which one of these two we are talking about. am i correct?

 

[Bandersnatch]

That's about right.

 

[Skiessa]

That's about right.

thank you for your time!