Metrics and distances in the Universe.

In the series: Note 4: Metrics and distances in the Universe.

Version: 0.0
Date: September 2022.
Status: In dev., and information will be added/edited, to make it more informative.
By: Albert van der Sel.

Here I like to spend a few words on metrics and distances in the Universe, at least as far
as human theories gets us there.

It's not a very easy subject. For example, suppose we have an "object" where some event occurred in the deep past,
and somehow, we know that the light of that event, travelled for 800 millions years (800.000.000 years) to reach us.
Now..., you cannot say that thus the distance of that object is 800 million lightyears. That would be incorrect.

In an expanding Universe, the object is probably much further away "now". Also, it is 800 million years ago,
that the event occurred, so probably, that object was much closer to us (at that time).

Well, what is the situation then? You may ask, where is that object "now", and where was it when that event occurred?
Or in better words, what are/were those both distances involved?

Here we will see some measures for distances, like the proper distance, and comoving distance, and others as well.

I will tell you, that when it goes about "distances" and metrics (especially remote distances) in the Universe, you will never be
completely "happy" (or satisfied), due to certain "uncertainties", and assumptions. But that's OK ofcourse.

Important: Since recently, the James Webb Space Telescope is operational. The preliminary results are quite stunning.
Also, on a more fundamental level, like "expansion of the Universe" and the "Big Bang" model, I think that we are going
to see some spectacular findings. Maybe even to the point where we might even have to revise models.

If I may, here are a few points before we explore any deeper.

=> (1). Let's first say something about "time". Einstein already learned us a lot how "flexible" SpaceTime is.
In different frames of reference, with different speeds, clocks run different as well. Also, the closer to a
large mass a testobject comes, the slower a clock with that object runs.
Ofcourse, a real equivalent of a clock, might serve the decay time of an elementary particle at high speed, compared
to that same particle at rest.

=> (2).