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I looked at this question. There's one answer that alludes to what I'm asking, but I don't find it satisfactory, because to me the following is still a paradox:

The most distant galaxies we have ever observed appear to be around 13 billion light years away. Here's my question: Suppose the universe were not expanding, and suppose an observer in a galaxy 10 billion light-years away from us RIGHT NOW were to look directly at our planet (or rather at least the section of space our planet is occupying) with some magical telescope powerful enough to do such a thing. In this hypothetical scenario, both our planet and this galaxy would be static. The physical distance between the two doesn't change throughout all time. If we can observe such a far away galaxy (albeit as it was 10 billion years ago), could an observer in this supposed galaxy see earth? You'd say no, because light from our earth hasn't had enough time to reach the galaxy, with Earth being only 4.5 billion years old. But how is it that we could see such a galaxy from our viewpoint? Agreed that when light left that galaxy the earth was still a twinkle in the Milky Way's eye. But the light made the distance. At the same instant the distant observer looks at us and finds nothing?

Why is it that we can see them and they can't see us? Again, static environment. Light works one-way only?

What are the conditions for simultaneous mutual observation??

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  • $\begingroup$ The most distant galaxy is over 30 billion light years distant, it's moved since the light started traveling our way. I can see the milky way and I'm less than 25,000 years old. Physics.se isn't the place to ask about hypothetical static galaxies, because the rules would be different than our universe. $\endgroup$
    – Jiminy Cricket.
    Jan 2, 2021 at 8:34

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You should take care when talking about a "now" on large distances. In special relativity, there is no such thing as a "now" which would be the same here and at a distant point; and you could hit at paradoxes if you stick to that idea (see here).

The best thing you can do is to think in terms of past and future light cones. The past light cone of an event $E$ in spacetime (an "event" being combination of a time and a position) is the set of all other events from which $E$ can receive a light signal. The future light cone of $E$ is the set of all other events to which $E$ can send a light signal. The event $E$ can only be influenced by events located inside his past light cone, and it can only influence events located inside his future light cone. We talk about it as the causal structure of spacetime.

Now, going back to your galaxies : there is nothing wrong once you drop the idea of "simultaneous mutual observation". Your far away galaxy should be inside our past light cone for us to observe it. But may there be observers out there, earth could not have entered their past light cone yet (a little drawing is incoming).

Here it is :

enter image description here

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  • $\begingroup$ Just so I understand.... we're not in their light cone. And there is no simultaneous. ..... light cones don't intersect each other implies no mutual observation....? $\endgroup$
    – MaximusFastidiousIrreverence
    Jan 2, 2021 at 9:24
  • $\begingroup$ In my drawing, we are indeed not in the past light cone that stems from the observer at this given time in the distant galaxy. But in the future of this galaxy, there may be other observers for which we are in the past light cone. There is no such thing as simultaneity or "mutual observation", and it has nothing to do with the intersection of light cones. It comes from the fact that there is a speed limit for any exchange, the speed of light. Since this speed is really fast, it is okay to think of simultaneity in our everyday life. But you are always observing things as they were in your past $\endgroup$
    – Emmy
    Jan 2, 2021 at 19:52
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Because, not accounting for the expansion of space, we are seeing what was in their galaxy 10 billion years ago if they are 10 billion light years away, we do not know what it looks like right now. If observers there are looking towards our part of space right now they will see what was here 10 billion light years ago, most likely the molecular cloud that we were formed from since our Sun is only about 4.6 billion years old. So, at this moment, we would both see only each others past.

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  • $\begingroup$ isn't it weird though that we can see them but they can't see us?? $\endgroup$
    – MaximusFastidiousIrreverence
    Jan 2, 2021 at 8:03
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If we and they are looking in each other's direction right now, they won't see us because we weren't here 10 billion years ago, and we won't see them because they weren't there 10 billion years ago. Perfectly symmetrical situation.

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  • $\begingroup$ we are supposing that we can see them. Just like how right now we can see galaxies 13 billion light years from us. My question is suppose the two galaxies are static, could they see us? No right?... because the earth wasn't here if were talking about distances more than 4.5 billion. But then how do we see them if they can't see us?? $\endgroup$
    – MaximusFastidiousIrreverence
    Jan 2, 2021 at 8:23
  • $\begingroup$ by your logic the furthest galaxies observers can mutually witness is are those within a 4.5 billion lightyear spherical radius from us.... how then can we witness 13 billion lightyear distant galaxies? $\endgroup$
    – MaximusFastidiousIrreverence
    Jan 2, 2021 at 8:27
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    $\begingroup$ We can't mutually witness any other galaxies. We're always seeing what was there millions of years ago. They are seeing what was here millions of years ago. Nobody ever sees what is in another galaxy right now. $\endgroup$
    – Kristoffer Sjöö
    Jan 2, 2021 at 11:29

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