Long rigid ship in cosmology One spaceship, rigid as a whole, 100 Megaparsecs long. Being aware of relativity, observing one end from the other is affected by cosmological redshift due to expansion of the universe. Now assuming the reference frame of one end, reality as it is observed from our end explains that the ship’s other end is moving away from us and that is indeed a physical fact. Yet, by the grace of the physical laws of the universe, we conclude that in reality, there is no moving away and it is simply the universe affecting the message to get here longer. These realities are contradictive. Here we have two opinions of our own. One being the observing side and the other being the calculating side. Based on principle of relativity, neither of which is preferred over the other. Yet, we always agree that the ship’s ends are not moving away.
In the interest of argument, we could say that the ship’s ends are moving away from each other because indeed we won’t be able to communicate at some point when the other end moves beyond the observable universe’s boundaries. But at the same time, we have to concede to the fact that by our calculations and accepted laws of inertia, the rigid spaceship is in fact still a whole and has not lost any ends since local effect of cosmological expansion is not strong enough to break the bonds between any atom or molecule. Yet, as a whole from one end to the other the ship is moving away.
In favor of the opposite argument, we could say the ship is rigid therefore its ends are not moving away but the observation is quite clear on this one. So, we have two opinions from one frame and they are contradictive. Which brings the question of which narrative is true? Yet principle of relativity tells us that we don’t have a preferred truth. Now if we say the ship’s ends are not moving away, we can observe them as they do. If we say ship’s ends are moving away, we know it’s not, because locally, cosmological expansion is not strong enough to affect the bonds between atoms so we know it’s not moving away.
To put things in perspective I want to remind myself of the fact that principle of relativity’s role here is critical. And I would say that it has a negative effect on the validity of the second narrative (the Not moving away narrative) because we could only claim it’s not moving away if we had a global side of the situation (to visualize it: see the entire ship as a whole so we could decide) and that is exactly what the principle is there for. There is no preferred reference frame which means there is no looking at universe from above (as a whole or globally). On the other hand, lack of global version of reality should emphasize on and strengthen the validity of the local version which tells us that there is no moving away; just an illusion.
The problem that stands is that if we say it’s not moving away, we are preferring one narrative over the other. So, does that mean that calculations come before observations? Why does our knowledge takes preference over our observation? What happens to the definition of reality in this case? How do we reconcile?
 A: Unfortunately this question is based on the mutually contradictory premises that (a) two distinct points can be both co-moving and yet (b) at constant proper distance in our standard cosmological spacetime. This is incorrect.
If the two points are indeed rigidly connected then it is possible for at most one of them to be co-moving with the FLRW background. The other point must be moving rapidly in the direction of the first point relative to the local background.
If on the other hand the two points are both co-moving with their respective local background then they cannot be rigidly connected. They will be receding from each other rapidly.
The two premises are incompatible and that incompatibility is the root of all of the contradictions described. At least one of the premises must be rejected. Once either of the incompatible premises are rejected then none of the contradictions arise. There is no conflict of narrative if given a non-self-contradictory scenario to narrate.
I will here assume that you would keep (b) and discard (a), so we have a long ship of constant proper length and one end is co-moving with the background. In the cosmological coordinates there will be a substantial cosmological redshift. However, the end that is not co-moving with the background is moving at high coordinate velocity towards the co-moving end. This will produce a blue-shift counteracting the cosmological red-shift in those coordinates. Note, in these coordinates because of the changing scale factor the constant-length ship will become "smaller" with respect to the coordinates. This is a coordinate artifact with no physical implication other than the velocity wrt the background at each location.
