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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?

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    $\begingroup$ Can you edit your title to be more descriptive of the content? $\endgroup$
    – user87745
    Apr 12, 2021 at 14:44
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    $\begingroup$ I agree with @DvijD.C. I would recommend something like "long rigid ship in cosmology" $\endgroup$
    – Dale
    Apr 12, 2021 at 14:46
  • $\begingroup$ You might want to specify the shape of the spaceship, as I believe special relativity requires its spatial contraction from the end nearest its destination. I don't think that that contraction has been verified either experimentally or observationally yet, mainly because astronomical objects are generally spherical, and an approaching sphere hides its backside as effectively as a retreating sphere hides its front side. There are two papers that may interest you: Terrell's "Invisibility of the Lorentz Contraction", & Roger Penrose's "The Apparent Shape of a Relativistically Moving Sphere". $\endgroup$
    – Edouard
    Apr 13, 2021 at 3:36
  • $\begingroup$ Penrose seems to have a knack for finding such situations: The two papers appeared at nearly identical times (several decades ago), and he managed to receive 1/2 of 2020's Nobel Prize for physics, mainly (but perhaps not entirely) for other reasons.... $\endgroup$
    – Edouard
    Apr 13, 2021 at 3:52
  • $\begingroup$ I say "perhaps not entirely", because Penrose has, in connection with his own cosmological model ("conformal cyclic cosmology"), recently made an allusion to "bouncing" models, which include Nikodem Poplawski's "cosmology with torsion": Although the two models seem very different, Poplawski's model relies (for that falsifiability which is required of scientific theories) on a prevalent direction of motion, which may present difficulties related to Lorentz contraction. (I see you've included a "cosmology" tag.) Both models have past- and future-eternality in common with each other. $\endgroup$
    – Edouard
    Apr 13, 2021 at 4:03

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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.

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  • $\begingroup$ I think that you, and maybe the OP, might be making the assumption that the ship is following a straight linear trajectory. In my earlier comments, I'd (maybe too obliquely) brought in the possibility that the ship might be following a spiralling trajectory as dirigibles have occasionally done (usually en route to an accident), which I think might require spherical coordinates. Would that make a difference in your answer, or require my suggestion of an edit to the question? (Of course, the distance scale suggests that the "ship" is a local universe within a multiverse.) $\endgroup$
    – Edouard
    Apr 13, 2021 at 17:32
  • $\begingroup$ The "cosmology" tag also suggests that inference. $\endgroup$
    – Edouard
    Apr 13, 2021 at 17:40
  • $\begingroup$ I disagree. Nothing about the cosmology tag nor the OP indicates that a spiral trajectory would be relevant $\endgroup$
    – Dale
    Apr 13, 2021 at 20:08
  • $\begingroup$ I appreciate your response, but I've re-read the original and edited versions of the question, and I haven't found anything that excludes a spiral trajectory for its ship, which I think might relate the question to the possible problem (with either Poplawski's model or Lorentz contraction) that I mentioned in my comments. $\endgroup$
    – Edouard
    Apr 15, 2021 at 2:30
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    $\begingroup$ If you want to include such non standard stuff then please write your own answer. I have not the remotest inclination to put it in mine $\endgroup$
    – Dale
    Apr 15, 2021 at 2:46

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