Quiescents state and uniform rectilinear motion are indistinguishable.
What: You will not even know it?
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Ñîñòîÿíèå ïîêîÿ è ðàâíîìåðíîå ïðÿìîëèíåéíîå äâèæåíèå íåðàçëè÷èìû.
×òî?: Âàì íå èçâåñòíî äàæå ýòî?
Under most real conditions and situation that is true.
The basic twin paradox (thought experiment) is a hypothetical. An imaginary situation designed to limit the question and puzzle to conditions consistent with SR.
In practice, no one can escape the conditions and effects associated with gravity and GR, when talking about spaceship's and planets.
No, no one can in a real situation assume that a planet is at rest.
The thought experiment ignores that to focus on the core issue of time dilation associated with velocity as defined, in SR.
In real life conditions, time dilation associated with GR would dominate.
GPS sattelite clocks run fast compared to those on earth. This is a combined GR and SR time dilation effect, where GR has a greater affect on the clocks.
Returning to your quoted post...
You are correct when you say that in practice one cannot say which of two objects is "really" moving with respect to the other.
We can say which of two objects or observers or twins, changes its velocity, when compared to a common origin. As I believe przyk was tring to point out, it is that change in velocity that the traveling twin experiences, that sets the two apart and determines which of the two experienced "more" velocity, during the traveling twins trip.
The basic twin paradox is an idealized hypothetical, that assumes a rest frame for the thought experiment... No there is no real rest frame.
The addition of acceleration for the traveling twin, is an attempt to project the thought experiment, in a more realistic way. Even then the hypothetical still ignores gravity and the existence of other external forces. It remains an imaginary situation. It still attempts to address or describe only time dilation associated with SR.