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  • $\begingroup$ So basically, you say Alice sees the time on the spaceship has slown down significantly. Because of this, when Joe returns to his post, according to Alice, Joe accelerates very_very_very slowly. Which is consistent with him gaining a lot of weight, so his muscles can propel him to the front only so fast (in this case, so slow). $\endgroup$ Commented Jul 11, 2019 at 18:06
  • $\begingroup$ "It isn't clear what your reasoning here is." I was thinking that if a spaceship has a constant trust X, according to an external, "stationary" observer (Alice), it gains less and less momentum from the same trust, as if its weight was growing. When Joe moves forward in the spaceship, it is not different from a spaceship gaining momentum by throwing stuff backwards. So Alice must see that Joe has gained weight, as if he was a spaceship himself, for the purpose of accelerating forward. $\endgroup$ Commented Jul 11, 2019 at 18:10
  • $\begingroup$ However, even though Joe gains weight, according to Alice, general relativity says nothing about having stronger muscles. The sentence "All observers agree that Joe accelerates but they don't generally agree on the magnitude of Joe's acceleration." put me in the right track, to understand why - from the viewpoint of the "stationary" Alice everything seems normal. $\endgroup$ Commented Jul 11, 2019 at 18:12
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    $\begingroup$ @ZoltanK. wrote "However, even though Joe gains weight, according to Alice..." - Joe doesn't gain weight (or mass) according to Alice and that's all I have to say about that. You may want to search this site and elsewhere for the term invariant mass. For example, see Ben Crowell's answer here $\endgroup$ Commented Jul 12, 2019 at 0:48