PeterDonis
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FactChecker said:The point that I have been trying to make this entire time is that there is a logical symmetry between the two twins unless some other fact (acceleration, light color shift, external objects, some other physical fact) is brought into the problem.
Some other fact besides what? Basically you're saying that there is a logical symmetry between the twins if we don't know any physical facts about them. Which I suppose is true, but seems rather pointless. Obviously we need to have some physical fact that differentiates the twins. I don't think anyone disputes that. I certainly don't.
FactChecker said:Essential parts (like inertial reference frame) of the Twins Paradox can not even be defined without talking about acceleration or some representation of it.
This, however, is wrong. I've given you an explicit counterexample.
FactChecker said:very good scientists (including Einstein) used acceleration to explain the twin paradox
Arguments from authority are not valid and carry no weight here.
FactChecker said:it is exactly at the point of the turn-around that one twin departs from an inertial reference frame due to acceleration that distinguishes him from the other twin
This is one possible physical fact you could have to distinguish the twins. But it's not the only one. The traveling twin can tell he is turning around even if he has no way to measure or feel his proper acceleration, by looking at the change from redshift to blueshift of the light signals that are coming from the stay-at-home twin.
In other words, it would be fine to say that acceleration is one possible way to distinguish the twins. But you are taking the position that it's the only way, or that it's a necessary way, that we can't distinguish the twins without it. That position is wrong.