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 Quote by DaleSpam No, "frame invariant" is not the same as "path independent".
I stand (or, rather, sit) corrected. Come to think of it, a simple calculation demonstrates that this cannot be the case (though I guess it should be obvious since the length can be extremized). The proper time of the rocketship between Earth and Betelgeuse is about 2 years, compare this with a path that stays at Earth for 2 years and then takes the spacelike path between the then simultaneous (according to Earth) points of the Earth's and Betelgeuse's worldlines. The latter path has a (proper) length of 640-2=638 light-years versus the -2 light-years for that of the rocketship. Even though these two paths connect the same two events, they do not have the same invariant length. (should have calculated before I wrote in my previous post)