Wednesday, December 2, 2015

special relativity - How to make appropriate statements concerning simultaneity or sequence of pitches?


This answer The example of relativity of simultaneity given by Einstein to a recent question related to Einstein's thought-experimental definition of (how to determine) simultaneity contained the following statement:



Suppose two people, $C$ and $D$, stand equal distances from you and are known to pitch balls at exactly the same speed. With everyone standing at rest, $C$ and $D$ each toss you a ball. You get the ball from $C$ before the one from $D$. This is not a logical inconsistency. It simply means $C$ threw a ball before $D$ in your reference frame [emphasis added].




I believe that I understand the described setup and the conclusion ("It simply means $C$ threw a ball before $D$") as such. But I question whether it is necessary to add the qualification "in your reference frame".


Carefully applying Einstein's definition of (how to determine) simultaneity, as referenced above, which for the given setup involves a suitable observer "at the midpoint between $C$ and $D$", is there even any reference frame at all (necessarily other than "your reference frame") "in which" $C$ threw a ball *simultaneous to* $D$ throwing a ball ?


Or is there even any reference frame at all (again necessarily other than "your reference frame") "in which" $C$ threw a ball *after* $D$ ?


(If there are no such reference frames, then the qualification "in your reference frame" is apparently not necessary; and, indeed, it would seem inappropriate and misleading to add such a qualification as if it were necessary.)




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