Choosing different ways of slicing spacetime into space and time equates to choosing a different coordinate system. The twin paradox arises from the fact that the duration of time you personally experience measures the interval traversed through spacetime. Just like two people walking different distances between the same two points in space, in the twin paradox, one twin moves only in time while the other travels a curved path in spacetime, demonstrating the difference between space-like and time-like paths.

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