In the discussion on sign swapping for spacelike intervals, it is established that for spacelike intervals defined by s² < 0, the sign of s can be swapped between s = x - y and s = y - x. This is possible due to the ability to select a reference frame where the events x and y occur simultaneously. In contrast, such a transformation is not feasible for timelike intervals. The continuous transformation is demonstrated through a 180° rotation about an axis that bisects the x and y axes.
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Take the axis which is 45° between x and y. Rotate 180° about that axis. Now you have swapped x and y, and since every rotation about that axis less than 180° is also a valid transform, the transform is continuous.Svendsen said:Supposedly there exists a continuous transform between x-y and y-x for spacelike intervals, but not for timelike ones. Can anyone show me that?