Sign swapping - spacelike intervals

[Svendsen]

Hello guys!

I´ve seen that for spacelike intervals, ie $s^2 < 0$ you´re able to swap the sign of s = x-y = y-x. Why is that?

Thanks!

 

[Svendsen]

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?

 

[Svendsen]

Figured it out! The reason is that for spacelike intervals it is possible to choose a reference frame such that the two events x and y occur at the same time. This however is not possible for timelike ones.

 

[Dale]

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?

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.