The discussion revolves around the properties of spacelike intervals in the context of special relativity, specifically focusing on the ability to swap the signs of the difference between two events, denoted as s = x - y. Participants explore the implications of this property and the existence of continuous transformations between the two events.
Participants express differing views on the nature of transformations between spacelike and timelike intervals, with some proposing the existence of continuous transformations while others focus on the implications of reference frames. The discussion remains unresolved regarding the specifics of these transformations.
Some assumptions about the nature of spacelike and timelike intervals and the definitions of continuous transformations are not fully explored, leaving room for further clarification.
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?