>>11529467It is true that for some (not all) events 'a' and 'b' that appear simultaneous, can appear with 'a' before 'b' according to a different observer, or with 'b' before 'a'.
These events will cannot be causally linked however. An example would be witnessing two simultaneous lightning strikes on either side of you when stood still on Earth. Since you're stood inbetween them and the light you see is the fastest thing that can travel between them, there cannot have been any causal link between the strikes. These types of events could be viewed in any order by a moving observer.
If two events are causally linked then the maths works out that for all observers that the events are observed in the right order.
I think part of your misunderstanding comes from that gif? But we can use the gif to rectify that.
In your gif you will notice that A, B, and C are not within any of each other's light cones (the light grey shading shows B's lightcone). This means they cannot be causally linked since travelling from A to B requires faster than light travel according to every observer. This means their order is relative, as shown by the gif.
Now focus on the grid square (1,2) in that gif and watch how it gets transformed. This point is within B's light cone but not A's (also C's but that's irrelevant). Notice how (2,1) is always occurring after B. This is because the Lorentz transformation moves each point along a hyperbola that is asymptotic to the 45 degree line that defines the edge of the light cone, pic related.
Obviously this hyperbola within the lightcone transforms (2,1) so it is always occurring after B, but the hyperbola in the dark region to the left will transform (-1.8, 0) from being before or after (or simultaneous) depending on what speed you're travelling.
Hope this helps :^)
