Consider 1-D space. Let S and S' be two inertial reference frames. Let A and B be two events.
Co-ordinates of A and B under S are A = (xA,tA) and B = (xB,tB).
When we say events coincide - it simply means they have same space-time co-ordinates.
i.e. if (xA = xB) and (tA = tB), then w.r.t S, events A and B coincide.
Let me state a theorem: If A and B coincide in S, then they will the coincide in S' (hence in every and any IRF i.e. two events being coincident is NOT a relative concept)
Q1 - Why is this theorem? Is there a deeper assumption and understanding regarding space-time behind this concept? (I'm not looking for an answer basis Lorentz Transformation - but a more physical / maybe more basic argument). Or is this just an assumption of Special Relativity?
Q2 - If 2 balls A and B collide - they will collide in every IRF. How can I derive this basis above theorem? i.e. how can I "precisely" express collision of 2 balls as two events which coincide?
(I'm asking the above question to better understand space-time, events etc at a little conceptual level and I'm having difficulty in understanding them, Thanks for your help)