1. The problem statement, all variables and given/known data Prove that for a timelike interval, two events can never be considered to occur simultaneously. 2. Relevant equations Δs'2=∆s'2 (∆s is invariant) s2=x2 - (ct)2 s'2=x'2 - (ct')2 3. The attempt at a solution I first imagined a reference frame K in which two events happened at (x1, t1) and (x2, t2) Here, ∆s2= x22 - x12 - c2t22 + c2t12 = s'2=∆x'2 - ∆(ct')2 where ∆(ct')2 = 0 (if I'm trying to prove that this CAN'T happen I thought it would be best to show what would happen if it were indeed zero) ...which can be rewritten as: ∆s2= x22 - x12 - c2t22 + c2t12 = s'2=∆x'2 = x2'2 - x1'2< 0 (my book says that for events with timelike separation that ∆s2<0) I guess I'm not really sure where to head from here. Should I substitute in x'=x-vt...(the lorentz transformations for velocity) and try and solve for some value of v such that (ideally) it might be v>c and thus false? I tried doing that but saw that the algebra seemed pretty long and so I thought that I might not be on the right track...I'm not exactly sure what I'm looking for here, I'm quite new to proof-based math (or physics or really anything). Any guidance would be appreciated.