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Prove that cause precedes effect in all inertial reference frames.
The interval from cause to effect is a future-directed timelike interval in some frame therefore it is a future-directed timelike interval in all frames.Prove that cause precedes effect in all inertial reference frames.
That's not true in general. Just because two events are in a particular temporal order in one frame does not mean that they are causally related.i want to prove that if the temporal separation dt between 2 events is positive in 1 inertial frame then it is positive in all inertial frames
As Doc Al was hinting at, this is only true if the events have either a time-like or light-like separation (meaning they could be causally related), but it's not true if the events have a space-like separation (meaning they couldn't be causally related, at least not unless there exist particles which travel faster than light, which would make a mess of causality anyway). If you're not familiar with the meaning of these different types of spacetime separations, see here.i want to prove that if the temporal separation dt between 2 events is positive in 1 inertial frame then it is positive in all inertial frames
Prove that cause precedes effect in all inertial reference frames.
that's exactly what i want. how can you prove it.Are you just asking for a proof that all inertial frames agree on the order of two causally related events--i.e. if A and B are causally related, and one frame says A happened before B, then all frames agree that A happened before B? This is not too hard to prove.
I already proved it above:that's exactly what i want. how can you prove it.
The interval from cause to effect is a future-directed timelike interval in some frame therefore it is a future-directed timelike interval in all frames.
For this question one also needs to prove that the order of two timelike-separated events can't change under the Lorentz transformation, not just that all frames agree the separation is timelike (and likewise for lightlike separated events).Yes, start with the formula for the spacetime interval and then prove that it is invariant under the Lorentz transform.
I think the question was specifically about SR.You can't prove it, because GR has solutions with closed time curves.
I think the point of the question was that for two causally-related events, all frames would agree which event came earlier and was therefore the "cause", and which event came later and was therefore the "effect". This is not true by definition, and it would be violated in SR if events with a spacelike separation could be causally related.But even in flat spacetime, "cause" and "effect" are just DEFINITIONS. So cause precedes the effect BY DEFINITION.
I think the point of the question was that for two causally-related events, all frames would agree which event came earlier and was therefore the "cause", and which event came later and was therefore the "effect". This is not true by definition, and it would be violated in SR if events with a spacelike separation could be causally related.