PART 1:
I was reading the article Relativity of simultaneity Wikipedia. I couldn't understand this line:
"if the two events are causally connected ("event A causes event B"), the causal order is preserved (i.e., "event A precedes event B") in all frames of reference."
Is this an assumption or a consequence of STR? Please explain.
Note: My question consists of 2 parts this is the 2nd part.
Below is a genral version of my previous question question:Breaking the simultaneity.
PART 2:
Let there be three events $A$,$B$ and $C$ s.t: $C$ is the result of Simultaneous occurrence of $A$ and $B$. In other words $C$ occurs iff $A$ and $B$ are simultaneous.
Now as we know in STR any two events separated in space are not simultaneous in different frames. So In some frames $C$ will occur and in some $C$ will not occur which will cause paradox.
I tried many thought experiments to make such a paradox but i failed. In all the experiments that i thought i could not break the causality even by breaking the simultaneity because everytime the fact: "all signals move slower than light" preserved the causality.
So why causlity remains preserved always? Is it due to the fact that nothing can move faster than light?
Best Answer
Causality is preserved, unless Tachyons exist.
Part 1: STR doesn't assume causality. Causality is violated when you have a flow of information that goes back to the same place in space AND time, creating a contradiction. Both newtonian and STR guarantee causality. STR is more complex, but it still prevents anything from going back in time with respect to another's frame, as long as nothing starts out faster than light in the first place (i.e. Tachyons). The policeman work by creating a "light barrier" that prevents anything from being accelerated past the speed of light.
Part 2:
"C is the result of Simultaneous occurrence of A and B. In other words C occurs iff A and B are simultaneous."
You can't do this. Lets try: A and B are excited atoms that emit flashes of light. Suppose a detector halfway in-between explodes because both atoms flashed at once. The atoms and detector are stationary. Sounds like a simultaneity detector? Not in a frame moving with respect to the set up! In a moving frame, the atoms emit light at different times (light still goes the same speed in any frame), and the detector is still halfway in-between the atoms. But the set-up moves just the right amount in the time it takes for the flashes to converge that the detector will hit them at thier meeting point, and still explode.