But I’ve never been able to grasp exactly why it would break causality.
It’s what I might call inferred logic. It’s not that traveling faster than light “breaks causality” it’s that light is observed to be constant in all reference frames. From that observation you build a system of motion which requires that nothing can travel faster than light. In that mathematical system, if you break that rule then the math says that you must go backwards in time to go faster than light.
So the “causality” is a side effect of the math system you created based around the rule that light is constant in all reference systems.
It’s like if you created a math system where you observed A=1 and let B=1 and state that A+B=2. Then someone says but what if A+B = -1. Your reply would be that means B = -2 because we observed A = 1 and B can be anything so if we add A + B and get -1 B must be -2. If B represented time you’d say, “Well that means you have negative time!” But it’s just the math and if you give physically impossible inputs you get physically impossible outputs.
It’s what I might call inferred logic. It’s not that traveling faster than light “breaks causality” it’s that light is observed to be constant in all reference frames. From that observation you build a system of motion which requires that nothing can travel faster than light. In that mathematical system, if you break that rule then the math says that you must go backwards in time to go faster than light.
So the “causality” is a side effect of the math system you created based around the rule that light is constant in all reference systems.
It’s like if you created a math system where you observed A=1 and let B=1 and state that A+B=2. Then someone says but what if A+B = -1. Your reply would be that means B = -2 because we observed A = 1 and B can be anything so if we add A + B and get -1 B must be -2. If B represented time you’d say, “Well that means you have negative time!” But it’s just the math and if you give physically impossible inputs you get physically impossible outputs.