To be clear, it breaks causality in every reference frame. It is the definition of causality and derived from the definition of reference frames. In fact, c is not really the speed of light, it’s the speed of causality. Light itself could theoretically go slightly slower.
Causality is always hard for me to understand. Imagine an MRI, where you take a 3D object and slice it into a sequence of 2D slices. When you view the 2D slices, is it really true that slice N has any causal relationship to slice N+1? No, of course not. However, when we view a 3D slice of the universe, which is a 4D object in space-time, we want the slices to have a causal relationship.
The big difference that makes causality work is that there is only one timelike dimension (but three spacelike ones).
A purely spacelike curve can wrap back around and close on itself like a circle. But a purely timelike curve just can't turn around: it's like a person on a tightrope who's not allowed to slow down. So it's stuck going to later and later times forever (or to earlier and earlier ones, depending on orientation). (Yes, changes in reference frame broaden that 1D tightrope to a whole "future light cone", but that only allows limited changes of "heading": the time coordinate is guaranteed to be increasing no matter what.) And, roughly speaking, it would cost infinite energy to change from a timelike path to a spacelike one.
You can perform the same thought experiment by pretending you can only “see” in 2 dimensions. Using the MRI example, pretend you “see” sequential slices of the MRI. Prior slices still don’t cause later slices even though one of the dimensions (the axis along which the MRI was taken) is special. And notice, your observation that 3D objects can loop back on themselves is still correct. But that doesn’t really impact how you see the 2D slices.
This could have been an interesting video, but PBS had some nutty production values. Why did they insist on filling half the screen with some guy waving his arms to distract you? I hope the producer moved on to his true calling - gasoline pump videos.
They have toned that down a bit over the years since that video was recorded six years ago. The videos are really informative, and you can always close your eyes and listen if you like.
