information:extraction, structural:summarization, information:highlighting
Causality and prohibition of motion faster than light

It is not necessary for signals to be instantaneous to violate causality. Even if the signal from D to C were slightly shallower than the x ′ {\displaystyle x'} axis (and the signal from A to B slightly steeper than the x {\displaystyle x} axis), it would still be possible for B to receive his message before he had sent it. By increasing the speed of the train to near light speeds, the c t ′ {\displaystyle ct'} and x ′ {\displaystyle x'} axes can be squeezed very close to the dashed line representing the speed of light. With this modified setup, it can be demonstrated that even signals only slightly faster than the speed of light will result in causality violation.