Stretch a sheet of rubber and put a giant, heavy object in the middle to stretch the rubber down. Measure the length of the rubber in the middle and the length on the edge. The path through the middle is longer. Now imagine a marble or some other object traveling across the rubber at a specific speed that cannot change. The marble going through the stretched region will take longer to reach the opposite side of the sheet than a marble traveling on the unstretched region.
Space-time is the rubber, and causality is the marble.
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