Understanding Information Propagation in Special Relativity: Explained

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This thread is slightly related to another question: https://www.physicsforums.com/showthread.php?t=109211
I was hoping someone here could give a better explanation since it's essentially a relativity problem.

In general however, what exactly does it mean to say that information propogates at the speed of light? What constitutes information? And how does it figure into special relativity?
 
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