Relativity and Cosmic Rays

Ethan Siegel has a post giving a good, comprehensible description of how cosmic ray muons demonstrate special relativity. Namely, that muons produced by cosmic rays colliding with the upper atmosphere, travelling downward at relativistic speeds can be detected at the ground despite a particle lifetime that is far too short for the travel time involved. The answer, of course, is time dilation; the proper time measured by the muon, the time which matters for the muon’s decay, is much, much shorter than that we measure.

An interesting additional point to consider, though, which Dr Siegel does not cover in his post, is to consider the trip from upper atmosphere to ground from the muon’s frame. Whatever speed the muon has in our ground frame, in the muon’s frame, the atmosphere and earth is coming at it at that same speed. So how, then, does the ground reach the muon in the short time the muon experiences? Length contraction! In the muon’s frame, the length of the atmosphere along the direction of motion is contracted to a shorter distance, just enough to make the time from upper atmosphere to ground consistent.

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