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When talking about how muons reach earth even though their half-life is very short the explanation of time dilation is given. From earth's frame of reference, the Muon's clock is "slowed down" so is has longer to live and keep racing at it's speed, I think I understand this.
However, will the length between the Muon and the earth when seen from earth's reference also contract? If so, why is this never included in the calculation of amount of muons reaching the earth?
Also, from the muon's perspective the earth contracts which I understand but nobody talks about the time dilation for the earth. (Although this I understand better because it doesn't really matter how "fast" time flows for the earth relative to the muon, the earth will still take the same amount of time to reach the muon wether time dilation is included or not) Examples of places where they discuss these phenomena without including the length contraction (from earth's frame of reference):