From the reference frame of the earth, the distance between the surface of the earth and the muon is longer, but the muon survives because time for the muon is slowed down.
From the reference frame of the muon, the time experienced by the muon is not slowed down but the muon survives because the distance between the surface of the earth and the muon is contracted. However, the time experienced by the earth is slowed down.
Please tell me if my logic is correct. I am not sure as to what time the muon's clock and the earth's clock would be showing when the muon and the earth's surface meet (supposing we could attach clocks to the two objects), since each object observes the other's clock slowed down from its own frame of reference.
Please forgive me if I seem ignorant!