muons have a very small half life comparable to 2.5 μs or so. But we know that it has to cover a very large distance from upper atmospheric layers to reach the particle detectors installed at earth's surface. How is this possible as there journey would take a large time and they should spontaneously decay into other sub atomic particles before even reaching the detectors? please help?
From our point of view, Lorentz time dilation causes the fast-moving muon to have a longer half-life before decaying than it does at rest. So it has enough time to reach the surface.
From the muon’s point of view, Lorentz length contraction causes the distance it has to travel through the atmosphere to be much less than what we think of as the thickness of the atmosphere. So, again, it can reach the surface before it decays.
What amazing evidence for both time dilation and length contraction! Without them we would not see cosmic muons.