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?


closed as off-topic by user191954, Jon Custer, M. Enns, Kyle Kanos, stafusa Mar 14 at 23:14

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  • $\begingroup$ Hi Aditya, could you edit the question to describe what you've already done to try to find the answer from other sources? $\endgroup$ – David Z Feb 24 at 4:44
  • $\begingroup$ i think that as muons move at a speed close to light the must have experience time dilation so a few seconds from our perspective might very large for them please just tell me if this is right $\endgroup$ – Aditya Garg Feb 24 at 5:13

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.

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    $\begingroup$ For the record, I'm not a fan of answering questions that are so easy to look up elsewhere online $\endgroup$ – David Z Feb 24 at 5:52
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    $\begingroup$ @DavidZ OK. I am of course aware that homework questions should in general not be answered, but I was not aware that “you could have looked it up” questions should not be answered. Is this policy your personal preference as a moderator or is it a community consensus? It seems to me that a large fraction of questions here could be answered with just a few minutes of web research. $\endgroup$ – G. Smith Feb 24 at 6:02
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    $\begingroup$ Sorry not to make that clear. This is something entirely different from the rule about giving answers to the underlying problem in homework-like questions. In this case, unlike with homework questions, it's not exactly prohibited to post answers, but a certain portion of the community sees it as rewarding laziness on the part of askers. See the meta post I linked for more info. $\endgroup$ – David Z Feb 24 at 6:13
  • $\begingroup$ @DavidZ Thanks for the clarification and the link to the meta post. $\endgroup$ – G. Smith Feb 24 at 6:17

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