Twin Paradox with radioactive twins

[PAllen]

I’ve always considered that many muons are created at much lower altitude than 10 km, where the atmosphere is denser. However, looking at the density as a function of altitude, it does appear 10 km would be a reasonable median creation altitude. But there is also the question of muon energy. I think many are created with $\gamma$ greater than 5, some much greater (even over 100).

Actually, I just checked and found the average muon energy at creation is well over 4 GeV, which is a $\gamma$ of over 40. Thus, my statement was correct. For some reason, hyperphysics is using a plausible creation altitude, but a way too low energy. There are even substantial numbers of muons created with $\gamma$ of 40,000 or more.

[edit: as a further aside, I note that the cosmic ray muon spectrum is regularly measured out to 100 TEV, which corresponds to a $\gamma$ of 1 million. For such a muon, it would appear only 1 cm of atmosphere passed by before the ground hits.]

 

[PAllen]

Actually, I just checked and found the average muon energy at creation is well over 4 GeV, which is a $\gamma$ of over 40. Thus, my statement was correct. For some reason, hyperphysics is using a plausible creation altitude, but a way too low energy. There are even substantial numbers of muons created with $\gamma$ of 40,000 or more.

[edit: as a further aside, I note that the cosmic ray muon spectrum is regularly measured out to 100 TEV, which corresponds to a $\gamma$ of 1 million. For such a muon, it would appear only 1 cm of atmosphere passed by before the ground hits.]

And this page of hyperphysics has the correct number - no idea why the muon experiment page uses misleading numbers:

http://hyperphysics.phy-astr.gsu.edu/hbase/Particles/muonatm.html