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I was reading the summary of most significant experiments done so far verifying muon's Special Relativity time dilation and lifetime extension here:

https://en.wikipedia.org/wiki/Experimental_testing_of_time_dilation

However it is not clear to me:

How do we know that the muons created by cosmic rays in the upper atmosphere are the same muons reaching our detectors at the surface?

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    $\begingroup$ Because we have measured them all the way up. High up lots of cosmic rays, few muons. Eventually lower down lots of muons and few cosmic rays. $\endgroup$
    – Jon Custer
    May 5 '21 at 13:08
  • $\begingroup$ What's your alternative explanation? What happened to those muons? What are these muons? $\endgroup$ May 5 '21 at 14:24
  • $\begingroup$ @CosmasZachos I prefer to hear an established explanation and methods used. $\endgroup$
    – Markoul11
    May 5 '21 at 20:00
  • $\begingroup$ What do you believe is cattywampus with the established explanation, then? What chapter of cosmic ray physics do you want rewritten? $\endgroup$ May 5 '21 at 20:02
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Here is a calculation , and here you can read about the air showers and how they are modeled .

The basic assumption in the calculation is that very high energy cosmic rays hit the atmosphere at a specific distance . The calculation is done because of the paradox of the muons reaching the earth, whereas their half life measured on the surface would have them decay before reaching the surface.

From the studies in accelerators one can generate the primary interaction, have Monte Carlo events and compare the distribution with the observed data from the showers. For the muons the important point is that they are decay products of pions, and pions decay faster by two orders of magnitude then muons.

As you can see here there is a mutual interaction between cosmic ray experiments, and particle physics running ones, as it seems there are questions about the density of muons. The link gives also an overview of the cosmic experiments. I just learned that they can see the shower starting on the top of the atmosphere! (search for telescope) So if specific air showers can be correlated with telescope detection, this makes the muon timing and modeling more strict.

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  • $\begingroup$ okay now I have even more questions? The subject seems to be much more complicated. From the provided "air showers" link diagram we see that although pions to muons decay is happening only at the upper atmosphere however we have muons production even up to the lower layers of the atmosphere by γ-rays bremsstrahlung cascade. Considering also the 8σ reported discrepancy of the layered muons density in the above link provided why then we are excluding the possibility of muos reaching the surface not due to the SR time dilation but because a cascade sequence? $\endgroup$
    – Markoul11
    May 6 '21 at 12:13
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    $\begingroup$ All that is taken into account in the generation of monte carlo events to compare with the distributions from the detectors. It is only an approximation given in the first link, assuming it for test muons created at the top of the atmospher. $\endgroup$
    – anna v
    May 6 '21 at 12:28
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There's no such thing as "the same muons" or "different muons". All muons are not just identical, they are indistinguishable. If there is a process:

$$ \mu + X \rightarrow X^* \rightarrow \mu + X$$

in which a muon and $X$ combine into an intermediate state which decays to a new muon, then two things happen:

1: the final state muon is not going to live longer than the initial state muon. There are plenty of PSE answers explaining that decay is memoryless.

2: that reaction will occur along with some kind of exchange, where them muon scatters off of $X$, meaning the final state muon is now entangled...but not really b/c it's identical particles.

So: there are no "new" or "old" muons. The question is basically nonsense. Relativity is correct.

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    $\begingroup$ I believe my question does matter. If you cannot prove that these muons are the same muons how then you can prove SR time dilation of the muon particles in the case of cosmic rays hitting the upper atmosphere? $\endgroup$
    – Markoul11
    May 5 '21 at 19:54
  • $\begingroup$ @Markoul11Is this a "chain of custody" qualm? Muons are the likeliest decay products of pion decays, and you get pion bursts at the primary vertex. You detect them the moment they die, and as per above, it is hardly sensible to have them regenerate. What is going on? $\endgroup$ May 5 '21 at 20:10
  • $\begingroup$ @Markoul11 But it doesn't matter if they are the same muons or not (see pt 1). New muons decay at the same rate as old muons. $\endgroup$
    – JEB
    May 5 '21 at 23:44

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