A very common example of time dilation is given for muons i.e. how presence of large number of muons reaching earth (which were created in upper atmosphere) can be explained using time dilation.
The argument is something like this: If person and muon are at rest with each other, Muon decays after 2.2 microsecond according to both. However, when they are created in the upper atmosphere, they are moving at 99% speed of light. Muon will say person (measuring Muon on earth) clock is running slow and person will say that muon clock is running slow.
So when muon reads 2.2 on it clocks, person will read 15.6 on his clock. That explains how Muon is able to cover more distance it ought to be covering according to an observer on earth to reach earth.
So 2 questions:
So when person reads 15.6 on his clock, he thinks muon reading is 2.2 and when muon reads 15.6 on its clock, it will think the person’s clock reads 2.2. Is this correct understanding of the symmetry?
if 1 above is correct, Decay of Muon is 2.2 according to both. When person's clock reads 15.6 and muon decays, Muon's clock reads 2.2 according to person.That makes sense to me. Other way around is not. So when Muon reads 2.2 according to its clock and decays, person's clock is reading only 0.31.?
My question was closed as duplicate saying it is same as how can time dilation be symmetric. I don't have that question as I understand that symmetry as per 1 above. The question is #2 above.
