I Is time dilation a real effect?

[PeterDonis]

Time dilation is a factor in explanation of muon count.

No, it isn't, because, as has been pointed out, it's not an invariant.

What explains the muon count is the proper time along the muon worldline, which is an invariant, compared with the muon half-life, which is just a physical constant.

Two muons might have smaller speed and they will not make it down.

That is not why some muons don't make it. Some muons don't make it because muons decay; they have a finite half-life. There is no difference in speed between the muons.

The actual issue is not that some muons don't make it; it's that more muons make it than "naive" Earth observers who don't take relativity into account would expect. That aspect is where "time dilation" is usually invoked as an explanation, but "time dilation" is not an invariant. As @pervect pointed out in an earlier post, a better name for the actual invariant involved would be "differential aging".

 

[Orodruin]

Time dilation is a factor in explanation of muon count.
There could be 10 muons created in the atmosphere but we might count only 8 at the Earth surface.
So B - muon count on the Earth surface is partly consequence of A - time dilation.
Two muons might have smaller speed and they will not make it down.

You are missing the point made. The point is that time dilation is not the physically invariant explanation. If you go to the muon rest frame, it plays no part whatsoever in the explanation. The invariant explanation refers to the invariant proper time of the muons.

 

[Jaaanosik]

Let us assume there is no time dilation.
How many muons we would count?

 

[PeterDonis]

Let us assume there is no time dilation.

Making an assumption that is contrary to the laws of physics is pointless. If you have a contradictory system you can deduce anything.

 

[PeterDonis]

Thread closed.