A supplementary length contraction question

[Glenn G]

Sorry community, I know I have another outstanding relativity question but something else is currently troubling me.

What got me thinking was the question of muons moving towards earth. Now according to their half lives very few of them should make it through 12Km of atmosphere...

ANALYSIS FROM GROUND
Now due to t = (gamma) t0 as they are moving very fast in a lab frame their measured half life is longer so it makes sense that more make it to ground level.

Due to L = L0/(gamma) If the muons were like spheres (just for sake of argument) then their dimension in the direction of motion would be squashed whereas dimension perpendicular to this wouldn't be ( so would the spherical particle appear like a flattened disc)?

FROM POINT OF ViEW OF MUON
Wouldn't feel as though it is really living any longer still experience the 2.2 micro seconds half life (or whatever it was?)

Length contraction: due to its motion it would feel as though it had only traveled L/(gamma) so ie less than the 12Km that would be measured in the lab frame.So my main question is about these two 'types' of length contraction one of the moving object itself as viewed from Earth and then the length contraction of the journey to Earth as experienced by the moving muon?

Sorry to bother I promise I'm trying to get it sorted in my head!
G.

 

[rumborak]

I'm not sure what your question exactly is regarding the contraction of the muon, as seen from Earth. Yes, in general the muon is squashed (as seen from Earth) by the same gamma as the travel distance is as seen by the muon, but the squashing of the muon as seen from Earth has no meaningful effect. It's the time dilation that makes the big difference in that frame of reference.

 

[Glenn G]

Thanks rumborak, I just wanted to check.

 

[Dale]

Length contraction: due to its motion it would feel as though it had only traveled L/(gamma) so ie less than the 12Km that would be measured in the lab frame

To be precise, it wouldn't feel as though it had traveled at all since it is at rest in its frame. Instead, just as the muon is a flattened disk in the Earth frame, so the Earth is a flattened disk in the muon frame. It takes less than 2.2 us for the flattened atmosphere to pass by the muon.