Muons Decaying on Mt Washington: Expert Answers

[bugatti79]

TL;DR

Length contraction from Muons perspective

Dear Experts,
Currently I am reading up on Special Relativity.
I struggle to understand how from the perspective of the Muon that the distance to the surface of the Earth is contracted and thus more Muons arrive at the surface based detector.
How can this be? To me the physical space is real between the muon and the surface and thus cannot be manipulated. How can this space be „contracted“ so that the muons arrive faster?
I am aware of length and time dilation and is related to observers etc but I am not referring to this. I referring to the muon reference frame...
Any clarity is appreciated! Thanks

 

[BvU]

It is one and the same thing: in the muon rest frame, the decay time is 2.2 $\mu$s. So, even at close to the speed of light the length decay distance would only be 660 m (in the Earth frame) without length contraction. In the Earth frame the time dilation factor is the dame as the length contraction factor in the muon frame. It's nicely described on the first pagehttp://www.pas.rochester.edu/~advlab/reports/pelcher_rapach_muon.pdf.

 

[PeroK]

To me the physical space is real between the muon and the surface and thus cannot be manipulated.

This is a conceptual hurdle to get over. If what you say were true, then there would be no SR. But, as there is SR, your preconceptions must be misplaced.

 

[Ibix]

The "real thing" is spacetime. How you divide that into space and time is a matter of choice, although there's an obvious way to do it for each observer.

Two reference frames in relative motion have different natural choices, so they measure different things and call them both "distance through space". So no-one is manipulating space - the two frames just mean different things when they talk about space.

 

[A.T.]

I am aware of length and time dilation and is related to observers etc but I am not referring to this. I referring to the muon reference frame...

"Observer" is often used as a synonym for "reference frame" in the context of SR, which leads to a lot of confusion.

 

[Herman Trivilino]

I am aware of length and time dilation and is related to observers etc but I am not referring to this. I referring to the muon reference frame...

Just have the observer be at rest in the rest frame of the muon.