# Decaying Muons on Mt Washington

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## Summary:

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

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BvU
Homework Helper
2019 Award
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 page here.

PeroK
Homework Helper
Gold Member
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.

PeroK
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.

Ibix
Mister T