Calculating Muon Half-Life: Length Contraction vs Time Dilation

[mananvpanchal]

This link is confusing me.

http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/muon.html

In this link, with non-relativistic method, half life is calculated as 21.8.

But with relativistic method half life is calculated as 4.36.

We calculate half life considering time dilation for muon in Earth frame.
And, we calculate half life considering length contraction for muon in muon frame.
We get same value using both method as 4.36.

So, the question is:
Would length contraction and time dilation both not exist for muon?
Would we not include both factor in equation to calculate half life?
Why are we using length contraction and time dilation one by one to calculate half life?

 

[Doc Al]

In this link, with non-relativistic method, half life is calculated as 21.8.

But with relativistic method half life is calculated as 4.36.

Those are not half lives, but the travel time expressed in terms of half life.

We calculate half life considering time dilation for muon in Earth frame.
And, we calculate half life considering length contraction for muon in muon frame.
We get same value using both method as 4.36.

Both observers agree that 4.36 half lives will occur during the muon's travel to the earth.

So, the question is:
Would length contraction and time dilation both not exist for muon?
Would we not include both factor in equation to calculate half life?
Why are we using length contraction and time dilation one by one to calculate half life?

The muon travels from some distance above the Earth to the Earth's surface. In the muon's frame, it has a certain half-life. Viewed from the earth, time dilation will apply to the moving muon's half-life; length contraction is not relevant since the distance is in the Earth frame. Viewed from the muon's frame, it's the distance traveled that will be contracted; time dilation is not relevant since the muon is at rest in its own frame. Those end up being two different yet equivalent descriptions of what happens; each description leads to the same observable result.

 

[ghwellsjr]

You might find a similar thread discussed last month interesting, Muons experiment, strange logic.