Relativity fails with quantum particles?

[PeterNoodles]

It seems to me there is a problem with special relativity - at least involving a particle which is commonly used as evidence to support it! Am I missing something?

Here it is:
A spaceship is stationary in space next to the moon. An interstellar muon traveling near the speed of light passes through the front of the ship, and - even though it's half life is much shorter than the time it should take to travel through to the back of the ship - it still survives to make it through the back end. This has been used to prove that time slows down as per SR when things travel fast.

Now, if instead, the muon is stationary, and the spaceship is traveling near the speed of light (the same as the muon was but in the opposite direction), the muon will be inside the spaceship for the same amount of time, but in this case it will decay before leaving the ship because it's time is not slowed.

So for the passengers of the ship, in one case the muon will decay, in the other, the muon will not decay. Where is the relativity?

 

[Dale]

Hi PeterNoodles, welcome to PF

You remembered time dilation but forgot length contraction. You can't use one aspect of the theory in isolation, you need to use all three aspects together (time dilation, length contraction, relativity of simultaneity).

 

[jtbell]

This looks like a variation on the classic "barn and pole paradox" which is resolved using relativity of simultaneity.

 

[Vanadium 50]

This looks like a variation on the classic "barn and pole paradox" which is resolved using relativity of simultaneity.

I think Dale's description is all you need.

From the spaceship's point of view, you see a fast muon which doesn't decay because it's time dilated.

From the muon's point of view, you see a length contracted spaceship, so you spend very little time inside.

 

[PeterNoodles]

Very cool. So simple. Thanks!