In the Earth frame the muon takes about 30 ms to reach sea level. (Longer time interval)In the Earth Frame, I am at rest with respect to my ruler, so I observe no length contraction. My clock is not at rest with respect to the muon, so I do observe time dilation.
In the muon frame the trip takes about 6 ms. (Shorter time interval)In the Muon Frame, I am not at rest with respect to the ruler (Earth), so there is length contraction. My clock is at rest with respect to me, so I observe no time dilation.
The Earth frame considers the interval measured in the muon frame to be time dilated (shorter) than the interval measured in the Earth frame.
THe Earth/muon experiment can not be directly equated with the twin paradox, because if we ignore gravitational time dilation then both the Earth frame and the muon frame are essentially inertial while in the twin experiment one of the twins is non-inertial.
This is not correct. The interval measured by the moving twin is shorter.However, it is said they run slowly and in the case of the Twin Paradox the Moving twin is younger. Why is it said it runs slowly when it yields a larger time interval?