This is a very common topic especially regarding the apparent slowing down of time, the twins paradox etc. I have come across the figures for a muon and the relativistic effects that allow it to reach the earths surface despite its very short life. The relevant transforms show length multiplied by the equation and time divided by the same (sqrt(1-v2/c2) ). Looking at this I think time expansion is probably a more accurate discription rather than dilation or the more comon use of slowing down. Back to the muon, the figures I saw were (approx) time dilation factor of 22 and length contraction of 10000mts down to 450mts also approx factor of 22. As I see these figures I get 1 muon second = 22 of ours and 1 muon meter = 45mm, it therefore has 22times longer to move 1/22nd distance relative to us in other words it moves very fast and is able to reach the earths surface in its short lifetime. Also time and length contraction are both dependant on velocity and must go hand in hand a fact that does not seem to be taken into account when talking about time slowing for things, normally people moving at near speed of light velocities, there seems to be an obsession with slowing the ageing process, so if time dilates by say a factor of 50 then distance must also contract by the same so you would get 50 times longer to do a journey that would seem 50 times shorter so the total journey would appear to be shrunk by a factor of 2500 (50x50) So if the muon was a person what would we see, after 22 of our seconds their watch would have moved only 1 second but would they actually be 21 seconds younger than the person standing on the earths surface waiting for them, they would certainly have appeared to be moving very fast though.