 Now let's look at things from the particles frame. So from the muon's point of view, it is stationary and the earth is rushing towards it at speed v. But now here's a problem. This muon is going to decay in some time tau. But now in the muon's frame, it's the earth that's undergoing time dilation. But now we've got a problem. The muon is going to decay in some time tau. But now time dilation can't lengthen that. Because from the muon's point of view, it's everyone on the earth that's living in slow motion. Not it. And tau is much, much smaller than l on v. So this is a paradox, right? How can someone on the earth think that the muon is going to make it to the surface, whereas the muon thinks that it's going to decay long before passing through the atmosphere?