How does the General theory of relativity affect the decay speed in time of a muon?
That’s special relativity, not general relativity. Muons are affected by time dilation like other things moving at high speeds. Their decay time (as it appears in our frame of reference) depends on how fast they are going to relative to us. See more info on time dilation here: http://www.mahalo.com/answers/physics/a-man-is-driving-a-car-at-the-speed-of-light-he-turns-on-the-headlights-what-happens http://www.fourmilab.ch/cship/timedial.html Time dilation can also be caused by gravity, but that is very small on the Earth and makes little difference to a muon’s observed lifetime.
