Confirming Evidence of Time Dilation The Mount Washington Mu-Meson(Muon) Experiment Watch the video of the Experiment: Video Link: Mu-Meson Experiment The muon is an elementary radioactive particle created when cosmic rays crash into the upper atmosphere of the earth. It has a half-life of 1.5 us. = 1.5 x 10*'s in its rest frame. Muons decay randomly into a positron and an anti-neutrino. 568 Meson counts at rest at 6300 f Time AS Only muons with a speed of 0.995c are stopped in the detector where they remain until they decay. Muons with less speed are stopped in the iron above the detector. Muons with greater speeds pass through the detector into Mount Washington below. 1. Calculate the speed (in m/s) of the muons moving at 0.995c 2. What distance do they travel in one microsecond? 3. Mount Washington is about 6,300 feet high. What are the appropriate S.I. units? Show that it takes about 6.4 microseconds for a muon to travel this distance. 4. The physicists counted 568 muons on the top of the mountain. Based on the average life span of a muon in the rest frame, the scientist calculated that 29 should reach the bottom of the mountain. That is, twenty-nine of the 568 muons should survive the 6.4 microseconds required to travel the height of Mount Washington. Show that this expectation is correct under classical mechanics. You can use the equation N=N./2" y = t/t1/2. No is the initial count and N is the count after time t where the half-life time is tiz When the physicist took the equipment to sea level (to the foot of Mount Washington), 412 muons were counted in a one-hour period (and not just 29 as expected!!!). Clearly, moving clocks do not keep time at the same rate as stationary clocks, or (perhaps) distances are not the same in a fixed or moving frame. We can analyze the results from either frame.EARTH FRAME Here we are at rest alongside the mountain and we observe the muons speeding towards us at a speed of 0.995 c. 5. Calculate the gamma factor for muons, y = 1 - 12 6. Calculate the time (in us) for half of the 568 muons to decay. 7. Calculate the distance a typical muon travels in 15 us. 8. Compare your answer to question (7) with the height of the mountain. Use this to appreciate why so many muons survived to sea level. Muon Reference Frame 9. Use the gamma factor, ), calculate the height of the mountain as it is seen to pass by. 10. Compare answer (9) with the height we normally ascribe to Mount Washington. 11. How far does the earth move towards the muons in a time of 1.5 us. Comment on how many of the muons should be hit by the earth. 12. Given the experimental fact that 412 muons reach the foot of the mountain, calculate the fraction of one-half life that elapsed, and so calculate the elapsed time in us from the muon's reference frame. For us (at rest on the earth) the time is clearly 6.4 us