Relativity Lite

10 | Relativity Lite c t c τ c t v t c t Figure 6. The sequence of fours steps for v = 0.9986 c . In this case, c t = 10 cm is much longer than c τ = 0.52 cm. The coordinate time is extremely dilated by a factor of 19. So thanks to relativistic time dilation you measure a muon’s half-life at 19 times its proper half-life, or 38 microseconds. This is about twice the time it takes for the muons to travel through the atmosphere. That is, roughly 1/4 of them will decay, and 13 muons make it through each second * to crash through your skull and increase your cancer rate. The typical yearly dose of radiation due to these muons is 400 µsv (microsievert), † 6 times higher than a typical yearly dose of radiation due to diag- nostic X-rays, 70 µsv. ‡ If there were no relativistic time dilation, the yearly radiation dosage * National Council on Radiation Protection and Measurements, Report No. 94, Exposure of the Population in the United States and Canada from Natural Background Radiation (NCRP, Bethesda, MD, 1987), p. 12, has a rate of 0.00190 muons per cm 2 per second at the surface. I obtained 13 muons per second by modeling a person by a cylinder with a radius of 15 cm. † Alan Martin and Samuel A. Harbison, An Introduction to Radiation Protection (Chapman & Hall, New York, 1979), p. 53, gives 500 µsv for all types of cosmic radiation, of which muons make up 80%, according to the National Council on Radiation Protection and Measurements, Report No. 94, Exposure of the Population in the United States and Canada from Natural Background Radiation (NCRP, Bethesda, MD, 1987), p. 12. ‡ Alan Martin and Samuel A. Harbison, An Introduction to Radiation Protection (Chapman &Hall, New York, 1979), p. 57.