Every second thousand of cosmic rays mostly hydrogen and helium nuclei strike every square meter of the Earth’s upper atmosphere. We don’t really know where they come from. But we do know that when cosmic rays crash into air molecules in the atmosphere. They create a shower of other fundamental particles pions crayons positrons, electrons neutrons neutrinos gamma and x-rays and muons. We know this because we have particle detectors in Labs down on the surface that detects the directions and energies of the particles in these. Showers, and use them to study the original cosmic rays, but there’s something fascinating about the fact that we detect a lot of the muons from cosmic rays down on the surface of the Earth because muons if you make them in a laboratory only have a 1 .5 microsecond half-life before they spontaneously Decay into an electron or positron and some neutrinos and yeah, the Greek symbol mu is used for both muon and four microseconds, which can certainly be a little confusing. But the lifetime of muons is really close to a microsecond. So it’s also kind of beautiful. We appropriate anyway, the point is that if you have a bunch of muons, you’ll only be left with about 50% after one point five microseconds and 25% after three microseconds and after 10 microseconds. There will only be point one per cent of the muons left muons. Don’t live very long just to point to microseconds on average to put that time into perspective light travels fast enough that in one second. It can go around the earth seven times but in two-point two microseconds light will only travel 660 meters or less than half a mile. So even
Muons travelling at essentially the speed of light wouldn’t make it more than a kilometre or two before the vast majority of them decayed Which is far less than the 10 or 20 or 30 kilometres that muons do regularly travel from the upper atmosphere to the ground. So how do muons travel dozens of kilometres through the atmosphere without spontaneously decaying when in fact they should only be able to travel less than one-kilometre time dilation. Yes, because the muons are travelling close to the speed of light their time literally passes more slowly. Slowly at a speed of 99.5 percent, the speed of light to point 2 microseconds for them would be about twenty-two microseconds for us enough time for the average muon to travel at least six kilometres before decaying instead of half a kilometre and even higher energy muons going even faster would even more easily reach our detectors on the Earth’s surface before they decayed at 99.995% The speed of light the average mu 1 would live for 220 microseconds and travel at least sixty six kilometres before decaying so from our perspective.
The fact that so many cosmic ray muons reach our detectors on the earth’s surface is direct evidence for special relativity and time dilation. But what about from the muon’s perspective where they do only live on average two points two microseconds. Well for them the answer to the apparent Paradox is also relativistic length contraction from the muon’s perspective. It’s the earth and the atmosphere which are moving at 99.995% The speed of light towards the muon and the lengths of moving objects are literally Contracted by a factor dependent on their speed in this case 50 kilometres of our atmosphere is to the muon literally only half a kilometre which is thin enough for even a muon with a lifetime of 2 points 2 microseconds to Traverse. Well, actually from this perspective the atmosphere and ground move past the muon but at a speed of 300 meters per microsecond and a distance of only 500 meters the ground has no problem reaching the muon before the muon decays this in my mind are one of the most awesome experimental verifications of special relativity the unequivocal time.
Action or length contraction depending on your perspective for objects moving close to the speed of light. They literally couldn’t get here if it weren’t for time dilation
Globe Eld 