4.2 Muons

Key Takeaways

welcome back to age 20 special relativity in the last section we discussed that moving clocks tick differently than those which are at rest and here i would like to discuss a real-life example of this the muon the muon is an elementary particle very similar to the electron its mass is about 200 times as heavy um the mune was discovered in the 1930s by anderson and nedermeier at caltech and it it's really one of my favorite particles because you can they're abundant they there's many of them in cosmic ear showers you can study them you can study their lifetime you can even calculate their lifetime on a on a piece of piece of paper so what anderson and nedermeyer did is they just basically you know went outside and discovered a particle which comes from the sky and so they studied cosmic radiation moons are produced in cosmic air showers and we look at one of those a little later basically proton sits the upper atmosphere and in a shower of various particles neurons are being produced and then those neurons are not stable particles but they are stable enough to reach us on average if you hold out your hand right now about one neuron travels through your hand every second how does how is this possible so if you look at this muon give you a little bit of particle physics explanation here again the muon is not a stable particle that decay the decay via the weak interaction for those who are interested uh this is the final diagram for this decay the muon couples to the w and as a result of the decay you find an electron an anti-electron neutrino and a neuron the lifetime is about 2.2 microseconds 2.2 times 10 to the minus 6 seconds and i just taught 8701 which is introductory class into particle and nuclear physics and the students calculated the lifetime of a muon in that class so you can calculate this and you need a few tools but it's not that hard after all the average velocity of the neurons when they're being produced is close to the speed of light or 0.998 times the speed of light and if you do a classical calculation and you want to figure out how long do the muons on average live fly you find that this is about 660 meters now they are produced in the upper atmosphere and nevertheless we can find them down here on the earth so something is not quite right what is not quite right you can already assume is that the clock in the muon uh as observed by us uh ticks much much slower than this then for the muon at rest and so the lifetime of the mural of 2.2 microseconds is basically extended um if you calculate this this average velocity we find a gamma factor of 15 using the equations we this you know for time dilation you just simply multiply 15 times 2.2 microseconds and you find that neurons indeed reach our hand on the surface of earth all right this is a really fun example again you can study uh those cosmic air showers with moons um and and learn about the neurons in very simple experiments this picture here shows you one of those air shower formations so the story is a little bit more complex as i explained this is a spectacular air shower or a picture of one where you have an important coming in with an energy of 10 to the 15 electron volt and so even at slower lower energies showers look like the one here you produce in collision with the atmosphere many many particles pions protons additional protons neutrons and ions again and those pions then they decay into neurons and this all happens in the upper atmosphere but also in some cases further down so here we have seen now an example which you can actually see and observe in nature where particles travel with high speed and there is relativistic effects we can measure and observe you