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  • Every second, thousands 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, kaons, 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 detect 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.

  • Oh yeah, the greek symbol, mu is both used formuonAND formicrosecond”,

  • which can certainly be a little confusing; but the lifetime of muons is really close

  • to a microsecond, so it's also kind of beautifully appropriate/fitting.

  • Anyway, the point is that if you have a bunch of muons, More specifically, if you have a

  • bunch of muons, you'll only be left with about 50% after 1.5 microseconds, and 25%

  • after 3 microseconds, and after 10 microseconds there will only be 0.1% of the muons left.

  • Muons don't live very long -2.2 microseconds on average!

  • To put that into perspective, light, which travels fast enough that it could go around

  • the earth 7 times in a second, only travels 660 meters, or less than half a mile, in 2.2

  • microseconds.

  • So even muons traveling at essentially the speed of lighta , wouldn't make it more

  • than a kilometer or two before the vast majority of them decayed . Which is far less than the

  • 10 or 20 or 30 kilometers that muons DO regularly travel from the upper atmosphere to the ground.

  • So how do muons travel dozens of kilometers through the atmosphere without spontaneously

  • decaying, when in fact they should only be able to travel less than one kilometer?

  • Time dilation.

  • Yes - because the muons are traveling close to the speed of light, their time literally

  • passes more slowly - at a speed of 99.5% the speed of light, 2.2 microseconds for them

  • would be ~22 microseconds for us , enough time for the average muon to travel at least

  • 6km (instead of half of a kilometer) before decaying.

  • 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

  • muon would live for 220 microseconds and travel at least 66 kilometers 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 muons' perspectives, where they DO only live on average 2.2 microseconds?

  • Well, for them the answer to the apparent paradox is also relativistic - 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, 50km of our atmosphere is, to the muon, literally only half a kilometer

  • - aka 500 meters - thick.

  • Which is thin enough for even a muon with a lifetime of 2.2 microseconds to traverse

  • - well, actually from this perspective the atmosphere moves past the muon - but at a

  • speed of 300 meters per microsecond and at a distance of only 500 meters, the ground

  • has no problem reaching the muon before the muon decays.

  • This, in my mind, is one of the most awesome experimental verifications of special relativity:

  • the unequivocal time dilation (or length contraction, depending on your perspective) for objects

  • moving close to the speed of light.

  • The specific time dilation and length contraction

  • factors I talked about can be calculated using the time dilation and length contraction formulas

  • - once you know how to use them, you can plug in any speed you want and see how much distances

  • and time intervals will be distorted.

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Every second, thousands of cosmic rays - mostly hydrogen and helium nuclei - strike every

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Impossible Muons

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    Summer posted on 2020/11/03
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