MIT's GameLab has a
fun example of how Special Relativity works. See also
Gamow's popular science book on Special Relativity.
CERN's DIY Cloud Chamber DesignCloud Chamber without Dry Ice (see also references within)
Other References:
Measurement of muon flux as a function of elevationICRP Paper on Aviation and RadiationRadiation Exposure During Commercial Airline FlightsRadiation from Air Travel as per the CDCCalculate Your Radiation Dose (EPA) Cosmic Rays
Part 3 - Cosmogenic Muons and Special Relativity
Muons - those heavy, unstable cousins of the electron - are all around us. All the time.
On average, every square centimeter of Earth sees a muon about once a minute. While that might not seem like a lot, if you consider your personal space. Say, about square meter around you - you know, 10 square feet . Over 160 muons pass through your personal space per second! Per second!
Those muons coming form the upper atmosphere. They are the debris left over from the constant bombardment Earth experiences from high energy cosmic rays.
If only there was a way to see them.
Do you remember when I said that a particle physicist will look for particles WHEREVER they can find them? Well, before weather balloons, before particle colliders, there were cloud chambers.
Cloud chambers are boxes full of super saturated vapor or some kind. Any little disturbance will cause that vapor to condense, as clouds do up in the sky.
High energy particles blasting through a cloud chamber leave tracks. Little clouds form around the path of the particle, just like the contrails of a jet flying through the sky.
The muon and the positron were both discovered this way!
Cloud chambers are fun because you can build them yourself at home! The main thing you need is a sustained temperature gradient and tiny bit of very pure isopropol alcohol.
We’ll link to two great examples of DIY cloud chamber designs in the show notes.
Building a cloud chamber at home is a great way to come face to face with the fact muons - the debris from cosmic rays - are passing through us all the time.
The Atmosphere as a Muon FilterThe magnetic field generated by the Earth’s core protects us from many incident particles from space. Especially all that plasma in the solar wind.
But those high energy cosmic rays blast straight through the magnetic field. It’s just not strong enough to contain them.
Our upper atmosphere is our next layer of defense. Cosmic rays collide with its molecules tens of miles above the Earth, creating a shower of debris that itself can be miles across.
In some sense, the atmosphere serves as a filter, converting all those particles like protons and pions into muons. Muons comprise the bulk of what we see down here at the surface.
Muons are unstable particles. They decay to electrons after about 2.2 microseconds. This means that while many muons make to the ground, not all of them do. The higher you are above sea level, the more muons you’re likely to see.
At 10,000 ft above sea level, this number can triple! Given that commercial airline flights typically occur above 40,000 ft, it’s important to realize that flying exposes you to more Cosmogenic Muons.
Fortunately for you frequent flyers, the extra does radiation exposure is still a very small amount of radiation exposure! The International Commission on Radiological Protection has well established professional limits to protect even commercial flight crews from exposure to all those cosmogenic muons.
Long Lived Muons
Despite the atmospheric filter, those Cosmogenic Muons are still traveling really, really fast. Like 99.9 percent of the speed of light fast. Muons moving that fast don’t behave like you’d expect. For one thing, they take far longer than they should to decay.
How do we know that?
As you might recall from their eponymous episode, muons only live for about 2.2 microseconds. That’s 2.2 millonths of a second. Even traveling near the speed of light, that’s simply not enough time to get from the upper atmosphere to anywhere near the surface of the Earth.
That’s a bit over 9 miles - or 15 kilometers. It takes light about 50 microseconds to travel that far.
Muons that make it to Earth, then, live over 22 times as long as they should.
Why that happens - what causes the muons to live so long - requires a small digression on the theory of relativity.
On Special Relativity
As they say, Nothing travels faster than the speed of light. Which is true, at least, in outer space and to some extent in the air around us. You see, it’s not so much that LIGHT is the fastest thing around. It’s that the universe itself has a maximum possible speed - a speed limit, if you like - which is just shy of 300 million meters per second.
When left to its own devices, light - or any particle with zero mass - travels at that speed.
That universal speed limit is just a fact of life, but we don’t notice is much because a typical human moves at about 1 meter per second. Not 300 million meters per second.
But having a speed limit like the speed of light leads to some pretty strange paradoxes.
For example: you cannot race a photon. Photons, you might recall, are particles of light.
If you ran towards a photon, the photon sill still move away from you at the speed of light.
If you drove towards the photon at 100 miles and hour, the photon will still move away from you at the speed of light.
If you jumped into a supersonic fighter just and chased a photon, the photon will still move away from you at the speed of light.
Even if you built and launched in a rocket ship so fast you were traveling at 200 million meters per second - you know, 67% of the speed of light - and chased that photon, the photon will still move away from you at the speed of light.
At least in the vacuum of space, light always moves at the speed of light. No matter how fast you are going. Frustrating, huh? Maddening even. But that’s how the universe enforces its speed limit. No matter how hard you try, you can never catch up.
But how could this be? What weirdness could explain this paradox?
Well speeds don’t really add like normal numbers do. This is Einstein’s famous theory of Special Relativity. There’s re some technical details and nuances of course, but essentially, relativity says that light always moves at the speed of light, relative to you.
The implication is that EVERYONE, ANYONE sees light moving at the same speed, no matter how fast they’re moving.That same universal speed limit, just shy of 300 million meters per second.
The way the universe affords this is by exchanging your perception of time for a perception of distance.
The faster you go, the LONGER the distance you have to travel. Your perception of one meter is LONGER than someone going slower than you. That’s why is so hard to get up to light speed. The faster you go, the further you have to go to catch up.
Of course, to account for this cheat, the universe also shortens your sense of time. So yeah you have to go further, but you don’t really notice that because time has slowed down for you. But the net result is even “doubling your speed” only really inches you closer to the speed of light.
In a VERY real sense, motion trades TIME for SPACE. At least that’s how the mathematics of special relativity work out. In some sense, trading time for space is literally what it means to be in motion.
If that’s too heavy to take in, don’t worry about it. If it excites you, AWESOME. I’ll link to some further reading on special relativity in the show notes. But in either case, all you need to know at this point is that those cosmogenic muons, those particles screaming in at over 99% of the speed of light, have traded a LOT of their sense of time for space. So their internal clocks ticks much, much, much slower. Well over twenty times slower! Which is why they take so long to decay.
In other words, the cosmogenic muons all around us near the surface of the earth - the things you can detect with your own cloud chamber at home - are a testament to the peculiarity of Einstein’s theory of special relativity.
Conclusion
Muons, borne of debris from cosmic rays collisions in the upper atmosphere, travel at outrageous speeds to surround us here on the surface of the Earth. They travel so fast that Einstein’s theory of special relativity directly manifests itself in the very existence of those muons.
Other particles created in those cosmic rays collisions - like pions or lambda baryons - are also moving at outrageous speeds, but since they contain quarks, they communicate via all of nature’s forces. They are much more susceptible to not only decay but collisions with other particles. Far more susceptible than the muons are.
Even the humble electron, when traveling at relativistic speeds, will quickly lose much of its energy via the brehmstrahlung radiation, which depends inversely on its small mass. Muons, being heavy, don’t have this problem.
So this is what we mean when we say the atmosphere behaves like an energy filter, catching all that cosmic ray collision energy, all except for those muons. They’re fast, heavy and don’t interact as frequently.
But they do eventually interact. With the molecules in our body. In the rocks. Or even, in the snow and ice the covers the high mountain tops and polar regions of our Earth. In our concluding episode in this mini-series, we’ll explore how cosmogenic muons have helped scientists understand the history of Earth’s atmosphere and the associated implications for its climate.