Cosmic Rays : Part 3 : Cosmogenic Muons and Special Relativity

The Field Guide to Particle Physics
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The definitive resource for all data in particle physics is the Particle Data Group: https://pdg.lbl.gov.

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The Particle Data Group's write up on cosmic rays. See Figure 29.8 for a representation of the "ankle" feature in the spectrum.
https://pdg.lbl.gov/2019/reviews/rpp2019-rev-cosmic-rays.pdf

Another representation of the power laws can be found in Professor Peter Gorham's Coursework on Ultra High Energy Cosmic Rays: http://www2.hawaii.edu/~gorham/UHECR.html

Natalie Wolchover has written two great articles in Quanta on Cosmic Rays, both which talk about what might accelerate these particles.
The Particle That Broke a Cosmic Speed Limit and Cosmic Map of Ultrahigh-Energy Particles Points to Long-Hidden Treasures

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 Design
Cloud Chamber without Dry Ice (see also references within)

Other References:
Measurement of muon flux as a function of elevation
ICRP Paper on Aviation and Radiation
Radiation Exposure During Commercial Airline Flights
Radiation from Air Travel as per the CDC
Calculate 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 Filter

The 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 ...