Spring Forecast: Muon Showers

In the March Mathness post I mentioned that one reason I love March is that it contains the Vernal Equinox, the official astronomical start of Spring. More importantly to me, it means six months of more daylight than darkness, and as much as I’m a night person, I prefer long, sunny days.

Well, today is the day! The equinox happened at 21:58 UTC (two minutes before 5:00 PM locally). What’s better is that, after all the miserable bitter cold and all that snow in February and into March, the weather is indeed finally turning. Deeply embedded in our mythologies is the idea of spring rebirth; New Year’s parties aside, this, today, is the true new year.

And the forecast is for muon showers!

Thought I was done talking about Special Relativity, didn’t you! Sorry, but no, there’s this one last bit.

It sprang (speaking of spring) from, in the previous year, at least two comment threads on a physics blog I follow. Both involved people denying the validity of SR (many of the same people in both cases).


It’s a weird phenomenon that anyone who spends time in the sciences runs into eventually:

People who are (A) certain all those trained scientists who devoted their lives to understanding their field are wrong, and (B) that they, without all those years of study and learning, have figured out the “error.”

In mathematics, people are convinced Cantor was wrong and that they have found a way to enumerate the reals. They are always wrong about that, often in ways that are easily demonstrated.

In physics, people are convinced Einstein was wrong, and all this Relativity stuff is nonsense. As I mentioned recently, Einstein continues to bat one-thousand; these people are also always wrong.

Some of them are so wrong they are, as the saying goes, “Not even wrong.”

That is, their ideas are so off the mark that they’re not even near the territory that would allow those ideas to be merely wrong. Their entire understanding of the subject matter is hopelessly ignorant.

Not only are they not “in the ball park,” they’re not even in the city the ballpark is located in.


The phenomenon is often labeled Dunning-Kruger effect, although one needs to be careful invoking it — it’s often mislabeled as a form of stupidity.

These people aren’t (necessarily) stupid, but they are massively ignorant, and Dunning-Kruger is about ignorance so massive it prohibits any clear understanding of how wrong their ideas are.

Simply put, one needs to understand a subject matter sufficiently to appreciate what one knows and has yet to learn. With massive ignorance, one can believe one understands.

Tragically, this ignorance often seems willful: Attempts to educate these people, to point out the errors in their thinking, tend to result in various forms of push-back.

These people are so deep in their own ignorance, they hear no one (which tends to make debating them an exercise in futility).


Sorry, didn’t mean to go on about that on this lovely spring day, but willful ignorance is a major hot button for me.

The view out my window one month ago (2/21/2019).

The view out my window today (3/20/2019).

What I wanted to talk about is muon showers!


A question I asked several times in these debates denying Special Relativity was: What about muons? (None of them took up the question.)

Let alone that GPS requires both General and Special Relativity to work, so that your (and everyone’s) GPS works proves Einstein’s Relativity. The problem, of course, is this requires an understanding of how GPS works, and we’re back to where we started.

And on that count, I suppose muon showers also require some very basic understanding of particle physics, but really not all that much.


Let me start at the beginning:

A muon is the heavier cousin of the electron (a bit over 200 times as heavy). It’s from the “second family” of matter. The electron’s even heavier cousin (almost 3,500 times as heavy), the tau, is in the third (and so far as we know, last) family.

The electron, the muon, and the tau, are identical in all ways their except mass.

Importantly, all the particles from the second and third families are too massive to not instantly decay into lighter particles.

The muon has an almost surprisingly long lifetime before it decays: on average, a muon lasts 2.2 micro-seconds (just over two-millionths of a second).

(Yes, that is long compared to other heavy particles, which decay much faster!)

Consider the math for how far a muon can travel at, say, 1000 mph:

\frac{6.336 \times 10^8 \frac{in}{mi}}{3.6 \times 10^9 \frac{\mu s}{hr}} = 0.0176 \frac{in}{\mu s} \times 2.2\ \mu s = 0.03872\ in

So, with their 2.2 micro-second life, at 1000 MPH, muons would only travel just under four one-hundredths of an inch.

But we’re all about relativistic speeds, so let’s consider a much higher speed, say 99 percent of light speed (without considering the effects of SR):

973,733,270 \frac{ft}{s} \times 2.2\ \mu s = 2,142.2\ ft

Which isn’t too bad, although it’s still under half a mile.


Muon Moon Shadow!

The thing about that is that one natural source of muons is cosmic ray collisions with the Earth’s atmosphere.

These occur up in the atmosphere, increasing with altitude. One source cites an average distance of 15 km for these collisions (the distance is hard to pin down as it occurs over a range).

So the question is, if even muons moving at relativistic speeds can’t make it (on average) even half a mile, how is it we detect them — lots of them — at the Earth’s surface?

Which we do. We can even detect the shadow our Moon casts from blocking cosmic rays!


The answer, of course, is Special Relativity and how it affects things that are in motion relative to other things.

Recall that a moving clock appears to run slower to observers. (The moving clock seems fine to those moving along with it.)

Remember that muon moving at 0.99c? From the (unmoving) Earth’s perspective, the muon’s clock is running only 0.141 (just under 15%) the rate of the Earth’s clock.

So, from the Earth’s point of view (and ours), muons have plenty of time to reach the surface.


As I said, the muon thinks its clock is just fine, and it fully expects — and gets! — an average lifetime of 2.2 micro-seconds.

But another effect of Special Relativity is foreshortening of length along the direction of travel.

From the muon’s point of view, the Earth is moving up towards them at relativistic speed. They see the Earth’s clock as running just under 15% of normal, but more importantly, they see the distance along their travel — the Earth’s atmosphere — shortened to just under 15% of its length.

So, rather than having to travel 15 kilometers, they only have 2.115 kilometers to travel to reach the surface.


And, per the math above, a muon would seem to need to either be closer than 15 km or to move faster than merely 0.99c.

An interesting thing about SR is the curve of change. Even at half the speed of light, the contraction is only 0.866. It’s not until we get very close to the speed of light that things really change.

Here’s a set of graphs that show how extreme this is:

The full range from 0c to 1c. These charts show the actual gamma, which is 1.0 at zero velocity and increases towards infinity with increasing speed. We calculate dilation by using its inverse (or just dividing).

This chart zooms in on the 0.9c to 1.0c range where things start to really pick up. But notice how similar it is to the full curve and how, even in this range, it’s not until 0.98c that things really pick up.

Seriously zoomed in on the last bit of the range, and the curve still looks like a late riser. But notice how the vertical scale has expanded in each case. In this chart, gamma increases beyond 300!

As you can see, it’s not until 0.86c that the difference is even double (or half), and it takes getting above 0.999 for things to really pop.


So if we apply this to the muon situation, we get this chart:

This chart is a little complicated, so let me explain:

Firstly, the chart covers the range from 0.9c to 1.0c. The vertical scale is both micro-seconds and kilometers. I’ve adjusted things so the numbers are correct for both scales.

The red line (muon half-life of 1.5µs) and the green line (muon average time of 2.2µs) indicate the number of micro-seconds a muon lives. As the speed increases towards c, that lifetime increases.

The blue line shows the number of kilometers an average lifetime muon can travel. The cyan line shows the distance dilation assuming a (very high) altitude of 50 km. At 0.98c, that distance has shrunk to only 10 km!

The yellow table provides some specific numbers for how far an average lifetime muon can travel. At extremely high speeds, that distance gets quite long!


I’ve mentioned before how we exist in a thick soup of radio waves — low frequency photons we cannot see.

Every radio station, every TV station, all those cell towers, every wireless device, they all add to the soup. If we could see them, we’d be constantly blinded. (Even closing your eyes wouldn’t help, those photons penetrate.)

And then there are the solar neutrinos, many billions of them sleeting through your every cubic inch every second. (They don’t really even notice you.)

We also live in a frosting of cosmic ray collision fallout. Muon showers all around!

Ain’t that somethin’!


Happy Vernal Equinox, my friends!

Enjoy the muon showers!

About Wyrd Smythe

The canonical fool on the hill watching the sunset and the rotation of the planet and thinking what he imagines are large thoughts. View all posts by Wyrd Smythe

17 responses to “Spring Forecast: Muon Showers

  • SelfAwarePatterns

    On the Dunning-Kruger effect, one of the things I’ve learned is to simply state the facts (at least as I know them) and then move on. Further argument is rarely productive, particularly when the person is spoiling for the argument. I’ve been accused of being closed minded for this, for not parsing and rebutting the details of someone’s hopelessly ill conceived arguments, but life is short and time is precious.

    Not that I don’t occasionally give in to temptation and have a debate anyway 🙂 But usually when I do, it’s more to test how solid my own thinking actually is than to convince someone wrapped tightly in their own narrative.

    • Wyrd Smythe

      Quite agree on both counts. A key characteristic is how impervious to argument they tend to be, but that very trait allows one to exercise their debate skills if one is in the mood. It’s almost like having a debate punching bag — they seem impervious to harm, and they always return to the same position for more.

      As you say, it’s an exercise for the self, not a serious attempt (or belief it’s possible) to change their thinking.

      And it can be interesting to explore the structure of their belief. It’s fascinating to me how humans can think the same in so many ways, yet also think so differently.

      In Westworld, Bernard has a line about how many mental states there are, but we consider only a narrow subset of them “sane.” In context, he’s implying we’re being narrow-minded and should expand our definitions, but I think there is some truth to what he’s saying. I define “sanity” as the closeness of one’s mental model to physical reality, so from that perspective, it is a fairly narrow range.

      So I’m deeply fascinated by those who seem so close, but have seemingly wandered just a little off the beam! Sometimes it feels that, if you could just nudge them right, they’d get back on track. (Of course, it’s a little presumptuous to think I know what the right track is, but I try to take physical reality and persistent, convergent human constructs as my model. 😀 )

      • SelfAwarePatterns

        That last point is something we always have to keep in mind. It’s always possible the other person has a point and our own biases are the issue.

        However, usually if the person has a valid position, they’ll be able to marshal enough of a line of reasoning to where you can at least see where they’re coming from, even if you continue to disagree. For example, I’m not an idealist, but I can see how someone can arrive at that position. Same for panpscyhism and a host of other notions.

        But when someone simply asserts that a well tested scientific theory is nonsense, and doesn’t offer an alternative framework, well, it doesn’t leave a lot to work with. Carl Sagan, when interacting with someone like this, observed that if you don’t value evidence, there’s not much common ground for discussion.

      • Wyrd Smythe

        “…they’ll be able to marshal enough of a line of reasoning to where you can at least see where they’re coming from…”

        Right! And following that reasoning, seeing their logic, is where it can get very interesting. It’s not impossible for the untrained to stumble over something; sometimes fresh eyes spot something everyone overlooked.

        Not often, of course, but possible enough that no one should be dismissed out of hand. Everyone gets a listen. (A very short listen in some cases, but still a listen. 🙂 )

        “But when someone simply asserts that a well tested scientific theory is nonsense, and doesn’t offer an alternative framework…”

        Yeah, those are worth the least amount of time.

        It’s the ones who’ve developed an elaborate framework of their own where you have to pause and see what they’ve got. Sometimes it’s just a lot of hand-waving, vague ideas without details, but I’ve run into a few with elaborate constructs. (There was a guy with an idea there were no actual neutrons or protons. The nucleus is just a soup of quarks and gluons.)

        But there are certainly enough unanswered questions in physics that you never know.

      • SelfAwarePatterns

        Hmmm. I might find a proposal for the non-existence of protons and neutrons interesting. Of course, it would have to account for everything protons and neutrons accounted for. If I recall correctly, the original motivation for protons and neutrons amounted to accounting for charge and atomic weight. But the fact that we haven’t thrown the concepts overboard probably means they’re needed to account for other phenomena?

        I used to periodically debate a guy on the old HuffPost comment threads whose posting name was QuarkGluonSoup. I wonder if he was the one you ran into.

      • Wyrd Smythe

        My thought was, “If protons aren’t real, what’s flying around inside the LHC?”

        Thing is, you could view it as (exactly what it is), a hydrogen nucleus and figure that whatever applies to the hydrogen atom would apply to the LHC.

        But I have no idea how his theory, which he called “quarkeosynthesis” (IIRC), dealt with hydrogen. I got all this second-hand from a buddy who actually received the letter (it was sent to the corporate help desk; not sure why… where else?).

        Just tried, “quarkeosynthesis” does get hits. Last time I checked (years ago), it only got four, one clearly to this guy’s paper. (I’m not bored enough right now to explore those hits to see if they even apply.)

      • SelfAwarePatterns

        Thanks. I have to admit I’m not interested enough myself to take the time to read up on it. This is one of those things that if a substantial portion of actual physicists haven’t bought into, I’m not willing to invest my own time in it.

  • Wyrd Smythe

    I completely forgot, but for the record, another thing that got me thinking about cosmic ray caused muons was a Bad Astronomy column (by Phil Plait).

    His post discusses the muon situation and links to a YouTube video I remembered from long ago:

    I just wanted to record both links here in case I need them again. (And now I can delete the email I sent myself to remind me to include them.)

  • rung2diotimasladder

    I’ll admit up front that I didn’t read this whole post. Or any charts that say “Gamma Factor”. Or anything with numbers.

    I’m amazed to hear that there are people in physics trying to prove Einstein wrong. I thought relativity was a given in that crowd. And I thought the GPS thing was pretty well known nowadays? I’ve seen it in PBS shows about Einstein and relativity—it’s one of the few things that sticks in my mind on that topic.

    Relativity itself, however, is another matter. I’m pretty sure I will never get it, so I’ll just assume it’s one of those things that makes mathematical sense.

    BTW, sorry it’s taken me so long to stop by! I have no good excuses…

    • Wyrd Smythe

      “I didn’t read this whole post.”

      😀 I hope you liked the snow pictures. (There’s even less, now!)

      “I’m amazed to hear that there are people in physics trying to prove Einstein wrong.”

      It isn’t really the people actually working in the sciences, it’s armchair wannabes. What I’ve noticed is that each branch of science not only has its own crowd of “visionaries” (let’s call them), but that there are specific topics that seem to attract their interest, like moths to a streetlight.

      Einstein and Cantor are a couple of very big streetlights with a large flock of moths! 🙂

      Relativity is, as you thought, very well established among those who understand it. There are some seeking alternative explanations, but they understand the uphill climb they face. The armchair guys figure they got all solved and it’s just unfair opposition from the status quo that keeps their ideas from full recognition.

      Mathematician John Baez has a Crackpot Index one can use as a checklist (Einstein gets several mentions on it)…

      “BTW, sorry it’s taken me so long to stop by!”

      You’ve been missed! But people have seasons, and sometimes they move on from things. So it goes.

      • rung2diotimasladder

        Funny, when I saw “Mathematician John Baez” at first I read it as “Joan Baez”… “Well, I’ll be damned,” I thought.

        Thanks! It’s nice to be missed. I’ll be back into the swing of things again at some point, I’m sure. Probably once the flamenco season is over. May 18th is the tentative date for our recital, so I’ll be practicing a lot until then. There has been some talk of moving the date to the beginning of June, which would mean dancing in brutal heat, and it looks like we’re figuring on doing it in the afternoon at the hottest time of the day. If it goes over 105 degrees, I might have to protest. If it’s 110, I won’t do it. No amount of shade can compensate for that.

      • Wyrd Smythe

        Turns out he is related! According to Wikipedia (emphasis mine): “His physicist uncle, Albert Baez (inventor of the X-ray microscope and father of singer and progressive activist Joan Baez), interested him in physics as a child.”

        You dance outside? Not in some nice air conditioned space? Maybe the “Flamenco Season” should be a winter thing, like bowling leagues! 😀

        Hope to see you more often! (Are you here because of March Mathness? 😀 )

      • rung2diotimasladder

        The Baez thing…How bizarre!

        Yeah, I wish we had the recital in the winter, or indoors. The thing is, the “Flamenco Season” coincides with the school year for the school kids, and for the rest of us who like to get the hell out of here in the summer. Luckily it’s looking like we’ll do it in May. Not ideal, but it’s not June! (Personally, I’d rather do it in the snow than in the heat.)

        “(Are you here because of March Mathness? 😀 )”
        I am here despite the mathness!

      • Wyrd Smythe

        I guess the question I have is why do it outside? Is that part of it being real Flamenco?

        “I am here despite the mathness!”

        Ha! Well, in that case I’m extra double-plus pleased to see you here!

      • rung2diotimasladder

        Ah, the reason we do it outside is because we need a lot of space for dancing and parking and we need it for free. I would’ve volunteered my house, but we don’t have the space for it, not even outside. There could be about 100 people or so attending. Luckily, someone has volunteered their backyard for our venue. From what I heard, the house used to be Linda Ronstadt’s…so I’m guessing lots of space. But now we have to rent a stage…so, yeah, it’s a big to-do for a student recital!

        But real flamenco is definitely not connected to being outside.

      • Wyrd Smythe

        Ah, I see; I was being dense. You don’t have a budget to rent a big enough space.

        Linda Ronstadt! Cool; I always liked her music, such a great voice! Should be fun. Good luck! (I’m pretty sure one does not say, “Break a leg!” to dancers! 😀 )

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