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