In my opinion, one of the coolest parts of astronomy is relativity, the theory describing the warping of spacetime. If you’ve ever seen Interstellar, you’ve been exposed to one part of the theory: time dilation. In short, time dilation is a phenomenon that causes time to pass more slowly in one place than another (relative to that other place). Time dilation can be caused by gravity or – as I’ll discuss today – high velocities.
Background information: “Muons have a mass roughly 200 times that of the electron, but decay moderately rapidly, with a half-life of 2.2 microseconds. Muons are formed in the upper atmosphere, when high-energy cosmic rays collide with atomic nuclei in the air. This raises the question: why don’t they all decay before they reach the ground? Even travelling at 99.5% of the speed of light, the time taken to reach the ground is many half-lives,” (source).
In other words, muons travel super close to the speed of light, and they should decay before reaching Earth. We receive muons on Earth, though, raising the question of why they don’t decay on their way down from the atmosphere.
As it turns out, as velocity increases, time slows down relative to a stationary observer (source). Let’s look at this in other words to try to understand it:
-Stationary muon: If I were to create a stationary muon, I could stand next to it and time its half-life to be 2.2 microseconds.
-Moving muon: If I were to hang out in the atmosphere and follow a muon down to Earth (I would travel at the speed of light with the muon), I would also time its half-life to be 2.2 microseconds.
So, each half-life is 2.2 microseconds. But here’s the kicker: those 2.2 microseconds are not equal when compared to each other. What does that mean? Imagine this: you stand still on Earth and time 2.2 microseconds, and at the same time, I travel through space at the speed of light and time 2.2 microseconds. We could compare our times after finishing, and we would find that my 2.2 microseconds took MORE TIME to conclude than yours did on Earth. In other words, relative to you being on Earth, time would have passed slower for me (traveling at the speed of light) than it would have for you (stationary on Earth).
Check out this video and this video for more information and illustrations of all this.
So, what do we know? A few things:
-Relative to a stationary observer, increased speed slows down the passage of time.
-Muons’ half-life is so short that they should decay in the time it takes them to travel to Earth after being created in the atmosphere.
-Muons travel at 99.5% the speed of light (let’s call it the speed of light for our purposes).
So, what does this mean? Because muons travel at the speed of light, their time is dilated relative to stationary-on-Earth muons. Therefore, the muons making their way from Earth’s atmosphere down to Earth have a “longer” half-life (again, relative to those 2.2 microseconds on Earth).
Significance of this: muons making it to Earth is one line of reasoning we use to support Einstein’s Theory of Relativity.
A final thought: though you and I aren’t muons, there are still some cool things we can do with all this information…
-Next time you hear someone say, “It’s all relative,” you can respond with, “Well, actually, yes. It is. Have you heard of muons?” and then proceed to show off your scientific brilliance by regurgitating all this information.
-When you walk outside, you can imagine the muons making their way to Earth from the sky.
-GPS systems find your location by pinging satellites in Earth’s orbit, and because those satellites move very quickly, time passes slower for them relative to time on Earth. As a result, GPS systems have to counter the effects of time dilation (the effects we discussed re: muons traveling to Earth). This is connected to muons only by extension, but it’s still cool to know!
#/media/File:AquariusCC.jpg){kind=link}