Motivation for Relativity

Hello, and welcome back to MPC! Last week, we went over some basic physics concepts, including displacement and velocity. This week, we are going to be jumping into the first field of modern physics that we will be discussing on MPC: relativity. The goal of this post is to show you what makes relativity so amazingly awesome and why you should care about it.

Let’s start off with a strange scenario. Say you are standing at the top of a cliff that is 100 meters in height. You pull out a timer, turn the dial to the 10 second mark, and throw the timer down (towards the base of the cliff) at a speed of 5 meters per second. Recall that this simply means that, for every one second of time that the timer is traveling at this speed, the timer will move 5 meters. Let’s just say, for the sake of simplicity, that we are on a weird planet that has no gravitational field (allowing us to ignore the acceleration caused by gravity). What is going to happen?

If you read last week’s post, this scenario should not be too difficult to analyze. We know that the timer will ring after 10 seconds have elapsed, and we also know that the timer is moving at 5 meters per second. Using these two facts, we can determine that the timer will ring after it has traveled 50 meters (you can reach this answer by using the formula for velocity or using intuition). In other words, when the timer has reached the halfway point between the top of the cliff and bottom of the cliff, it will buzz.

Now, let’s imagine that the timer is something else: a muon (mew-on). You can think of a muon simply as a particle, a speck of matter. The interesting thing about a muon is that its lifespan (time before it “disappears”) is very short. If we were to imagine the muon as our timer, we could say that the muon disappearing corresponds to the timer buzzing. Let’s imagine that a muon, with a lifespan of 10 seconds, was thrown down from the top of the same cliff as before (100 meters high) with a speed of 5 meters per second. How can we analyze this scenario? Once again, think about the timer: just as the timer buzzes after 10 seconds, the muon will disappear after 10 seconds. So, the muon would only travel halfway to the bottom of the cliff prior to disappearing — the muon would never actually hit the bottom of the cliff.

And with that, we are done, right?

Wrong. The analysis we just performed was based on the assumptions of classical physics. Remember, here on MPC, we are talking about modern physics. How does modern physics change everything? Well, what if I were to tell you that the muon actually does hit the base of the cliff? How amazing would it be if that were true?

Scientists have experimentally observed this phenomenon. Alright, they have not observed this exact phenomenon — it is very difficult for someone to just grab a muon and toss it (not to mention the difficulty of finding a planet without a gravitational field) — but they have observed something similar to it. Muons are typically found in the Earth’s atmosphere and sometimes come falling down to the Earth’s surface. Just as the lifespan of the muon in our other scenario prohibited it from reaching the base of the cliff, the lifespan of the muons in the real-world should prohibit them from hitting the surface of the Earth. Nonetheless, they do hit the surface of the Earth, and scientists have confirmed that these collisions occur rather frequently. I know — pretty awesome.

So how does all of this happen? Relativity! What do I mean? You’ll have to wait and see — we have a lot to learn first! Relativity has many important applications, and we will be using relativity to discuss light, speed, time travel, and more! Be sure to stick around for next week’s post, where we will be discussing more about relativity! See you then!

**Side note: The timer that you threw from the top of the cliff would not hit the base of the cliff without buzzing (even when relativity is taken into account) and the muons would not hit the bottom of the cliff. The cliff example was simply meant to provide a conceptual understanding of this intriguing phenomenon. Don’t worry, the muons in the real-world example do actually hit the surface of the Earth. The reason why the real-world muons hit tbe Earth’s  surface but the “fake” muons do not hit the bottom of the cliff has to do with the very high speed of the real-world muons (much, much greater than 5 meters per second), which we will be discussing in a future post.**