Special Relativity 1: The beginning — trains and tennis balls.
You may have heard of the words special relativity before and you may connect these words with Einstein himself, as it was he who developed both special and general relativity theories. You might also know that the speed of light is the universal “speed limit”. Some of you may even have heard of the strange effects that can happen when one tries to go close to the speed of light. All of this and more is what my small course on special relativity aims to explain.
In this article, I will go over the very basics and the groundwork we need to instil before we can proceed with the quirky stuff. This will mostly be obvious to many of you, but it is important that we define even the most basic of things properly before we move on. I will go over something called a “frame of reference” and how we will use these extensively to think about relativity. I will also go over trains… yes you heard me. More specifically, I will go over what happens when we throw a tennis ball while on a train. I know I know, the final two topics seem to burst with fun and interest, but I promise it will all mean something.
Inertial frames of reference
I hinted at the term “frames of reference” in the section above. Now is the time to go through what this really means. To put it simply (and how I think about it personally), a frame of reference is, as the name suggests, nothing more than a viewpoint. Let’s make an example, suppose you are in a car and your friend is outside the car. There are two “viewpoints” here, one is the point of view from yourself within the car (you can see your friend outside the car), and the other is the point of view of your friend (they can see you inside the car). A frame of reference is just a fancy physics name for this (of course it comes with a bit more spice than that, but we will not need this to understand what’s happening!).
Now that we have established what a frame of reference is, I want to go over why it is important and why I am even bringing it up at all. Well, the theory of special relativity, is as the name suggests, about things which are “relative”, i.e. measured or viewed with respect to something else. This sounds familiar, doesn’t it? A reference frame is what we use to describe this perfectly and so we will need these whenever we want to think about it.
Trains
Trains. Imagine yourself inside one which is moving at say… 60mph (clearly not a train in the UK!). Now, imagine you pass a platform without stopping and out of the window you lock eyes with another person. You see this person flash by at 60mph. They also see you flash by at 60mph. Let’s look at this again but this time using our new physics tool, the frame of reference. As before, there are two frames of reference: yourself and the person who is on the platform. The key difference now is, we want to be more careful and specific about things such as direction, speed and time. In this scenario, from both of the frames of reference, the speed and time are the same. You see them the same time they see you and you both see each other whizz by at 60mph. However, when we think about direction, that changes between the frames. You see the stranger pass by you going one way, while they see you pass by them going in the other way.
Now, I admit, I may have lied to you earlier when I said the speeds were the same in both frames. While it’s true that you both see each other going at 60mph, you also both see _yourself_ as being completely still. To you, you are simply sitting down and the stranger on the platform is moving at 60mph in the opposite direction. This is the essence of relativity! You are both correct and both of your reference frames are correct…relative to each other! Now, let’s add some spice to this so we can start to see the real effects of relativity.
Trains and Tennis Balls
Oh yeah, now I have added tennis balls into our thrilling discussion about trains, but trust me, it’ll be worth it. Let’s imagine the exact same scenario, you are on your train at 60mph and you pass the same platform and see the same stranger. Now, let’s imagine you are in possession of a tennis ball, a very nice one, and for some reason, you decide to throw it at 5mph at the exact time you pass the stranger on the platform. In this scenario, there is an additional, third frame of reference — that of the ball itself (let’s imagine the ball is sentient and can also have a point of view). Let’s imagine you throw the ball in front of you at 5mph. From the frame of reference of the stranger on the platform, what do they see? Well, they will see you going at 60mph, but they will also see the ball travelling too. Since you just threw the ball at 5mph, the ball in the frame of reference of the stranger is now travelling at 65mph. This is mostly common sense. If you throw the ball behind you at the same speed, the stranger will see it travelling at 55mph. We see this effect a lot if we try to walk the wrong way on an escalator.
Now, what does the ball see? In any case, it will see you (the thrower as it were) travelling away from itself at 5mph. But this time, it will see the stranger travelling at either 65mph or 55mph. What have I shown here, well, the key point of adding the tennis ball is to see that when more than two frames of reference are in the mix, there are lots of different viewpoints especially when it comes to how fast things are moving. What I haven’t mentioned, but what I hope is obvious, is that in all these cases, the time and even where this happens is the same. Why do I point this out? Well, as we get closer to the speed of light, those things can (and do!) change, and in very weird ways!
I hope you enjoyed this story about trains, and tennis balls and can think of the world around you in terms of “frames of reference”. This physics tool will be extremely important when we start to think of crazier scenarios when we are close to the speed of light.
