So, on special relativity - What's up with reference frames?

Now special relativity is a concept that is strange to no one. I mean, everyone knows of its existence while not understanding what it means, and everyone has heard of the famous, E = mc^2, arguably the most famous equation in physics... But still what is special relativity all about? I recently decided to learn a bit more about the history of physics that led to that theory and the whole thing is fascinating. So fascinating, that I decided to create a blog only to talk about it, from a more personal point of view. But I am digressing from the subject.

Well, first of all, the concept of relativity isn't new. And by not being new, I mean that it started as what we can call the foundations of physics as a science of its own. So what is relativity all about? In a simple way, relativity is all about reference. Or better saying frame of reference. Now what is a frame of reference?

As you know from high-school physics, one of the exercises you constantly solve is about motion. I would dare to say that motion is one of the most important things in physics, and from where some of the greatest questions were derived. But I also believe you heard of frame of references (or reference frames). To visualize frames of reference, you should imagine being in a moving train, watching someone standing outside this same train. If you switch places with the person, you see the train and the person inside of it moving. But you switch back positions, you will see the person outside moving, while you remain sitting still. So while you are still, the person appears to be moving "relative" to you. And you appear to be moving to the person standing still outside. While we do know that in this case, the train is the one actually moving,  the whole question of things moving relative to others is important. And the fact you change the perspective from one person to the other alters the way things move. In physics, there is a more general term than perspective, and that would be frame of reference. You could say you are in a different frame of reference and a good way for you to visualize this would be for you to imagine yourself in a graph, on the center. You can think of it as a plane, divide it into pieces of equal size (like a bathroom floor with its tiles) and give each point a certain value. An example, if you have a ball that is 2 tiles to your right and 3 tiles in front of you, in your reference, you could say that the ball is in the position (2,3), and those two values are called the coordinates of your reference frame. (Keep in mind that there are many kinds of reference frames, so you divide it in a different way, it could give a different value)

Well, I could draw my own graphs,

 but I am not really willing too so just 

endure this one. Courtesy of K. Bolino,

 on Wikipedia (Cartesian coordinate system)

So you are the center. And let's say you have something moving from the blue spot towards the red spot. Since this is your frame of reference, you are called the observer. And the observer is usually at the center of the frame of reference or the origin, so when someone says you are not in center of the world, from your reference, actually you are in the center (this, my friends, is the first example of bad physics jokes you will see here. Beware of more of these). But again, the thing moving from the blue to the red point has its own reference frame, and in that reference frame, you are the one moving. So each of you has a relative movement compared to others. In fact, in its reference, the observer is always at rest. That may not be true in another reference. In your reference, you are still, and you don't move, but in other people's reference you are moving. Also, keep in mind that this is the physical definition for a frame of reference. In mathematics, there is a lot more to do with your coordinate system, and the way you define your vectorial space, and there is hardly any necessity for a observer, that is exclusive to physics. In fact, the physical frame of reference is called the observational frame of reference, to give emphasis to this. But what  you take from this is that understanding the frame of reference may be the first thing you need not only to understanding relativity, but all of physics.

Now we may think that this whole talk about reference frames is boring. I mean, it is not exactly the best in relativity, but to me it is important to understand the concept of reference frames well, because that helped me actually figure out what relativity is all about, it led me to actually understand the significance behind all the consequences it brings, and that gave me a bigger fascination for special relativity.