Space

In Physics, we study the motion of objects. And, as discussed, motion is the change of position after a period of time. However, what is position? And what does “a period of time” mean? We will explore these ideas the same way we did in the previous discussion.

Space is, simply put, an environment in which objects exist. We can intuitively imagine it like this: a toy boat is floating on the surface of water in a box. Can the boat float beyond the box? Obviously, it cannot, because it will hit the side of the box (unless you intentionally take it out). So, in this case, the “space” here can be understood as the box area. Now, it is essential to note that we used an important assumption there: the boat cannot exist outside of the box, which is obviously false. However, it is essential for us to use such an assumption to really imagine what space is. So, in reality, we consider everywhere that an object can exist to be “space”.

Now, can two things exist in the same point in space? Let us return to the boat example and ask that question again: can the boat… exist right where the edge of the box is? The answer is obviously no: you cannot “merge” a toy boat into a box, unless they were previously merged together (and thus become an object itself).

Now that we have defined space, let us tackle the next question: what is position in space? That is a question that requires a very complicated answer, so we will put it simply here. Let us start from observation again: in real life, how do we know where an object is? For example, when we play hide and seek in team (say the hiders are one team and the seekers are one team). Each team has more than 1 player. You are on the seeker side, and you suddenly spot a hider nearby who is hiding behind a tree (given that the playground has only one tree. I know it is absolutely odd, but it will simplify our example much more). Now, how do you tell the member in your seeker team where the hider is? If you say “Hey, there is a hider there!” (without pointing your finger at the tree), the other members of your team cannot know where “there” is, and cannot find the hider. So, you need to tell them “The hider is behind the tree!”, so that other members know where to look for. Why does this work? Because your teammates know where the tree, and since the position of the hider is tied to the tree (that is, the hider is behind the tree), they then know where the hider is. There is another notable thing here: your members do not know where they are on the playground, they only need to know where the position of the tree relative to their positions is. For example, if the playground is really vast, so large that you cannot see the edge of the playground, and you do not know where you are on that playground. However, you do know where the tree is compared to you. Again, this is the same idea of the tree and the hider.

So, how do we apply this idea into space? Let us recall the core idea we gained from our example: you do not need to know the position relative to the space (that is, the edge of the space), we only need to know where things are relative to us, or to another object that we can observe to physically “know” where the object is. There is a useful Mathematics concept we can use here, that is the Cartesian coordinates. Now, notice that there are other coordinates that you can use too, such as cylindrical coordinates that can also be used to describe this. Obviously, the choice of coordinates is an expression of the idea of specifying position, and it is not a necessity.

That is, from now on, we shall use the definition of a three-dimensional space for “space” in Classical Physics.