We are about to see the last building block of nature! After this week we will have all the pieces ready for the chess game, and we will start looking at the rules of the game.
You will often hear that we live in a Universe with four dimensions. It sounds like a grand statement, but it is not really that complicated. If I want to invite you to my house, I could give you three numbers to locate it using a GPS: the latitude, the longitude and the altitude (I could also just give you my address, but never mind that). We will often use x, y, z coordinates to describe those three numbers.
If I want to make sure that you don't barge in during the middle of the night, I should probably give you a time as well. Instead of just being a location in space, you now describe an event in spacetime . This is all we mean when we say that time is the fourth dimension. Now time is clearly a different kind of dimension than the other three. Some people prefer to say that we live in a 3+1 dimensional spacetime, where the notation is three dimensions of space + one of time. This is to clearly differentiate time and space.
The most remarkable thing about time is that it seems to flow forward irrevocably. We seem to have no control over our motion in time while we obviously can affect our motion in space. This is not quite right. As it turns out, we can affect our "time position" but we need to go fast.
In summary, we live in a Universe with three dimensions of space and one of time and we can move from point to point (from event to event). As we will see, not all motion is allowed. We often represent spacetime in a diagram like the diagram below. The horizontal axis (distance) is really all three spatial coordinates but for visual necessity we just reduce it to one dimension. The vertical axis is time, while
Nobody knows why the Universe is 3+1 dimensional. We could have lived in a Universe with four dimensions of space and one of time (4+1). Or maybe two space dimensions and two time dimensions (2 + 2). Obviously, the laws of physics would change quite a bit if the number of dimensions were different.
Let us not think about time as a dimension for now and let us return to motion in space. We are interested in describing how objects move in space as a function of time. This means that the position coordinates x,y and z are really functions of time x(t), y(t) and z(t). That means only that your position can change as time passes (ie. you could have a velocity!).
Let's imagine that we move at a constant velocity in some direction such that the velocity
We will always consider motion in a single line to simplify the discussion and so the velocity is just some numbers of meters per second. A positive number means that we are moving right while a negative number means that we are moving left.