The Beauty of Space-time - Minkowski space (Part1)

One of my favorites - Minkowski space-time. It is a very useful way of imaging the structure of space and time, especially when working with relativity theory.

Recipe:
Things you'll need:
-3 dimensions of space
-1 dimension of time
-a very unique inner product

Steps:
Take your three dimensions of space in the way you're used to it.
Now add your extra time dimension! Congratulations! You'r Minkowski space-time is almost finished! All you need to do is mix in your inner product and bake for a few million years.

Ok, what's this "inner product" I'm talking about?

---math start---

Ordinarily if you have two vectors, you can "multiply them", or create their scalar product. by multiplying their coordinates and adding those together:

For example, here you would get (1,5)*(4,2) = (1*4 + 5*2) = 4+10=14.
Yay!

Now just to simplify things, let's take the graph above, and let's call the 'x' axis our (traditional) space axis, and 'y' the time! So basically we're only going to be observing movement along one line.

Ok, so the inner product we will use will be the following: multiply and add the coordinates of the spacial parts of the vector as you usually do so, and subtract the multiplication of the time part of the vector from it!

It's really simple. So now, (1,5)*(4,2) = (1*4 - 5*2) = 4 - 10 = -6

(or generally: v*w = v_1 * w_1 + v_2 * w_2 + v_3 * w_3 - v_4 * w_4)

---math over---

What does this result in? Amazingly cool things! So the more interesting things will come in part 2! I decided to split this Minkowski topic in too, because I'm lazy right now, and this way next time I won't have to even mention math!