 We can now graph light using our space-time coordinates. For this, we use the distance light travels in one second for the units on the x-axis. This gives us the line running diagonally up the right side for light moving in the positive direction. At this scale, we cannot distinguish between the speeds achieved by snails, animals, cars, planes, and rockets from the line that represents standing still. Here's the line for protons at the end of the large hydron collider's linear accelerator traveling at one third the speed of light. And at this scale, the line for protons in the LHC itself is indistinguishable from the speed of light. Now we can run the light line up the left side for light moving in the negative direction. If we then extend the x-axis line to be a plane that we'll use to represent three-dimensional space, we can rotate the light line 360 degrees to create a cone, the light cone. This is the four-dimensional space-time graph. A point on this graph represents an event with four coordinates, x, y, and z for space and t for time. A mathematician named Hermann Minkowski developed the geometry for Einstein's space-time. So you may sometimes hear space-time referred to as Minkowski space. The four-dimensional length of a line in Minkowski space is referred to as proper time or proper distance. Space-time inside the cone is called time-like because the length of connected points have positive proper time. This makes all points inside the light cone reachable. In other words, it is possible for an event at an earlier time within the cone to be the cause of an event at a later time within the cone. At the speed of light, the lines connecting the events run up the edge of the cone and the four-dimensional length of the line connecting these events, proper time, is zero. Cause and effect can still hold. The space outside the cone is called space-like. The proper time of the line connecting a point inside the cone with a point outside the cone will have a negative length. And like the boat example in our speed of light segment, where negative times simply meant that you could not get there from here, so the negative proper time simply means that you cannot get from one of these points inside the cone to the other point outside the cone. In other words, no event from within the cone can ever be the cause of an event outside the cone. If we go back in time as well as forward in time, we get the full space-time diagram. Here we see that no past event outside the cone can be the cause of any event we see today.