Light Has Constant Speed

Find The Midpoint

page1 If we assume the speed of light is constant, we can use it to find the midpoint between two other points. I'm adding two people to my scene, $P_1$ and $P_2$ and then I'm adding a flash of light at each of them.

page2 As we move forward in time, we see that the two beams of light meet at the midpoint. I'll add an event where the two cones intersect. I'm going to name it " $X$ " and make it red.

page3 Now let's go back to time zero and add a third person at the midpoint. I'll call that person $M$ , and choose blue.

page4 I'll turn off the Lorentz transformation and see that this picture would give us a paradox. When I change our observer's velocity, the two beams of light do not meet at the same location as $M$ . That can't be: the third person would see different behavior depending on the velocity of the observer!

page5 Let's go back to the zero velocity and turn the Lorentz transformation back on. Now when I change the observers velocity, the two beams of light always intersect at the same event $X$ , and $M$ 's world line goes through $X$ .

page6 The surprising thing is that from this observer's frame of reference, $P_1$ flashed a light before $P_2$ . This is an important part of the Lorentz transformation: saying two events happen at the same time is relative to the observer. Since $P_1$ , $P_2$ and $M$ are not moving relative to each other, they agree that the light cones start at the same time.

page7 Another observer, however, who is moving relative to the other three, does not agree that the light cones start at the same instant. This is probably the hardest idea to come to grips with in relativity: different observers do not agree on which events happen at the "same time".