 One of the most dramatic consequences of general relativity is how gravitational redshift leads directly to the conclusion that a gravitational field slows time. We'll use the elevator thought experiment to illustrate how clocks closer to the source of gravity run slower than those further away. Picture a wave sent from the bottom to the top. Let the leading edge of the wave mark the start of a time interval. And let the trailing edge of the wave mark the end of the time interval. At the receiving end, the viewer sees that because the length of the wave has been stretched due to gravitational redshift, the length of time observed is slower than the viewer's clock. The lower clock's time is dilated. To help see how this works, we'll take another look at the lightning strike for the person on the train and the person on the ground that we used in our segment on special relativity. Only this time, we'll map the events to our spacetime graph. The whirl line for the person standing on the ground is shown in purple. We label the lightning strikes A and B and place the two events on the spacetime graph with A to the left of the person on the ground and B to the right. The plane containing A and B contains all the points that are simultaneous for the person on the ground at the time of the two strikes. We call this the simultaneity plane. The light from both events travels at the speed of light so their whirl line always moves at a 45 degree angle. They reach the person on the ground at the same time. This of course is what makes them simultaneous from the point of view of the person on the ground. Now let's repeat the lightning strike so that from the point of view of the person on the moving train, they strike at the same time. In order for the light to reach the person on the train at the same time, the strike behind him will need to hit first from the person on the ground's point of view because it will have to travel further to get to the moving person than the light from the strike that hits in front of him. So we see that the simultaneity plane where the moving person is necessarily tilted up on the right. Now we can map the movements of A and B in the accelerating elevator to the spacetime graph. The center is the source of the acceleration or gravity. A is to the right of it and B a bit further to the right reflecting their distances from the source of the gravity. As the elevator accelerates, the whirl lines on the spacetime graph are not straight lines. They curve outwards because their velocity increases with every second. Here we have clocks that measure the proper time elapsed along each person's whirl line. They mark the time in their own reference frame. At the start, they are both at rest, so their simultaneity plane is horizontal and they each read each other's clocks reading zero. In this example, we see that after two seconds, we have a slightly tilted simultaneity plane. B sees that at the same time his clock ticks two, A's clock ticks one. A also sees his own clock reading one when B's clock reads two, continuing to a higher velocity with a steeper slope for the simultaneity plane. B sees A's clock reading two when his own clock reads four. A also sees his own clock reading two when B's clock reads four. A and B both agree that A's clock is ticking slower than B's clock. The equivalence principle tells us the same thing will happen near a massive body. Gravity slows down time. Newton's gravitation has no such implication. In 1971, Joseph Haffiel, a physicist, and Richard Keating, an astronomer, took four cesium atomic clocks aboard commercial airliners. They flew twice around the world, first eastward, then westward. And compared the clocks against others that remained at the United States Naval Observatory. When reunited, the three sets of clocks were found to disagree with one another, and their differences were consistent with gravitational time dilation. Today, we see this with our GPS systems. In our segment on special relativity, we saw that time dilation, due to velocity differences, have GPS satellites losing time every day, time that must be corrected for to get the right position on the surface of the Earth. They must also take into account gravitational time dilation, due to their being further away from the Earth than clocks on the ground. Based on the Schwarzschild metric, calculations show that the satellite's clocks will gain over 45,000 nanoseconds a day due to this general relativity effect. The accuracy of our GPS system is strong evidence for the correctness of general relativity.