### Moving Clocks: how each observer sees the other observer's clock as running slow.

This shows two inertial frames moving past each other, each equipped with a set of clocks. One frame is "stationary" (with respect to you, the viewer of this movie), and the other is moving to the right at a large fraction of the speed of light (corresponding to gamma=2). The red clocks are at the origin of each inertial frame, and are set to read the same time at the instant the two clocks pass each other. The clocks in each reference frame are synchronized (according to the observer in that reference frame).

The first thing one notices when one runs the movie is that all the clocks in the "stationary" referece frame are synchronized, but those in the moving reference frame are not. From the point of view of an observer on the moving reference frame, however, the clocks in that frame are synchronized and the clocks in the "stationary" frame are not. (See the movie demonstrating the relativity of simultaneity.)

As demonstrated in another movie the observer in the stationary frame will observe the moving clocks as advancing more slowly. This can be seen as this movie runs by noticing that the moving red clock gets further and further behind the clocks in the stationary frame (careful observers will notice that the moving clock runs a factor of 2 slower than the stationary clocks). (Notice that the moving clocks are all compressed along their direction of motion. This is the result of length contraction).

What does the moving observer say about the stationary clocks? To answer this, consider the red clock in the "stationary" frame. According the observer in the "moving" frame, this clock is moving to the left. As the stationary red clock passes each of the clocks in the "moving" frame, we see that it gets further and further behind the corresponding clock in the moving frame. Thus, from the point of view of an observer in the moving frame, the stationary clocks are running slow.

From the point of view of the "stationary" observer, this slowness of the stationary clock (as viewed by the moving observer) arizes from the fact that the moving clocks are not synchronized with each other. Thus, it is the relativity of simultaneity that makes it possible for each observer to measure the other observer's clocks as running slow.