SPECIAL RELATIVITY
and
THE CONCEPT OF SIMULTANEITY

Han Erim
29 October 2009

I explained the subject of simultaneity in detail in Alice Law Version 5. Here I will explain it once more.

Let us suppose we are watching a news program on television. Let the news topics be divided into 5-minute segments and consist of three small parts:

• At the beginning of the topic, the anchor is on screen (red bar).
• In the middle of the topic, the picture is fully visible (green bar).
• At the end of the topic, the image moves away (blue bar).

Let us watch the news program by pressing the START button.

The diagonal lines on the left represent the television station. There are three different reference systems receiving the broadcast. The clocks used in the animation show when the signal leaves the television station. By moving the slider, we can see in which position each of the three reference systems is watching the broadcast.

We know that electromagnetic waves move at speed c with respect to the field in which they exist. Therefore, each reference system receives the television broadcast through its own field. For moving airplanes, the (c+v)(c-v) mathematics arises.

Rule 1: If objects moving relative to each other are at the same position in space, they see different moments of the same event.

Let us press the Rule 1 button. Although all three reference systems are at equal distance from the television station, they are watching different images.

Rule 2: If objects moving relative to each other see the same moment of an event, they are located at different positions in space.

Let us press the Rule 2 button. Although the three reference systems are at different distances, they are watching the same image.

The animation above shows that the television broadcast starts at the same time for the three reference systems. By slowly moving the slider, first let the broadcast reach the observers, and then let it reach the end of the program for the top airplane. Instead of this, we can also press the “Rule 3” button.

We see that although the broadcast has ended for the top airplane, it is still continuing for the other observers. According to this situation, we can define a new rule:

Rule 3: When a moving object looks forward, it sees events as if they are happening faster than normal; when it looks backward, it sees events as if they are happening more slowly than normal.

The (c+v)(c-v) mathematics reveals such relative effects. In this animation, we have seen the effect of (c+v)(c-v) on the concept of simultaneity. As the velocity difference between reference systems increases, these effects become more pronounced.