DIMENSION SHIFT AND INVERSE IMAGE FORMATION
IN FASTER-THAN-LIGHT MOTION

DETAILED ANIMATION

Before watching the animations of Alice Law, I recommend reading Alice Law - The Transition to (c+v)(c-v) Mathematics in Electromagnetic Theory.

This animation demonstrates how Dimension Shift occurs in faster-than-light motion. However, there is no limitation on speed. By changing the observer's speed, you can analyze the situation for any speed value. The animation operates in the speed range of 0.5 to 2. A value of 1 represents the speed of light. For faster-than-light motion, values greater than 1 should be used.

EXPLANATION:
"How does an observer perceive when moving faster than light?" We will see the answer to this question here in more detail. This topic was also explained in the Inverse Image animation, but not in as much detail as here.

The signals emitted in the animation carry a color code. Signals emitted from the right side of the Sun carry a Blue color code, while signals emitted from the left side carry a Red color code. As the signals reaching the observer form the Image Object with the information they carry, they also color it with their color code. In this way, we can understand which parts of the Image Object are formed by signals coming from which part of the Sun.

When we start the animation (let's set the speed value to 1.25), the signals are emitted. However, due to the observer moving faster than the speed of light, we see that the signals reaching the observer shift towards the left side of the Sun.

The signals moving towards the observer travel within the observer's domain and move at the speed of c within that domain. As the observer moves, they carry their domain in the direction of motion. Since the observer moves faster than the speed of light, the signals traveling within the observer's domain shift to the left relative to the Sun's reference frame, instead of moving towards the observer.

When the observer reaches the Sun's position, the Image Object begins to form. However, note that at this stage, signals now reach the observer from two directions: the signals that remained in front of the observer and are coming directly towards them, and the newly emitted signals from the Sun arriving from behind. As a result, we see two distinct Image Objects forming: the Inverse Image Object in front of the observer and the second Image Object forming behind them.

When all the signals from the front reach the observer, the Inverse Image Object in front of the observer disappears. The Image Object of the Sun forming behind them, however, remains permanent.

What is the "Shadowing Factor" option in the animation?
Normally, the Sun's material presence should block some signals from reaching the observer. In faster-than-light motion, signals with a Blue color code shift to the left, and the Sun's mass should shadow these signals. In slower-than-light motion, the Sun should shadow the signals with a Red color code. When the "Shadowing Factor" option is activated in the animation, the signals exposed to the Sun's shadowing become ineffective. The Image Object is formed only by signals that are not subject to shadowing. This type of modeling aligns better with the realities of nature. From the observer's perspective, there is no difference in the Image Object seen between the two cases. Keep in mind that we are observing the animation from the side, whereas the observer sees it from the front and back.

By changing the observer's position on the Y-axis and their speed, you can analyze different scenarios. The behavior of the signals and the resulting Image Object are worth observing in every aspect.