SPEED SHIFT

The speeds of the Source Object and the Image Object of a moving object are always different. This difference is called Speed Shift.

Since what we observe are the Image Objects of the objects, the speed value obtained from a measurement we make visually does not represent the actual speed of the object. This may not matter for small speeds, but as speed values increase, this issue becomes increasingly important. There is no upper limit to the speed for an Image Object. At times, it can be thousands of times faster than the speed of light.

While writing the book, I somehow skipped adding the topic of Speed Shift. However, it was not a new discovery for me. I mentioned this topic in Alice's Law Version 7 (Time Dilation, page 12). If you check the post-book publications section, you can find my latest publication on this topic.

THE MATHEMATICS OF SPEED SHIFT
You can see how Speed Shift occurs in this animation. In the animation, we see two adjacent Doppler Triangles. These are the OAB and OBC triangles. The OBC triangle is included here to provide continuity of motion. Calculations will be performed on the OAB triangle.

By moving the slider, I first want you to see how the event develops. To arrive at the mathematics of Speed Shift, we write down the sequence of the event we see in the animation.

The airplane (Source Object) sends a signal towards the observer while at point A.
The signal travels along line d0 at speed c and reaches the observer.
When the signal reaches the observer, the observer sees the Image Object of the airplane at point A.
The time it takes for the first signal to reach the observer: t0=d0/c , (t0=tΔ)
During this time, the airplane travels the distance AB, that is, line d1, at speed u1 and reaches point B. d1=u1.(d0/c)
When the airplane reaches point B, it sends a second signal towards the observer.
The signal travels along line d2 at speed c and reaches the observer.
When the signal reaches the observer, the observer sees the Image Object of the airplane at point B.
Let’s calculate the time it takes for the second signal to reach the observer: t1=d2/c
During this time, the airplane travels the distance d3 and reaches point C.
During the same time, the Image Object of the airplane travels the distance d1 at speed u2 and reaches point B. d1=u2.(d2/c)
As can be seen, while the Source Object of the airplane travels the distance d1 at speed u1 in d0/c time, the Image Object of the airplane travels the same distance at speed u2 in d2/c time.
A speed difference has formed between the Image Object and the Source Object. This effect is called Speed Shift.

With this information, we can now write the mathematics of Speed Shift.
The figure shows the steps of deriving the mathematics of Speed Shift in sequence.

THE SPACE SHUTTLE MOVING AWAY FROM EARTH
This and the next animation were created using the Speed Shift equation. The animation is controlled by timers. Therefore, depending on the performance of your operating system, there may be minor errors in the animation.

Conduct a time test in advance: When you run the animation at a "1 c" value, if the Source Object’s arrival time is between 0.98 - 1.05 seconds, we can say things are going well. The ideal case is 1:00.

The animation shows how an observer on Earth perceives the speed of the Image Object as the space shuttle moves away from Earth. We could already understand how the event unfolds using the Speed Shift equation. However, I wanted to show it here as an animation as well.

The animation compares how long it takes for the Source Object and the Image Object of the space shuttle to cover a "1 light speed/second" distance as the shuttle moves away from Earth. The Radio Buttons on the left set the speed of the shuttle (Source Object). Enter a value from here into the animation and press the Play button to see the result.

THE SPACE SHUTTLE APPROACHING EARTH
Depending on the performance of your operating system, there may be errors in the animation. In this animation, the Source Object and the Image Object must always reach the finish line simultaneously. The Image Object can never reach the finish line earlier. If they do not arrive at the same time, do not watch the animation, as it will provide incorrect information. I am making this warning because it happened to me. When I restarted my computer, this situation was resolved.

Conduct a time test in advance: Run the animation at a "1 c" value. If the Source Object’s arrival time is between 0.98 - 1.05 seconds, we can say things are going well. The ideal case is 1:00.

The animation shows how an observer on Earth perceives the speed of the Image Object as the space shuttle approaches Earth.

If you enter a value of 1 into the animation and run it, the speed of the Image Object will reach infinity, meaning it will become undefined. With the arrival of the Source Object at the destination, the Image Object will appear at the destination.

The animation compares how long it takes for the Source Object and the Image Object of the space shuttle to cover a "1 light speed/second" distance as the shuttle moves away from Earth. The Radio Buttons on the left set the speed of the shuttle (Source Object). Enter a value from here into the animation and press the Play button to see the result.