TIME SHIFT I

Among the Relativity Effects, the most significant one is undoubtedly Time Shift. The difference in the flow rate of time in Absolute Space-Time and Apparent Space-Time is called Time Shift. The Time Shift effect occurs between reference systems moving relative to each other. More specifically, Time Shift refers to the difference in the flow rate of time between the Source Object and its Image Object.

Before starting the animations, I recommend reading the book and informing yourself on this topic. To understand what is shown here, you need prior knowledge of critical topics such as "Image and Source," "Doppler Triangle," "Absolute Time," and "Apparent Time." In other words, you should read my book beforehand. The animations here are not going anywhere and will remain available.

DERIVATION OF THE MATHEMATICS OF TIME SHIFT
This animation shows how we can derive the mathematics of Time Shift. In the animation, there are two adjacent Doppler Triangles, OAB and OBC. You can observe the flow of events by moving the slider. Now, let’s write down the event in the animation step by step:

• The airplane moves along line AC.
• When the airplane is at point A, it sends the first signal to the observer.
• The signal travels along line d0 at the speed of c and reaches the observer.
• When the signal reaches the observer, the observer sees the Image Object of the airplane at point A.
• During the time it takes for the signal to reach the observer, the airplane (Source Object) travels along line d1 at speed u1 and reaches point B.
• Let’s pay attention to the time it takes for the airplane (Source Object) to cover distance d1. This time is t0 = d0/c.
• Let’s write the equations: t0 = d0/c = d1/u1 and t0 = tΔ
• When the airplane reaches point B, it sends the second signal to the observer.
• The signal travels along line d2 at the speed of c and reaches the observer.
• When the second signal reaches the observer, the observer sees the Image Object of the airplane at point B.
• During this time, the airplane (Source Object) travels distance d3 and reaches point C.
• Let’s pay attention to the time it takes for the airplane (Source Object) to cover distance d3. This time is t1 = d2/c.
• Notice that during time t1, the Image Object of the airplane travels distance d1 and moves from point A to point B.

We see that while the Source Object of the airplane travels distance d1 in time t0 = d0/c, the Image Object of the airplane travels the same distance in time t1 = d2/c. The difference between these two times gives us the mathematics of Time Shift.

The mathematical derivation of Time Shift is shown step by step in the figure.

EXPLANATION:
From this point on, we will see how Time Shift occurs in continuous motion and what effect it causes.

Before watching the next animation, I would like to inform you about it. Observe the flow of events by moving the slider.

The Source Object is represented by a clock in motion.

The clock sends a signal to the observer while moving along its path.

Each signal sent by the clock in the animation is marked with a number. In this example, the clock sends signal number 7.

When the clock sends the signal, a marker is placed at the current position of the clock, as seen. The red hour and minute hands on the marker indicate when the signal was sent, the number indicates which signal it is, and the marker’s position shows from where the signal was sent.

In the above example, the Source Object sends signal number 7 at 1:13:00, and at that moment, a marker is placed at the signal’s emission point. When signal number 7 reaches the observer, the observer sees the Image Object at the position of marker number 7. At this moment, the observer sees that the clock on the Image Object shows 1:13:00.

Thus, we have seen the operating principle of the next animation. If signal number n has reached the observer, the observer will see the Image Object of the clock at the position of marker number n and at the time indicated by the red hour and minute hands on the marker. Since the signals are continuous, the Image Object will follow the markers in the order the signals arrive.

TIME SHIFT ANIMATION
The operating principle of the animation is explained above. The playback speed of the animation may vary depending on your operating system and programs. You can optimize the playback speed of the animation using its main controls.

Main controls of the animation:
Light Speed: Adjusts the speed of the signals.
Delay: Changes the intervals between signal emissions.
Frame Speed: Adjusts the playback speed of the animation.
Slider: Changes the speed of the clock (Source Object).

Explanation of the animation:

Here, the flow rate of time in the Image Object is compared with the flow rate of time in the Source Object. While the animation is playing, two clocks side by side in the bottom-left corner show us this comparison. The clock on the left shows the time value of the Source Object, and the clock on the right shows the time value of the Image Object. The clock in the Source Object represents Absolute Time, while the clock in the Image Object represents Apparent Time.

Let’s press the play button, run the animation, and watch it.

Time Shift

Pay attention to the signals coming toward the observer in the animation; if the observer receives signals emitted while the Source Object is moving away, the flow rate of time in the Image Object slows down. If the observer receives signals emitted while the Source Object is moving toward them, the flow rate of time in the Image Object speeds up. You can more easily see the deceleration and acceleration of time in the Image Object by comparing the clocks in the bottom-left corner.

Speed Shift

You must have noticed. If the observer receives signals emitted while the Source Object is moving away, the speed of motion of the Image Object slows down. If the observer receives signals emitted while the Source Object is moving toward them, the speed of motion of the Image Object increases. The change in speed of the Image Object in this manner is called Speed Shift. Speed Shift is another Relativity Effect that expresses the difference between the speed of the Image Object and the speed of the Source Object.

I forgot to include the topic of Speed Shift in the book, although it was shown in Alice's Law version 7. You can find updated information on this topic in the post-book publications section.

Observer Moving and Clock Stationary
If you select this option from the Radio Buttons in the animation, the animation will make the observer move and the clock stationary. However, the situation you will encounter will probably surprise you. To interpret the animation more comfortably, I recommend activating the "Show Observer’s Field" option. Recall the animation "Woman Sitting on a Chair" in the Image and Source section; that animation will help you here.

In this option, the (c+v)(c-v) mathematics is at work. The Source Object places its signals inside the observer’s field. The markers placed on the field indicate where the signal enters the field. Note that the markers are carried by the observer’s field in the direction of motion. The Image Object moves according to the markers placed on the observer’s field. In fact, the same applies when the observer is stationary and the clock is moving. However, when the observer and thus their field are stationary relative to our reference system, such an explanation is unnecessary. Whether the observer is stationary or moving, the signals will travel within the observer’s field.

FLOW RATE OF APPARENT TIME
In this animation, the Source Object is represented by three balls moving inside a box. The logic of the animation is entirely the same as the previous one. The red, blue, and green balls replace the hour and minute hands on the marker here. The marker placed at the point where the signal is emitted shows the current positions of the balls in the Source Object. The balls in the Image Object move by following the balls on the markers.

The subject of the animation is how the observer perceives the balls (Image Object) depending on the speed of the box (Source Object). The flow rate of Apparent Time is seen more clearly here. The Demo Button sets the animation’s parameter values to a suitable position for viewing.

Notice; if the observer receives signals emitted while the Source Object is moving away, the motion of the balls in the Image Object slows down. If the observer receives signals emitted while the Source Object is moving toward them, the motion of the balls in the Image Object speeds up. Thus, we have observed how the flow rate of Apparent Time changes.