TIME SHIFT I

The most important one among Relativity Effects is undoubtedly Time Shift. The fact that the speed of flow of time in Absolute Space-Time and the speed of flow of time in Visible Space-Time are different from each other is called Time Shift. Effect of Time Shift occurs between reference systems that are in motion relative to each other. More specifically, Time Shift represents the difference between the speed of flow of time in an object’s Source Object and the speed of flow of time in its Image Object.

I suggest you read the book and getting informed before you start watching the animations. In order to understand what is shown here, you need to be familiar with the critical topics such as “Image and Source”, “Doppler Triangle”, “Absolute Time”, “Visible Time” and the like. In other words, you need to read my book first. The animations are not going anywhere and will never do so.

OBTAINING THE MATHEMATICS OF TIME SHIFT
We see how we can obtain the mathematics of Time Shift in this animation.
There are two adjacent Doppler Triangles in the animation. These are OAB and OBC triangles. You can see the flow of events by moving the slider bar. Now, let’s write about the event taking place in the animation in accordance with the order of flow:

  • The plane travels by following the AC line.
  • When the plane is at point A, it sends the first signal to the observer.
  • The signal reaches the observer by covering the d0 line at c speed.
  • When the signal reaches the observer, the observer sees the Image Object of the plane at Point A. 
  • Within the travel time of the signal to the observer, the plane (Source Object) covers d1 at u1 speed and reaches Point B.
  • Please pay attention to the time it takes for the plane (Source Object) to cover d1 distance. This time is: t0= d0/c
  • Let’s write the equations: t0= d0/c= d1/u1 and t0= tΔ 
  • When the plane reaches B, it sends the second signal to the observer.
  • The signal covers the d2 line at c speed and reaches the observer.
  • At the moment the second signal reaches the observer, the observer sees the Image Object of the plane at Point B.
  • Within this time, the plane (Source Object) covers the d3 distance and reaches Point C.
  • Let’s pay attention to the time it takes for the plane (Source Object) to cover d3 distance. This time is: t1=d2/c
  • Please pay attention: the Image Object of the plane covers d1 distance in t1 time and travels from Point A to Point B.

As we can see, while the Source Object of the plane covers d1 in t0= d0/c time, the Image Object of the plane covers the same distance t1= d2/c time. The difference between these two different time periods gives us the mathematics of Time Shift. 

How we obtain Time Shift mathematically can be seen in order in the figure.

EXPLANATION:
After this step, we will see how Time Shift occurs in continuous movements and what kind of an effect it has. 

Before you watch the next animation, I would like to inform you about it. 
Please move the slider bar and examine the flow of the event.

The Source Object is represented by a clock that is in motion. 
The clock sends a signal to the observer while following its path.

In the animation, each signal that the clock sends is marked with a number. In the example here, the clock sends the signal numbered 7.

At the moment the clock sends the signal, a marker is placed on the location where the clock is. The red hour and minute hands on the marker show us when the signal sets out, the number on it shows which signal it belongs to, and its location shows from which point the signal sets out. 

In the example above, the Source Object sends Signal 7 at 1:13:00 and, at that moment, a marker is placed on the place where the signal is emitted. When Signal 7 reaches the observer, the observer sees the Image Object on the location where the marker is placed. At this time, the observer sees the clock in the Image Object showing 1:13:00. 

In this way, we saw the working principle of the next animation. If Signal numbered “n” has reached the observer, the observer will see the Image Object of the clock on the location at which the marker numbered “n” is and with the hour values that the red hour and minute hands in the marker show. As the signals are continuous, the Image Object will follow the markers in the order of arrival of the signals.

TIME SHIFT ANIMATION
The working logic of the animation is discussed above. The play speed of the animation may differ depending on the operating system and programs you use. You can optimize the play speed of the animation for yourself by using the main controls of the animation.

Main controls of the animation:
Light speed: Increases or decreases the speed of signals.
Delay: Changes the intervals between the signals emitted. 
Frame Speed: Changes the play speed of the animation. 
Slider bar: Changes the speed of the clock (Source Object).

Explanation of the animation:
Here, the speed of flow of time in the Image Object and the speed of flow of time in the Source Object are compared. The two clocks on the bottom left corner show us this comparison while the animation is playing. The clock on the left shows us what the time is in the Source Object and the clock on the right shows what the time is in the Image Object. The clock in the Source Object represents the Absolute Time while the clock in the Image Object represents the Visible Time.

Let’s click on the “Play” button and watch the animation.

Time Shift
Let’s pay attention to the signals coming towards the observer in the animation. If the observer receives the signals that the Source Object emits while it is moving away from the observer, the speed of flow of time in the Image Object decreases. If the observer receives the signals that the Source Object emits while it is coming towards the observer, the speed of flow of time in the Image Object increases. You can see the slowdown and acceleration at the time on the Image Object more easily by comparing the clocks on the bottom left. 

Speed Shift
I am sure it attracted your attention. If the observer receives the signals that the Source Object emits while it is moving away from the observer, the movement speed of the Image Object decreases. If the observer receives the signals that the Source Object emits while it is coming towards the observer, the movement speed of the Image Object increases. This change in the speed of the Image Object is called Speed Shift. Speed Shift is another Relativity Effect that explains the difference in the speed of an object’s Image Object and its Source Object. 

I skipped the topic “Speed Shift” in the book, but this topic was covered in Alice Law Version 7. You can find the up-to-date information on this topic in the part "Publications after the book". 

The Observer Is in Motion and The Clock Is Motionless
If you choose this option from the Radio Buttons in the animation, the observer will be in motion and the clock will be motionless. However, the situation that you will encounter will probably surprise you. I suggest you click on the option “Show the field of the observer” in order to interpret the animation more easily. Remember the animation with “the Women Sitting on the Stool”; that animation will help you here. 

In this option, the (c+v)(c-v) mathematics is at work. The Source Object leaves its signals into the observer’s field. The markers placed on the field show the points where the signals enter the field. Please pay attention to the fact that the markers are carried in the direction of the movement by the observer’s field. The Image Object moves in accordance with the markers placed on the observer’s field. In fact, things explained here happen also when the observer is motionless and the clock is in motion. However, when the observer, and thus its field, is motionless relative to our reference system, there is no need for such an explanation. The signals will travel in the observer’s field no matter if the observer is in motion or motionless.

SPEED OF FLOW OF TIME IN VISIBLE TIME
In the animation here, three balls moving inside a box represent the Source Object. The logic of the animation is exactly the same as the previous one. The hour and minute handles in the marker are replaced with red, blue and green balls here. The marker left on the point where the signal is emitted shows the location of the balls in the Source Object at that moment. The balls in the Image Object move by following the balls in the markers. 

How the Observer sees the balls (Image Object) depending on the speed of the box (Source Object) is the topic of this animation. How the speed of flow of time of Visible Time changes can be seen here more clearly. The Demo Button adjusts the settings to an appropriate level for observation. 

Please be careful: if the observer receives the signals that the Source Object emits while it is moving away from the observer, the movement speed of the balls in Image Object decreases. If the observer receives the signals that the Source Object emits while it is coming towards the observer, the movement speed of the balls in the Image Object increases. In this way, we have seen how the speed of flow of time in Visible Time changes.

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