If you would like to improve your scientific knowledge individually, being informed about the topic “Image and Source” will be quite beneficial for you because it is really necessary to know this topic, even if to some extent, to be able to understand the effects of physics in our daily life.

“Image and Source” is a topic of vital importance as almost all the Relativity Effects are directly relevant to this topic. If we think of Relativity Effects as a tree, the topic “Image and Source” represents the trunk and (c+v)(c-v) mathematics represents the roots of the tree. 

In the animations here, I covered the general principles of the topic “Image and Source”. However, this topic is not that limited. In the parts where Relativity Effects such as Time Shift, Dimension Shift, Speed Shift, Doppler Shift, Byte Shift, and Reverse Image discussed, you will see that the topic “Image and Source” immediately shows up, expands phase by phase, and gradually gets more detailed. 

I suggest you read the book “Alice Law – Transition to (c+v)(c-v) Mathematics in Electromagnetic Theory”. In this way, you can better understand the animations here. All the animations here are related to the topics in the book.

I will start talking about the topic with a simple and basic animation. The observer is looking at the planet Neptune. While the planet (Source Object) is moving on its orbit, it sends signals that form its own images. The observer, with the signals coming to him, sees the planet (Image Object). 

Source Objects, as I mentioned in the book as well, are never visible under any circumstances. What we see are always Image Objects that belong to them. As this is an animation, we can see the Source Object here. Source Objects belong to Absolute Space-Time while Image Objects belong to Visible Space-Time.

The point that we will emphasize in this animation is as follows:
Whichever point the signal going to the observer sets out, the observer will see the image of the planet at that point. As the planet is in motion and it takes time for the signals to reach the observer, the observer sees the Image Object behind the Source Object. If the distance between the Source Object and the observer was longer, the Image Object would follow the Source Object from further behind. (You can see this effect by decreasing/increasing the speed of light in the animation. It will seem as if the distance between has increased/decreased and the signal has covered a longer/shorter distance.)

In some of the animations I create, I use graph paper to show the field. 
I showed the observer’s field here in a bit different way. If you are pay attention, you will see that the signals that come to the observer always follow the field lines.


Doppler Triangle and Doppler Quadrangle gives us clear and accurate information about where an image object will be seen. 

The figure on the left: 
The signal tower sends a signal towards the plane. The animation gives the answer to the question “At which point will an observer on the plane see the Image Object of the signal tower?”. Let’s slide the slider bar to the end. At that point, the location of the red O point is where the Image Object will be seen. And why is that? Because, relative to the reference system of the plane, the signal reached the plane by following the red d0 line. As the signal was emitted from the red O point relative to the reference system of the plane, the point where the Image Object will be seen is the red O point. 

The figure on the right:
In order to find out where the image object of the signal tower will be seen relative to the reference system of the plane, a method like the one here can be used. Let’s use the Galilean Relativity Principle. Let’s assume that the plane is motionless and the Signal Tower is in motion. In this case, the signal is sent to the plane from Point A. As the signal comes from Point A relative to the observer on the plane, he will see the Image Object at A. 

The equality between the figures on the right and on the left
In both figures, there are two reference systems that are in motion relative to each other. It does not matter which one is in motion and which one is not. The result obtained should be identical in every aspect. When we compare the two figures above, we can see that this identity is proven. Alice Law protects the Galilean Relativity in itself.

This animation is like an open buffet that shows how (c+v)(c-v) mathematics occurs in all its details. 

In the first animation, the observer was motionless and the Source Object was in motion. In this animation, however, the Source Object is motionless and the Observer is in motion. After clicking the play button, drag the observer with your mouse. 

The Source Object in the animation (the woman sitting on the stool) sends the signal that forms its own image to the observer. With the signals reaching him, the observer sees the Image Object of the woman.

  • The following are what we need to play attention in this animation:
  • We see that the observer carries his own field along with him. 
  • Source Object leaves its signal to the point of the field it is in contact with.
  • The location of the point where the signal is left on the field always remains fixed relative to the reference system of the observer. When the observer moves, this point is also carried along with the field. Therefore, the location of this point never changes relative to the observer.
  • When the distance between the point where the signal is left on the field and the observer is covered by the signal and the signal reaches the observer, the observer sees the Image Object at the point where the signal enters the field.
  • The speed of a signal that is left on the field is always equal to the constant, i.e. the speed of light “c”, relative to the field.
  • The direction of the movement of the signal inside the field is always towards the center of the field. The signal does not and cannot move in any other direction. There is a simple reason behind this: The signals inside the field are signals that set out to reach the observer who is in the center of the field. If they were going to travel to another object, they would be in that object’s field, not here. 
  • The signals that move inside the field are also carried along with the field. Move the observer up and down. You will see that the signals do not change direction relative to the observer. Move the observer to the left or right. Speeds of the signals relative to the field will not change.
  • A change in the speed or direction of the observer’s movement does not change the speed or direction of a signal coming towards the observer in the field relative to the field. 

An Image Object is a virtual reality that can only be seen by the owner of the field. I cannot see the Image Object that you see and you cannot see the Image Object that I see.

You should drag the observer in the “Free” position in the animation. When you choose the demo modes, the observer will move on his own.

There is the opposite of the first animation here. The observer is in motion while the planet is motionless. In the animation, we see at which point the observer will see the image of the planet. You may think “Doesn’t it look weird?”. But it is not. It looks different only because we changed our “observation window”. When we examined the event in the previous animations, we looked from the observer’s window. There is no such chance here; we are looking at the event from the outside. Where the location of the Image Object is relative to the observer could have been found only through mathematical calculation method, and it is what we do here as well. Otherwise, there is no difference from the ones covered above in terms of the events. 

In this last animation, you will find what we have covered so far and a bit more. The King and the Queen are looking at each other. The animation shows where they see each other’s image objects in cases when the King, the Queen or both of them move. Please click on the play button and drag the King or the Queen with your mouse. The Image Objects that belong to the King and the Queen are represented by figures that are surrounded by glowing colors. In the animation, Red represents the events that belong to the Queen and Blue represents the events that belong to the King.

You will see a few samples available in the demo mode. Please pay attention to which direction the King, the Queen or the Image Objects look at in the demo mode. Of course, Image Objects do not look or see, but they give us this information: “A while ago, my Source Object was looking at that direction.”.

Go back to the Animation List Page