Alice Law Version 7

Simultaneity and Coexistence

Han Erim

May 7, 2012

SIMULTANEITY AND COEXISTENCE

The topic “simultaneity” in the Alice Law reached a solution in the first place because the first thing that (c+v)(c-v) mathematics shows us is how simultaneity occurs. However, after many years, along with the inclusion of the topics “Image and Source” and “the Doppler Effect”, the topic of simultaneity developed further.

Simultaneity is a really crucial topic because the description of being present at a location at a certain time is included in it. The synchronization of the clocks according to each other is also closely related to this topic. Simultaneity becomes a critical topic that should be known accurately in case the difference in speed among the reference systems is very big. It is vital for an application in practice. On the other hand, there is the topic of coexistence (I use this term to define the situation in which the reference systems sharing the same location) that is as important as simultaneity; I will also touch upon this topic here.

Figure 1, The Reason of Relativity

Let’s see how the electromagnetic interaction occurs here one more time as a summary. We can control the speed of both the observer and the light source in the animation. As we have seen before, the distribution of the signals coming from the lamp changes if both the frames are mobile according to each other. The change in the distribution is primary subject that should be known in the electromagnetic interaction. The change of the electromagnetic waves on the field leads to some effects that we call relativity effects. That is what should be understood from relativity.

Simultaneity is directly related to how electromagnetic waves are distributed on fields. In addition, the fact that speed of electromagnetic waves is constant (c: light speed constant) according to fields they travel determines the general principles of simultaneity.
Figure 2 As you see, there are three different frames in the animation. There is a signal station on the right. The station sends signals in constant intervals. While the signals travel towards their target frames, they will, in accordance with the functioning mechanism of the electromagnetic interaction, travel on the fields belonging to the frames. We have seen before that the signal intervals change in mobile frames. Therefore, for each frame here, the signal intervals coming to them will be different from the others.

The signal intervals going to the city that is immobile according to the station will not change.
The signal intervals will be shorter for the plane approaching to the station and will be longer for the plane moving away from the station that they actually are.

Think that there is a TV station instead of a signal station here. The flow rate of the broadcast would be different for each frame as all the frames will watch the broadcast according to the signals reaching them, which we will see shortly.
Figure 3The mathematics of perception speed.

We see how the perception speed changes here.

As it is the signal intervals that determine the perception speed, we can figure out how the perception speed changes by calculating the time between two consecutive signals. We benefit from (c+v)(c-v) mathematics for the calculations as the graphic shows.

If the frames are approaching each other, the signals on the field will get jammed and this situation will bring about an increase in the perception speed.

If the frames are moving away from each other, the signal intervals on the field will get longer and, as a result, the perception rate will decrease.

 Figure 4, In the following animations, I will use this TV here. Press the “Start” button to turn on the TV. There is a news program broadcasted on TV. Each news topic is broadcasted in three parts and in equal periods.  The beginning of the news (the speaker is in front of the topic) The middle of the news (the topic) The end of the news (the topic move out of the image)
Figure 5, Now, let’s think that each frame is watching this news program on the TV.

The flow rate of the TV broadcast will be different for each frame.
The flow rate will be in normal rate for those in the city.
In the plane approaching the TV station, the TV broadcast is faster than it actually is.
In the plane moving away the TV station, the TV broadcast is slower than it actually is.

I would like to show you two rules regarding simultaneity.

Let’s push the button “Rule 1”. As can be seen, all three frames have the equal distance to the TV station. However, if we look carefully, at this moment, each frame watches a different image on their own TVs.

Let’s push the button “Rule 2” this time. Here, all the frames watch the same image on the TV. However, we see that the distance that each frames has to the stations are different at this moment.

From this point of view, we can identify an important rule regarding simultaneity. Frames that are mobile according to each other, if they have the equal distance to the scene, they will see different moments of images belonging to the scene. As the opposite of this situation, if they see the same image, they will have different distances to the scene.
Figure 6, Here, we see the effect of the movement on our perception speed. While the TV broadcast started for each frame at the same time, the flow rate of the broadcast is different for each frame.

Let’s push the “Rule 3” button to watch the event occurring.

We can define another rule here for simultaneity. When frames that are mobile according to each other look at a scene, they see the event occur in a different speed.
Figure 7 Now, I will show you a very interesting event now. There are spaceships that are approaching and moving away from the world in the animation. If you were a passenger in those spaceships and look towards the world, you would see the world rotating in a different speed.

The world will rotate more slowly than it normally does for the passengers in the spaceships moving away from the world while the world will rotate faster than it actually does for those approaching the world.

We have named the object as Spring and its image as Ghost. Of course, what the passengers see is not the world’s Spring but its Ghost. We know that the passengers observe the Ghost rotate in a different speed according to the direction of their movement with the relativity effect. The rotation speed of the world’s Spring does not change for certain. The passengers also see length deformation on the world; however, I have not included it in this animation.

This information is crucial. In order to find out the actual speed of a celestial body while observing from a distance, we should use a reverse calculation method from Ghost to Spring. These details may be unimportant for low speeds; however, as the speed difference between the reference systems increase, this details become more and more significant. For instance, while creating the world map by means of satellites, if you want sensitivity in the centimeter scale, you should definitely take the effects of Ghost and Spring into consideration.
Figure 8, Simultaneity in Ghosts and Springs

According to what the simultaneity occurs is certainly important. Most of time simultaneity in springs is more important because how a physics event occurs is about springs. Springs are the ones that collide with each other, undergo chemical reactions and have gravitational force. However, as explained in the previous sections, objects’ springs are invisible.

In this animation, the TV station broadcasts and the two televisions in the city receive the broadcast. As the televisions have the same distance to the station, they have the same image on their screens. Accordingly, we can say that springs of both these televisions are simultaneous.

However, an observer looking at the televisions from the left side will see that there are different images on the television. The ghosts of the televisions are not simultaneous according to this observer. There are no movements in this animation. If there were movements in it, it would have been taken into consideration, too.
Figure 9Being located at the same coordinates

Let’s think that two observers approaching each other are looking at a flag. (Please remember that there is one red flag instead of two.) Pay attention to where the observers see the flag when they reach the same alignment. Although they share the same alignment, the flag has different distances for both of them.

The flag’s  is, of course, at the same distance to both of the observers when they are at the same alignment. However, you live in the environment that you can see. Your perception of your environment depends on what you see. Therefore, where the observers see the flag is their own virtual reality. For these observers, the flag is in the position that they see it.
Figure 10, Seeing at the same distance

We see a different version of the previous animation. The observers are again approaching each other. When they reach the same alignment, the flag’s spring has equal distance to them. At this very moment, we take the signals from the flag into consideration. When the signals reach the observers, the distance that flag has will be equal for both of them. But what they see is the flag’s ghost. The flag’s  is at different distances to them at that moment. Please pay attention to the fact that the observers do not share the same coordinates at the moment they see.