SIMULTANEITY AND COEXISTENCE RULES

I defined some rules regarding the topics of Simultaneity and Coexistence in the book. I included animations related to those rules here. In order for you to understand these animations completely, you should read the book beforehand.

Please drag the slider bar slowly and bring it to the last situation. If you click on the Play button, the animation will do the dragging itself. 

Simultaneity Rules 1 - If observers that are moving at different speeds relative to a place of the incident are also at the same distance to the place of incident, each observer sees a different moment of the place of incident.

You may think ďWhat we see is Byte Shift, isnít it?Ē. Yes, Byte Shift can be seen here. However, the animation gives us other information as well. The people watching TV on the planes and mountain see different images on their TV although they are at the equal distance from the Signal Tower. The signals that enable us to see Image Objects and communication signals are subject to the same rules. Letís think that there are observers on the planes and the mountain. If these observers look towards the Signal Tower, each of the observers will be seeing a different time in the Image Object of the Signal Tower. The animation here shows this situation too.

Simultaneity Rules 2 - If observers that are moving at different speeds relative to a place of incident see the same moment of the event, the distance of each observer to the place of incident is different.

Letís pay attention to the starting point here. When the animation starts, the planes and the mountain station is at equal distance to the Signal Tower. Therefore, the TV broadcast starts at the same time in all three reference systems. As the speed of the INCOMING signal to itself relative to a reference system is always c, the travel time of the first signal that belongs to the TV broadcast will also be the same for three reference systems (t=r/c). Therefore, the news broadcast starts at the same in all three reference systems. At the moment the news broadcast reaches the reference systems themselves, the distances of the reference systems to the signal tower are different from each other as can be seen here.

Letís think that, in the last state, i.e. at the moment the signal reaches the planes, the observers on the mountain are looking towards the signal tower. All three observers will see the Image Object of the Signal Tower at the same moment. But again, we need to be careful. The Image Object that an observer sees belongs to only that observer itself. As we are talking about three observers, we have three Image Objects here.

Simultaneity Rules 3 Ė Speed of flow of time of a place of incident is different for observers that are moving at different speeds relative to a place of incident.

You may think ďThe broadcast for the plane that approaches the signal tower will of course end sooner.". However, that is not the main point here. The important point here is that the speed of the flow of the broadcast is different for all three reference systems. For instance, while the mountain station receives the broadcast as 30 frames/second, the plane that is moving away receives it as 20 frames/second and the plane that is approaching receives it as 40 frames/second.
Letís imagine that the observers on the planes and the mountain are looking towards the signal tower. The speed of flow of time in the Image Objects that they see is as in the change in the speed of frame in the TV broadcast. While the speed of flow of time for the observer on the mountain takes place at a normal speed, the speed of flow of time for the observer on the plane that is approaching has accelerated and the speed of flow of time for the observer on the plane that is moving away has slowed down. You can find more detailed information on this topic in the part Time Shift.

Coexistence Rules 1 - If observers that are moving at different speeds relative to a place of incident see that they are at the same distance to the place of incident, they are not at the same distance to the place of incident.

I guess there is no need for additional explanation here. Everything seems quite clear. 

Coexistence Rules 2 - If observers that are moving at different speeds relative to a place of incident are at the same distance to the place of incident, they see the place of incident at different distances.

As can be seen in the animation, letís consider the moment when the distances of the planes and the mountain to the signal tower is equal. At that moment, the signals that reach them has set out at different times. Therefore, they will see the Signal Tower at different distances. 

Coexistence Rules 3 - For observers that are moving at different speeds relative to a place of incident, coordinates of the place of incident they see are always different from each other.

Although the observers on the planes have reached the place of incident at the beginning of the animation, they see themselves as if they have not reached the place of incident. On the other hand, at the end of the animation, they have already left the place of the incident, but they see themselves as if they are right at the place of incident. But the coordinates of both planes are different at that moment. In conclusion, the observers on the planes will judge the coordinates of the place of incident differently.

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