In the book, I defined some rules regarding Simultaneity and Co-location.
Here, I have included animations related to those rule definitions. To fully
understand these animations, you must have read the book.
Slowly drag the scrollbar in the animations to the final state. If you press
the play button, the animation will do the scrolling itself.
Simultaneity Rules 1 -
Observers moving at different speeds relative to an event location, if
they are at equal distances from the event location, each observer will
see a different moment of the event location.
You might think, "Isn't this the Byte Shift we see here?" Yes, Byte Shift
is visible here. However, the animation also provides other information.
Observers in airplanes and on the mountain, even though they are at the
same distance from the Signal Tower, see different images on their
televisions. The signals that allow us to see Image Objects and the
communication signals are subject to the same rules. Imagine observers
in airplanes and on the mountain. If these observers look at the Signal
Tower, each one of them will see a different time in the Image Object of
the Signal Tower. This animation also demonstrates this situation.
Simultaneity Rules 2 -
Observers moving at different speeds relative to an event location, if
they are observing the same moment of the event, their distance to the
event location is different.
Let’s pay attention to the starting point here. At the beginning of the
animation, the airplanes and the mountain station are at the same
distance from the Signal Tower. Therefore, the television broadcast
starts at the same time in all three reference frames. Since the speed
of the signal coming TO them is always c for a reference frame, the
arrival time of the first signal belonging to the television broadcast
will be the same for all three reference frames (t = r/c). Therefore, the
news broadcast starts at the same time in all three reference frames.
At the moment the news broadcast reaches them, the distance of the
reference frames to the Signal Tower, as seen, differs from each other.
In the final state, that is, when the signal reaches the airplanes,
imagine that the observers in the airplanes and on the mountain are
looking at the Signal Tower. All three observers will see the Image
Objects of the Signal Tower at the same time. But pay attention again.
The Image Object seen by an observer is unique to them. Since we are
talking about three observers, we are talking about three Image Objects
here.
Simultaneity Rules 3 - For observers
moving at different speeds relative to an event location, the time flow
rate of the event location differs for each observer.
"Of course, for the airplane approaching the signal tower, the broadcast
ends earlier," you might think. But that’s not the main issue here.
What matters is that the flow rate of the broadcast is different for all
three reference frames. For example, the mountain station receives the
broadcast at 30 frames per second, the receding airplane at 20 frames
per second, and the approaching airplane at 40 frames per second.
Imagine the observers in the airplanes and on the mountain looking at
the Signal Tower. The time flow rate in the Image Objects they see
happens like the change in the frame rate of the TV broadcast.
For the observer on the mountain, the time flow rate in the Image Object
occurs at normal speed, while for the observer in the approaching
airplane, the time flow rate in the Image Object accelerates, and for the
observer in the receding airplane, the time flow rate in the Image Object
slows down. You can find more details on this topic in the Time Shift
section.
Co-location Rules 1 -
Observers moving at different speeds relative to an event location, if
they see themselves at equal distances from the event location, they are
not actually equidistant from the event location.
I think there is no need for additional explanation here. Everything is
very clear.
Co-location Rules 2 -
Observers moving at different speeds relative to an event location, if
they are at equal distances from the event location, they see the event
location at different distances.
As seen in the animation, let’s consider the moment when the airplanes
and the mountain station are equidistant to the Signal Tower. At this
moment, the signals reaching them started at different times. Therefore,
they will see the Signal Tower at different distances.
Co-location Rules 3 - For observers
moving relative to an event location, the coordinates of the event
location they observe are always different from each other.
At the beginning of the animation, the observers in the airplanes, even
though they have reached the event location, see themselves as not yet
having arrived at the event location. At the end of the animation, they
have left the event location, but they see themselves as being directly
over the event location. However, at this moment, the coordinates of the
two airplanes are different. As a result, the observers in the airplanes
will evaluate the coordinates of the event location differently.