Simultaneity and Co-location

Han Erim

May 7, 2012

SIMULTANEITY AND CO-LOCATION

In the Alice Law, the issue of simultaneity was resolved from the very beginning. Because the first thing that (c+v)(c-v) mathematics demonstrates is how simultaneity works. However, years later, with the addition of the "Image and Source" and "Doppler Effect" concepts to the Alice Law, the topic of Simultaneity was further developed.

Simultaneity is truly a very important subject. Because the definition of being at a certain place at a certain time is embedded within it. The synchronization of clocks relative to each other is also closely tied to this. When the speed difference between reference frames is large, simultaneity becomes a critical issue that must be understood. It is of vital importance for many practical applications. On the other hand, there is also a topic just as important as simultaneity — co-location (I use the word co-location to mean the sharing of the same position between reference frames), which I will also address here.

Figure 1, As a summary, let’s once again observe how electromagnetic interaction occurs. In the animation, we can control the speeds of both the observer and the light source. As we’ve seen before, when both frames are moving relative to each other, the distribution of signals from the lamp over the field changes. This change in distribution is the highest-priority topic to be understood in electromagnetic interaction. The change in how electromagnetic waves are distributed over the field leads to various effects — which we refer to as relativistic effects. This is what relativity fundamentally means.

Simultaneity is directly related to how electromagnetic waves are distributed over a field. In addition, the fact that the speed of electromagnetic waves is constant relative to the field they travel in (c: the speed of light constant) defines the general principles of simultaneity.

Figure 2

As seen in the animation, there are three separate frames. On the right side, there is a signal station. The station sends out signals at regular intervals. As the signals travel toward their target frames, they will pass through the fields of those frames in accordance with the functioning of electromagnetic interaction. We’ve already seen that the signal intervals change in moving frames. Therefore, the signals received by each of the three frames here will have different intervals.

The signal intervals heading toward the city — which is stationary relative to the station — will remain unchanged.
For the airplane approaching the station, the signal intervals will be shorter than normal, and for the airplane moving away from the station, the intervals will be longer than normal.

Now imagine replacing the signal station with a TV station. Since each of the three frames watches the TV broadcast depending on the signals reaching them, the flow rate of the broadcast would occur at a different speed in each frame — and we will observe this shortly.

Figure 3, THE MATHEMATICS OF SIMULTANEITY

Here, we see how the perception speed changes.

Since the perception speed is determined by the signal intervals, we can calculate how the perception speed changes by computing the time between two successive signals. As shown in the graph, we use the mathematics of (c+v)(c-v) for these calculations.

If the frames are approaching each other, the signals in the field will become denser, which will lead to an increase in perception speed.

If the frames are moving away from each other, the intervals between signals in the field will widen, and as a result, the perception speed will decrease.

flash4

Figure 4, In the following animations, I will use this TV. Click the Start button to turn on the TV. A news program is being presented. Each news item is shown in three segments, each of equal duration. Beginning of the news (Anchor in front of the topic) Middle of the news (the topic) End of the news (topic fades out)

Figure 5, Now let's imagine that all three frames are watching this news program on TV.

The flow rate of the TV broadcast will differ across the three frames.
For those in the city, the broadcast will proceed at its normal speed.
In the airplane approaching the TV station, the broadcast will appear faster than normal.
In the airplane moving away from the station, the broadcast will appear slower than normal.

Here, I would like to introduce two rules about simultaneity.

Let’s click the Rule 1 button. As seen, all three frames are equidistant from the TV station. However, if we pay attention, at that moment, each frame is watching a different video frame on their TVs.

Now let’s click the Rule 2 button. Here, all three frames are watching the same video frame on TV. However, we see that each frame is at a different distance from the TV station at that moment.

From this, we can define an important rule about simultaneity:
If relatively moving frames are equidistant from the event location, they will see different moments of the image related to that event. Conversely, if they see the same image, they must be at different distances from the event location.

Figure 6, Here we also see the effect of motion on our perception speed. Even though the TV broadcast started at the same moment for all three frames, the flow rate of the broadcast proceeded at different speeds for each.

Let’s click the Rule 3 button to observe the actual event.

We can define another rule for simultaneity here: When relatively moving frames observe the same event location, they perceive the event as unfolding at different speeds.

Figure 7, Now let me show you a very interesting phenomenon. In the animation, there are spaceships approaching and receding from Earth. If you were a passenger on one of those ships and looked toward Earth, you would see the Earth rotating at a different speed.

For passengers on the spaceship moving away from Earth, the Earth will appear to rotate slower than it actually does. For passengers on the ship approaching Earth, the Earth will appear to rotate faster than it actually does.

We had called the actual object the Source and its image the Ghost. Of course, what the passengers see is not the Source of the Earth, but its Ghost. Due to relativistic effects, passengers see the ghost rotating at different speeds depending on their direction of travel. The actual rotation speed of the Earth’s source does not change. Passengers will also see a length deformation on Earth, but I did not include that in the animation here.

This type of information is naturally very important. When observing a celestial object remotely, its true rotational speed can only be determined by calculating backward from ghost to source. For small velocities, such details may be negligible, but as the speed difference between reference frames increases, these details become more significant. For example, when mapping the Earth using satellites, if centimeter-level precision is desired, you must take into account ghost and source effects.

Figure 8, Simultaneity Between Ghosts and Sources

What simultaneity is defined by also matters. Often, simultaneity at the sources is more important. Because the way a physical event occurs is determined by the sources. It is the sources that collide, enter chemical reactions, or apply gravitational force. But as explained in earlier sections, the sources of objects are not visible.

In this animation, a TV station is broadcasting, and two TVs in the city are receiving the broadcast. Since both TVs are equidistant from the station, the same image is shown on their screens. Therefore, we can say that the sources of both TVs are simultaneous.

However, an observer looking at both TVs from the left will see different frames playing on each TV. According to this observer, the ghosts of the TVs are not simultaneous.

There is no motion involved in this animation. If motion were included, that would also need to be taken into account.

Figure 9, Being at the Same Coordinate

Let’s imagine two observers approaching each other, both looking toward a flag. (Think of the two red flags as a single flag.) When the observers are aligned, notice where each sees the flag. Even though the observers share the same position, the flag appears at a different distance for each.

Of course, when the observers are aligned, the source of the flag is at equal distance to both. But you live within the space you perceive. Your interpretation of your surroundings depends on what you see. Therefore, where they see the flag is each observer’s own virtual reality. For them, the flag is where they see it.

Figure 10, Seeing from the Same Distance

Here we see a variation of the previous animation. The observers are again approaching each other. When they align, the source of the flag is at equal distance from both. At this exact moment, we consider the signals emitted from the flag. When the signals reach the observers, the ghost of the flag will appear equidistant for both observers. However, what they see is the ghost. At that moment, the flag’s source is at a different distance for each. Let’s also note that at the moment of seeing, the observers do not share the same coordinates.

About Simultaneity

In truth, without understanding the concept of a field and how light travels within fields, it is impossible to truly understand electromagnetic interaction, relativistic effects, or physics in general.

Here, we explored what simultaneity means, how it should be understood, how our perception speed changes, and how it can be calculated. Make sure you learn the Relativity Theory of the Alice Law quickly. Protect yourself from misinformation, and if you've been misinformed, cleanse yourself immediately. The Alice Law is currently the only source on Earth showing you the truth. Right now, no physicist or university knows what you are seeing and learning here. How sad. I struggle to answer when I wonder what physicists really know.

What I’ve explained here is really general knowledge. These are the kinds of things that anyone interested in or fond of physics can easily understand. That’s usually the kind of thing I talk about. I hope you enjoyed this section.