ALICE IN PHYSICS

Touristic Tour – Second Stage

WONDERLAND

Han Erim

30 November 2011

WONDERLAND

By briefly summarizing the Airport and In Flight sections, we can move on to the main subject: why Gryphon sees time dilation in the right-hand clock.

Animated figure 1- Since both clocks approach Alice from equal distances at equal speed, it is already evident that the inclination of the rod will not change according to Alice. This shows that both clocks work simultaneously according to Alice.

Animated figure 2- At this stage, we need to understand whether both clocks work simultaneously according to Gryphon. If we answer this, our job becomes much easier. For this, it is enough to understand whether the inclination of the rod changes according to Gryphon. For this purpose, let us mount a pen on one end of the rod and assume that the Main Frame is moving along the X-axis. Let the pen mark its own position. What kind of curve will it draw?

We already know that the inclination of the rod will not change according to Alice. Therefore, the pen must draw a line according to Alice’s reference frame. The line drawn for Alice will be a proper sine curve. If we assume that the inclination changes according to Gryphon, the line drawn by the pen cannot be a proper sine curve.

Since the pen cannot draw two different lines at the same time, the line drawn for Alice will also apply for Gryphon. The line drawn is unique and always a proper sine curve. This shows that the inclination of the rod does not change for Gryphon either, and therefore, both clocks work simultaneously for Gryphon as well.

Thus, a very important result emerges from this: Time dilation is not a real effect. Time dilation is a perception.

Animated figure 3 - First, let us understand how Gryphon sees the rod. Everything we see comes to us from the past. Electromagnetic waves that carry images travel a distance before reaching our eyes. The farther the light comes from, the older the information it carries.

Since both ends of the rod are at different distances according to Gryphon, a deformation caused by time difference forms on the image of the rod. As a result of this deformation, even if the clocks do not move on the X-axis, Gryphon will inevitably see the rod as inclined.

In my own studies, I call the image of objects GHOST and the objects themselves SPRING. These definitions make it easier to explain visual phenomena. What we see is always the GHOST. We can never see the SPRING of an object.

Animated figure 4 - The animation below provides information on how the rod will appear according to Gryphon's position. A rod parallel to the ground is moving up and down. As can be seen, since the rod is in motion, Gryphon never sees it as straight. The image of the rod changes depending on the oscillation speed and the length of the rod. By changing Gryphon's position, you can test how the rod appears from different points.

Animated figure 5 - While we are here, let us also see how length contraction occurs. Using the concepts of "GHOST and SPRING", we can easily explain how Length Contraction is formed. At the foundation of length contraction lies the same visual principle we saw in figures 3 and 4.

Again, we are dealing with frames moving relative to each other, but here we also take into account the dimensions of the object and consider the signals coming from the front and the rear of the object. Objects that are receding appear compressed in length.

Animated figure 6 - It is more accurate to describe the event of length contraction as Length Deformation. Because length deformation can occur in both directions — either compression or extension. When objects approach each other, length extension is observed. When objects are moving away from each other, length contraction is observed.

Length deformation is a perception, not a real effect. In other words, length changes occur not on the Spring but always on the Ghost.

Animated figure 7 - Now we can move on to the question of why Gryphon observes time dilation. A signal emitted from the clock essentially conveys two pieces of information to Gryphon: the coordinate of the clock at the moment the signal is emitted (relative to Gryphon), and the time value at which the signal was emitted. When the signal reaches Gryphon, he sees the image of the clock at that coordinate and at that time value.

Animated figure 8 - To see how time dilation occurs, it is sufficient to consider the consecutive signals emitted sequentially together with the principle above. In the animation below we see this situation.

The clock on which Alice is sitting emits signals at regular intervals. In the animation we see a ruler attached to Gryphon's reference frame. The ruler is an auxiliary that shows the coordinate of the emitted signal. Each signal travels toward Gryphon with speed "c", the speed of light. Therefore, the speed of the signals relative to this ruler is also "c".

When a signal reaches Gryphon, he sees the image of the clock (GHOST) at the coordinate where the signal was emitted and at the time instant when the signal was emitted.

In the animation, if you set the radio buttons to "Show the principle", you can clearly see the details of the processes that occur in the time dilation phenomenon.

Let us set the radio buttons to "Show Intervals". Let us pay attention to the intervals at which the signals reach Gryphon. When Alice accelerates or decelerates, it changes the time between two successive signals reaching Gryphon. Because of this change, Gryphon detects a time dilation in Alice's clock.

Let us set the radio buttons to "Show the FULL EVENT". The signals arriving at Gryphon come from the Spring. But of course, Gryphon does not see the clock on the Spring, and where and how he sees the clock is determined by the signals that reach him. What he sees is the clock on the GHOST, and he sees that this clock runs at a different rate.

As we have seen, time dilation is a perception. We have already seen above that the clock on the Spring and Gryphon's clock must work simultaneously. In the animation, the rod standing on the minute hands shows that both clocks work simultaneously.

Let us set the radio buttons to "Show the Math". In the window that appears, we see what kind of mathematics Gryphon encounters when he compares the signals reaching him with the signals of his own clock. This mathematics represents the real mathematics of time dilation.

This equation has another very important meaning, because this mathematics is directly related to the mathematics of the Doppler Effect. In other words, the reasons for the Doppler Effect and for time dilation depend on the same principles and causes that we see here. Although it is not written above, the mathematics of length deformation also depends on this mathematics.

Let us set the radio buttons to "Compare the clocks". In this mode, you can more easily compare Gryphon's clock with the clock on the Ghost. Just like length deformation, time dilation can occur in both directions. That is, we may see a clock running slower, but we may also see a clock running faster than normal. For this reason, it is more accurate to call it time deformation.

Let us set the radio buttons to "Speed of Ghost". In this animation, a value of 5 pixel/frame is used for the speed of light. Alice's speed can take any value between 0 and 5 pixel/frame, that is, between zero and the speed of light. Since what matters is the ratio of the speeds, this animation reflects the real situation in nature one-to-one.

You may have noticed that the speed of motion of the Ghost is different from the speed of motion of the Spring. This is an effect that relativity produces on our perception speed. The speed of perception is inversely proportional to time dilation. We see that events in the direction of our motion occur faster, and events behind us occur more slowly. Since our topic here is time dilation, length deformation has not been included in this animation.

Here we have considered only the situation for Gryphon; Alice will also observe a time dilation on Gryphon's clock. I will deal with this in the next section.

Universal Velocity of Light Postulate:

The speed of a signal is independent of the source that emits it. I would like to point out that this was stated by Albert Einstein.

Universal Velocity of Light: The light is always propagated in empty space with a definite velocity c which is independent of the state of motion of the emitting body.

In the animation we also clearly see that this postulate of his is preserved. The signals emitted from Alice's clock do not have speed "c" relative to Alice, but relative to Gryphon they are always "c". The Alice Law uses this postulate of Einstein in a very beautiful and proper way.

The cause and mathematics of time dilation are never within the "Lorentz Transformations". The error in the theory of relativity stems from a deficiency in electromagnetic theory.

Focus your thoughts and your work rapidly on the Alice Law. The future lies within the Alice Law.

WONDERLAND

"Welcome to Wonderland. If the White Rabbit offers you something to eat, absolutely do not eat it. You may shrink and get lost among the grass."