Alice Law Version 7

 

Time Dilation

 

Han Erim

May 7, 2012

Copyright © 2012 Han Erim, All Rights Reserved.

 

 

TIME DILATION

With the inclusion of the topic “Image and Source” to the Alice law in 2009, the Relativity Theory of the Alice Law gained great momentum and reached its final shape. “Image and Source” was really an important topic and it brought along much information. The understanding of the topics like Time Dilation and Length Deformation became possible thanks to this topic. 

One of the leading topics occupying physics is Time Dilation because it we encounter it in many situations. Therefore, it is necessary to understand this topic and to know its formation mechanism. We will see how and why Time Dilation occurs in all its details in this section. 

Time Dilation occurs as a result of the electromagnetic interaction between frames that are in motion according to each other. It is described with (c+v)(c-v) Mathematics like all other relativity effects. 
 

Figure 1, Let’s think two clocks moving towards each other. Think that a bar is placed on the bulges on minute hands of the clocks and that Alice is sitting on this bar. We assume that Alice’s position always remains in the midpoint of these two clocks. 

Will both these clocks work simultaneously according to Alice? This is not a difficult question at all. As both the clocks comes closer and moves away from Alice at the same speed and they always remain at equal distance, the clocks will work simultaneously according to Alice.
Figure 2,  The situation does not change for Alice if one of the clocks doesn't moves and the other one moves. As both the clocks come closer and move away from Alice equally and the distances of the clocks to Alice remain same, both the clocks will work alike for Alice here as well. 

In fact, Alice observes a time dilation on the clocks here. However, this time dilation occurs on both the clocks, these clocks work coequally to Alice. But let’s move slowly if you do not mind. Time Dilation is a topic that should be taken into account and it is also a little bit difficult.
Figure 3, Now, let’s place a second observer on the left clock. Here, Gryphon, who is also one of the heroes of the story “Alice in Wonderland”, will accompany us. 

There is this following interesting situation: When Gryphon compares the ticktack intervals of the right clock that is in motion according to him with the ticktack intervals of the clock that he is sitting on, he discovers an obvious time dilation. In other words, he sees that the ticktack intervals of two clocks are different. However, this is not the case for Alice. To Alice, both the clocks work simultaneously; the ticktack intervals of the clocks are equal. Why and how can such a thing happen? This will be question that we will seek the answer of.

In order to answer this question, we first need to understand whether the time dilation that Gryphon sees/discovers/measures is a real effect or a perception effect. 

If the time dilation seen on the moving clocks come about as a real effect (if it leads to a change in the working speed of the clocks), the clocks must work at different speeds according to Gryphon. In this case, the hour and minute hands of both the clocks must rotate at different speeds. In such a situation, the slope of the bar that Alice sits on must change. 

However, we see that Alice sits on such a position that it does not allow us to make such reasoning because that both the clocks works simultaneously according to Alice is the primary information that we are sure of. The bar must be parallel to the ground according to Alice.

 

Figure 4, Let’s give a concrete answer to the question whether the slope of the bar changes for Gryphon or not. If we can shed some light on this topic, we will be able to reason the incident. 

Let’s mount a pencil at the right end of the bar. The pencil will mark the bar’s position when the bar is in motion. The line that the pen draws will be determinative according to both Alice’s and Gryphon’s reference systems. 

It is clear that, if the slope of the bar changes, the pencil will draw an irregular sine curve; if it does not, the pencil will draw a regular sine curve. We already know that the slope of the bar does not change according to Alice’s reference system. Therefore, the pencil will certainly draw a regular sine curve for Alice’s reference system. While the pencil draws the line for Alice, it cannot draw a different line for Gryphon in the meantime. The pencil cannot draw two different lines at a time. The line that is drawn as a regular sine curve will also be valid for Gryphon’s reference system. From this point of view, we come up with this conclusion: The slope of the bar does not change for Gryphon’s reference system either. 

The fact that the slope of the bar does not change shows that both the clocks always work simultaneously for not only Alice but also Gryphon. We draw a very important conclusion here: Time dilation is not a real effect. The clocks that are in motion do not slow down mechanically. 

So we left behind the difficult part of Time Dilation. The rest is really easy. Now that we reached the conclusion that both the clocks must work simultaneously, we can pass on to how and why Time Dilation occurs by using the information we obtained from the sections (c+v)(c-v) Mathematics and Image and Source.

I would like to add a few sentences here. If you read the Alice Law Version 5 or the previous versions, you probably noticed that they also came up to this point. Namely, it was shown years ago in the Alice Law that both the clocks would work simultaneously. However, as the topic “Image and Source” did not take from yet, it was not possible to go further. Now we can take this further. 
Figure 5, By the way, let’s first discuss how Gryphon sees the bar. As both sides of the bar have different distances to Gryphon and the bar moves vertically up and down, Gryphon never sees the bar straight. 

Due to the movement of the bar, a deformation will occur on the image of the bar and, as a result, Gryphon will see the bar as bent. What we sees is not the spring but the ghost of the bar. The ghost of the clock will also be in a different position. We have seen these in the section “Length Deformation”. 

Of course we are talking on principles here. The speed of light, 300.000 km/s, does not simply let us perceive these kinds of effects. However, as we show the speed of light with small speed values here, we are able to see what kinds of effects occur in every detail. No matter how fast light is, these effects always occur, even if just a bit. 
Figure 6 Now let’s get our hands on how Gryphon sees the clock. Gryphon will see the image of the clock instead of the clock itself. The signal emitted will reach Gryphon in accordance with the rules that we saw before. (I use the word “signal” for electromagnetic waves.)

In this animation, only one clock signal is handled. After the clock emits the signal, it continues its own move. When the signal reaches Grpyhon, he will see the image of the clock in the position from which the signal is emitted. The hour and minute hands on the clock face will indicate the emitting moment. 
Figure 7, It is clear that, in order for us to be able to tell whether a time dilation occurs on a clock, we should pay attention to consecutive signals. Time dilation can only be found out by measuring intervals between successive signals. As you guess, the reason why Gryphon observes a time dilation is about the change in the interval between two successive signals coming to him.

I created this animation for the purpose of pre-understanding. Let’s assume that the clock emits a new signal every second. When a signal reaches Gryphon, he will see the clock in a new position and with a new value on the clock face. However, please be careful; Gryphon sees the Ghost of the clock, not its Spring. 
THE PRINCIPLE 

This animation that we will take as base hosts all the information about the topic “Time Dilation”. From now on, we will examine the details of the animation respectively. First, I would like to explain according to which principle this animation was created. 

The Principle:

Let’s start the animation.

The clock that Alice sits on comes towards or moves away from Gryphon. In the meantime, it emits signals at equal intervals. The red hour and minute hands show the position and the emitting time of each signal. These signals are enumerated. We can see which signal is emitted, when and where it is emitted, which ones are on the way and which ones reach Gryphon.

The clock showing the Ghost of Alice moves by following the signals emitted by the Spring of Alice. The movement of the Ghost takes place according in accordance with the rule that we saw on the previous page. For instance, the moment the fourth signal reaches Gryphon, the Ghost is in the coordinate on which the fourth signal is emitted and the value on the clock face shows the emitting time of the fourth signal. I am always saying this, but please pay attention to the fact that Gryphon sees the clock in the Ghost. He does not see the Spring’s clock. 

In order to prevent visual pollution, only one signal for each 25 signal is set as visible. You can change the intervals of the signals with the Numeric Stepper below. The invisible signals enable the animation to be smooth by working on the background. 

The transparent grey bar swinging up and down is the bar that shows that the clocks in the springs of Gryphon and Alice work simultaneously. (The bar Alice was sitting on in the beginning of the section)

You can change Alice’s speed with the help of the slider on the left. 5 pixel/frame was used for the light speed value in the animation. Alice’s speed can change between 0-5 pixel/frame. Accordingly, the animation can show what kind of an incident takes place for the movements whose speed is close to the speed of light and even for the ones at the light speed. 

Of course, we are discussing only time dilation here. A deformation occurs together with time dilation; however, length deformation was not included in the animations.
INTERVAL

The signals that Alice emits reach Gryphon at “c” speed by travelling on Gryphon’s field. The time interval between two successive signals reaching Gryphon will determine the time dilation for Gryphon. We can see the duration of the signal intervals in the second table from the left below.

As the clocks in the Springs work simultaneously, the intervals of both the Springs are equal. However, the movement of Alice changes the distance between the signals travelling on Gryphon’s field. As a result, Gryphon observes a time dilation. We can again see the results Gryphon obtains when he measures the intervals of the signals coming to him. 

If Alice moves away from Gryphon, the signal intervals get longer;
If Alice goes towards Gryphon, the signal intervals become shorter;
The signal intervals can be equal only if Alice stays still.

THE MATHEMATICS OF TIME DILATION

Please press the Math button. As we will see, Time Dilation is described and calculated through (c+v)(c-v) Mathematics. You can see how the interval between two signals changes in the pop-up window. 
THE SPEED OF THE GHOST

I do not know whether it attracted your attention, but please pay attention to the speed of the ghost now. The ghost moves more slowly when Alice moves away from Gryphon and moves faster when Alice approaches Gryphon. 
For a better observation, please set Alice’s speed to a value close to the speed of light and follow the value in the text box that shows the speed of the ghost. We will see that the ghost can move a lot faster than the speed of light. The image is not a material object; it is not an electromagnetic wave either. The ghost is a virtual reality consisting of electromagnetic waves. Therefore, the speed of light is not a limit for the ghost. The ghost can easily exceed the light speed. 

If you press the Speed button, you can see how the speed of the ghost changes in the pop-up window. The speed of the ghost is again described with (c+v)(c-v) Mathematics. 

 

COMPARING

We are going to compare the clocks on this page. After starting the animation, press the Compare button. In the windows, you will see the clocks side by side. The animation will continue on the background. We will be able to compare easily what kind of a situation occurs when Gryphon compares his own clock with Alice’s clock (Ghost). 

Gryphon sees that, while Alice is coming towards him, Alice’s clock works away faster than it actually does and that Alice’s clock works slower than it actually does while Alice is moving away from him. Of course Gryphon sees the clock of the ghost. He cannot see the spring. We already know that the springs of the clocks will work simultaneously. 

As a result, Time Dilation may occur in both ways: deceleration and acceleration. Time Dilation is not a real effect; it is just a perception. 


Although Time Dilation is a perception, it carries a real meaning for us because we continue our lives inside the places we perceive. Time Dilation is our virtual reality. 
GRYPHON

We discussed the topics that are important for Time Dilation on the previous pages. Here, you can examine the time dilation for Gryphon as a whole.
THE PRINCIPLE FOR ALICE

We have discussed every incident according to both the reference systems up to now. We will do the same here. We have seen how time dilation occurs for Gryphon. Now, we will examine how time dilation occurs for Alice because she also sees-identifies-measures time dilation on Gryphon’s clock. Here, we will discuss the principles that we considered for Gryphon before for Alice as well. As Alice and Gryphon are two frames that are in motion according to each other, an incident occurring for one frame will take place simultaneously for the other frame.

Gryphon’s clock sends signals towards Alice in equal intervals. The emitting times and coordinates of the signals are shown by the red hour and minute hands.

Here, as Alice’s frame is in motion and the signals go to Alice, we should pay attention to the fact that the signal coordinates are described according to Alice’s reference system (according to Alice’s field). Therefore, these coordinates move along with Alice’s reference system. We discussed this situation in detail in the section “Length Deformation”. We apply the same principles in a similar way here. 

The movement of Gryphon’s Ghost will take place in accordance with the signals. For example, when the fifth signal reaches Alice, the ghost of Gryphon’s clock will be at the place where the fifth signal was emitted and the clock face will show the emitting time of the fifth signal. Gryphon’s ghost will carry out its own movement by following the signals respectively according to this rule.

If you have any space on your screen beside the program windows, stretch the windows horizontally as much as you can. In this way, you will be able to watch Gryphon’s ghost better.
FINALE

Lastly, we see the incident occurring for both the frames together. All the controls are open here. You can manage the animation as you like by using these controls. 

Suppose that there is a symmetry axis that always stays in the midpoint between Alice and Gryphon (their springs). The incidents occurring in both sides of the symmetry axis must be equal. The symmetry axis acts as a checking means that confirms the correctness of the animation. 

About Time Dilation

To tell the truth, this section was the one that I had the most difficulty in writing among the sections. I knew what I would write, but still it was difficult. I hope I was able to explain you what Time Dilation is.

Naturally, this section will start an uproar in physics because it changes many things in physics. It will affect all the theories on time and require the already written studies to be re-written and corrected and necessitate the applications in practice to be re-handled. The things I explained here will get into school curriculums as well. I do not know when these will happen; but it was really enjoyable to explain these things. 

Ah Alice, you sat on such a nice place that the whole world could not stop looking at you.

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