Alice Law and Relativity Theory

Chapter 4

What Is Time Dilation and How Does It Occur?

Han Erim

19 May 2011

The “Alice Law and Relativity Theory” series consists of consecutive topics that follow one another. From here on, we move on to the results of the (c+v)(c-v) mathematics. If you have not read the previous chapters of the series, I strongly recommend that you come back here later.

What is Time Dilation?

Electromagnetic waves emitted by moving objects are inevitably deformed as a consequence of relativity. We will now and in the coming chapters examine step by step, in a comprehensive way, how these deformations form and what results they lead to.

One of the most important results of the deformations that occur on electromagnetic waves is, without a doubt, the observation and measurement that moving clocks run at different rates. This situation has been called “time dilation” in physics. It would be more accurate to call time dilation “Time Deformation,” because it can also be observed that a moving clock runs faster than normal. (By a moving clock, I mean a clock that is in motion relative to a reference frame.)

The fact that a clock is in motion does not, by itself, create an effect on the clock’s operating rate (its tick-tock intervals). If two identical clocks placed side by side on a table run in synchrony, then no matter which one we move, they will continue to run synchronously. But despite this, when we measure the tick-tock intervals of the clock we moved, we inevitably see that a difference arises. Note carefully: we compare the tick-tocks of the clock moving relative to us with the tick-tock intervals of the clock standing beside us. The reason we measure a difference in the moving clock’s tick-tock interval is that we must interact with the signals (electromagnetic waves) coming from the clock.

It is clear that we can talk about the tick-tock intervals of a moving clock only after interacting with the signals that reach us from the clock. If there is a velocity difference between two reference frames, relativity will enter the picture. This is what we must understand. Relativity causes the signals reaching us from the clock to be deformed. As a result, we observe and measure that the moving clock’s tick-tock intervals are different. “Time Deformation” is an inevitable consequence of relativity.

In this chapter, we will see the mechanism by which time deformation occurs.

Effect of force on clocks:

Before entering the subject, we need to briefly touch on the effect of force. Whether it moves or not, it is of course quite natural that the tick-tock interval of a clock under the influence of force changes, because the force will affect the operating rate of the clock mechanism to a greater or lesser extent. The effect of force can slow the clock down, or it can also speed it up.

Let us consider pendulum clocks, which are extremely sensitive to force. The same pendulum clock will run at different rates on the Moon, Earth, and Jupiter, where gravitational forces are different (Animated Figure 1). In summary, under the effect of force, the operating rate of a clock depends on how the clock mechanism is affected by the force. A change in a clock’s operating rate due to force is not a topic related to relativity.

The effect of force relates to relativity in the following way: since a clock moving under the influence of force will accelerate (or decelerate), the intensity of the deformation caused by relativity changes. The deformation strengthens as the clock accelerates and weakens as it decelerates. Relativity arises when there is a velocity difference between reference frames.

How Does Time Deformation Occur?

In the figure below, there is a clock moving relative to the observer. We will examine a signal sent by the clock while the clock is at point P. Let us list, in items, the events that occur after the signal is sent, in order. (Animated Figure 2)

1) While the clock is at point P, it sends a signal. Let the dial of the clock show 8:00 at that moment.

2) The signal traveling toward the observer will travel within the observer’s field.

3) The travel time of the signal to reach the observer will be as follows:

Distance between point P and the observer (d)
travel time = d / c (speed of light constant)

The speed of a signal is always c (the speed of light constant) with respect to the field in which it travels. Therefore, to find the travel time of the signal, we divide the distance between the point where the signal enters the field and the point where the signal arrives by the speed of light.

Let us note that point P is defined with respect to the observer’s reference frame. We use the ruler that represents the observer’s field to make this distinction clear. Point P is a point on the observer’s field. Even if the observer is in motion, for the observer, the coordinate of point P remains unchanged.

4) At the moment the signal reaches the observer, the observer will see the image of the clock (Ghost) at the point where the signal entered the field, namely at point P. Since the signal started at 8:00, the observer will see that the clock (Ghost) shows 8:00. (The topic “Ghost and Spring” was explained in the previous chapter: Principles of seeing and perception in electromagnetic interaction. Ghost and Spring.)

5) During the travel time of the signal, since the clock (Ghost) will continue its own motion, at the moment of seeing it will be at a different point such as P′. Since the clock continues to operate during the time until the signal reaches the observer, the value shown by the clock (Spring) at the arrival moment of the signal is as follows:

The observer does not see the real clock (Spring), but its image (Ghost). Let us always pay attention to the existence of this rule.

Up to here, we considered the flow of the act of seeing for a single signal.

Events in nature are continuous. Normally, the observer will interact with signals arriving from the clock continuously. If we convert the case we considered for a single signal into a continuous one, we see how time deformation takes place. (Animated Figure 3)

In the animation, a pendulum clock operates at a constant rate. We assume that 1 second must pass for the pendulum to return from the vertical position to the vertical position again. Each time the pendulum reaches the vertical position, the clock emits a signal. The signals move toward the observer within the observer’s field. It is clearly seen that if the observer and the clock are at rest, the observer will observe and measure that the signals arrive at 1-second intervals.

Now let us move either the observer or the clock.

Alice Law Notice in the animation: no matter who moves, the speeds of the signals never change with respect to the observer’s field. The speed of electromagnetic waves with respect to the field in which they travel is constant and always equal to c (the speed of light constant). The signal’s speed does not have to be c with respect to another reference frame. This is the essence of the (c+v)(c-v) mathematics.

Let us consider the case where the observer is moving and the clock is at rest; depending on the observer’s speed and direction, we see that the distance between two neighboring signals traveling on the field changes. If the observer moves toward the clock, the signal intervals shorten; if the observer moves away, the signal intervals lengthen. As a result of the change in the distance between signals, the intervals of signals reaching the observer are not 1 second. Therefore, when the observer measures the clock’s operating rate, the observer will measure that it runs at a different rate, because the observer can only measure the signals that reach them.

Will the observer only measure it? No — the observer will also SEE that the clock runs differently, because together with the tick-tock signals, the signals carrying the clock’s image also reach the observer. Whatever happens for the tick-tock signals, the same happens for the signals carrying the clock’s image.

The signals reaching the observer also carry the information about where the image (Ghost) of the clock will be seen. Wherever the signal enters the observer’s field, the observer will see the Ghost there. Because the observer and the clock are in relative motion and because the signal requires a certain time to reach the observer, the position of the Ghost is always different from the Spring.

If we consider the case where the observer is at rest and the clock is moving, we see that events occur in a way completely similar to the above. If the clock moves toward the observer, the signal intervals shorten; if it moves away, the signal intervals lengthen. As a result, the observer observes and measures that the clock runs faster or slower.

We see that it does not matter who is moving, or whether both are moving. If the observer and the clock are in relative motion, time deformation inevitably occurs, and the observer will see and measure that the clock runs at a different rate. Time deformation is a PERCEPTION.

Here we saw the formation rule of the deformation that occurs on electromagnetic waves. A velocity difference between reference frames changes the normal distribution pattern of electromagnetic waves in the field. Deformation forms in this way. As a result, as we have seen here, “time dilation,” or in the terminology of Alice Law, Time Deformation, occurs.

Animated Figure 4 – In order to see the difference between the tick-tocks of the clocks located at GHOST and SPRING more clearly, in this animation the emission durations of the signals were kept very short. As a summary, let us write the results we see in the animation:

Time deformation that occurs while the clock and the observer are in relative motion;

• As the clock approaches the observer, the observer sees that the clock runs faster.
• As the clock moves away from the observer, the observer sees that the clock runs slower.
• The observer sees the image (Ghost) of the clock at a different location than the clock (Spring).
• It does not matter whether the observer or the clock is moving.
• The clock mechanism (atomic, digital, wound, pendulum, etc.) does not matter.
• The moving clock (Spring) will run in synchrony with any other clock. Synchrony between clocks can break only if a force intervenes in the event.
• Of course, if the clock mechanism does not operate correctly, synchrony between clocks will also break. We probably should not expect the atomic clock in Greenwich to run synchronously with the wound clock on our desk :)

You can download the source codes of the animation from here. The animation was prepared with Flash CS3 ActionScript 3.0.

We clearly see here how important the topic “Ghost And Spring” is. Ghost And Spring is, in a sense, the essence of relativity. The effects of relativity are always observed on the GHOST.

You can find the proof that moving clocks (Spring) will run in synchrony in my works Manifesto of Alice Law and Tin Soldiers. (Alice Law Version 5 also demonstrates this situation, although at that time I had not yet reached the Ghost and Spring knowledge.)

Alice Law Seeing and measuring that it is so does not mean that it is actually so.

Other Consequences of Time Deformation

Because they are related to this chapter, I would like to touch on two topics.

1) Change in the speed of perception:

Another important result of relativity is that it changes our speed of perception. Suppose there is a television instead of a pendulum clock above. For the observer, the speed at which the images on the television change will be different if the observer approaches the television than if the observer moves away from it.

Imagine that the observer is moving toward an apple tree and, during this time, an apple breaks off and falls from the branch. The falling speed of the apple will be faster than normal for the observer. If the observer is moving away from the tree, the falling speed of the apple will be slower. Relativity leads to truly interesting results. (Animated Figure 5)

Alice Law We see that events in the direction of motion (approaching) occur faster, and events in the opposite direction of motion (receding) occur slower.

The closer the velocity difference between reference frames approaches the speed of light, the more the effects of relativity increase. I will discuss this more broadly in the chapter on simultaneity. You can find information about this topic in the Alice Law Version 5 program.

2) The Relationship Between the Doppler Effect and Time Deformation

The Doppler Effect observed in electromagnetic waves is directly linked to the (c+v)(c-v) mathematics of Alice Law; it is a consequence of it. The effects of relativity (time deformation, speed of perception, space deformation, etc.) can be easily calculated by using Doppler equations. The amount of change in the wavelengths or frequencies of electromagnetic waves is a measure of the degree to which relativity effects occur.

Alice Law The Doppler Effect observed in electromagnetic waves is direct proof of Alice Law and the (c+v)(c-v) mathematics.

The mechanism of how the Doppler Effect forms is seen with complete clarity in Alice Law. You can find the information on Doppler in my publications “DOPPLER EFFECT and SPECIAL RELATIVITY” and “THE RELATIONSHIP BETWEEN THE DOPPLER EFFECT AND SPECIAL RELATIVITY”. I will return to the Doppler topic again in a later chapter of this series.

19 May 1919 The publication date of this article coincided with May 19. Turkish youth, I congratulate you here on your “Commemoration of Atatürk, Youth and Sports Day.” As one grows older, one understands much more clearly that Mustafa Kemal Atatürk was a great leader and a world leader. Dear young people, your youth will be more beautiful with him, your intelligence brighter, and your thoughts much deeper.

Existing publications on Aliceinphysics.com related to this chapter:

• Special relativity and time synchronization
• The reason beneath special relativity
• Alice law – manifesto
• Ghost and spring (image and source)
• Doppler effect and special relativity
• The relationship between the Doppler effect and special relativity
• Alice Law Version 5
  
  

Han Erim