The article series “Alice Law and the Relativity Theory” consist of consecutive topics. From this point on, we are moving to the outcomes of (c+v) (c-v) mathematics. If you haven’t read the previous chapters of this series, I strongly recommend that you check this chapter out later.

What is Time Dilation?

Electromagnetic waves emitted by moving objects always experience deformation as an inevitable result of relativity. Here and in the forthcoming chapters, we will thoroughly see how these instances of deformation occur and how their results are step by step.

One of the most significant results of the deformation occurring on electromagnetic waves is undoubtedly observing and measuring moving clocks as working at different speed levels. This case is named as “time dilation” in physics. It is better to call time dilation as “time deformation” as it is also possible to observe a moving clock working faster than a normal clock. (What is meant with “moving clock” is a clock in motion according to a reference system.)

The case that a clock is in motion does not influence the working speed (intervals between ticks and tocks) of that clock. If two identical clocks on a table are working simultaneously, they will always keep this simultaneousness, no matter if we move any of them. Nevertheless, when we measure the ticking intervals of the clock we have moved, we inevitably see that there is a difference. We should keep in mind that we are comparing the tick tocks of the clock which is in motion according to us and the tick tocks of the one standing nearby. The reason why the ticking intervals of the moving clock are measured to be different is that we have to interact with the signals (electromagnetic waves) coming from the clock. It is obvious that we can determine the ticking intervals of the moving clock only after interacting with the signals coming from the clock towards us. If there is a speed difference between the two reference systems, then relativity gets involved. This is exactly what we need to understand. Relativity caused the deformation of the signals reaching us from the clock. Consequently, we observe and measure the ticking intervals of the moving clocks as different. “Time Deformation” is an inevitable outcome of relativity. 

In this chapter, we will see the mechanism of deformation occurrence.

Force impact on the clocks:

Before getting straight to the point, we need to mention force impact shortly. A change in the ticking intervals of a clock under force impact , no matter whether it is inert or in motion, is completely natural, as the force will more or less influence the working speed of the clock. The impact of the force can either decelerate or accelerate the working speed of the clock. Let’s think of pendulum clocks, which are extremely sensitive to force. Due to difference of gravitation, the same pendulum clock has to operate at different speeds on Moon, on Earth and on Jupiter (Animated Figure 1). To sum up, the working speed of a clock under force impact is dependent on how the clock mechanism is influenced by the force. The change in the working speed of a clock due to force impact is not a topic related with relativity. 

The connection between force impact and relativity is as follows: as a clock affected by force impact accelerates (or decelerates), the size of the deformation caused by relativity changes. Deformation increases as the clock accelerates, and it decreases if the clock decelerates.

How does Time Deformation Occur?

In the figure below, there is a clock in motion according to the observer. We will examine a signal sent by the clock when it is at point P. Let’s itemize the events occurring after the signal is emitted. (Animated Figure 2)

1. The clock emits a signal on point P. Let’s say the clock points at 8.00.
2. The signal travelling towards the observer enters his field.
3. The time passing until the signal reaches the observer is as below:

                                                The distance between point P and the observer

Travel Time for the signal = ---------------------------------------------------------------
                                                        c (speed of light constant)

The speed of the signal is always c (speed of light constant) according to the field on which it travels inside. Therefore to find the travel time of signal, the distance between the place where the signal enters the field and the destination of the signal is divided by the speed of light. 

Please pay attention that point P is identified according to the reference system of the observer. The reason why we use the ruler representing the field of the observer is to clarify this distinction. Point P is a point on the field of the observer. Even though the observer is in motion, the coordinate of point P remains unchanged for the observer.

 

4. At the moment when the signal reaches the observer, he will see the image of the clock (ghost) at point P, that is, where the signal entered the field. As the signal has set off at 8:00, the observer will see that the clock (ghost) points at 8:00. (The issue of “Ghost and Spring” has been discussed in the previous chapter. Principles of vision and perception in electromagnetic interaction, Ghost and Spring)

5. As the clock (spring) continues its own movement during the time until the signal reaches the observer, it will be at a different point, such as P', at the moment of seeing. As the clock goes on working until the signal reaches the observer, the time value shown by the clock (spring) at the moment when the signal reaches the observer is as follows:

The observer sees not the actual clock (spring), but its image (ghost). We should always keep in mind the presence of this rule.

Until now, we have approached the phenomenon of seeing for only one signal.

Events have continuousness in nature. The observer will normally interact with the signals reaching him incessantly from the clock. If we turn this situation, which we have discussed for only one signal, into a continuous stance, we can see how time deformation occurs (Animated figure 3).

In the animation, a pendulum clock is working at a fixed speed. We assume that it takes 1 second for the pendulum reaches the vertical position for the second time. Each time the pendulum is vertical, the clock emits a signal. The signals travel towards the observer on his field. It is obviously seen that if the observer and the clock are inert, the observer will see and measure that the signals reach himself with intervals of 1 second.

 
Now, let’s move the observer or the clock. 

Let’s consider the situation in which the observer is in motion and the clock is inert. We see that the distance between two neighboring signals travelling on the field changes depending on the speed and the direction of the observer. If the observer is moving towards the clock the distance between signals is shortened, while it is longer when the observer is moving away. As a result of the change in the distance between signals, the intervals between the signals reaching the observer are not 1 second. Therefore, the observer will measure the working speed of the clock and see that it operates at a different speed, since the observer is only able to measure the signals reaching him. Will the observer only measure them and do nothing else? No, he will also SEE that the clock works differently, as the signals carrying the image of the clock reach him, together with the ticking signals. What happens in the case of ticking signals of the clock will also be valid for the case of signals carrying the image of the clock.

Signals reaching the observer carry the information about where the image of the clock (ghost) will be seen. The observer will see the ghost at the exact point where the signal entered the field of the observer. As the observer and the clock are in motion relative to each other and as a certain period of time is necessary for the signals to reach the observer, the position of the ghost is always different than that of the spring.

If we consider the case in which the observer is inert and the clock is in motion, we see that what happens is quite similar to the situation above. Intervals between the signals are shorter if the clock is moving towards the observer, whereas they are longer if it is moving away. As a consequence, the observer measures the clock to work either faster or more slowly.

It is clearly seen that it does not matter which one is in motion, or if both of them are moving. If the clock and the observer are in motion relative to each other, time deformation is an inevitable outcome, and the observer sees and measures that the clock works at a different speed. Time deformation is a kind of PERCEPTION.

Here, we have seen the rule for the occurrence of the deformation on electromagnetic waves. A difference of speed between reference systems changes the normal dispersion of electromagnetic waves in the field. This is how deformation occurs. As a result, “time dilation”, or time deformation as named in Alice Law, occurs as is seen.

 

Animated figure 4 – In order to have a clear vision of the difference between the tick-tocks on GHOST and those on SPRING, the intervals between the moments when the signals are emitted are deliberately short in this animation. Let’s summaries the outcomes we observe in the animation: 

The time deformation occurring when the clock and the observer are in motion relative to each other:

• When the clock moves closer to the observer, the observer sees the clock working faster.
  As the clock moves away from the observer, the observer sees the clock working more slowly.
• The observer sees the image of the clock (ghost) at a place different than the actual place of the clock (spring).
• The type of the clock mechanism (whether it is atomic, digital, clockwork or pendulum) does not matter.
• The clock in motion will work simultaneously with any other watch.
• The simultaneousness between the clocks can be disturbed only by the interruption of a force.
  Naturally, if the clock mechanism does not work accurately, the simultaneousness between the clocks will be disrupted. Obviously, we cannot expect the table clock on our desk to work simultaneously with the atomic clock in Greenwich :)

You can download the source codes for the animation here. The animation has been prepared with Flash CS3 ActionScript 3.0.

Here, we see how important a topic “Ghost and Spring” is. In a sense, the issue of Ghost and Spring is the essence of relativity. The impacts of relativity are always observed on the ghost.

You can find the proof for the simultaneousness of moving clocks (springs) in my works named "Alice Law The Manifest" and "Tin Soldiers". (This proof is also provided in Alice Law 5 software. Back then, I hadn’t discovered the concepts Ghost and Spring.)

Other Outcomes of Time Deformation

1) Change in the speed of perception:

Another significant outcome of relativity is that it changes our speed of perceiving. Let’s think of a TV instead of the pendulum clock above. For the observer, changing speed of the visuals on the TV will be different when he gets closer and moves away from the screen. 

Let’s assume that the observer is walking towards an apple tree and that an apple falls down in the meantime. The falling speed of the apple is faster for the observer, while it is slower when he is walking away from the tree. Indeed, relativity causes quite interesting results. (Animated figure 5)

The closer the speed difference between reference systems is to the speed of light, the bigger the impacts of relativity will be. I will discuss this issue in simultaneousness chapter more thoroughly. You can find information regarding this issue in Alice Law Version 5 software.

2) The Relationship between Doppler Effect and Time Deformation

Observed on electromagnetic waves, Doppler Effect is directly related to (c+v) (c-v) mathematics of Alice Law. In fact, it is an outcome of this mathematics. The impacts of relativity (time deformation, speed of perception, space deformation, etc.) can easily be calculated by utilizing Doppler equalities. The change in the wavelength or the frequency of electromagnetic waves is an indicator of the extent to which relativity impacts have occurred. 

The mechanism of Doppler Effect is clearly seen in Alice Law. You can find information about Doppler Effect in my publications titled "DOPPLER EFFECT AND SPECIAL RELATIVITY" and "THE RELATIONSHIP BETWEEN DOPPLER EFFECT AND SPECIAL RELATIVITY.” I will touch upon the issue of Doppler Effect in the forthcoming chapters of the series.

Available publications dealing with this chapter on aliceinphysics.com are:

• SPECIAL RELATIVITY AND TIME SYNCHRONIZATION
• THE REASON BEHIND SPECIAL RELATIVITY
• ALICE LAW- THE MANIFEST
• SIMULTANEOUSNESS CONCEPT
• GHOST AND SPRING (IMAGE AND SOURCE)
• DOPPLER EFFECT AND SPECIAL RELATIVITY
• RELATIONSHIP BETWEEN DOPPLER EFFECT AND SPECIAL RELATIVITY
• Alice Law Version 5 (Index>Special Relativity>Special Relativity)

Han Erim

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