Alice Law and Relativity Theory

Part 5

What Is Length and Space Contraction and How Does It Occur?

Han Erim

23 May 2011

8 June 2011 (Update)

What is Relativity? Let’s get to know it.

Relativity occurs because of the existence of two fundamental rules. The first rule is that electromagnetic waves travel within the fields of objects, and the second rule is that the speed of an electromagnetic wave with respect to the field it travels in is constant (the speed of light constant c). If there is a velocity difference between reference frames, then due to these two rules electromagnetic waves are deformed while they are emitted from the source. The formation of deformation changes the normal distribution pattern and the energies of electromagnetic waves on the field. Observation and measurement values obtained by interacting with such electromagnetic waves deviate from normal values by the amount of deformation. The name of these deformation effects is relativity. We can briefly define relativity as deformations occurring on the electromagnetic interaction.

Dimension and Space Deformation

In the previous chapter, we saw how relativity causes Time Deformation. Like time deformation, Length and Space Deformation is also a result of deformations formed on electromagnetic interaction. It arises from the effect of relativity on our perception, and as a result we see objects in a deformed form. Length and Space Deformation is a more realistic description of this effect, because length and space expansion can also be observed.

The mechanism behind the formation of Length and Space Deformation is again based on two principles related to relativity. The first is “Ghost and Spring,” and the second is “the packet-forming property of electromagnetic waves.” I mentioned both of these principles in the chapter “Principles of Seeing and Perception in Electromagnetic Interaction.”

Objects occupy a volume in space. They have width, length, and height. If the knowledge obtained from “Ghost and Spring” is generalized to three dimensions (width–length–height), how length and space deformation occurs can be seen easily. Let us examine the examples below.

Animated Figure 1 In this example where we look toward the ruler, the observer is stationary. We write in order how the seeing event occurs. The signal that starts from point P1 of the ruler goes toward the observer by using the observer’s field. When the signal reaches the alignment of the other end of the ruler, point P2, it forms a group with the other signal emitted from point P2 at that moment. A packet has formed. Both signals in the packet will arrive at the observer at the same time. When the signals reach the observer, the observer sees the ruler. Since the ruler and the observer are stationary with respect to each other, the length of the ruler’s image (Ghost) and the ruler (Spring) are equal.

Let us recall from “Ghost and Spring”: the point where the signal enters the field becomes the place where the image will be seen. Since we are thinking in terms of length here, we perform the same operation for each of the signals emitted from the ends of the ruler. The image of the ruler will be placed between points P1 and P2. The reason we pair the signals is that we must think with two signals that arrive at the observer at the same time.

Animated Figure 2 Here the observer is moving away from the ruler. When the signal that departs from point P1 reaches the other end of the ruler, at that moment it forms a group with the signal emitted from there. However, if we pay attention, due to the observer’s motion the entry point of the second signal into the field becomes point P3 instead of P2. When the signals reach the observer, the observer will see the image of the ruler within the interval P1–P3. We see that the interval P1–P3 is shorter than the interval P1–P2. A deformation has occurred, and as a result the observer sees the length of the ruler as shortened.

Alice Law Objects and space contract in the direction of recession.

Animated Figure 3 In this example, the observer is approaching the ruler. We calculate in a similar way as above. The observer will see the image of the ruler within the interval P1–P3. Here, the interval P1–P3 is longer than the interval P1–P2. The observer sees the length of the ruler as elongated.

Alice Law Space and objects expand in the direction of approach.

Animated Figures 4 and 5 In the examples examined above, we considered motions occurring along the X-axis. In length and space deformation, the main effect is observed in front of and behind the direction of motion. However, partial deformation also occurs along the Y and Z axes. The examples here show the results of deformations occurring along the Y-axis.

We apply the same principles described above. The signal emitted from point P1 later forms a group with a signal emitted from point P2. (By drawing a circular arc centered on the observer, we can find when and where the signals will form a group.) As a result, as seen, the observer will not see the ruler in a vertical position.

I did not use a ruler representing the observer’s field here. P1 and P2 are two points on the observer’s field and are defined according to the observer’s reference system.

Animated Figure 6

The animation below has been prepared in accordance with the principles explained above. By dragging the observer with the mouse, you can observe where and how the observer sees the GHOST. This animation reflects the exact real situation of relativity. By dragging the red control points, you can also change the shape of the SPRING if you wish.

You can download the source codes of the animation from download. Flash CS3 ActionScript 3.0.

Deformation on Perspective

Length and space deformation mainly occurs along the axis of motion. Here we are watching the events from the side. However, the observer is looking at the Spring from the front or from behind. The animations here are prepared in two dimensions. Preparing them in three dimensions is quite difficult for me. Therefore, it is not really possible for me to fully convey what the observer exactly sees. You need to think about this effect in three dimensions and within a perspective. Here, we have seen why and how length and space deformation occurs, and its rules. That is what is important.

NEW ADDED – 8 June 2011
The animation below is the world’s first realistic 3D Space Deformation Relativity animation. This is its second version. You can watch the first version on YouTube. But this one is much better. The animation uses intensive code. I recommend closing other applications before running it. If you reduce the speed of light in the animation, you can observe the resulting effects more clearly.

The relation of the Doppler effect to length and space deformation

Many of the effects of relativity are closely related to the Doppler Effect. The degree to which Length and Space Deformation occurs can be calculated easily by making use of Doppler equations.

Current publications on aliceinphysics.com related to this chapter:

• Ghost and spring (image and source)
• Orbit and special relativity
• Doppler effect and special relativity
• The relationship between the Doppler effect and special relativity

Han Erim