Alice Law Version 7

 

Length and Dimension Deformation

 

Han Erim

May 7, 2012

Copyright © 2012 Han Erim, All Rights Reserved.

 

 

LENGTH AND DIMENSION DEFORMATION

We always see images of objects rather than themselves. We have seen in the section Image and Source that an object and its image may be on different coordinates. Images are brought to us by electromagnetic waves; that is, light. If there is a speed difference between reference systems, a deformation occurs on electromagnetic waves carrying images. Accordingly, there also occurs a deformation on images of objects and these objects may seem in shorter, longer or bent/curved shapes than they actually are. The Length Deformation always occurs on images, not on objects themselves. The Length Deformation also means the Dimension Deformation. The effect for a moving object is, in common perspective, perceived as the contraction or extension of the space. The topic of the Length Deformation is not only interesting but also quite fun. 

In the section of Image and Source, mainly the question where the image of an object is seen was discussed. We will relate the results of that section with sizes of objects here, so we will be able to see how a length deformation occurs.

The Length Deformation, like all other relativity effects, is closely related to (c+v)(c-v) mathematics and is described by this mathematics. Just like all relativity effects, it occurs between frames that are moving according to each other.

 

Ay ve Ağaç.

The principles of seeing 

In order to describe the Length Deformation, we should first discuss the stages of seeing. Let’s think our eyes as a camera. Suppose that our eyes took only one frame of photograph. Let’s name the moment we took the photo as seeing moment and examine this frame. When we look at the photo, we see lots of objects. If we had taken the photo of the sky under a tree, we would have seen both stars and branches of the tree. There are many marks of lights coming from different times and place on the same photograph. While the electromagnetic waves coming from stars set forth millions of years ago, those from the branches of the tree set out a few nanoseconds ago. This situation gives us the information that electromagnetic waves reach our eyes by forming a group. There are numerous electromagnetic waves set forth from different objects and different times in a group. Naturally, what we see is the information brought by each group reaching our eyes. 

The Length Deformation is directly related to how this grouping occurs among electromagnetic waves. The formation rules of groups are the main information of the topic of the Length Deformation. 

Figure 1, How an electromagnetic wave group occurs:

We have seen that electromagnetic waves always travel to their targets at “c” speed. Imagine a shining, huge globe who inside is transparent. Think that you are inside this globe and the center of the globe is your eyes. Now, imagine that the radius of the globe gets smaller with “c” speed and comes towards you. While the globe is getting smaller, it will pass through many objects around you. Imagine that the objects contacting the surface of the globe stick their own electromagnetic waves on the surface of the globe. The group that I mentioned above becomes the surface of this globe. When the globe completely contracts and gets inside our eyes, our eyes will perceive the electromagnetic waves in this group and see the image that this group brings to them.

 

Figure 2, The formation rule of signal group in moving frames 

To make things easier, I will call electromagnetic waves as signals from now on.

In this example, there is a moving car according to the observer. In case the car moves, the duration of formation of a signal group belonging to the car changes. The signal group of the car occurs in a shorter time while the car moving away from the observer; the group occurs in a longer time while the car is coming closer to the observer. Please take attention to the fact that the speed of the globe’s surface is according to the observer. The speed of the globe’s surface is not “c” according to the car; it will be (c+v) or (c-v) according to the direction of the car. Accordingly, the formation duration of a signal group belonging to an object determines the deformation amount on the image of the object. 

We saw where an image (ghost) of an object is observed in the section of Image and Source. The coordinate that the signal is emitted from was the coordinate on which the image (ghost) is observed according to the reference system of the observer. We apply this rule for each and every point of the car here. As can be seen, the car will be observed shorter or longer by the observer depending on its movement direction and speed. 

Here, as the observer is still, (c+v) (c-v) mathematics remained in the background (at the side of the car).

 

Figure 3

 

In our previous example, the observer was still and the car was moving. Now, let’s discuss the situation in which the car is still and the observer is moving.

As the general principle, two reference systems are moving according to each other and it is not important which one is moving. The result occurring for the observer in the previous example is also occurs here in the same way. However, we need benefit from (c+v)(c-v) mathematics and the concept of fields in order to explain the event here. Two factors should be taken into consideration while doing these kinds of analyses for a moving frame.

1) As the signal comes to the observer, the center of the circle belonging to the signal group is the observer. As the observer is moving, the circle will also move with the observer because the signals are going to the field of the observer and moving at “c” speed according to the observer.

2) The coordinates that signals are emitted are defined according to the reference system of the observer. Therefore, these points will also move together with the observer. 

The coordinates where the signals go into the field of the observers will be the ones that the image of the car will be seen on. The observer will see the image of the car inside these coordinates defined according to him. As a result, we get the same result as we did in the previous page. This figure and the previous one are exactly equal. 

 

Figure 4THE MATHEMATICS OF THE LENGTH DEFORMATION

Here we will see how to calculate the length deformation.

Radio Button 1: The event occurring while the observer comes closer to the city:
If the observer had not moved, the signal set out from the right side would have covered d1 length of the city at c speed in t1 time. (d1=c.t1)

However, as the movement direction of the observer is towards the city, in order for the signal to travel the city thoroughly, the signal needs to cover d3 distance instead of d1. (because, the signal is going inside the observer’s field.) It will cover the d3 distance on the field at c speed in t2 time (d3=c.t2)

The observer, during the signal’s t2 duration to reach it, covers d2 distance at v speed. (d2=v.t2)

From this information, we can calculate to what extent the length deformation occurs. The equation below describes the length deformation for the frames approaching each other.

Observed Size = Original Size . c/(c-v)

Radio Button 2: The situation occurring while the observer is moving away from the city:
If the observer had not moved, the signal set out from the right side would have covered d1 length of the city at c speed in t1 time. (d1=c.t1)

However, as the observer is moving away from the city, in order for the signal to travel the city thoroughly, it was enough for the signal to cover d3 on the field, which is a shorter distance, at c speed in t2 time because the signal is moving into the field of the observer. (d3=c.t2)

Throughout the t2 time that is the arrival time of the signal, the observer covers d2 distance at v speed. (d2=v.t2)

We can calculate the length deformation here in a similar way. 

The general equation belonging to the length deformation:

Observed Size = Original Size . c/(c±v)
If the frames are approaching each other, the sign is (-);
If the frames are moving away from each other, the sign is (+).

(c+v)(c-v) mathematics, as in all the relativity effects, is a determiner for the length deformation. 

 

Figure 5EQUALITY

We see how the length deformation occurs according to the movement directions of the frames one more time in this page. As can be seen in the animation, the result is the same whether the observer moves and the ruler stays still or the ruler moves and the observer stays still. 
Figure 6The Length Deformation on the X Axis

The distribution of the “cross” signs shows us how the length deformation on the image occurs.
Figure 7 The Length Deformation on the Y Axis

Although the Length Deformation occurs in the direction (Let’s call it the X axis) of the movement, it also has an effect on the Y axis. Here, we see a deformation occurring on a long object vertical to the ground. 
Figure 8The Deformation Occurring on the Rotation Movement

We can understand how the deformation occurs on rotating objects by looking at the distribution of cross signs.

 

On the Length Deformation

Here, we have seen how the speed difference between frames leads to the length deformation and given basic information. Of course, this subject is not limited with these. We can find many subjects that can be regarded as results of the length deformation and can obtain interesting results. 

The Length Deformation is a crucial part of the relativity effects. As we perceive the world as we see it, the Length Deformation is, in fact, a factor determining what kind of a setting we live in. There is no doubt that, in order to feel this effect clearly, it is necessary to be very fast. Who knows, maybe someday we can travel at speeds close to the speed of light and see this effect with our eyes. We have only talked about its formation principles here. Scientists will decide after which speeds this subject will be important for them in their own study fields themselves. 

Maybe we can see the same effect, created by clinging to its original, in movies and computer games soon. To be honest, it would be really nice.

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