FOLLOW THE RABBIT Han Erim 5 October 2005 Copyright 2008 © Han Erim All Rights Reserved.
FOLLOW THE RABBIT
I will publish some new papers on the Special Relativity Theory under the name "Follow the Rabbit". This is the first paper in this series. I preferred a friendly name because the website of aliceinphysics.com is a public website and most of its readers are layman. In this article, I took up the first two parts of Special Relativity section of the Alice Law program and I interpreted them in a more simple way. I hope this paper will contribute to your understanding of Special Relativity. I assume that you downloaded Alice Law program and you read it. If not, DOWNLOAD it before reading this paper. Otherwise you may not follow the rabbit and you may lose so many things.
Thank you very much my dear readers.
Han Erim 

Figure 1: Here, the man is on the symmetry axis of the car and there are two lamps mounted on both sides of the car. Here is AO = OB. When the lights are lit simultaneously, the lights cover the distances AO and BO from both sides and reach the man simultaneously. Regardless of the speed of the car, this event doesn't change. This rule belongs to the nature and we learned this rule by experiments. As we see in the previous parts of Alice Law, this rule is accepted without discussion and this is the REFERENCE POINT of Special Relativity section of Alice Law.As you see, I take up a similar sample as in the previous parts of the program but I made some small changes on it, therefore the figures and its logical explanations will not be strange for you. 

Figure 2: Now, let's focus on the figure and let's try to find some basic principles of the "Reference Point".
Reference Point: The man in the moving car sees both lights simultaneously, if the lamps are lit simultaneously and the distances of the lamps are equal.
We can write the following principles related to the Reference Point.
1) The distances AO and BO are equal to each other at the emitting moment. AO = OB 2) The event is independent from the speed of the car. 3) The event is independent from the length of the car. 4) The man in the car always measures the speed of light as "c".
Let's assume that, the lamps are lit at moment t0 and arrived the man at moment t1.
In this case traveling time of the lights is t = t1 t0 and c = AO/t = BO/t (c: speed of light)
Now, let's change our observing position and let's observe the "Reference Point" from the ground as our reference system.
1) The middle point of the car is on the X0 point of the ground at the emitting time of the lights. 2) When the lights travel in the cars, the car travels on the road. 3) When the lights arrive the man simultaneously, the middle point of the car is on the X1 point of the ground. 4) During the event the car covers the distance "d". The distance "d" is equal to: d = v . t (explanation is on the figure 2).
Defined principles here are enough to explain the Special Relativity Theory. 

Figure 3: Now, we are mounting a ruler to the car. After now, the car will carry the ruler. Drag and drop the slider button on the page and change the positions of the lamps relative to the ruler and take them out of the car.
As we see, we are always keeping the positions of the lamps equal, relative to the axis of symmetry, also relative to the man. For that reason, regardless of the distance of the lamps from the axis of symmetry, the man will see the lights simultaneously when he is at the axis of symmetry. Here, we are protecting the first principle of the "Reference Point". AO = OB 

Figure 4: You may have some hesitations because of the new places of the lamps, because now, they are outside of the car. I remind you the third principle; The event is independent from the length of the car. The length of the car may be short, long or too long. The result must not change. So, if it will comfort you, you may choose a longer car for yourself, its length may even be longer than the ruler. 

Figure 5: Let's join this part to the previous parts of Alice Law.
There are two light sources on the ground and there is a man between the lamps. The distances of both light sources are equal relative to the man. When the lights are emitted simultaneously, the man sees the lights simultaneously. In this part, I will use a different light source. (Figure 5)
I used red triangles on the ground, which are mounted on a pole and the poles are mounted to the ground at equal distances from axis of symmetry. 



Figure 8: I will not include the outcomes of the current Special Relativity (length contraction, space contraction, time dilation, etc) into this logical experiment, because I showed its incorrectness at the previous parts of the Alice Law. But you may still have some doubts or you may believe its existence and you may want to include its outcomes in this chapter. You can do this easily by dragging the slider button above; in this case the length of the ruler and the car will contract. Animation simulates that, because of the velocity of the car, the length of the ruler and the car are contracting. Drag the button and bring the triangles to the same line. You will see that this effort will be ineffective in this logical experiment. Because of this, you may consider the following pages with or without the length contraction of the car.
In this logical experiment the distance between red triangles and the distance between green triangles are equal. When a triangle touches the other one on the left side, the other triangle also touches the other one on the right side.
I changed the observer in the car. After now, it is a woman. 

Figure 9: The car comes with speed "V" from the left side towards the right side and the woman arrives to the axis of symmetry. The woman is on the symmetry axis of the car.
At this moment WE ABSOLUTELY KNOW THAT the triangles face and touch each other and the lights are emitted, but the lights don't start to travel yet.
This figure is a copy of "REFERENCE POINT" which is at the beginning of the part. We changed only type of the light sources and their places. We protected all its principles. 

Figure 10: Let's see what will happen after now. WE ABSOLUTELY KNOW THAT, the woman will see the lights simultaneously at the right side of the axis of symmetry of the ground. This is the natural outcome of "REFERENCE POINT".
The lights coming from the triangles will also arrive the man on the ground. But at this stage, let's focus only on the woman in the car and the lights traveling towards her. You can turn coming of the light to the man on the ground by using Turn Off button.
If we pay attention enough to the figure, we see that, RELATIVE TO THE MAN ON THE GROUND the speed of traveling lights towards the woman in the car from both sides ARE NOT "c", because, relative to the man, they are emitted from equal distances from both sides at the same moment. Is there something wrong or not? Let's check the event more carefully at the next figure. 

Figure 11: To reach a very clear outcome, let's add a second car to the figure and let's use the symmetry principle. You may not see the second car in the figure but it is just behind the front car. When you press the "Play Button" you will see it. It is moving from the right side towards to left side with the same speed.
WE ARE ABSOLUTELY SURE THAT because of the principle of symmetry, the same events will happen for both cars simultaneously. If a woman sees the lights simultaneously, the other woman will see the lights simultaneously. Let's make this sentence clear: RELATIVE TO THE MAN ON THE GROUND all events happening in both cars occur simultaneously.
Now, we obtained the same outcome very clearly. RELATIVE TO THE MAN ON THE GROUND the speeds of traveling lights from both sides towards the women ARE NOT "c". 

Figure 12: Now, let's watch the same event from the upper view. We know that, the emitting moment (t0) is the same for the three reference systems. 1) The woman (at the top) sees the lights at the t1 moment at the distance X1. The t1 moment of the woman will come across to a t' moment of the man. Therefore we can write t1 = t' 2) The woman at the bottom sees the light at t2 moment at the distance X2. Because of symmetry principle we can write t2 = t', Because of equations between t1=t' and t2=t' we can write t1 = t2 = t' In this case, relative to the man on the ground, the speeds of traveling lights towards the cars are as follows: c1= x1/t' and c2= x2/t'. Here, we clearly see that c1 > c2. This result shows that RELATIVE TO THE MAN ON THE GROUND the speed of traveling lights from both side towards the women ARE NOT "c" (c: speed of light). Thus, we obtained the mathematical evidence of this event. 

Figure 13: With the results we have obtained from this logical experiment, we reach the Special Relativity Theory.
All the observers are on the axis of symmetry at the emitting moment. And naturally, when the women see the lights, THEY WILL NO LONGER BE AT THE AXIS OF SYMMETRY. One of the women will be on the left side and other woman will be on the right side of the axis of symmetry.
You may find the above outcome very natural and simple but THIS OUTCOME KILLS THE CURRENT SPECIAL RELATIVITY THEORY AND BUILDS A NEW SPECIAL RELATIVITY THEORY. 

BUTTON 1: According to the current Special Relativity, the emitting time of the lights must be realized before the women arrive at the axis of symmetry and all the observers HAVE TO see the lights at the axis of symmetry at the same time. (See: Alice Law Program, Part Time Travel)
BUTTON 2: We can see clearly in our logical experiment that, realization of the above paragraph is impossible, because the triangles cannot touch each other and the lights cannot be emitted if the women don't arrive at the axis of symmetry. If they arrive at the axis of symmetry, this becomes Alice Law, doesn't it?


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