RELATIVITY OF SIMULTANEOUSLY and THE MAIN PROOF OF ALICE LAW
March 2005 Copyright 2005 © Han Erim All Rights Reserved
Summary: This paper is published together with Alice Law Version 5 physics program in March 2005. It contains an important physics proof related in Special Relativity Theory that proves the speed of light can not be constant relative to all reference frames. This proof is named as "The Main Proof of Alice Law". The proof continues with an another proof and defines a new mathematic for Special Relativity Theory. The second proof is named as "The Final Proof of Alice Law" which is in the "Relative Velocity of Light" paper that is also published in Alice Law Version 5. Both proofs show us the new and correct mathematics of Special Relativity Theory and it is what.
Relativity of Simultaneously and Special Relativity.
The starting point of the "Special Relativity" theory is based on the proof that the definition of the term simultaneous is "RELATIVE". For that reason, while I explain you the theory of Special Relativity, I reserved the first section for the definition of the term "simultaneous". While Albert Einstein was proving the relativity of the term which we call "simultaneous", he had given the TRAIN example. Here I used an example similar to the train example.
While you read you will see that the term simultaneous has become more improved, more consistent and more understandable with the Alice Law. As a result of this improvement a very important progress has been made in the Special Relativity theory and some inconsistencies that the Special Relativity theory used to include have been removed. Therefore, for this section I believe that it would be appropriate to name the section as "The New Principle of Special Relativity Theory". All the consequent topics have been consistently developed with the results obtained from this section and as a result Special Relativity theory is clarified in detail.


Figure 1  Now think about two lamps mounted on the ground. We assume that you are in the middle of the two lamps. You can turn on the lamps whenever you want by pushing the button at that point. (I ask you to join the animations on the page. Now turn on the lights by pushing the button please.)
If I ask you the lights are turned on simultaneously or not, I believe that you will answer me like this: "Considering the lights are at equal distances from me and in addition assuming that the cable installations for the two lamps are equal in length, (more explicitly, according to the principle of symmetry the lefthand side is symmetrically equal to the righthand side) if I push the button I see that two lamps are turned on simultaneously.
In this fashion you have defined the term "simultaneous" with respect to you. It is not possible to disagree with your explanation. (We assume that the lefthand side is symmetrically equal to the righthand side with respect to the axis of symmetry.)


Figure 2 Now let's assume that you are in a rectangular shaped vehicle which has a light source at the center that is moving with a constant velocity. When you turned on the light if I had asked you : "If the light reaches to the front and the back of the vehicle simultaneously or not?", you would answer me like this if you are a physicist: "The vehicle that I am in is moving with a constant velocity, of course when I turn on the light it will reach to the front and the back of the vehicle simultaneously with respect to me."
If I object to you such as "While the vehicle that you are in is moving, how can you claim that the light emited from the lamp will reach to the front and the back of the vehicle simultaneously", you will allege that your claim has experimental verification and its related theory is based on the two physics postulates of Albert Einstein.
Two Physics postulates of Albert Einstein:


Figure 3  After having such an introduction to the subject, now we are expanding our example.
After this moment we will look for an answer to the question; when the lamps that are on the ground are turned on simultaneously relative to the observer on the ground, are the same lamps turned on simultaneously relative to an observer in the middle of the moving vehicle?
Indeed Albert Einstein had already answered this question mainly about one hundred year ago. Since our purpose is to indicate the causes that lie behind the term "simultaneous" more explictly and to make the "Special Relativity Theory" more apparent, I am explaining the subject with the following different example.


Figure 4  I am assuming the following experiment:
We figure out if the experiment is successful or not in the following way: If the observer on the vehicle has seen the lights turned on simultaneously he runs up the green flag or else if he sees one of the lights first then the other light he runs up red flag. (Use the buttons. You can move the vehicle with the "Move" button and turn on the lights at any time.)


Figure 5  As a method to eliminate the difficulty of setting the time for turning on the lights, you can place the button (brown triangle) on the path of vehicle. When the vehicle touches the button the lights will turn on automatically. If the vehicle is moving with the same velocity in all the tries (in the experiment we are assuming that it moves with the same velocity), we can change the time for turning on the lights by moving the button (please try) to the left or right side. If the button is placed on the proper point, the light will reach to the observer on the vehicle simultaneously.
Of course we are keeping the cable installations that go to the light sources equal in length. Thus, as long as you stand on the axis of symmetry the two light sources will turn on at the same time and the lights will reach you simultaneously no matter where you place the button on the path.
Before starting to the experiment we must make an important addition to remove the mistakes of the animation. Such as; let's take into consideration that the lights that are turned on simultaneously relative to you are not turned on simultaneously relative to the observer on the vehicle. Because at the moment the "Special Relativity" theory predicts that the lights which are turned on simultaneously relative to you are not simultaneously turned on relative to the observer on the vehicle.
Therefore we can think that: As long as you stand on the axis of symmetry, no matter where you place the button, according to you the light sources will turn on at the same time and the lights will reach you simultaneously. For the observer on the vehicle the situation is such that; if you place the button on the proper point, although the time of turning on the light sources may be will not be simultaneous, but the two lights will reach him simultaneously. Relative to the observer on the vehicle the light sources may be at different distances or may turn on at different moments but since the lights will reach the observer simultaneously he will see that the lights are turned on simultaneously. However, we are trying to provide this condition in the experiment.


Figure 6  Now I ask you to be very careful.
First of all, for the observer on the vehicle to see the lights turned on simultaneously the lights must enter inside the vehicle from the front and back sides simultaneously. This condition is necessary, otherwise the observer on the vehicle can not see the arrival of the lights simultaneously. I call this situation as "fulfillment of the necessary provision."
If the two lights has entered inside the vehicle simultaneously, the lights will definitely reach the observer simultaneously.
At the moment the logic of the experiment has been mostly constructed. In the case of placing the button on the proper point, the light will reach to the front and the back side of the vehicles at the same time and then they will reach to the observer who is standing at the center of the vehicle simultaneously. And you see that the two lights are simultaneously turned on. Up to this point I don't think that I have proposed anything that you disagree.
As an exception, we have not considered the phenomenon that we call "Space Contraction" (shortening of an objects physical space due to the velocity) in the logic of the experiment. I will take it into account in the preceding pages.
Since we have made our preparations we can now start to our experiment.


Figure 7  From this moment on, I will make a proof that leads to very important results. So I ask you to give all your attention.
I add one more vehicle into the figure and I will make a proof base on law of symmetry. If you think according to you, all the events that take place on the left side of the axis of symmetry must occur on the right side of the axis of symmetry simultaneously since you are standing on the axis of symmetry.
The requirements we have met for the vehicle on the left side are also met for the vehicle on the right side simultaneously. 

Figure 8 First let's consider the situation when the light reaches to the front and the back side of the vehicles, namely the situation when the requirements are met
("fulfillment of the necessary provision"). Since the requirements are met for the vehicle on the left, the requirements for the vehicle on the right side are also met. Pay attention to the condition of the light. With respect to you the light that comes from the same source (let's say the source on the left side) had gone to both of the vehicles with different
velocities.
You can drag the vehicle on the left (with the help of the mouse) to the right or left sides and examine the result for each position. The position of the vehicles when the light reaches them and the velocity of the vehicles does not have any importance. We assume that the necessary requirements are met at the point where you drag and drop the vehicles.
We see that there is an interesting situation that must be answered. Because the figure above shows that the light that goes to the vehicles does not travel with the velocity "c" with respect to you. However "Special Relativity" theory says that the velocity of the light that goes to the vehicles must be "c" namely a constant.
Let's consider that this strange situation is due to the exclusion of the phenomenon called "Space Contraction" in the logic of the experiment. Then at this level we must take the "Space Contraction" phenomenon into account in the logic of the experiment. We do that in the following way:
Let's assume that the private spaces of both of the vehicles, the private times and dimensions of both of the vehicles have changed with respect to your own space, your own private time and dimensions. And let's add here that we are not going to be able to explain the events mentioned above by the figure drawings.
Against the problem we have faced I suggest to have an overview of the information that we have.
Let's look for a reference system that we can trust on it in all aspects since we can not trust the reference systems of the vehicles in the figure. If we think for a while we can realize that we already have such a reference system. It is the reference system of your own. Secondly, with respect to your reference system we are sure that the events that occur in both of the vehicles must be simultaneous with respect to you due to the law of symmetry. And the third information we have is that since the observers on the vehicles will see that the lights are turned on simultaneously with respect to you, whatever the positions of the vehicles would be, the light will enter to both of the vehicles simultaneously with respect to you. Then let's consider these three information together.


Figure 9 I suggest you the following to reach a solution: Let the observers drop their flags that are at the back and the front sides of the vehicles at the moment when the light reaches to the back and the front sides of the vehicles. Later we can go near the flags and study the positions of the them. Since we are sure that both of the observers will drop the flags simultaneously with respect to you, we will have the chance to figure out the positions of the vehicles when the light reaches to the vehicles. The position of the flags will give us a definite information about what has happened.
Since we are going to try to find out the position of the flags via logic, we cover the place where the experiment is taking place with a cloth not to have our thoughts dispersed.
We start our experiment assuming that we have placed the button on the proper point.
First we will study the situation when the necessary requirements are met, namely the situation when the light reaches to the back and te front sides of the two vehicles simultaneously. 

Figure 10 Now we study the position of the flags that the vehicles have left behind.
In the case of considering the light which goes to the vehicles with a constant velocity "c", we will see that there is only one probable position for the flags. We should find the edge flags at equal distances from the axis of symmetry as shown here.
Now to get the results obtained here, let's sift the other probable positions of the flags where we can find them.
In the figure above we see two probable positions of the flags where we can find them. In the figures; the green flags are the 1st vehicle's edge flags and the blue flags are the 2nd vehicle's edge flags.
Figure 10  C and D : Another probability is the probability of C and D. We immediately eliminate those alternatives since they neglect the law of symmetry. In those alternatives both of the vehicles have not moved with the same velocity with respect to you who stands on the axis of symmetry.
Figure 10  E : It is seen that if we think that the light must travel with the "c" velocity to both of the vehicles, we should find the flags coinciding and at equal distances from the axis of symmetry as shown in the figure below. This is the only position that meets the necessary requirements.


Figure 11Thus, by taking into account the phenomenon called "Space Contraction" in the logic of the experiment, we have reached to a conclusion in which at the moment when the light arrives to the back and the front of the vehicles, the back and the front sides of the vehicles should be coinciding.
Although we assume that the length of the vehicles have shortened due to the Length Contraction (Length Contraction is another foresight of the existing "Special Relativity" theory and assumes that a change will take place in the length of an object's physical dimension due to its velocity), this shortening will be symmetrical with respect to you. At this moment the position of the observers who stands at the center of the vehicles will be on the axis of symmetry with respect to
you.
Since we have studied the case when the light enters to both of the vehicles simultaneously and where the necessary requirements are met, we may go to the next level and study the situation when the light reaches to the observers simultaneously.


Figure 12 Let's make the motion continue (click to move button please). As the vehicles move along their paths, the light that has entered into the vehicles will travel through to the observers. At the moment when the light reaches to the observers, the observers are not on the axis of symmetry anymore with respect to you. Obviously there is no possibility of finding the center flags that the observers have
dropped coinciding with each other.
The situation above, again shows that the light travelling to the observers did not travel with the velocity "c" with respect to you. Thus with the proof done here I demonstrate that it is impossible for the light that is travelling to the vehicles travel with the velocity "c" with respect to you. The results obtained here give us very important information about what the "Special Relativity" is and show the error in the source of "Special Relativity" theory.
Now, I would like to make an addition and finish the proof.
In any circumstances, it is impossible to find the center flags on the axis of symmetry and coinciding each other. First of all this situation means the immobility of the vehicles after the necessary requirement are met which is not possible.
Secondly, both of the observers in the vehicles which are going in the opposite directions would see the light that is coming from the same source at the same space position, which is impossible and already has been proved by Albert Einstein with the train example.
In the proof we have the result of finding both of the center flags (either on the right or left side of the axis of symmetry) at equal distances from the axis of symmetry. Both of the observers has dropped the flags to your own space simultaneously with respect to you. This situation shows that the light that goes to the vehicles does not travel with the velocity "c" with respect to you. Thus we are concluding the 1st part of the proof.


Figure 13  Previous proof shows the existence of a result as shown in the figure above. Since light is composed of photons, all the photons emitted from the same source does not travel with the constant velocity "c". The photons that go to the vehicles had not travelled with the velocity "c" with respect to the observer on the ground.
The proof of the Alice Law you have seen here is the first part of the two parts that is required to show that the velocity of light is "RELATIVE". I will continue to the 2nd part of the proof with the next part called "Relative Velocity of Light". Briefly the proof done here shows that the "Special Relativity" theory includes a big deficiency in its own and the behavior of light is not known well.It is obvious that without understanding at what velocities the light travel that goes to the vehicles, it is not possible to improve the definition of the term which we call "simultaneous". In the part of "Relative Velocity of Light" where the second proof is done we will see at what velocities the light travels to the vehicles.

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