RELATIVITY OF SIMULTANEITY

and

MAIN PROOF OF ALICE LAW

Han Erim

March 2005 

Abstract: I published this work inside the Alice Law Version 5 physics program in 2005. This publication, which contains an important physical proof related to the Special Theory of Relativity, clearly shows that the speed of light cannot be constant for all reference systems. This proof, which I call the "Main Proof", is the first of two proofs of Alice Law related to Special Relativity. In the second proof (Relative Light Speed), the behavior of light is revealed and how Special Relativity arises is explained. I have called the second proof the "Final Proof". Together, these two proofs show how Special Relativity must be and define its new mathematics.

Relativity of Simultaneity and Special Relativity.

The starting point of the theory of “Special Relativity” is based on the proof that the definition of “At the Same Time” is “RELATIVE”. For this reason, while explaining the theory of Special Relativity here, I have devoted the first section to the definition of “At the Same Time”. When Albert Einstein proved that the concept we call “simultaneous” is relative, he used his famous TRAIN example. Here I use a similar example to the train example.

As you will see while reading, with Alice Law the concept of “At the Same Time” has been developed and has gained a more consistent and understandable structure. As a natural result of this development, a rather significant advance has been achieved in the theory of Special Relativity and some inconsistencies contained within the theory have been eliminated. Therefore, I think that a designation such as “the new foundation of the Special Relativity theory” would be correct for this section. Every subsequent topic has been developed in harmony with the results obtained in this section and, as a result, the theory of Special Relativity has been clarified in quite a detailed way.

Figure 1 - Let us consider two lamps mounted on the ground. We assume that you are standing in the middle between the two lamps. By pressing the button here, you can switch on both lamps at any time you wish. (I kindly ask you to participate in the animations inside the page. Now please press the button and switch on the lamps.)

If I asked you whether both lamps light up at the same time for you, I think your answer would be as follows: “Since these lamps are at equal distance from me and, in addition, if I assume that the wiring to both lamps is of equal length (and more explicitly; if, according to the symmetry principle, the left side is exactly equal to the right side), then when I press the button I will see both lamps light up at the same time.”

Thus you have defined the concept of “At the Same Time” for yourself. It is impossible not to agree with the explanation you have given. (In all animations, we assume that the left side is exactly equal to the right side with respect to the symmetry axis.)

Figure 2 -Now let us assume that you are inside the rectangular vehicle shown above, which is moving at a constant speed and which has a light source located at its midpoint. If I asked whether, when you switch on the lamp, the light reaches the front and rear of the vehicle at the same time, your answer, if you are a physicist, would be something like this: “The vehicle I am in is moving at a constant speed. Of course, when I switch on the lamp, the light will reach the front and the rear of the vehicle at the same time for me.”

If I object by asking, “How can you say that, even though the vehicle you are in is moving, the light coming from the lamp will reach the front and the rear of the vehicle at the same time?”, you will say that your statement has experimental verification and that the relevant theoretical explanation is based on Albert Einstein’s two physical postulates.

Albert Einstein’s two physical postulates:

Principle of Relativity: For all reference systems, the same electrodynamic and optical laws are valid in such a way that they include the equations of mechanical physics.

Universal Light Speed: Light propagates in empty space with the constant speed c, independently of the speed of the source from which it is emitted.

If I object again, you might say the following: “I cannot argue with you about whether his physical postulates are correct or not. You may or may not understand those postulates; that is up to you. But let me tell you this much: it is impossible to explain the above physical event without relying on these two physical postulates. The light emitted from the lamp at the midpoint of the vehicle will definitely reach both ends of the vehicle at the same time. This is the reality of physics.”

Figure 3 - After introducing the subject in this way, we now extend our example.

From this point on, we will look for the answer to the question of whether the lights that are simultaneous for the man on the symmetry axis are also simultaneous for the man in the moving vehicle.

In fact, about a hundred years ago Albert Einstein largely answered this question with his train example. The aim here, however, is to reveal with greater certainty the reasons underlying the concept of “At the Same Time” and to make “Special Relativity” more understandable. For this reason, I explain the same topic with a different example as shown here.

Figure 4 - I assume the following experiment:

The vehicle on the left moves with constant speed towards the light source on the right. You remain at your place on the symmetry axis. Since the button that switches on the lamps is under your control, you determine the instant at which the lights turn on. Your aim is to make the man inside the vehicle see both lights turning on at the same time. While the vehicle is moving, you must press the button at such a moment that the light from the lamps reaches the man inside the vehicle simultaneously. If you press the button too early or too late, naturally the man will not see both lights turning on simultaneously.

We determine whether the experiment has succeeded or failed as follows: if the man in the vehicle sees both lights turning on at the same time, he raises a green flag on his vehicle; if he sees one first and then the other, he raises a red flag. (Use the buttons. With the Start button you can set the vehicle in motion and you can switch on the lights at any instant.)

Figure 5 - In order to eliminate the difficulty you face in adjusting the switching time of the lights, as a method you can place the button you use (the brown triangle) onto the path of the vehicle. When the vehicle comes into contact with the button, the lights will turn on automatically. If the vehicle always moves at the same speed in all trials (and in the experiment we assume that it always moves with the same speed), then by moving the button to the left or to the right (please try it) you can adjust the switching time of the lights as you wish. If the button is placed at the correct position, the light from both lamps will reach the man inside the vehicle at the same time.

Of course, we keep the wiring from the button to both lamps of equal length. Thus, as long as you stand on the symmetry axis, no matter where you place the button along the road, both lights will always switch on at the same time for you and the light from both lamps will reach you simultaneously.

Before starting the experiment, in order to eliminate animation errors, we must make an important addition. Let us take into account that, although the lights are simultaneous for you, they may not be simultaneous for the man in the vehicle. Because the current theory of “Special Relativity” predicts that the lights which are simultaneous for you will not be simultaneous for the man in the vehicle.

In that case, we can think as follows: as long as you remain on the symmetry axis, no matter where you place the button, the lamps will turn on simultaneously for you and the light from both lamps will reach you at the same time. For the man in the vehicle, however, the situation is as follows: if you place the button at the correct position, even if the switching instants of the two lamps are not simultaneous for the man in the vehicle, the light from both lamps will reach him simultaneously. For the man in the vehicle, the light sources may be at different distances or may turn on at different times, but because the light reaches him at the same time, he will see both lamps as having turned on simultaneously. In the experiment, this is exactly the condition we want to achieve.

Figure 6 - Now I kindly ask you to be very careful.

For the man in the vehicle to see both lights turning on at the same time, it is first necessary that the light enter the vehicle from the front and from the rear simultaneously. This condition is necessary; otherwise the man in the vehicle cannot see the light reaching him simultaneously from both sides. I call this “satisfying the necessary condition”.

If, for the man in the vehicle, the light from both lamps enters the vehicle at the same time, then the light will definitely reach the man at the same time.

At this point, the logic of the experiment has largely been established. If you place the button at the correct position, the light will reach the front and rear of the vehicle simultaneously and then will reach the man standing at the midpoint of the vehicle simultaneously. You, on the other hand, will see both lights turning on simultaneously and reaching you simultaneously.

I do not think that, up to this point, I have put forward any proposition that your reasoning cannot accept. As an exception, the physical phenomenon called Space Contraction (the shortening of the physical space of a body due to its speed) has not yet been included in the logic of the experiment. I will include it a little further on.

Now that we have made all our preparations, we can start the experiment.

Figure 7 - From this point on, I will carry out a proof that leads to very important consequences. Therefore, I ask you to give it your full attention.

I add one more vehicle to the frame and base the proof on the symmetry rule.

Since you are standing on the symmetry axis, if you think in terms of your own reference frame, all events taking place on the left side of the symmetry axis must occur simultaneously with the events taking place on the right side, as far as you are concerned.

The conditions we have fulfilled for the vehicle on the left are also fulfilled for the vehicle on the right, simultaneously for you.

Figure 8 - First let us examine the configuration in which the necessary condition is satisfied, that is, the moment at which the light reaches the front and rear of the vehicles. Since the necessary condition is satisfied for the vehicle on the left, it is also satisfied for the vehicle on the right. Let us pay attention to the situation of the light. As far as you are concerned, the light coming from the same source (for example, the light source on the left) has travelled to the two vehicles with different speeds.

By dragging the vehicle on the left (with the help of your computer mouse) to the right or to the left, you can examine the situation that arises at each position. It does not matter at what position the light reaches the vehicles or what the speeds of the vehicles are. We assume that at the position where you leave the vehicles, the necessary condition has been satisfied.

We see that there is an interesting situation that needs to be answered. Because the figure above shows that, for you, the light going to the vehicles does not move with speed “c”. However, the theory of “Special Relativity” states that the speed of the light going to the vehicles must be “c”, that is, constant.

Let us assume that this strange situation arises from the fact that the physical phenomenon called “Space Contraction” has not been included in the logic of the experiment. In that case, at this stage we must also include the phenomenon of “Space Contraction” in the logic of the experiment. We do this as follows:

Let us accept that the spaces belonging to both vehicles, their own proper times and their own lengths (length contraction) have changed with respect to your space, your own proper time and your length measurements, and let us add that, for this reason, we cannot represent the events that occur in the vehicles at this moment by drawings such as those above.

In the face of this problem, I propose that we review once again the information we have in hand.

Since we cannot represent the reference systems in which the vehicles reside in a drawing in every detail, let us first see whether there exists a reference system in which we can trust from every aspect. After a little thought, we see that we already have such a reference system. This is your own reference system. Secondly, because of the symmetry rule, we are sure that, in your reference system, the events occurring in both vehicles must always be simultaneous for you. The third piece of information we have is this: since the men in the vehicles will see the lights turning on simultaneously according to you, the light will enter both vehicles simultaneously for you, no matter what the positions of the vehicles are. So let us use these three pieces of information together.

Figure 9 - I propose the following in order to reach the solution:

When the light reaches the front and rear of the vehicles, the men in the vehicles drop the flags located at the front and rear ends of their vehicles onto the ground. Then we can go to the places where the flags were dropped and examine their positions. Since we are sure that both men drop their flags onto the ground at the same time according to you, we will, in this way, gain the possibility of understanding the positions at which the light has reached the vehicles. The positions of the flags will give us definite information about this.

Because we will try to determine the positions of the flags by pure reasoning, in order not to let our thoughts be scattered, we cover the place where the experiment is performed with a curtain.

Assuming that we have placed the button at the correct position, we start the experiment.

First we will examine the situation in which the necessary condition is satisfied, that is, the moment when the light reaches the front and rear of both vehicles simultaneously.

Figure 10 - We examine the flags that the vehicles have left behind.

If we assume that the light goes to both vehicles with speed “c”, that is, constant, we will see that there is only one possible alternative for the positions at which we can find the flags. We must find the edge flags of both vehicles at positions such that they are at equal distance from the symmetry axis and coincide with each other, as shown here.

Now let us obtain this result by successively eliminating the other possible positions in which we could find the flags.

In the figures above, we see two possible configurations for the positions of the flags. In the figures:

The green flags are the edge flags belonging to vehicle 1.
The blue flags are the edge flags belonging to vehicle 2.

Since the edge flags of both vehicles have been dropped onto the ground at the same time according to you, if the flags are in either of the two configurations above, this will show that the light has not gone to the vehicles with speed “c” according to you. Let us consider the light going from the lamp on the left to the vehicles. The light coming from the left has reached both vehicles at the same time according to you, but we see that at that instant the distances of the two vehicles to the same lamp are different for you.

Figure 10 - A and B: Therefore, Figures A and B here show that the light coming from the lamp has gone to the two vehicles with different speeds according to you. If we assume that the present theory of “Special Relativity” is correct (that is, the assumption that light moves with speed “c” with respect to all reference systems), such a situation must not exist. Therefore, we eliminate these options for now.

The other possibilities are those in Figures 3 and 4.

Figure 10 - C and D: Since these options violate the symmetry principle, we immediately eliminate them as well. In these options, the two vehicles have not moved with equal speed according to you, who is standing on the symmetry axis.

Figure 10 - E: It is seen that, if we think that the light must not go to the two vehicles with different speeds, we must find the flags as shown in the figure below, coinciding with each other and at equal distance from the symmetry axis.

This is the only configuration that satisfies the necessary condition.

Figure 11 - In this way, by including the physical phenomenon called “Space Contraction” in the logic of the experiment, we have reached the conclusion that at the moment when the light reaches the front and rear of the vehicles, the front and rear ends of the two vehicles must coincide with each other. Even though we assume that the lengths of the vehicles have been shortened because of “Length Contraction” (it is another prediction of the present theory of “Special Relativity” and assumes that the physical length of a body changes due to its speed), this shortening will again be symmetric for you. At that moment, the positions of the two men standing at the midpoints of the vehicles are on the symmetry axis according to you.

Since we have examined the position in which the light enters both vehicles simultaneously, that is, the position where the necessary condition is satisfied, we can proceed to the next stage and examine the configuration in which the light reaches both men simultaneously.

Figure 12 - Let us continue the motion. While the vehicles move along their directions of motion, the light that has entered the vehicles also moves towards the men. At the moment when the light reaches the men, neither of the men is on the symmetry axis any more according to you. Naturally, there is no possibility of finding the central flags they have dropped onto the ground coinciding with each other.

The situation above again shows that the light going to the men in the vehicles does not go with speed “c” according to you. Thus, with the proof carried out here, I show that it is impossible for the light going to the vehicles to move with speed “c” according to you. This result gives us very important information about what “Special Relativity” is and shows the source of the error in the theory of “Special Relativity”.

If you allow me, I would like to make one last addition and then finish the proof.

Under no circumstances is it possible for us to find the central flags at positions that are on the symmetry axis and coinciding with each other. Firstly, such a situation would mean that, after the necessary condition has been satisfied, the vehicles have not moved, which is impossible.

Secondly, both men in the two vehicles moving in opposite directions would have seen the light coming from the same source in the same position in space, which is impossible; Einstein has already proved this with his train example.

Since, in the proof, we have arrived at the result that we must find the two central flags on the right and left of the symmetry axis at positions that are at equal distance from the symmetry axis, both men have dropped their flags into your space at the same time according to you, but at different positions. This shows that the light going to the vehicles does not move with speed “c” according to you. In this way we complete the first part of the proof.

Figure 13 - The proof in this section reveals the existence of a result as shown in the figure above. Since light consists of photons, not all photons emitted from the same source move with the constant speed “c”. According to the man on the ground, the photons going towards the vehicles have not moved with speed “c”.

This proof of Alice Law that you have followed is the first of the two proofs needed to show that the speed of light is “RELATIVE”. I will continue with the second part of the proof in the next section, titled “Relative Light Speed”. In summary, the proof here shows that the theory of “Special Relativity” contains a serious deficiency in itself and reveals the existence of some different physical facts concerning the behavior of light.

It is clear that, without understanding at what speed the light going towards the vehicles moves, it is not possible for us to develop the definition we call “At the Same Time”. In the section "Relative Light Speed", where the second proof is made, we will see at what speed the light travels towards the vehicles.