TUBE

and

THEORETICAL PROOF OF ALICE LAW

Han Erim

30 August 2025

Hello,

The content of this article is based on a study I published on 23/October/2000 under the title "(c+v) (c-v) proof – The speed of light is relative". I wrote that paper to provide a theoretical proof of Alice Law, and it was my first article about Alice Law. In my later works, I included the same proof in computer programs explaining Alice Law. For example, in the physics program "Alice Law Version 5", which I published in 2005, the sections "Relativity of Simultaneity" and "Relative Speed of Light" present this proof.

In later years, I aimed to share this study with my readers in a clearer and more understandable way, and in 2010 I published my article titled "TUBE". The work you are now reading is the updated version of that article.

Since this article contains the existence proof of Alice Law, it is extremely important. The name of the article comes from a theoretical device designed in the form of a tube. The simplicity and clarity of the device are sufficient to produce correct theoretical assumptions. The proof of Alice Law is also based on the theoretical precision provided by this device.

Introduction of the Device:
The device we will use is a vacuumed tube with a light source on each side. Inside the tube, there are two carriages moving on rails. On both sides of each carriage there is a sensor, and a third sensor is located in the middle of the carriage. The side sensors are equidistant from the central sensor. The sensors are sensitive to light and detect the moment when the light reaches the ends and the middle of the carriage. The carriage can also measure the speed of the light coming to it.

By using the control panel, the speed of the carriages can be set to any value between 0 and c (the speed of light) relative to the ground reference system. The lamps located on both sides of the tube can be lit at any desired moment by button mechanisms. The device can be controlled entirely from outside, and here you will control it. The figure below introduces the device and shows its parts. Please take a look.

Important points:

The device is designed in accordance with the principle of symmetry.
The lamps at the ends of the tube are always triggered at the same time.
Both carriages are identical.
The carriages can move at any speed, but their speeds are equal and opposite.
The distances of the carriages from the symmetry axis are always equal.
There is no special condition for the lengths of the carriages.

The timing of the lights is adjusted with the help of small brown triangular buttons that can be moved left and right. At the moment when this button touches the orange triangular button located at the bottom-center position of the carriage, the lamps at the ends of the tube are triggered. It is assumed that once the contact occurs, the lights turn on without any time delay.

Due to the principle of symmetry, we can confidently say: Events occurring on the left side of the symmetry axis will also occur in the same way on the right side of the symmetry axis. For example, when the light moving from the left reaches a carriage, the light coming from the right will also reach the other carriage.

Golden Rule:

The goal is to ensure that the lights coming from both sides reach the central sensor of the carriages at the same time. This is possible when the lights are triggered at the correct moment.

I call this the "Golden Rule".

Golden Rule: Since we can control the speed of the carriages and the ignition time of the lights as we wish, there must necessarily be a situation where the lights reach the central sensors of the carriages at the same time.

Therefore, the claim that "there is no solution" can never be put forward.

Moreover, the theory that can satisfy the Golden Rule is the correct theory.

You may think that the condition to satisfy the Golden Rule should be as follows: When the midpoints of the carriages reach the symmetry axis, the lights must also reach the symmetry axis; if the speed of the carriages and the ignition moment of the lights are chosen to provide this situation, then the Golden Rule will be satisfied and the lights will reach the central sensors at the same time. (You can simulate this assumption by pressing the Show Button in Figure 2.)

Use of the tube device:

The speed of light is simulated in the animation as 5 pixels/frame.
The speed of the carriages can take any value between 0–5 pixels/frame.

1) Choose a speed value for the carriages.

2) Drag the brown triangles left and right to set the ignition time of the lights.
3) When you press the Start button, the device will animate the event according to your choices.

The small lamps on the carriages are indicator lights, showing the result. By turning red or green, they indicate whether the lights reached the sensors simultaneously. When you achieve the Golden Rule, all of these lamps will light up green.

But reaching the result is not easy. Because there is another condition that must be fulfilled: For the lights to reach the central sensor at the same time, they must first reach the side sensors of the carriages at the same time. Only if this condition is satisfied can the lights reach the central sensor at the same time. (Figure 3)

(Let us imagine that a lamp is placed on each side of the carriage. If the lamps are lit simultaneously while the carriage is moving, the lights will reach the central sensor at the same time. This is a well-known physical phenomenon explained by Galileo’s Principle of Relativity. As a result, for success, the lights must first reach the side sensors of the carriages at the same time.)

Paradox:

1. When the midpoints of the carriages reach the symmetry axis, suppose the lights have reached the side sensors. In this case, however, the lights will not reach the central sensors at the same time. (Figure 4-A)

2. If the lights meet the central sensors on the symmetry axis, then the lights will not have reached the side sensors at the same time. (Figure 4-B)

3. There is no specific limitation for the lengths of the carriages.

4. The carriages must measure the speed of the incoming light from both directions as "c".

5. Any solution that violates the principle of symmetry will not be valid.

I invite my physicist colleagues to seek a solution: Try to produce a solution that satisfies the Golden Rule using the Theory of Special Relativity.

Solution of Alice Law

To reach the solution, let us focus our thoughts on the light emerging from the device.

My proposal is this:
Each photon travels at the constant speed c relative to its own target.

In this case, the beam of light, which was initially a single piece, will split, and photons heading to different carriages will form separate groups. (Figure 5)

The groups formed will fulfill all the necessary conditions for their target carriage and will satisfy the Golden Rule.

What I call Alice Law is the solution that assumes that light (photons) behaves as described here. In the following animation, you can use the device to obtain the Golden Rule. Figure 6

This solution also shows us without hesitation when the lights must be ignited.

• The lights must be ignited when the central points of the carriages reach the symmetry axis. At that moment, the distances of the central sensors to the lamps are equal. Since the light will travel at speed c relative to its targets, the arrival times at the central sensors will be equal.
• The lights will also reach the side sensors of the carriages simultaneously, because at the ignition moment the side sensors are at equal distances from the lamps.
• The lengths of the carriages do not matter for the experiment. The carriages may be chosen at any desired length.
• The carriages always measure the incoming light at speed "c" under all conditions.
• The principle of symmetry is strictly preserved; regardless of the speeds or lengths of the carriages, all the necessary conditions are fulfilled.

Result:

The fact that there is only one solution that satisfies the Golden Rule elevates Alice Law mathematically to the status of the "correct theory."

The fact that light (photons) behaves as shown here is very critical information that must be taken as a basis for Electromagnetic Theory. When this is done, Electromagnetic Theory will have filled a major gap. Special Relativity, however, will have to drop out of the agenda since it cannot provide a solution.  

Years ago, when I started working on physics, I considered Alice Law as an alternative relativity theory.  After twenty years of study, I realized that I had actually found the missing link of Electromagnetic Theory.  In other words, Alice Law is Electromagnetic Theory based on the (c+v)(c-v) mathematics. Personally, I think Theoretical Physics is the most difficult job in the world. Of course, I may be wrong, but I believe Alice Law will carry physics to a much better point.

I address my readers: Use this theoretical device to test your own knowledge, meet the necessary conditions, and obtain the Golden Rule.
I wish you success in your studies.

Note: "I do not think that the tube experiment can be practically implemented under today’s conditions, due to the extremely small time resolution required. Therefore, the setup should be regarded as a theoretical existence proof and a thought experiment of Alice Law."

Sincerely
Han Erim