07 Understanding the principle of invariant light speed

  In an inertial system, the speed of light is always constant. It is a very short sentence, but today this proposition is not fully understood. If you thoroughly understand and adhere to two principles of relativity theory, the principle of relativity and the constancy of the speed of light, you can naturally conclude against a reasonable relativistic length. If we keep these two principles constant, without preliminarily setting a conclusion about length, we can make a surprising discovery. Especially about length.

The two principles of special relativity theory speak about symmetry and conservation. The first principle, the principle of relativity, says that all inertial systems are symmetrical to each other, and the second principle, the constancy of speed of light, says that the light speed is always preserved.

At first glance, these two principles seem to oppose each other. However, if these two principles work in harmony, you get amazing conclusions. After reading this article, I am confident that you will be able to understand the constancy of speed of light more deeply than before. But before that, let's go over the two principles precisely.

First, you must understand that it is the inertial system. An inertial system is a space in which time, space and direction are guaranteed to be symmetrical everywhere. Therefore, the first principle of relativity theory, 'principle of relativity', is that all physical laws in the inertial system are equal to each other. This is a natural requirement. If this is guaranteed, you and I will be able to exchange physical laws and information with each other.

Second, the second principle of relativity, the constancy of speed of light, is that the light speed in a vacuum is always constant, regardless of the speed of the light source. You have to keep the same conditions here. The condition of vacuum is also important, and the speed of the light source is also important. And this is not just a human idea, but a very important conclusion drawn from experimental observations. No basic principles have yet been found to make the speed of light a dependent variable.

Now these two principles are enough. If this is guaranteed, it is not difficult to judge whether the length contraction is correct or the length expansion is correct. If you do not deny these two principles, you can reach the right conclusion.

James and Alice are in different inertial systems. They are both moving relative to each other. From James's point of view, Alice is moving to the right at v speed.

Figure 1. James and Alice in two inertial systems

Suppose both are in a spherical mirror. The center of the sphere is the origin of the coordinates. The figure below shows James's coordinate system. The light spreads from the origin of James, then returns. When James observes himself, the reflection plane will look like the picture below.

Figure 2. When James observed, his reflection sphere of light

When James's light hits the sphere and returns, the reflective surface of the light always forms a sphere. Since the constancy of the speed of light and the isotropy of light propagation are ensured, the sphere forms precisely. We assume that James's system is inertial, so this is natural.

Figure 3. Two basic principles that are opposed to each other

James seems to have stopped himself, but Alice is running to v to the right. The problem arises here. Suppose that the origin of the coordinates of James and Alice match, and the light is fired. The reflective surface of light always forms a sphere for James, but it is no longer a sphere for Alice.

According to the principle of relativity, Alice must feel that the light originating from her origin is always spherical. According to the principle of relativity, no one should be discriminated against, and light should always have a constant speed regardless of who sees it. In the picture above, James has a constant sphere, but Alice does not have that sphere any more. Is this not a violation of the first principle of relativity? Do you have a way to resolve this contradiction?

Assuming that the speed of light is constant, it is not constant for Alice, so it violates the principle of relativity. If we focus on the principle of relativity and form a sphere for Alice, it will not become a sphere for James anymore. Then the constancy and the isotropy of light propagation is now broken. It is no longer an inertial system.
.
.
.
.
.
.
.
.
Here we are mistaken by one important thing. The constancy of speed of light is that the speed of light is constant, not that the distance traveled by light is constant. In the above situation, Alice also observes the reflection surface of the light in the form of a sphere and observes it as a sphere to James. And if the speed of light is constant, then all conditions are satisfied. There is a way to prove this. Let's take a closer look.

Figure 4. Starting point, reflection point and end point

Now let's assume that James observes Alice, who is relatively moving. Then the light originating from Alice's origin A will be reflected on B and return to point C. When James observes himself, he does not move, so he has the same starting and ending points, but when James observes Alice, the start and end points are different.

Figure 5. The ellipse that appears when you connect all the reflective surfaces

When James observes Alice, of course, the principle of constant velocity of light must be established. This is inevitable. When we discuss the theory of relativity, it is an absolute principle that must be followed. If so, the photon starts from starting point A, hits the reflecting surface, and returns to destination C. In this case, the length of all light paths is the same.

Since all photons have the same length of path, this exactly matches the definition of an ellipse.

The definition of an ellipse is 'a set of points with a constant sum of lengths from two points in the plane'. If so, the above reflection surface exactly matches the shape of the ellipse. In other words, for Alice running, the path of all photons must be an ellipse, and Alice will recognize this as a circle. So, both James and Alice are satisfied with both the principle of relativity and the principle of flux constant. Therefore, the shape of the spherical mirror James observes James himself, and the shape of the mirror when James observes Alice are distinctly different. Its shape is as follows

Figure 6. If you are observing yourself, and observing your opponent

The following is a very simple summary of all the above statements. When a person observes himself, it is a circle because the starting point and the ending point of light are the same. And when someone observes the moving frame, the starting point and the ending point of light are different. Therefore, the two points are the focal points of the ellipses, and the key is that they are observed as follows.

Figure 7. Different starting and ending points

This is the difference between a circle and an ellipse. Compared with general objects, this is shown below.

Figure 8. Expansion of a general object

That's it. This is the length expansion. Suppose an object is observed in the form of a circle when it is stationary. When moving at relativistic speed, it is observed as it expands in the direction of travel. The length expansion exactly follows the principle of relativity and the constantancy of the speed of light.

Keeping both principles thoroughly will never lead to length contractions. It is always concluded that the length expands. This is also evident in the equation. As can be seen from the equation below, the length contraction never satisfies the constancy of the speed of light.

How can you use the name theory of relativity, even if you cannot keep the constancy of the speed of light? Length contraction is a pure classical ether theory, but it is by no means a theory of relativity.

Figure 9. Contradiction between length contraction and constancy of the speed of light

However, when interpreted as the expansion of the length, it will naturally satisfy the constancy of the speed of light.

Figure 9. Matching between length expansion and constancy of the speed of light

Therefore, the relativistically accurate length should be like this:

In fact, length contraction is a deformed theory created by historical distortions. There is a reason why Lorentz and Fitzgerald and Einstein were forced to argue. So I do not want to criticize them. Once you know that distortion exists, you can correct it. I will introduce many distorted scenes in the following posts.

Here, we apply two principles thoroughly to the conclusion that 'the length expansion'. This phenomenon continues to repeat. This is repeated in all scenes such as the Minkoski spacetime diagram, K Calculus, and Lorentz transformation etc..

If you truly adhere to the basic spirit of relativity theory, you will conclude that it is the length expansion. If there is any disagreement, please present your objection.

Lehgth Expansion(Amazon books)