16 Understanding the principle of invariant light speed 2
But there is one thing more fundamental than this. The path of light should be 'continuous'. Can the photon disappear at some point while it is transmitting in space, and can it reappear at another point? In relativity, this never happens. This is an extraordinary science, beyond modern science. Therefore, these things cannot be accepted or recognized in the theory of relativity.
This is a series of posts. It is better to read the following article first.
When we talk about light in relativity, there are a few things that we should basically assume. This is the constancy of speed of light proposed by Einstein, but there are some more basic than Einstein proposed. If this basic story is not acknowledged, the scientific discussion of light is meaningless and this post is pointless.
The basic properties of light are as follows. And the fourth is the nature of the general object, not the light.
i) Constancy of the speed of light: The speed of light in vacuum always has the same value c.
ii) Isotropy of light propagation: Light propagates at the same speed c in all directions.
iii) Continuity of light propagation: Light travels continuously without breaking.
iv) Continuity of object movement: The object moving at constant velocity has constant distance to move per unit time.
i) and ⅱ) are so well known, there is no need to explain. iii) means that the light travels continuously, and iv) requires a little explanation. When the light travels about 3 x 108 m in one second, it assumes that the points move like the blue dot in the figure below every second. So, when an object runs at a speed of 86.6% of the speed of light, the spacing is a bit smaller than the speed of light, but the spacing is always constant. (Assuming that the velocity of the object is 0.866c, because, the value of the Lorentz factor γ is simply about 2. The light is represented by the blue dot, the object by the red, and the reflection point by the black dot.)
 |
| Figure 1. Constant speed |
In the above figure (a) it shows that the light moves by 3 x 108 m per second. If the interval either decreases or increases, the scientific description is impossible. The increase and decrease of the intervals do not match the constancy of the speed of light. Likewise, the interval corresponding to 0.866c is constant. The unit distance the light travels is indicated by the blue dot, and the unit distance of the object moving to 0.866c is indicated by the red dot. Now the center point of an object moving to 0.866c should always move at the same interval as the red point. If this is not acknowledged, the future description is pointless.
Ellipse with path of light
The theory of relativity often deals with photo-clocks. When photon vibrates in a cylinder, it can be seen as a kind of clock. It is the simplest and most intrinsic clock because it oscillates at a constant time interval. And by using this, time dilation can be easily derived. Let's take a look at the photo-clock here.
 |
| Figure 2. Photo-clock |
James and Ellis are in relative inertia, moving relative to each other. James sees James' photo-clock. If so, its shape will look like Figure 2. However, if James sees Ellis moving relatively, it will be as follows.
 |
| Figure 3. Relative moving photo-clock (the distance between the starting point and the ending point is now expressed in 2 time units) |
In Figure 3, if the starting and ending points are the same, they are circles. If the starting and ending points are different, they are ellipses. So let's draw an ellipse with the focus on the starting and ending points. Current textbooks only record when the photo-clock is oriented vertically. This is the way Kutliroff proposed. There is a special story that is recorded only when it is vertical, not when it is tilted. In the current relativity, it is only possible if the direction of the photo-clock is vertical. Even if the direction of the photo-clock tilts a little, the photon jump takes place and the above four properties are not kept.
 |
| Figure 4. Shape created by connecting all reflection-points, Ellipse |
The red dots in the figure 4 above are the reference points of the object moving to 0.866c (in the above figure 4, between the start point and the end point in 2 unit times). Therefore, the interval between these red dots must always be constant. If the spacing of these points is constant, then the assumption that an object moves to 0.866c is properly guarded.
The definition of an ellipse is 'a set of points with a constant sum of distances from the two foci'. And the path of light should always be equal to the sum of the distance to the starting point - the reflection point - the end point. This is an easy way to explain the constancy of the speed of light. And there should be no directionality. This is called 'the isotropic propagation of light'. In light propagation, the speed of light is the same in all directions. It is just another name for the constancy of the speed of light.
The problem with this photo-clock is the same as the problem of spherical mirrors that we have seen in the previous post (Relativity theory with fire and water in the other ). When you tilt the direction of the photo-clock, it immediately becomes a circular mirror. So if you treat the photo-clock and spherical mirrors equally, you may find it convenient.
 |
| Figure 5. The 'spherical mirror' and the 'photo-clock of arbitrary angle' are the same |
Now in Figure 4, we will move the reflection-point back and forth without moving the starting and ending points. If the constancy of the speed of light is established, the lengths of the different paths must be the same. If it is not the same, the constancy of the speed of light will collapse.
Now, let's adjust the slope of the photo-clock. Light starts from the starting point (red), passes through the reflection point (black), and returns to the end point (red) again. At this time, the distance between red is 0.866 × (3 x 108m). In the figure below, there is a gap of 2 unit times between the starting point and the ending point.
 |
| Figure 6. Vertically erected photo-clock |
The picture below is slightly inclined. The starting and ending points are the same. The only difference was the location of the reflection point. However, it is a fact that the reflection point is on the ellipse.
 |
| Figure 7. Tilted photo-clock |
The picture below shows how the light travels in the same direction as the photo-clock. It's hard to see, so it's a little less tilted. The starting and ending points are the same. And though the reflection points are different, they are still on the ellipse.
 |
| Figure 8. Horizontal oscillating photo-clock |
If you draw all the different paths, it will look like the picture below. This exactly matches the definition of the ellipse.
 |
| Figure 9. Light clocks oscillating in all directions |
Gathering various tilted paths of light, it becomes an ellipse as shown in Figure 8. Different colors represent different paths, and the length is the same. If the constancy of the speed og light is right, it must be the same. If not, a fatal error has occurred in the theory of relativity. Let's summarize the description so far.
 |
| Figure 10. The path of vertically oscillating light |
For constancy of light speed and continuity of light propagation, the starting and ending points should be the focus of the ellipse, and the reflection-point should always be on the ellipse
For the above emphasized phrase, I think we should name it. I will call it 'elliptic theorem' for focus and reflection points. No matter what angle the photo-clock is inclined to, the reflection points must always be on the surface of the ellipse. If the reflection points are not on the surface, something is wrong and it does not satisfy the constancy of the speed of light. In current relativity, there is only one case below when light continuity is established.
This is the path that appears when you observe a photo-clock that vibrates vertically while moving. This is the only path that can be explained by length contraction theory. At this time, there is no discrepancy. However, if we change the direction of the photo-clock a little bit, the error will come out soon.
 |
| Figure 11. Elliptic theorem |
Pay particular attention to the red path in the figure above. The red path shows the case where the two directions match. We should note that in the red path, the oscillating direction of the light clock is the same as the direction of motion of the object. The length contraction theory does not explain this, but the length expansion theory naturally explains it.
Let's start with the case of length contraction. Let's see if it works according to the philosophy of relativity. There are a few things to consider before writing. Whether we observe a photo-clock that vibrates vertically, a photo-clock that vibrates in the same direction, or a photo-clock that tilts at an arbitrary angle, the starting and ending points of the photo-clock must always be the same. If this is not the case, it is not a photo-clock.
In the above three figures, although the reflection points may be different, the starting point and the ending point must be the same. This is because the photo-clock is moving at a constant speed of 0.866c and simply tilts the angle of the photo-clock. Now, let's see if this is true for length contraction cases.
Length contraction and discontinuity
The speed of light is always constant, but the path of the light should not be discontinuous. Light must always be delivered continuously. However, if the length contraction is correct, this is not possible. Let's take a closer look.
 |
| Figure 12. Photo-clock with length contraction applied |
In the picture above, the light started from the starting point. However, due to the length contraction, the length of the photo-clock is shortened, so it reaches the new reflection point shorter than the original point. The speed of light is always constant and the length of the photo-clock is shortened, so it must be like this. If this happens, the reflection-point does not reach the ellipse and the light is reflected. This is a violation of the elliptic theorem for focuses and reflection points. So the reflection points are different and the end points are also different. Since the end point does not reach the focus of the ellipse, a discontinuity section must be created.
 |
| Figure 13. Light leaping into unknown space |
Ether hypothesis → Length contraction hypothesis → light-leap hypothesis → ○○ hypothesis → hypothesis → hypothesis → hypothesis → → →
 |
Figure 14. A vertical photo-clock and a horizontal photo-clock |
If we create a hypothesis every time we have a problem, science as a whole will be filled with hypotheses. Once a person lies, he must constantly create lies to protect the lie. This is exactly the same situation as the length contraction hypothesis. Let's just look at the path of light, and more simply.
In the figure above, the red dot indicates the origin of an object moving to 0.866c. Here we will use the center point of the bottom of the photo-clock. And the time interval or speed of (a) or (b) is completely the same. If there is anything else, the orientation of the photo-clock is different. In (a), the light path is continuous. But in (b) the story is a little different.
In the case of (b), the length of the photo-clock was shortened by the Lorentz contraction. If so, it reflects earlier than if it was not shortened, and it would reach the blue dot without reaching red. In this case, it is not established that moving continuously to 0.866c. The light arriving at the blue dot has no path to go back to red. How then can the photo-clock vibrate continuously?
If we plot the path by speed, we can see clearly as shown in the figure below. In the picture below, the lower the picture is, the faster the speed of the object. A photo-clock with a faster speed is expressed as a shorter one.
 |
| Figure 15. Increasing blanks |
In order to let the light oscillate continuously, let's get rid of the blank spaces. Then it will be like the picture below.
 |
Figure 16. Path of light when blank is removed |
In order for the light clock and light to vibrate continuously, we have eliminated the blank space. Ironically, as the speed of an object gets faster, the light can only go a little further. When the speed is extremely high, both the object and the speed of light are stopped. The equations are:
"If the length contraction is correct, the light stops."
Continuity of light path and length expansion
 |
| Figure 17. One-shot vibration of light |
Now let's look at the case of two successive vibrations. The feature of this figure is that the ending point of the first vibration is the starting point of the second vibration. It is so natural. If you connect it continuously, it becomes a natural light vibrating picture as follows. So far, the theory of length contraction is also possible.
 |
| Figure 18. Continuous oscillation of light |
But when it tilts and vibrates, it changes completely. When tilted and vibrated, the first ending point is the starting point of the second, as long as it keeps the constancy of the speed of light. Because the ending point and starting point match, they will vibrate continuously. Whether it is be three times or four, it can be repeated infinitely.
 |
| Figure 19. Tilted continuous oscillation of light |
 |
Figure 20. Horizontal continuous oscillation of light |
And the picture above shows the case where the moving direction of the photo-clock is the same as the vibration direction. This is also the case with other vibrations. The ending point of the first vibration matches the starting point of the second vibration. Therefore, light can continue to vibrate continuously.
There is one thing in common in all three of these cases. It is reflection points, all of which are above the ellipse. Therefore, they keep the constancy of the speed of light, and the path lengths are the same. Because the lengths of the paths are the same, the time taken to vibrate and the reciprocating vibration distance all match. So the interference pattern did not appear in the Michelson Morley experiment.
The starting and ending points of a photon are in focus, and the reflection-point of a photon is an ellipse.
light path and length
The last thing to notice is "What is length?" It is the length measured with a ruler. In general, there is a way to measure the length more precisely than it is measured by a ruler. It is the length measured by the laser. We call it 'asynchronous length'. The length measured with this laser is more accurate than the length measured with a ruler.
In fact, the vibration of a photo-clock is a measure of time, and at the same time a measure of length. You will be familiar with the definition of 'one second' and the definition of '1m' in modern civilization, all related to light. Both time and length are based on the speed of light.
 |
Figure 22. Photo-clock in stationary state |
Therefore, when the light oscillates once and the time taken for the reciprocating motion is 2to, the total reciprocating distance when vibrating once can be called 2ℓo. Distance is the product of time and speed. If so, there is a relationship between proper distance and proper time:
The time needed to vibrate once (starting point - reflection point - ending point) is 2t, and the length of the vibration (starting point - reflection point - Ending point) is 2ℓ.
2 cto = 2 ℓo
∴ cto = ℓo
The time needed to vibrate once (starting point - reflection point - ending point) is 2t, and the length of the vibration (starting point - reflection point - Ending point) is 2ℓ.
|
| Figure 23. Photo-clock in moving state |
2 ct = 2ℓ
∴ ct = ℓ
This is the shape when the light is fired vertically. But now, let's look at what happens when the direction of the object is the same as the direction of light oscillation. The figure below shows the vibration in the same direction. Even when stopped in the same direction, it is natural that the round trip time is 2to and the round trip distance is 2cto. The light should be established as it does not depend on the direction.
 |
| Figure 24. Horizontally Vibrating Photo-Clock |
And when the photo-clock vibrates in the same direction, it looks like this:
 |
| Figure 25. Length of photo-clock in motion |
The red path shown in the figure above exactly matches the red path shown in the ellipse below.
 |
| Figure 26. Length tilted at various angles |
You should pay attention to this red path. This red path is twice the length of the light clock. This is the method used to measure the length accurately. Use this method to measure the distance from the earth to the moon, and use this method when fishing boats are trying to locate fish. In other words, the path of the red line is exactly the same as the way to measure the length in modern civilization. If this is acknowledged, the debate on length is over.
The path to the red line is shown in video below. In the figure above, we gave a slight angle to show the path. The first thing that comes out of the video is the stationary state, and the second one is the moving state.
If the video does not play, click once more.
If the video still does not play,
you can watch the 10: 31 ~ 10: 45 portion of the YouTube video below.
The principle of invariant of light speed and asynchronous length (Korean version)
 |
Figure 27. Comparison of proper length and length expansion |
(a) and (c) are the same length, and (b) and (d) are the same length. Relativism is not something that has a mystical philosophy. It's simple. In the above picture, we only look at the length of the light path. The red path has a longer path than the blue path with a proper length. Therefore, the expansion of the length is correct.
When James measures the length of the relatively moving Ellis, it looks asymmetrically as the picture or video. However, Ellis himself, who is relatively moving, looks like this symmetrical proper vibration. Then the relativity principle of relativity is satisfied. Therefore,
The length of the light is the same when it vibrates vertically or vibrates in the same direction. The principle of invariant light speed ensures this. If you now prove the length of the vertical oscillation, it is the same as proving the length of the oscillation in the same direction. And now I will prove. The mathematical methods used here are all Pythagorean Theorem.
(1) The principle of relativity is satisfied,
(2) It can keep the principle of invariant light speed,
(3) The continuity of light propagation can be maintained,
(4) It can keep isotropy of light propagation because it is constant regardless of direction,
(5) We can also keep the elliptical theorem about the focus and reflections.
Everything will be satisfactory. This theory cannot be solved by the theory of length contraction. The contraction of the length only creates a contradiction, but the expansion of the length is very easy to solve.
In addition to the above proofs, there is a direct proof of when the light vibrates horizontally. This is done in a way called K Calculus, which I will prove later in the K Calculus section. My writing is too long. Thank you for reading the long story.
Comments
Post a Comment