21 The contradiction between the theory of relativity and causality
Quantum mechanics is difficult to accurately apply causality. There are many phenomena out there that don't make sense. However, relativity does not go beyond causality like classical mechanics. If there is anything outside the causality in relativity, it is a very serious phenomenon.
However, unlike this naive desire of relativity, relativity can go beyond causality. It's time to deal with Bell's paradox. Bell's paradox is not just a small paradox within relativity. The problem of minor black-body radiation has spawned quantum theory, completely reversing the paradigm of science. In order for a paradigm to be maintained, nothing that rejects it must exist. In this respect, the current theory of relativity is challenged by various paradoxes. There are too many paradoxes in relativity.
Among the paradoxes of relativity, Bell's paradox and Ernest's paradox are the most difficult. In particular, Bell's paradox is a very important issue that can shake traditional thinking about what exists in the world. Today we will open the door to Bell's paradox, and deep into the philosophy of relativity. Please be prepared.
Overview of Bell's spaceship paradox
In the theory of relativity, the problem of causality arises in the process of solving Bell's spaceship paradox. So let's look briefly at the outline of Bell's spaceship paradox.
Two spaceships with perfectly identical conditions connected the thin string. If you move together in the same state, what will this string be? It is the question of Bell's spaceship paradox. Many scholars have studied this problem and concluded that:
They concluded that the spaceships were shrinking due to the Lorentz contraction and that the spaces between them were expanding. So they concluded that the string should be broken like this: This is the conclusion of most scholars' claims.
Maudlin presents a very unique logic about this conclusion. However, most scholars argue that the line will be cut off. These opinions are the mainstream, and the opinions of Maudlin are classified as small groups. Now let's look at why many scholars have come to this conclusion.
Basic solution of space-time diagram
The graph below is a basic model of the construction diagram. Xo represents the time axis, and X1 represents the space axis. Space is three-dimensional, but only one axis is represented. And the diagonal dotted line represents the world line of light. So the picture below is a two dimensional space-time diagram. I am satisfied with this. Later, in a 3D space-time diagram, more information is available.
 |
| Figure 1. Space-time diagram showing proper physical quantities |
The graph above is a graph used by a relatively stationary observer to express his or her physical quantities. However, when I observe other people moving at relative speed, I use the graph below.
 |
| Figure 2. Relative moving inertial coordinate system |
In this graph, the world of light is maintained at 45 °. This indicates the invariance of the speed of light. There is a relationship between tan θ = v/c between relative velocity and angle. Where θ is the angle between the axes in Figure 1 and Figure 2. Let's assume that the speed of light is 3 × 10^8 m / sec.
 |
| Figure 3. Two world-lines of light in a stationary coordinate system |
Figure 3 above is a graph that observes one's physical quantities in one's system. James observes various physical quantities on Earth. A is one light second (3 x 10^8 m) away from its origin, and B is two light seconds (6 x 10^8 m) away from its origin. (Of course, you need to make assumptions that the Earth is very large.)
X1 is the space axis and it also represents the simultaneous line. So when A and B shoot light at their origin at the same time, it will look like Figure 3 above. So how many seconds do the two signals arrive at? This can be calculated by the invariance of the speed of light.
We know this, but let's assume that the person at the origin does not know how far A and B are. To the person at the origin, the first signal arrives in 1 second, and the second signal arrives in 2 seconds. If so, the distances between them can be easily determined by applying the constancy of the speed of light. The time interval between two signals can be obtained by the following equation.
So we can see that the distance between the two initial spaceships A and B is 3 x 108 m. This, of course, should be done if the invariant of light speed is guaranteed. Then it is a problem now. These two spaceships, at the same pace with the same propulsion, started at exactly the same time as they looked and finally reached relativistic speed. The picture below shows the situation.
 |
Figure 4. Two spaceships moving at constant distance |
In this picture, when spaceships A and B were moving, they fired at the same time from their point of view. And these signals arrived at their origin at 1'sec and 2'sec. If so, the spacing between the signals is 1 sec. We know that 1 sec and 1'sec are in the relationship below.
So what happens in the above oblique coordinate system? Since the speed of light is always constant, the following relation holds.
Therefore, if James on earth is watching this scene, the time interval for the lights to reach the origin is recognized as γto, and the distance between them is recognized as γlo. If so, the length will actually look like this:
If the velocity of these spacecraft is 0.866c, the gamma value is 2, so that the interval of the signal arrives at about 2 times larger than the first to observe from the earth. Since the speed of light is always constant, the distance between them must of course double. If so, this is not a contraction of length, but an expansion. You may think this is ridiculous, but this is what most scholars agree to be true.
Now let's apply this situation to the space-time diagram. If the spaceships accelerate more and more, the world line in the space-time diagram is as follows. 1)
 |
Figure 5. Accelerated spaceship's world-line |
An angle of 0° to the time axis indicates a stationary state, and a 45° angle indicates the world of light. However, if two spaceships accelerate side by side, it becomes as follows.
 |
| Figure 6. Two spaceships' world-line moving together |
When observing a moving partner, it should be expressed as a oblique coordinate system. So the distance between two spaceships should be as follows.
 |
| Figure 7. Comparison of proper length (AB) and moving length (PQ) |
Initially, the interval was (AB), but later (PQ). The following relationship holds between (AB) and (PQ).
Therefore, there is no Lorentz contraction between them. It is a rather common objection. Let's hear from many scholars about this.
The views of many scholars
The views of many scholars about the distance between the two spaces are largely consistent. Only one person has a very unusual view. Now, let's hear the story of many scholars.
"The distance between the two points expands.
As a result, the strings are broken."
 |
Vesselin Petkov |
The interval between two points PQ is L '= γL.
As a result, the existing Lorentz contraction does not solve the problem.
3. Michael Weiss, Don Koks
math.ucr.edu/home/baez/physics/Relativity/SR/BellSpaceships/spaceship_puzzle.html
5. Brcowell, Physics Forums Insights, www.physicsforums.com/insights/what-is-the-bell-spaceship-paradox-and-how-is-it-resolved/
"The interval between two points PQ is L '= γL."
4. Dewan and Beran (proponents of Bell's spacetime paradox) and John Bell (proliferators) en.wikipedia.org/wiki/Bell%27s_spaceship_paradox(2017.67): Dewan, Edmond M. (May 1963). "Stress Effect due to Lorentz Contraction". American Journal of Physics. 31 (5): 383-386.
 |
John Bell |
The spacing of two spatially separated points is L '= γL.
 |
Figure 8. Comparison of proper length and moving length |
The later length is obviously larger than the initial length.
L2>L1
As such, most scholars agree that (PQ) is γ times longer than (AB). I think there are very few scholars who deny this. If you accept the constancy of the speed of light and the principle of relativity, you must inevitably acknowledge that (PQ) = γ (AB).
Destruction of causality
If the arguments of these scholars are correct, then serious problems arise. There is a very important problem that can shake the roots of science. This is both a matter of the theory of relativity and a philosophical one. It is implicated in the question of how we should recognize nature.
Two spaceships are stationed at the space station. These two spaceships are relatively stationary and assume no movement. In the picture below, A and B are two relatively stationary spaceships. By the way, another spaceship C is passing by relative speed rapidly.
 |
| Figure 9. In terms of spaceships A and B, C passes at relativistic speed |
Now, let's take a look at the position of ship C. From spaceship C's point of view, A and B are moving fast backwards. If so, should it be cut off according to the position of many scholars? Or does it not have to be broken? Of course, if many scholars are right, the distance between spaceship A and B must be increased and the string broken.
 |
| Figure 10. The situation from the point of view of spaceship C |
If you look at spaceship C, it will look like Figure 10 above. Embarrassingly, the thin string is stretched, and both spaceship and space station appear to have contracted. Although not logically understood, it should be a strange situation as shown in Figure 10 above, as the mainstream scholars claim.
 |
It's amazing. You believe this! |
The reason for this is that main scholars have argued that 'rigid objects cause Lorentz contraction and space expands'. A thin string is a filled object, not an empty space. Nevertheless why do they say it is expanded? What happens if you connect A and B with a wire instead of a thin string? There are many questions, but we will try to develop the logic.
Now, let's go back to spaceships A and B. They were standing still without doing anything, and suddenly the string was broken. The only thing that has changed is that C is gone. When spaceship C passes, why should the string of A and B be cut off? From A and B's point of view, there is no reason to break the string.
From A and B's point of view, something very embarrassing happened. They did not provide any cause, but the string between the two spaceships was broken. From A and B's perspective, there was no cause. A and B ask.
There is no cause. But why does the result appear?
Can you give a logical answer to this question? Many scholars try to answer this question, but there is no good solution. If you insist that C's observation is the cause, this world we live in cannot exist. For this, see what I posted last week.
'If there is a cause, there is a result' This is the causality. There is no escape from causality in the macroscopic world we live in. This is an important idea that has supported the civilization of mankind for thousands of years. At least in relativity, things that are out of causality should not appear.
Following the conclusions of relativity, the causality will collapse, and protecting the causality will cause serious problems in relativity. Causality and relativity collide in front. In this situation, a brave warrior appears to rescue the causality. His name is Maudlin.
Argument for the Preservation of Causality
Most scholars who support relativity agree that distance between two points (PQ) is expanding. But one person does not agree here. In his book, "Philosophy of physics," Maudlin says:
Length contraction due to coordinate transformation
and physical length contraction should be distinguished.
and physical length contraction should be distinguished.
What does this mean? Most scholars have concluded that the string breaks after relationally and carefully interpreting the Minkowski space-time diagram. However, Maudlin argues that this cannot be applied to the length of reality because it is simply a conclusion from interpreting coordinates.
In other words, even though Minkowski's space-time diagram or coordinates may show a length expansion, it actually means that the length does not expand. To speak directly, it is just to deny the crucial conclusion of relativity.
 |
| Maudlin's book |
If the length changes according to the coordinates are different from the actual length contractions, what can we do with the theory of relativity? The theory of relativity is to explain the actual phenomena of nature. If we do not accept coordinate transformations, should we respect relativity?
Most main scholars admit that the distances between the PQ are expanding because the message given by the relativistic space-time diagram is too simple and obvious. This cannot be denied if anyone knows a little bit about the relativity space-time diagram. Maudlin would have known this.
.
.
.
Tearful reality.
Harmony of relativity theory and causality
I do not think there is a paradox in science, especially relativity. There may be contradictions in mathematics or logic, but in science or relativity, we can experiment to find out the truth.
Let's look at the issue of relativity or causality. Relativity is right, and causality is right. There is nothing wrong with the interpretation of the space-time diagram of relativity, and there is no error in the concept of expansion that main scholars claim. And there is no error in the concept of causality. But just remember one thing.
Lorentz length contraction is not a theory of relativity
Relativity is right, causality is right, but length contraction is not right. To be precise, the theory of relativity of length contraction must be replaced by the theory of relativity of length expansion. If so, relativity theory and causality do not contradict each other. The existing interpretation of Bell's paradox is as follows.
 |
Figure 11. The view of current relativity theory. The spacecraft must shrink and the spaces between spaceships must expand. Therefore, the string should be cut off. |
In Figure 11 above, the distance between (AB) is increased (PQ). But look at the ship. The ship has contract. The distance between the two spaceships has increased, and both spaceships have contracted. Therefore, the interpretation of Dewan and Beran is as follows.
 |
Figure 12. The process of breaking a string |
However, the interpretation of the length expansion is as follows.
Because other observers observe me, my causality does not collapse. The rules of relativity are right, and the causality is right. The main scholars of relativity argue that L '= γL is just as it is claimed, and the causality does not collapse as well. Finally, Relativity theory and causality have reconciled.
According to the current theory of relativity that supports length contraction, there are a lot of logically painful things happening. From the perspective of Earth's observers, it is also impossible to interpret the phenomenon of sea level reaching Muon. And there are many paradoxes in relativity theory. These paradoxes are all caused by the theory of length contraction. However, many of these paradoxes also disappear cleanly when interpreted as the theory of length expansion.
Today's topic is similar. If it is interpreted as a length expansion rather than a length contraction, it is solved very simply. Thank you for reading the long post.
Below is a post related to this article. It would be better if you read it together.
 |
Figure 13. Bell's spaceship paradox interpreted as a length expansion |
The distance between two spaceships increases, and both spaceships increase. This is shown in the space-time diagram below.
 |
Figure 14. Space-time diagram of spaceships that is interpreted as a length expansion |
The string is not cut off because everything is stretched together. From spacecraft C's point of view, the space station, spaceships A and B, and the string between the two spaceships are all seen moving backwards. They all increase in proportion to γ. It does not expand only partly, it all expands together. Therefore, nothing is subject to strain. Therefore, there is no break or explosion at all.
 |
| Figure 15. Observation scene of spaceship C, interpreted as a length expansion |
Because other observers observe me, my causality does not collapse. The rules of relativity are right, and the causality is right. The main scholars of relativity argue that L '= γL is just as it is claimed, and the causality does not collapse as well. Finally, Relativity theory and causality have reconciled.
 |
© DasWortgewand, Pixabay |
According to the current theory of relativity that supports length contraction, there are a lot of logically painful things happening. From the perspective of Earth's observers, it is also impossible to interpret the phenomenon of sea level reaching Muon. And there are many paradoxes in relativity theory. These paradoxes are all caused by the theory of length contraction. However, many of these paradoxes also disappear cleanly when interpreted as the theory of length expansion.
Today's topic is similar. If it is interpreted as a length expansion rather than a length contraction, it is solved very simply. Thank you for reading the long post.
Below is a post related to this article. It would be better if you read it together.
Comments
Post a Comment