Length contraction thought experiment, figures 1, 2, 3.
We create the following systems and constructions on the surface of the Earth.
We construct a system which looks much like a belt conveyor system, but the belt-like material goes only one way and does not return back.
We have a very long line of rollers and we put an extremely long white belt-like material up on the rollers(figure 1).
We build a construction of steel beams, and we arrange so that the line of rollers and the white belt-like material are passing under and through this construction, like you see on the figure 1.
We want to make the white belt-like material to move at a speed close to the speed of light relative to the construction and the Earth, and so we must find a way to do that.
But we can find many ways to do that.
For example some of the rollers can be powered and so they can move the belt-like material, or we can attach the one end of the belt-like material to a car or a wagon or a plane or a spaceship, and it can pull the belt-like material.
{ Of course, the white belt-like material must be extremely long, but this is only a thought experiment, and like all thought experiments, it was created in order to make a point.
But of course, if we want we can really create a belt-like material which will have many thousands or even millions kilometres length.}
In the construction we attach two identical green mechanisms, like you see in the figure 1.
The two green mechanisms are having a red wheel which they can move a few centimetres down and up at very high speed(figure 1).
When the two red wheels are having contact with the white belt-like material, they are leaving yellow marks on its surface(figure 1).
The two green mechanisms are not positioned in line, and so the marks that the red wheels are leaving on the white surface are not collide with each other.
The red wheels are having a few centimetres distance from the white surface when they are up.
Normally the two red wheels are up, and both red wheels are having the same distance from the white belt-like material.
The two identical green mechanisms are electromechanical high precision mechanisms.
Each of the two green mechanisms has an atomic clock and a computer which controls the operation of the mechanism.
Each atomic clock displays the time in digital-style.
We have the two atomic clocks(one on each mechanism) in our possession for many months, we have made various tests at them, and we have seen that they always have totally identical indications.
A simple way to synchronize the two atomic clocks is if a human, with its equipment that help him for the synchronization, is standing exactly between the two clocks.
Due to the fact that the two atomic clocks are at the same distance from the human, if the human sees the same time on the two clocks when he is looking at them, this means that the clocks actually display the same time.
The two atomic clocks are having totally identical ticking rate, and they will always keep having identical ticking rates because they are always stationary relative to each other.
Due to the fact that the two atomic clocks are at the same distance from the human, if the human sees the same time on the two clocks when he is looking at them, this means that the clocks actually display the same time.
The two atomic clocks are having totally identical ticking rate, and they will always keep having identical ticking rates because they are always stationary relative to each other.
We are programing the computer of each mechanism, to move down or up the red wheel of the mechanism when the atomic clock displays a specific indication of time.
We make the same programing on the computers of the two green mechanisms, and this means that when the two green mechanisms are moving the two red wheels down or up, their atomic clocks are having exactly the same indications.
And that means that the two red wheels are moving simultaneously down and up.
For example, let's say that we have programmed the computers on the two green mechanisms, and they will arrange so that the two mechanisms will move the two red wheels down, when the two atomic clocks are having the following indications:
3 hours 25 minutes 10 seconds and 0,4050010020 seconds.
Both mechanisms will move the red wheel down when their clocks are having this indication, and that means that the two red wheels will move simultaneously, and that means that the two red wheels will be touching the white belt-like material simultaneously.
So we are sure that the two red wheels are touching and leaving the surface of the belt-like material simultaneously.
We have tested the two green mechanisms many times and we have made the necessary adjustments at them, in order to be sure that they are working completely the same, and with the technology that we have nowadays we can be extremely precise about that.
The fact that the two red wheels are moving simultaneously down and up has nothing to do with what someone may see, meaning that has nothing to do with the ''relativity of simultaneity, but it has to do with the fact that the two red wheels are moving according to the indications of the two atomic clocks!!!!!
Because of the fact that the two red wheels on the two mechanisms are moving down and up according to the indications of the two atomic clocks, and because the two atomic clocks having always the same indications, we have no doubt about the fact that the two red wheels are moving simultaneously, regardless of what someone may see, and regardless if humans are present when the experiment is taking place.
The fact that the two red wheels are moving simultaneously down and up has nothing to do with what someone may see, meaning that has nothing to do with the ''relativity of simultaneity, but it has to do with the fact that the two red wheels are moving according to the indications of the two atomic clocks!!!!!
Because of the fact that the two red wheels on the two mechanisms are moving down and up according to the indications of the two atomic clocks, and because the two atomic clocks having always the same indications, we have no doubt about the fact that the two red wheels are moving simultaneously, regardless of what someone may see, and regardless if humans are present when the experiment is taking place.
We measure the distance between the two red wheels, and let's say that it is 10 metres.
We put the white belt-like material in motion, and it reaches a speed close to the speed of light relative to the construction.
The two green mechanisms are moving simultaneously the two red wheels down, according to the programs of their computers and the indications of their atomic clocks, the two red wheels are touching the white belt-like material and start leaving yellow marks on its surface, and then the two mechanisms are moving simultaneously the two red wheels up.
After that, we stop the motion of the belt-like material.
( Or we can repeat the same procedure many times in different speeds, in order to be sure about the results.)
The point A is the starting or ending point of the mark that the one wheel is leaving, and the point B is the starting or ending point of the mark that the other wheel is leaving(figure 2).
We go to measure the distance between the two yellow marks, meaning between the points A & B, which the two red wheels are leaving on the surface of the belt-like material( figure 2).
We measure which is the distance between the two yellow marks( meaning between points A & B) when the two red wheels touching the surface(where the two yellow marks started), and when the two red wheels are leaving the surface(where the two yellow marks stopped).
What we will find????????
Which we expect to be the reality on the construction's frame of reference????
According to the theory of relativity, on the construction's frame of reference, the belt-like material would really be contracted during this relative motion.
If the belt-like material was really contracted when it was in a relative motion with the construction and the two red wheels were having contact with its surface, when the motion of the belt-like material is stopped, the distance that we will measure between the two
marks(between points A & B) on the surface of the belt-like material must be bigger than the distance between the two red wheels.
marks(between points A & B) on the surface of the belt-like material must be bigger than the distance between the two red wheels.
Because the marks were made when the belt-like material and the construction were in relative motion with each other.
And the reality on the construction's frame of reference is that the belt-like material was really contracted when the marks were made, meaning during the relative motion.
So when the relative motion stops, and the belt-like material goes back to ''not being contracted'', at that moment, the distance between the points A & B on the surface of the belt-like material, will be bigger than the distance between the red wheels, because the marks were made when the belt-lile material was ''contracted''.
When the belt-like material, from the state of not moving goes to the state of moving relative to the construction, we say that it ''contracts''.
Instead of saying that, when the belt-like material stops moving will go back to ''not being contracted'', we can say that it will ''expand'' and it will go to its previous condition.
So when the belt-like material, from the state of moving relative to the construction goes back to the state of not moving, we can say that it will ''expand''.
The marks were made when the belt-like material was on the move relative to the construction, and so when the belt-like material ''expands'' because the relative motion is stopped, also the distance between the marks will expand.
During the relative motion, the distance between the marks( point A & point B) on the belt-like material was the same with the distance between the red wheels of the construction(figures 2 & 3).
According to the humans on the frame of reference of the construction, when the red wheels will move up and stop leaving marks, and while the relative motion between the construction and the belt-like material continues, at that time, the distance between the marks( point A & point B) on the belt-like material will be the same with the distance between the red wheels of the construction(figure 3).
But at that time the belt-like material was contracted.
So when the belt-like material ''expands'' because the relative motion is stopped, the distance between the point A & point B will also ''expand'', and it will be larger than the distance between the red wheels of the construction.
Which will be the reality on the reference frame of the belt-like material, according to the theory of relativity?????
According to the theory of relativity and the belief of the scientific community, the reality on the frame of reference of the belt-like material is that the construction is moving, and that the construction is actually contracted.
If we say that the reality for the belt-like material is that the construction was really contracted during the relative motion, we end up with a different result of the experiment!!!!!!!
When the marks were made on the surface of the belt-like material, the belt-like material and the construction were in relative motion with each other.
When the relative motion stops, if something was ''contracted'' will go back to not being ''contracted'' or in other words it will ''expand''.
On the frame of the reference of the belt-like material, the reality is that the construction was really contracted.
This means that when the marks were made on the surface of the belt-like material, the construction was really contracted.
When the relative motion between the construction and the belt-like material is stopped, and the construction goes back to not being contracted, at that moment, the distance between the red wheels of the construction will be bigger than the distance between the
marks ( between points A & B) on the belt-like material, because the marks were made when the construction was contracted.
marks ( between points A & B) on the belt-like material, because the marks were made when the construction was contracted.
On the frame of reference of the belt-like material, the construction is on the move and it is contracted.
When the construction, from the state of not moving goes to the state of moving relative to the belt-like material, we say that it ''contracts''.
Instead of saying that the construction will go back to ''not being contracted'' when the relative motion stops, we can say
that it will ''expand'' and it will go to its previous condition.
that it will ''expand'' and it will go to its previous condition.
So when the construction , from the state of moving relative to the belt-like material goes back to the state of not moving, we can say that it will ''expand''.
The marks were made when the construction was on the move relative to the belt-like material, and so when the construction expands because the relative motion is stopped, also the distance between the red wheels of the construction will ''expand'', but the distance between the marks on the belt-like material will remain the same.
During the relative motion, the distance between the marks( point A & point B) on the belt-like material was the same with the distance between the red wheels of the construction(figures 2 & 3).
According to the humans on the frame of reference of the belt-like material, when the red wheels will move up and stop leaving marks, and while the relative motion between the construction and the belt-like material continues, at that time, the distance between the marks( point A & point B) on the belt-like material will be the same with the distance between the red wheels of the construction(figure 3).
But at that time, according to the reality on the frame of reference of the belt-like material, the construction was contracted.
But at that time, according to the reality on the frame of reference of the belt-like material, the construction was contracted.
So when the construction ''expands'' because the relative motion is stopped, at that time, the distance between the point A & point B will be smaller than the distance between the red wheels of the construction.
So, if we say that the length contraction is a reciprocal effect, we end up with two different expected results!!!!!!!!!!!
According to the reality on the construction's frame of reference, when the relative motion between the belt-like material and the construction stops, the distance between the marks( between points A & B) on the white belt-like material, will be larger than the distance between the two red wheels of the construction.
But the reality on the frame of reference of the the belt-like material is that, when the relative motion between the belt-like material and the construction stops, the distance between the marks( between points A & B) on the white belt-like material, will be smaller than the distance between the two red wheels of the construction.
Which of the two is going to happen?????????
The humans in both frames, on the reference frame of the construction and also on the reference frame of the belt-like material, will agree that during the relative motion, the distance between the marks(points A & B) on the belt-like material will be the same with the distance between the red wheels on the construction(figures 2 & 3).
But the human in the two frames will disagree on what will happen when the relative motion stops!!!!!!
The humans on the reference frame of the construction will say that the belt-like material will go back to not being contracted, meaning it will expand, and the humans on the reference frame of the belt-like material will say that the construction will go back to not being contracted, meaning it will expand.
This is leading to contradicted expected realities!!!!!!!!
When i say that the two red wheels will touch the white surface simultaneously, this is not a case where someone will see that the two wheels will be touching the white belt-like material simultaneously, but this is case where we know that the two red wheels are touching the belt-like material simultaneously, regardless of what we see, and this has to do with the way that the two green mechanisms are working, and the fact that the two red wheels are moving down and up according to the indications of the two atomic clocks.
If someone is looking towards the two red wheels, maybe will see that they are not touching the belt-like material simultaneously, because what he will see depends on his position.
But the human understands that what he sees is not what is really happening, and he understands that the two red wheels are actually touching the white belt-like material simultaneously.
The facts are very simple:
- There is relative motion between the belt-like material and the construction.
- The two red wheels touching the surface and leaving marks on the belt-like material during this relative motion.
So, which distance we will measure between the marks in the points A & B, when the belt-like material and the construction stopped being in relative motion with each other??????
We have relative motion and then the relative motion stops.
We say that we can't really tell who is moving and who stops moving.
Instead of saying that the belt-like material was moving we can say that the construction was moving.
The only thing that matters is that we have relative motion and then the relative motion stops.
We have relative motion between the construction and the belt-like material, we have contact between them because the wheels touching the surface, we have marks on the surface of the belt-like material, and then the relative motion stops.
At first, the two participants(construction & belt-like material) on this experiment were not in relative motion with each other.
At some point they go to a different frame of reference due to their relative motion.
And when the relative motion is stopped, everything is again on the same frame of reference.
The relative motion could stop in a different way.
Instead of the belt-like material to stop moving, we can arrange so that the construction will move at the same speed and towards the same direction, that the belt-like material is moving relative to the Earth.
It is the same thing, because the participants on the experiment will be again in the state of not moving relative to each other, and the results of the experiment will be the same.
We can create a little different version of this thought experiment.
Instead of having the two green mechanisms that are moving the red wheels down and up, we can have two mechanisms that are spraying paint towards the white belt-like material.
The computers on the two mechanisms will arrange so that the mechanisms will start spraying and stop spraying simultaneously, according to the time that the two atomic clocks display, and the paint will be sprayed on the white belt-like material.
Probably this version is better.
You can choose which version do you like, but in both versions the results will be the same.
We can also create another version of the thought experiment, which will also have the same contradicting assumptions.
We can put the two green mechanisms at the front and at the back end of a railroad wagon.
Inside the railroad path, we will put for a long distance a white material.
When the red wheels of the green mechanisms are having contact with the white material, they leave yellow marks on its surface.
The wagon will be moving at a speed close to the speed of light relative to the ground when the two red wheels will have contact with the white material.
The two atomic clocks that the green mechanisms have, will always display the same time because they are always on the same frame of reference, because they are always on the same wagon.
While the wagon is moving, the green mechanisms will move the two red wheels simultaneously down and up.
The humans that are inside the wagon, will be expecting the opposite result than the result that the humans on the ground(not moving relative to the ground) will be expecting.