Length contraction thought experiment, figures 12, 13, 14.
We put a flatbed railroad wagon in a railroad line( figure 12).
We can have a closed wagon instead of a flatbed wagon. In the figure 12 we see a flatbed wagon.
Each pair of wheels of the
wagon is affixed to a straight solid axle, and so the wheels of
each axle rotate in unison.
Also, the two pairs of
wheels are connected by a coupling rod/side rod, like the one
that the old locomotives have( figure 12 ).
We put the coupling rod
not because we want to
transfer power from the one axle to the other,
but because we want all
the wheels of the wagon to rotate in unison, and
the coupling rod serves that purpose.
Instead
of the coupling rod, we can create other systems which will have the
same result.
We put a coupling rod only on the wheels on the one side of the wagon.
On the wheels on the other side of the wagon, we affix a spike on each wheel.
We put the spikes in such position, so that while the wagon is moving and the wheels are rotating, the two spikes are hitting the ground simultaneously( figure 12 ).
The wheels of the wagon rotate in unison, and so the two spikes will always hitting the ground simultaneously.
As
you can understand, the distance between the two spikes is always the
same with the wheelbase of the wagon.
But
the spikes are not hitting on the ground.
Next to the railroad
line we put a line of small white tiles, and so the spikes are
hitting on the tiles and leaving marks on
them( figure 12).
Let's
say that each tile is 1 square centimetre, and when
a spike is hitting the tiles, it destroys
about a dozen of them.
The
spikes are made of a very hard material, and the tiles are made of a
very soft material.
Each
tile is having a number printed on its surface so we can see which
tiles are destroyed.
When
i say that the two spikes will be hitting the tiles simultaneously, this has
nothing to do with what someone will see, but it has to do with the
way that the whole system works.
It
has to do with the position that we have put the spikes, and the fact
that the wheels rotate in unison,
which means that the fact that the two spikes will hit the tiles simultaneously has nothing to do with
the ''relativity of simultaneity''.
which means that the fact that the two spikes will hit the tiles simultaneously has nothing to do with
the ''relativity of simultaneity''.
So,
there is no need to look towards the two spikes and see what they are
doing, because we understand that they are always hitting the tiles
simultaneously, regardless of what someone may see.
The
two spikes are not having the same shape, and so they are leaving
different marks on the line of the tiles,and so we can distinguish
where each wheel was, meaning where each axle was(figure 12).
We
don't want the spikes to leave a mark on the tiles in every rotation
of the wheels.
If
the spikes hitting the tiles in every rotation of the wheels, the
marks on the tiles will be mixed and we were not be able to find the
distance between the axles of the wagon, and additionally, at some
speeds maybe the two spikes will hit on the same place.
So on
each wheel we create a system, built-in to the wheel, which counts the rotations of the wheel and rotates the
spike, and most of the time keeps the spikes facing inwards
so they are not always facing outwards and they are not always
hitting the tiles.
For
example, in 9 rotations of the wheels the system is putting the
spikes facing inwards, and so the spikes are not hitting the tiles,
and in the tenth rotation the system will rotate the spikes so
they are facing outwards, and so they are hitting on the line of
tiles.
Or,
another example, in 99 rotations of the wheels the system is putting
the spikes facing inwards, and in the hundredth rotation the spikes
will be rotated and they are facing outwards.
Of
course, the systems on the two wheels are counting the same rotations,
until they rotate the spikes.
Next
to the railroad line, and next to the line of tiles, we have put a line of wooden poles.
When
the wagon is not on the move relative to the ground, the distance
between the wooden poles is the same with the wheelbase of the wagon.
Also,
a human is standing on the ground and another human is on the
wagon.
We start the experiment.
The wagon is starting to move and the spikes are hitting repeatedly the tiles.
The spikes are leaving marks on the line of tiles.
By looking at the marks on the tiles, we can see which spike made each mark because each spike makes different mark, meaning that we can see where each wheel was.
So we can see where the first wheel was and where the last wheel was, meaning where the two axles of the wagon were when the spikes hitting the tiles.
Therefore, we can measure the distance between the two different marks, that the two spikes have made on the tiles, and we see if the wheelbase of the wagon is changed when the wagon is on the move.
Question: When the wagon is moving at 10 km/hour relative to the ground, which will be the distance between the two marks that the spikes will made on the tiles????
Answer: The distance between the marks on the tiles will be the same with the wheelbase of the wagon, and the same with the distance between the wooden poles.
The spikes are hitting the tiles again and again, and they will stop only when the wagon will stop moving.
The speed of the wagon relative to the ground continuously increases, and the spikes repeatedly hitting the tiles.
Question:
While the relative speed increases, the distance between the marks on the tiles will be different?????
When the speed of the wagon relative to the ground is close to the speed of light, which will be the distance between the two marks that the two spikes will made on the tiles???????
According to the theory of relativity and the belief of the scientific community, the reality on the frame of reference of the human on the ground is that the wagon is really contracted, and the reality on the frame of reference of the human on the wagon is that the ground is really contracted.
Answer to the question, according to the human on the ground:
If the reality for the human on the ground is that the wagon is really contracted, that means that the distance between the axles of the wagon(wheelbase) is smaller than the distance between the wooden poles, and that means that the distance between the two marks that the spikes will made on the tiles, will be smaller than the distance between the wooden poles.
Answer to the question, according to the human on the wagon:
The reality for the human on the wagon is that the ground is really contracted, and that means that the distance between the wooden poles is contracted, and that means that the distance between the wooden poles is smaller than the distance between the axles of the wagon(wheelbase), and that means that the distance between the two marks that the spikes will made on the tiles, will be larger than the distance between the wooden poles.
The reality for the human on the wagon is that the ground is really contracted, and that means that the distance between the wooden poles is contracted, and that means that the distance between the wooden poles is smaller than the distance between the axles of the wagon(wheelbase), and that means that the distance between the two marks that the spikes will made on the tiles, will be larger than the distance between the wooden poles.
We see that, according to the theory of relativity, we have two different expected realities!!!!!!!!!
But of course, the tiles that are having contact with the spikes, are specific!!!!!!
Meaning that the real answer to the question, is only one!!!!!!!
So, which of the two is happening??????
Each tile has a specific number.
When a spike hits the tiles, it destroys about a dozen of them.
So, this is the question that the human on the wagon and the human on the ground have to answer:
The
tiles with which number, are the ones that are destroyed by the
spikes???????
The
answer to that is one!!!!!
There cannot be two acceptable answers about that!!!!The human on the ground and the human on the wagon, will give the same answer because each spike destroys specific tiles, which anyone can see, which means that the comparison between the marks and the wooden poles must be the same for the two humans, which leads to the conclusion that the length contraction cannot be a reciprocal effect!!!!!!
The
spikes are having contact with specific tiles.
The
spikes are destroying tiles with specific number.
This is ONE reality, not two!!!!!!
This is one reality not two, at any relative speed!!!!!!!!!!
Therefore, the ''length contraction'' cannot be real and reciprocal.
The spikes are destroying specific tiles.
And of course, when a spike has contact with the tiles and destroys them, anyone can see which are those tiles, regardless of his position or his motion!!!!!
All the humans, regardless of their positions or their motions, will give the same answer, because the answer to which tiles
each spike destroys, is ONE!!!!!
each spike destroys, is ONE!!!!!
And even if someone sees, that the shape of the wagon or the ground, is ''contracted'' or ''expanded'', he will also give the same answer.
And he will understand that the ''contraction'' or the ''expansion'' that he sees, is not the reality.
Where
each spike leaves its marks???
When
we answer that, we have really answer where each wheel was at a given
moment!!!
Because
each spike is where each wheel is.
The distance between the spikes
is always the same with the wheelbase of the wagon.
When the spikes are hitting the tiles, are exactly below the centre of each wheel.
Each mark on the tiles, has been made
exactly next to the point of contact between wheel and railroad,
at a given moment.
And
so, each mark on the tiles, is showing to us exactly where the centre
of each wheel was at a given moment, meaning that we see the distance
between the two axles at a given moment,
because the spikes are hitting the tiles simultaneously.
Therefore, the distance between
the marks, is the distance between the axles of the wagon during the
relative motion.
And so we can see if it is really
contracted!!!!!!
With
this experiment, we compare by direct contact, the wagon and the
ground, at any relative speed.
The
spikes are parts of the wagon.
The
spikes again and again are having contact with the tiles, and that
means that repeatedly we compare the wagon with the ground and the
wooden poles.
When
the spikes are hitting the tiles, we have direct comparison by
contact, between the wagon and the ground!!!!!
While the wagon is on the
move at different speeds relative to the ground, we compare the marks
which the spikes are leaving on the tiles at those different speeds.
And
of course, we also compare the distance between the marks with the
distance between the wooden poles.
In
order to understand better the problem, let's see the scenario in the
figure 13(
in the image we don't see the wagon).
The
figure 13
shows which will be the expected reality
according to the two humans(the one on the wagon and the one on the ground), if the wagon is abreast with two wooden poles( like it is on the figure 12) when the spikes are hitting the tiles, and the relative speed is close to the speed of light.
In the figure 13 we see the two different groups of tiles that are going to be destroyed, according to the two humans, if we accept that the length contraction is a real and reciprocal effect.
The reality for the human on the wagon is that the distance between the wooden poles is
smaller than the wheelbase of the wagon, but the human on the
ground says the opposite.
The reality for the human on the ground is that the wheelbase of the wagon is smaller
than the distance between the wooden poles.
The human on the ground says that the spikes are going to hit the tiles between the two wooden poles, but the human on the wagon says that the spikes are going to hit on tiles which are not between the two wooden poles(figure 13).
This means that the two humans will expect that different tiles are going to be destroyed!!!!!!!
The human on the ground and the human on the wagon, will point out different groups of tiles(figure 13), as the ones that they will be destroyed by the spikes!!!!!!
The human on the ground and the human on the wagon, will point out different groups of tiles(figure 13), as the ones that they will be destroyed by the spikes!!!!!!
But the tiles that are going to be destroyed by the spikes are specific!!!!!!!!!!!!!!!!!!
To better understand what i'm saying, let's assume that the line of
tiles is not continuous, and at some places we did not have put tiles.
For example let's say that in the figure 13, we have put tiles only between the two wooden poles that you see on the image.
Therefore, if the human on the wagon says that the distance between the wooden poles is smaller than the distance between the axles of the wagon, he must say that the spikes will not have contact with tiles at all!!!!!!!!!!
Because, according to the human on the wagon, the spikes are not going to hit between the two wooden poles, and at the place that the spikes are going to hit, meaning the points A & B(figure 13), there are no tiles.!!!!!!!!
But the human on the ground says the opposite!!!!!!!
The human on the ground says that the spikes will be having contact with tiles, because according to him, they are going to hit between the two wooden poles(figure 13)!!!!!!!
But the reality is only ONE!!!!!!!!!!
Which of the two will happen???????
The spikes are going to hit on tiles or not?????????
Someone
may think that the circumference
or the radius of the wheels will be different due to their extremely
fast rotation( i'm talking about the Ehrenfest paradox).
If the circumference or the
radius of the wheels is different,
larger or smaller, ''contracted'' or
''expanded'', this will not make any difference to the
assumptions of the experiment, because the change
on the size of the wheels will not change the wheelbase of the wagon,
and there will be no change on the distance between the two spikes.
Like
if we put larger or smaller wheels on the wagon, the wheelbase
will remain the same, and the distance between the two spikes
on the wheels will always remain the same.
The
distance between the two spikes is always the same with the wheelbase
of the wagon, regardless of the size of the wheels.
We
can create a different version of the thought experiment.
Basically
it is a different version of the spikes.
In
that different version, the spikes are not hitting the tiles.
In
that different version, the spikes are sprayers that are
spraying paint.
While
the wheel rotates, when a sprayer/spike is spraying towards the
tiles, is leaving marks on their surface.
The
two sprayers will have paint with a different color, in order to
distinguish which wheel made each mark.
We
don't want the sprayers to leave marks on the tiles in every rotation
of the wheels.
So
we can create a system on each wheel, which arranges so that, for
example, in 9 rotations of the wheels the sprayers will not spraying
paint, and they will spray paint only in the tenth rotation.
On
this version there is no need for the sprayers/spikes to rotate and
facing inwards, because the sprayers will not spraying paint all the
time, and so they will always facing outwards.
We
can create another version of the thought experiment
(figure 14).
On this version the difference
is that the wheels are very large.
On this version, the
circumference of the wheels is larger than the wheelbase of the
wagon( figure 14),
and the spikes are always facing outwards.
If
the circumference of the wheels is larger than the wheelbase, there
is no need to have rotatable spikes, because there is no possibility
for the two spikes to hit at the same place.
The
spikes are leaving marks on the tiles in every rotation of the
wheels, but there is no problem with that because the marks on the
tiles will not be mixed.
The spikes
are leaving different marks on the tiles, and so we can see where
each wheel was and therefore we can see the wheelbase of the
wagon.
When the
wagon is not on the move relative to the ground, the distance between
the wooden poles is the same with the wheelbase of the wagon, and the
same with the distance between the two spikes.
When
the wagon is moving at a speed close to the speed of light relative
to the ground, the distance between the two marks( by the two spikes)
in the line of tiles, will be larger or smaller than the distance
between the wooden poles??????????
Probably this version is better, because there is no need to have rotatable spikes!!!!
{In the figure 14 we see a closed wagon and not a
flatbed.}
