Thought experiment 1 describes what you see when a train moves in a circle.
Consider your self in a great round hall or arena.
In front of the wall their is a rail track.
At the rail stands a very long train.
The length of the train is half the circumference.
The picture more or less looks like:
L1
---->
TTF......
TTT ...
TT ..
T .
T .
T .
T O .
T .
T .
T .
TT ..
TTT ...
TTTTTB...
L2
The Observer (O) is in the centre.
The train is identified with the letter T.
F is Front of the train. B is Back of the train.
The rail track is identified with dots.
The movement of the train is in the direction of the arrow i.e. clockwise.
Near the rail track there are also two lamps. From the observer point of view they are behind the rail track. The two lamps are identified as L1 and L2
The "sketch" shows that the front of the train is behind the line L1 to O. This means from the Observer point of view the lamp L1 is ON.
The "sketch" also shows that the back of the train crosses the line from O to L2. That means from the Observer point of view the lamp L2 is OFF.
From the observer point of view the state of the lamps L1,L2 is: ON, OFF
Now consider what happens when the train start to move.
When the train starts to move the lamp L1, near the front of the train, will
stay on, until the front of the train crosses the line from L1 to O,
then the lamp L1 will go OFF.
At the same time, because the length of the train is half the circumference
the back of the train will cross the line from L2 to O and the lamp
L2 near the rear of the train, from the observer point of view will go ON.
From the observer point of view the state of the lamps L1,L2 will change from ON, OFF to: OFF, ON
The front of the train now enters the right hand side of the circle.
The lamps will stay in the same position until the train comes close to L2. When the train moves between the lamp L2 and the observer the lamp L2 will go OFF and at the same time L1 will go ON.
From the observer point of view the state of the lamps L1,L2 is: ON, OFF and we are back to the initial state.
When the train continues to move we get:
The state of the lamps becomes: OFF, ON
and later: ON, OFF etc.
Now the train starts to move faster.
When both lamps are OFF means that the length of the train is becoming longer
and is longer than half the circumference.
This will not be the case.
When both lamps are ON means that the length of the train is becoming shorter and is shorter than half the circumference.
It is possible that both lamps are ON. This is the case when the train starts to loose mass and becomes smaller as a result of heat and friction.
However when the train stops this reduction in length will be permanent.
The main objective of the simulation is to show what an observer sees the train when the speed of the train increases and decreases
In the simulation the length of the train is not half the circumference but smaller. Beginning and end of the train are identified with 2 red dots.
When the train starts to move the two red dots move back i.e. lag behind. This comes because it takes a certain time t for the light to move from the front of the train to the eye. In that period the train has moved a certain distance.
The two dots lag behind the same distance. This is because the train runs in a circle and the observer is in the centre. The distance from the front of the train to the observer is equal to the distance from the back of the train to the observer.
In thought experiment 2 we will see what happens when this is not the case
The simulation only consists of one test: test 1
On the train are two red circles. One at the beginning of the train and one at the end of the train. They represent the virtual position.
In order to move the train use the UP and DOWN arrows. The UP arrow is used to increase the speed of the train. The DOWN arrow is used to decrease the speed of the train.
The length of the train is shown in the middle.
The speed of light c = 30 is shown in the top right corner.
The speed v of the train is shown in the top left corner. Observe what happens when the speed reaches the speed of light.
The question is: is this according to reality ?
Return back to CHAPTER3.TXT
From the Parameter Selection Display the following parameters can be changed:
0 = Select test display
1 = Set standard parameters.
2 = Screen mode. Valid values are 7,8,9 and 12. Standard value = 9
3 = Wait time in second. Physical wait time between each simulation
cycle. Standard value = 0.01
4 = Speed of light. Standard value = 30
5 = Delta time in seconds between each calculation cycle.
Standard value is 0.1
The angle alpha between the front of the train and the red dot is calculated as follows:
The radius of the circle is r. Speed of light is c The time it takes from the front of the train to reach the observer is :
r
t = -
c
In that time the train with speed v will move a distance = v * t
The angle alpha between the actual position, the observer and the
virtual position is then equal to:
v * r * 360 v * 180
alpha = -------------- = ------- degrees
c * 2 * pi * r c * pi
This is true for both the front and the back of the train. (any point of the train)