## Changing Length - part 2

### Question

Is the length of train, when the speed drastically increases, getting any shorter when the observer O does not stand in centre of the circle?

### Purpose

The purpose of the question is to exclude any illusion, based on what we see or observe, when the concept of Length Contraction is used.

### Description of Thought Experiment

The Thought Experiment and the question is almost identical as for: Changing Length - part 1. The only difference is that the observer does not stand in the centre of the circle. For proper understanding let us assume that the observer is positioned left from the centre and that the length of the train is much smaller as in part 1 i.e. than half the circumference.
```            ---->
x
x         x 1              The observer is at O
x               x             At position 2 the train is
x                 x                the smallest.

x   O               x 2

x                 x
x               x
x         x 3
x
<----
```
The train moves in the direction of the arrow.
When the train is at 1 the train becomes smaller.
When the train is at 2 the train is the smallest.
When the train is at 3 the train becomes larger.

In order to make this visible, a simulation in the form of a program in Quick Basic, is supplied.
To get a copy select:TRAIN.BAS

The answer is the same as for part one: the physical length of the train will not change. On the other hand there is a big difference if you look to the length of the train that you see; that length will change.
There are two effects that cause this.

1. First when the train moves to the right, the distance with the observer increases and the observed length of the train becomes smaller. This effect is independent of the speed of the train. When the train stops the observed length stays smaller.

2. The reverse is true when the train approaches the observer; the train becomes longer. When the train stops the observed length stays longer.

3. Second, assume at a certain moment t0 that the back of the train is a distance l1 away from the observer. The observer will see the back of the train at that position a time t1 = l1/c later as t0. c is the speed of light.
At that same moment t0 the front of the train is a distance l2 away from the observer. The observer will see the front of the train at that position a time t2 = l2/c later as t0. t2 is later as t1 because the train moves away.

What sees the observer at t1?

At t1 the observer will see the back of the train a distance l1 away.
At that same moment t1, the observer will not see the front of the train a distance l2 away, because light from that position will reach the observer at t2 i.e. later as t1.
At t1 the observer will see the front of the train. However not from a distance l2 away, but from a slightly shorter distance. As a consequence the train seems even shorter.

4. The exact opposite we see when the train is approaching the observer: The train seems longer. Assume at a certain moment t0 that the front of the train is a distance l1 away from the observer. The observer will see the front of the train at that position a time t1 = l1/c later as t0. c is the speed of light.
At that same moment t0 the back of the train is a distance l2 away from the observer. The observer will see the back of the train at that position a time t2 = l2/c later as t0. t2 is later as t1 because the train approaches.

What sees the observer at t1?

At t1 the observer will see the front of the train a distance l1 away.
At that same moment t1, the observer will not see the back of the train a distance l2 away, because light from that position will reach the observer at t2 i.e. later as t1.
At t1 the observer will see the back of the train. However not from a distance l2 away, but from a slightly further away distance. As a consequence the train seems longer.

### Feedback

None

Created: 8 september 1997.