## Changing Length - Introduction

This page services as an introduction to explain the concept of Length contraction.
• the issue that the length of a rod changes as a function of the speed of the rod.
• the issue that any length changes ie space.
Length contraction is discussed in five different pages:
1. Changing Length part 1 The train experiment. Observer in the centre
2. Changing Length part 2 The train experiment. Observer not in the centre.
3. Changing Length part 3 Is it physical?
4. Changing Length part 4 To push or to pull
5. Is length contraction visible ? Terrell Rotation

Also study the following two examples Example 1 and Example 2 which give more detail about the mathematics involved.

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### Changing Length two Experiments

If you want to study Length contraction the first step is to demonstrate that length contraction actual exists. In order to do that we perform two experiments.

In both experiments we use a train which has a certain length l. We study the train under two conditions: At rest and not at rest. In the last case, when the train moves, we should find that the length becomes shorter.

The following sketch shows the experiment at rest.
 ``` a-----------o-----------b -------A-----------O-----------B------- Track O = Observer ab = Train ```

The sketch shows a Track, an observer O near the Track and the train ab at rest.
The point o is the corresponding point of the position of the observer at the train.
The points A,B are the corresponding points of the points a,b on the track.
The observer stands in the middle of the train. That means the distance ao = ob or AO = OB = 0.5*l

In order to calculate the position of the observer O

• We can use a rod of exactly half the length of the train l
• A different way to establish that O stands in the middle of points A and B is to use a light signals and two mirrors at the points A and B (or a and b).
O sends out a light signal to the left and to the right towards those two mirrors. O stands in the middle when O recieves the two reflected signals simultaneous.

In the first experiment in order to demonstrate length contraction we place the train left of point A and the train moves towards the right. At the points a and b on the train we place two lights. When a meets A we send a light signal. The same when the point b meets B.
Length contraction is demonstrated when the observer O does not see the two lights simultaneous.

The second experiment is almost identical except that at the points a and b there are no lights but mirrors. O sends out a light signal to the left and to the right. The starting position of the train is towards the left of point A and the train moves towards the right. The experiment is done in such a way that exactly when a meets A also the signal from the observer O is received.
Again Length contraction is demonstrated when the observer O does not see the two lights simultaneous.

The following sketch shows the situation when no length contraction is involved.
The two experiments are combined.
 ``` a b / / / / / . / / . . / / . . / /. . / . . / . ./ / . . / / . . / ----a---A-------O---b---B--- ```
Dots represent the light signals. Time runs vertical
The train moves from left to right.
The second experiment starts that O issues two light signals. The two signals are reflected when they meet either the lines aa or bb. Those two points coincide with the points A and B. The reflected signals meet simultaneous at O. No length contraction is involved.

The first experiment starts when the front of the train (point b) reaches point B and when the back of the train (point a) reaches point A. At those moments two light signals are generated. Those two signals meet simultaneous at O.

The sketch shows that both experiments when no length contraction is involved give the same result.

The following sketch shows the situation when length contraction is involved. The two experiments are combined.
 ``` a-------------b / / / . / / . / / . . / / . . / / . . /. / . . / / . . / / . . / . ./ ----a---A-------O-b-----B--- ```
Dots represent the light signals. Time runs vertical
The train moves from left to right.
The second experiment starts that O issues two light signals. The two signals are reflected when they meet either the lines aa or bb. The reflected signals do not meet simultaneous at O. The signal via the front of the train is observed first. Length contraction is involved.

The first experiment starts when the front of the train (point b) reaches point B and when the back of the train (point a) reaches point A. At those moments two light signals are generated. Those two signals do not meet simultaneous at O. The signal via the front of the train is observed the last.

The sketch shows that both experiments when length contraction is involved give different results.

### Changing Length - the speed v

When you want to study length contraction and more specific the Lorentz Transformations the speed of the object in your rest frame is very important.
How do you measure this speed? In practice how do you take care, considering the train in the previous experiment, that the train has a constant speed v.

In order to do that you need two things:

• A set of measuring rods of all the same length. For example 1 km each.
• A set of clocks.
In order to perform a train experiment at a constant speed you do three things:
• You place the rods one behind each other in a straight line.
• You place a clock at each end of each rod.
• You synchronize the clocks such that they show all the same time in your reference frame

The train has a constant speed if exactly after each time delta t you reach the next clock.

### Changing Length - visual illusion

If you want to study Length Contraction you have to be very carefull not to mix with visual illusion
Visual illusion takes place in the following experiment:
• Place a long rod in front of your nose
In practice you should take a rod made from glass with at the other end a lamp
• Move the rod away from you
• What will happen ?
The issue is that immediate when you move the rod, the part of the rod against your nose moves away, while it will take some time before you see that the other end starts to move. That means the rod seems smaller than the rod really is. That is visual illusion.

What you can also is to move the rod towards you. Than the opposite will happen.
Immediate when the rod reaches against your nose, than it will still take some time before you see that the other end stops to move. That means the rod seems longer than the rod really is. That is visual illusion.

This subject is extensively discussed in Changing Length part 1 and Changing Length part 2

### Changing Length - to push or to pull

However there is more. There are two ways to move the rod away from you:
• You can place your fingers at one end, against your nose and push the rod away. In that case the rod physical becomes shorter.
• You can place your fingers at the other end and pull the rod away. In that case the rod physical becomes longer
With the train experiment the same problem arises:
• You can place the locomotive at one end and push the train forwards. In that case the train physical becomes shorter.
• You can place the locomotive at the other end and pull the train forwards. In that case the train physical becomes longer
The problems with to push or to pull is also discussed in: Changing Length part 4

### Changing Length - rigid rod

To solve this pushing or pulling effect with a train is to use a train which only consists of locomotives.
However this creates a new problem: how do you start this train. The solution is more or less as explained in Changing Length - the speed v : you need rods with the same length as each locomotive and you need clocks.
Using the clocks you can take care that all the locomotives start at the same time and have the same speed.

For a rod you should take a rigid rod.
A rigid rod is a rod which internally does not posses and motion.
In principe when you push or pull against any one part of a rigid rod, the whole rod moves instantaneous. This requires instantaneous communication.

### Changing Length - summary

In the above paragraphs issues related to Length Contraction are discussed.
One important remark is that all the issues are discussed from the view point of one frame: ie the rest frame.
No moving observers are involved. No moving clocks are involved.

The most difficult part is the issue of rigid rods
IMO such a rod does not exist and or can not be used in any experiment.
On the other hand rods can be used for experiments when gravity is considered.
However gravity does not cause constant speed which is the starting point of Special Relativity implying that length contraction can not be studied in this way.

### Feedback

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Created: 3 February 2002
Modified: 6 October 2002
Modified: 18 January 2006

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