## Comments about "Length Contraction" in Wikipedia

This document contains comments about the document "Length contraction" in Wikipedia
• The text in italics is copied from that url
• Immediate followed by some comments
In the last paragraph I explain my own opinion.

### Introduction

In that document we read:
In physics, length contraction is the phenomenon of a decrease in length measured by the observer, of an object which is traveling at any non-zero velocity relative to the observer.
Two comments:
• In this text of 2015 we read: "phenomenon". In the Wikipedia 2008 we read "physical phenomenon". See Reflection 4 - Length Contraction in Wikipedia 2008 I will comment on the physical aspect later.
• In the definition of Length Contraction twice the word observer is used. This is confusing, specific if here is meant an observer at rest or moving.
I would change this definition as follows:
In physics Length contraction, is the physical phenomenon of a decrease in length in objects that move at any non-zero velocity measured in a frame at rest.
The issue is if an observer and a clock in the moving object also are affected by length contraction. This is important for the Michelson-Morley experiment.

Next we read:
It is only when an object approaches speeds on the order of 30,000 km/s, i.e. one-tenth of the speed of light, that it becomes important.
This line is correct
Next we read:
where
• L is the proper length (the length of the object in its rest frame),
• L' is the length observed by an observer in relative motion with the object,
• V is the relative velocity between the observer and the moving object,
I would change this as follows:
Where
• L is the length of an object when v = 0
• L' is the length of the object when v is non zero.
• v is the speed of the object.

Next we read:
Note that in this equation it is assumed that the object is parallel with its line of movement.
Nothing is mentioned if this should be in a straight line.
The two questions are:
1. What happens if the object does not moves in a straight line ?
2. What happens if the object moves in a circle ?
This last question is important because on the surface of the earth we also move in a circle parallel to the equator.

Next we read:
Also note that for the observer in relative movement, the length of the object is measured by subtracting the simultaneously measured distances of both ends of the object.
This is a very tricky sentence. The problem is that an observer in relative movement measuring a rod in relative movement should measure L. I expect that is not what you want. I expect what you want to measure is L'
The second problem is how is simultaneous defined. In the frame at rest or in a moving frame.

IMO there are two ways that this line can be rewritten:
1. Also note that for the observer with speed v, the length of the object at rest is measured by subtracting the simultaneously measured distances of both ends of the object in the moving frame.
2. Also note that for the observer at rest, the length of the object with speed v is measured by subtracting the simultaneously measured distances of both ends of the object in the frame at rest.
In the first line moving clocks are introduced. When this is the case then time dilation becomes an issue. IMO this should be avoided, as much as possible.
The second line is simpler, but still complicated. The problem is how do you perform this experiment in detail
This line was as of 2008. In 2015 are added: Next we read:
An observer at rest viewing an object travelling at the speed of light would observe the length of the object in the direction of motion as zero.
This line is theoretical correct.

### 1. History

Length contraction was postulated by George FitzGerald and Hendrik Antoon Lorentz to explain the negative outcome of the Michelson-Morley experiment and to rescue the hypothesis of the stationary aether (Lorentz–FitzGerald contraction hypothesis).
It is more to refute the aether theory.
Eventually, Albert Einstein (1905) was the first to completely remove the ad hoc character from the contraction hypothesis, by demonstrating that this contraction did not require motion through a supposed aether, but could be explained using special relativity, which changed our notions of space, time, and simultaneity.
Special relativity does not explain length contraction assuming it is something physical.

### 2. Basis in relativity

If the relative velocity between an observer (or his measuring instruments) and the observed object is zero, then the proper length L_0 of the object can simply be determined by directly superposing a measuring rod.
IMO a better sentence is:
If the relative velocity between the measuring instruments and the measured object is zero, then the proper length L_0 of the object can simply be determined by directly superposing a measuring rod.
This is better because it removes any human involvment.
The observer installs a row of clocks that either are synchronized
a) by exchanging light signals according to the Poincaré-Einstein synchronization, or
b) by "slow clock transport", that is, one clock is transported along the row of clocks in the limit of vanishing transport velocity.
What should be added is in the frame at rest i.e. along the track.
Compare this with: Reflection 1 - The simplest (?) experiment to detext length contraction which only requires two clocks (and a much simpler method to synchronise clocks)
After that, the observer only has to look after the position of a clock A that stored the time when the left end of the object was passing by, and a clock B at which the right end of the object was passing by at the same time.
 ``` 5 5 <--------------> 5 5 ^ 4 4 <--------------> 4 4 | 3 3 <--------------> 3 3 | 2 2 <--------------> 2 2 | 1 1 <--------------> 1 1 1 2 3 4 5 6 7 8 9 10 Figure A v=0 ``` ``` 5 5 5 5 5 <--------> 5 ^ 4 4 4 4 <--------> 4 4 | 3 3 3 <--------> 3 3 3 | 2 2 <--------> 2 2 2 2 | 1 <--------> 1 1 1 1 1 1 2 3 4 5 6 7 8 9 10 Figure B v>0 ```
Figure A shows a train at rest. Figure B show s a moving train.
The horizontal line shows a track with 10 clocks. The vertical axis is the time in counts. The inside shows the time of each clock.
Suppose in both cases you want to measure the length of the train at count 3.
• Figura A Shows that the front end of the train is near clock 8 and the Back at clock 3. That means L0 is 5.
• Figura B Shows that the front end of the train is near clock 7 and the Back at clock 4. That means L is 3, implying Length Contaction
Using this method, the definition of simultaneity is crucial for measuring the length of moving objects.
That is why it is terrible important to demonstrate length contraction without any moving clock
Another method is to use a clock indicating its proper time T0, which is traveling from one endpoint of the rod to the other in time T as measured by clocks in the rod's rest frame.
 That means you are using a moving clock. That is "strange". Figure C shows a moving train with a clock at a fixed position. t1 is the time when the front passes the clock. t2 is the time when the back passes the clock. The length of the train is (t2-t1) * v. There are two major problems: What is the speed v? You cann't demonstrate length contraction using this method. ``` ------v-------> t1 -------v-------> t2 ----------------------------------- Figure C ```
A serious problem also is how to measure the speed v and the speed of light c.

### 3. Symmetry

The principle of relativity (according to which the laws of nature must assume the same form in all inertial reference frames) requires that length contraction is symmetrical: If a rod rests in inertial frame S, it has its proper length in S and its length is contracted in S'.
What the text tries to describe is that a rod at rest has a proper length but observed from a moving train or frame has a shorter length and when you increase the speed of this train or frame to the speed of light than the length of the rod is zero.
There is no doubt that this is mathematical true using the Lorentz transformation but is it also physical true? See also Reflection 3 - The simplest experiment with a complication
Second image: A train at rest in S and a station at rest in S' with relative velocity of v = 0.8*c are given.
In S a rod with proper length L0 = AB = 30 is located, so its contracted length L' in S' is given by:
L' = AC = L0/gamma = 18 cm
The (contracted) length of the moving train L is 18 cm in S.

### 4. Experimental verifications

Any observer co-moving with the observed object cannot measure the object's contraction, because he can judge himself and the object as at rest in the same inertial frame in accordance with the principle of relativity (as it was demonstrated by the Trouton-Rankine experiment).
What this means is that neither an observer at rest with a train at rest nor a moving observer in a moving train can demonstrate its own length contraction. This seems reasonable because length contraction always implies that you measure the length of something under two conditions.
So Length contraction cannot be measured in the object's rest frame, but only in a frame in which the observed object is in motion.
This sentence is wrong. In order to measure length contraction you should do it twice in the same frame under two different conditions i.e. at rest in the frame and moving in the same frame.
In addition, even in such a non-co-moving frame, direct experimental confirmations of Length contraction are hard to achieve, because at the current state of technology, objects of considerable extension cannot be accelerated to relativistic speeds.
Why not call the non-c-moving frame the rest frame?
Because of physical limitations you should try only to demonstrate that there is length contraction involved. Not how much.
The same also means why it is so difficult to demonstrate the Lorentz transformations physical.
• So, only with the aid of length contraction and the relativistic Doppler effect, the extremely small wavelength of undulator radiation can be explained

### 5. Reality of length contraction

In 1911 Vladimir Varicak asserted that length contraction is "real" according to Lorentz, while it is "apparent or subjective" according to Einstein. Einstein replied:
The author unjustifiably stated a difference of Lorentz's view and that of mine concerning the physical facts. The question as to whether length contraction really exists or not is misleading. It doesn't "really" exist, in so far as it doesn't exist for a comoving observer; though it "really" exists, i.e. in such a way that it could be demonstrated in principle by physical means by a non-comoving observer.
IMO when you study what Einstein wrote the situation is clear:
Length contraction of a moving object is a physical effect. It can be observed from an observer at rest. It can not be observed from a moving observer.
He presented the following thought experiment: Let A'B' and A"B" be the endpoints of two rods of same proper length.
Let them move in opposite directions with same speed with respect to a resting coordinate x-axis.
Endpoints A'A" meet at point A*, and B'B" meet at point B*, both points being marked on that axis.
Thought experiments are always "dangereous".
When two identical rods L0 move in opposite directions with the same speed there length L are always (?) identical.
When the end points at one end meet then also the end points at the other end should meet for a split second.
The line that the two meeting points connects is not a physical object.

### 6. Paradoxes

Due to superficial application of the contraction formula some paradoxes can occur.
This is first of all not an issue based on mathematics.
However, those paradoxes can simply be solved by a correct application of relativity of simultaneity.
Paradoxes should be solved by performing different experiments.

### 7. Visual effects

Regarding Terrell rotation:
Length contraction refers to measurements of position made at simultaneous times according to a coordinate system. This could suggest that if one could take a picture of a fast moving object, that the image would show the object contracted in the direction of motion.
Terrell rotation involves both length contraction and length expansion. See: Program4 - Length Contraction
A visible illusion ?
However, such visual effects are completely different measurements, as such a photograph is taken from a distance, while length contraction can only directly be measured at the exact location of the object's endpoints.
What should be mentioned IMO is in the same frame.

### 8. See also

Following is a list with "Comments in Wikipedia" about related subjects

Comments on the article Quantum_and_classical_clocks.htm "Einstein’s quantum clocks and Poincaré’s classical clocks in SR" by Yves Pierseaux

### Reflection 1 - The simplest (?) experiment to detect length contraction

IMO there are three issues, which require an answer:
1. What is the simplest experiment in principle to observe length contraction.
2. What is the simplest experiment in principle to detect and measure length contraction
3. Is it possible to perform those experiments in practice.
Let us study these issues one by one
• IMO the simplest (?) experiment to detect Length Contraction is by means of a moving train, two contacts along the track which generate light pulses, and an observer at half distance between the two contacts. As follows:
```  >-----Train----->
----------------------A------------X------------B--------------------
O
Figure 1
```
A and B are the two contacts
The observer O is at X. i.e. AX = XB
The train starts left from A and moves towards B

The first step of the experiment goes as follows:

• You place the train above the observer, with the front of the train slightly left of point B and the back just slightly left of point A.
• You move the train towards the right, just that the front makes contact with point B and the back with point A.
• The observer should see the light pulses from the two points simultaneous.
• This means that the distance between the contacts is equal to the proper length or rest length of the train.
• This also means that if the observer sees them simultaneous, that the two light signals are generated simultaneous at the points A and B.
Now we are going to perform the real experiment in order to observe length contraction. You place the train as shown on the sketch. You start the engine and the train will move towards the right. The observer at point X should see the following if length contraction is involved :
1. The front of the train touches point A. As a result the observer observes a light pulse from point A, but this signal is ignored.
2. The back of the train touches point A and as a result the observer observes a second light pulse from point A.
3. However slightly later the observer observes a light pulse from point B. This pulse is generated when the front touches point B.
4. It is important that the observer does not see those two light pulses simultaneous, because this means that the pulses were not generated simultaneous, but A first and B later.
5. This means that when the back was at point A the front was not at point B but before point B. This means that Length contraction is involved and the train has to move a little further in order to reach point B and to generate the light pulse.
6. The back of the train touches point B. As a result the observer observes a second light pulse from point B, but this pulse can be ignored.
• In order to quantify Length Contraction you have to modify this experiment slightly.
You need two clocks, one at point A and an and one at point B. You also need two observers at both points inorder to observe each 2 events.
The experiment consists of two parts.
1. You have to synchronise the two clocks. That means the Observer at point X sends out a light signal. When the observer at point A sees this signal, he starts his clock. The same for the observer at point B. After this the clocks are synchronised.
2. You start the train, the same as above, when the Observer at A sees the front of the train he writes down his clock reading and again when the he sees the back of the train. As such you get two clock readings t1 and t2.
3. The same for Observer B at point B. You also get two clock readings t3 (front) and t4 (back).
The following sketch shows those 4 events:
```      >-----Train----->t1
----------------------A------------X------------B--------------------
t2>-----Train----->
>-----Train----->t3
t4>-----Train----->
Figure 2
```
4. The speed v can be calculated as follows: v = l/(t3-t1) = l/(t4-t2)
5. There is no Length Contraction when then back is at point A and that simultaneous the front is at point B. i.e. when t2 = t3.
6. The length contraction L' = v * (t2-t1) = L * (t2-t1)/(t3-t1) = L * (t4-t3)/(t4-t2)
t2-t1 is the time between that the front versus the back of the train passes at point A.
• The problem is that neither one of those two experiments can be done in reality.

### Reflection 2 - The simplest experiment to detect length contraction

In Reflection 1 a simple experiment to demonstrate Length Contraction is described.
However an even simpler is possible by means of a moving train, three lamps A, B and C along the track which generate light, and an observer at half distance between the two lamps A and C.
The experiment consists of two parts.
1. In the first part the train is positioned at rest in front of the observer such that the observer just can not see both lights A and C simultaneous.
That means he cannot see A but he can see C, but when the train moves a very little bit towards the right he cannot see C but now he can see A.
The observer is half way between the two lights A and C and in front of light B.
```                       A...........B...........C
>---------Train-------->
-----------------------------------X---------------------------------
O
Figure 3
```
Figure 3 shows the situation when the train is at rest in between the three lamps and the observer at O can see Lamp C.
2. In the second part the train moves starting left from A until somewhere towards the right of C.
```                       A...........B...........C
>-----Train----->	   >-----Train----->        >-----Train----->
-----------------------------------X---------------------------------
O
Figure 4
```
Figure 4 shows the situation at three instances:
(1) when the train starts left from Lamp C (2) when the train is half way between lamp A and C (3) when the train is at the right of lamp C.
There is length contraction involved when the observer can see both lights A and C simultaneous but not light B.
The importance of this experiment is that no moving clocks are involved.

### Reflection 3 - The simplest experiment with a complication

In Reflection 2 the simplest experiment to demonstrate Length Contraction is described. In that case we have one train which moves with a constant speed v towards the right.
Now we are going to make this experiment more complicated.
On top of Train 1 we are going to install a whole new train (Train 2).
1. First the speed of Train 2 is zero and we measure the length of the Train 2 when the speed of Train 1 is v.
This is the distance between the points A2 and C2 in Figure 5
2. Next we give the Train 2 also a speed v to the right.
Figure 5 shows this situation.
```                           A2      B2      C2
>--Train-2->
-------------------------------------
A1....................B1....................C1
>---------------Train-1------------->
-----------------------------------X---------------------------------
O
Figure 5
```
Figure 5 shows two important concepts:
1. Length contraction of Train 1 which has a speed v1. The distance A1 C1 is the length of the train when v1=0.
2. Length contraction of Train 2 which has a speed v2 relative to Train 1. The distance A2 C2 is the length of the train when v2 is zero (and v1>0)
What Figure 5 shows that also for Train 2 there is length contraction involved (twice)
Figure 5 raises a serious issue:
To what extend can you place inside a moving frame a different moving frame going in the same direction?
The maximum situation arises when Train 1 moves close to the speed of light and speeds higher than c can be considered.

Assuming that this is in agreement which what is observed we are going to modify this experiment.

• In stead of given Train 2 a speed to the right, we are going to give Train 2 a speed to the left.
What will happen? IMO:
1. When the speed v2 = 0 the length of Train 2 is A2 to C2
2. When we increase the speed v2 towards the left the length of the Train 2 will become larger. untill v2 = v1. In that case Train 2 does not move relative to the Observer.
3. After that the length of Train 2 will decrease.

### Reflection 4 - Length Contraction in Wikipedia 2008

In the 2008 document we read:
Length contraction, etc, is the physical phenomenon of a decrease in length detected by an observer in objects that travel at any non-zero velocity relative to that observer.
Two comments as of 2008:
• First we read: "physical phenomenon". The fact if length contraction is a physical phenomenon is under discussion. I will comment on that later.
• In the definition of Length Contraction twice the word observer is used. This is confusing, specific if here is meant an observer at rest or moving.
I would change this definition as follows:
Length contraction, etc, is the physical phenomenon of a decrease in length measured in objects that travel at any non-zero velocity relative to an observer at rest.
Next we read in the 2008 document:
It is only when an object approaches speeds on the order of 30,000 km/s, i.e. one-tenth of the speed of light, that it becomes important.
This line is correct

### Reflection 5 - Length Contraction in DESY Flash experiment

The Flash (The Free electron LASer in Hamburg) experiment is explained in: http://flash.desy.de/sites2009/site_vuvfel/content/e395/e2188/FLASH-Broschrefrs_web.pdf
At page 8 we read:
HoW It WorKs. The free-electron laser principle and the FLASH accelerator
At the bottom part of this document we read:
now we put ourselves into a wagon moving through the undulator with the average speed of the electrons, which is very close to the speed of light. As the undulator moves towards us its period appears length-contracted, and the electrons in the wagon oscillate at a high frequency and emit their radiation.
 ``` P N P N P N P N P N e e e e e eee e e e e e e e e e eee e e e e e --v--> Figure 6 ``` Figure 6 shows the undulator. This are the sequence of letters P N P N etc. The length of each section P N is 30 mm. The letters eee identify the path of one electron. What you can see is that this path is not straight but sinusoidal, caused by the undulator. This sinusoidal path causes that the electron emit photons. The frequency of this photons depent about the speed of the electrons. The faster this speed the higher the frequency of the photons and the shorter the wave length of the photons. IMO this decreases has nothing to do with length-contraction of a rod. The word 'appears' is appropiate.

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Created: 7 January 2008
Modified: 31 August 2008
Modified: 25 Januari 2015 - Added Reflection 2

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