## Moving Train Experiment

### Train Feedback Form

The purpose of this Feedback Form is to get feedback about the moving Train Experiment as discussed in literature:
1. "Spacetime Physics:introduction to special relativity" by E,F, Taylor and J.A. Wheeler Pages 62-64
2. "Introducing Einstein's Relativity" by Ray d'Inverno the pages 23-24
The purpose of this Feedback Form is also to get a better insight what the moving Train Experiment really means.

The same subject is also discussued in sci.physics.relativity: SR is succesfully debunked, spread the word. Part of the reason of this questionary can be found in the last posting of this thread.

Nothing for nothing. There will be a lottery between the persons who answer all the questions in this questionary before 1 January 2003. Two boxes of Belgium Chocolate are at stake.

### Questions

Once you have answered all the questions, click on the button.

If you would like to start over again, click on the button.

### Reflection.

The proposed Moving Train
experiment #3 as discussed in the questions 4 and 5 gives more insight what SR is compared with the experiments 1 and 2 used in the questions 1, 2 and 3. In fact what you perform in this experiment is called: clock synchronisation.

The Moving Train experiment in literature is used in order to explain relativity of simultaneity, with two observers as done in question 3.
An Observer can see (observe) two events (light signals) simultaneous. The question is than to decide if those events actual happend simultaneous.
You can also raise this question in a different way: Suppose two events happened simultaneous. Where is the plane from which you can see those two events simultaneous. To answer that question (experimental) is very difficult.
If two observers (A and C) are together in that plane at the moment when those two simultaneous events happen and observer C moves away from that plane then ofcourse A has a chance to see those two events simultaneous and C not. That is what the first to experiments demonstrate. Also Newton will agree with this.

If you measure the length of the Moving Train (in all experiments) as a function of v you get accordingly to SR a function like:

```               |l
|
.....
...  |  ...
..     |     ..
.       |       .
|
|
---------------0-------------
V  -->

figure 6
```
The problem is you can not test this curve in reality
What is more a problem is that at any speed the whole train should have contracted along its whole length "in a similar fashion", which requires some form of instantaneous communication, what is physical very difficult to crasp.

### Mathematics of Train Experiment 2 (d'Inverno)

The following sketch explains what happens if length contraction is involved in the train
experiment #2 as explained by d'Inverno. The sketch shows that neither observer A (at the centre near the track) or C (at the centre of the train) will in See the two flashes simultaneous.
```                    /           /
/           .t3
/          ./           /
/         . /           /
/        .  /           /
/       .   .t4         /
/      .    /  .        /
/     .     /     .     /
/    .      /        .  /
/   .       /           .t5
/  .        /           /|
/ .         /           / |
/.          /           /  |   ----> v
L1----------C-----------L2  |
------FD1------------A---------|--FD2------- track ----
| .           |          \  |             x, t
|   .         |           \ |        FD1= 0, 0
|     .       |            \|        A  = 0.5*l0, 0
|       .     |             .t5      FD2= l0, 0
|         .   |           . |        L1 = 0, 0
|           . |         .   |        C  = 0.5*l, 0
|             .t1     .     |        L2 = l, 0
|             |     .       |
|             |   .         |
|             | .           |
|             .t2           |

figure 7
```
1. The bottom part explains what Observer A sees in the rest frame. The two firing devices (FD's) are at FD1 and FD2. The distance between FD1 and FD2 represents the length l0 of the train at rest.
2. The top part explains the moving observer C. The front of the train L2. The back is L1. L2 is also the lamp at the front, L1 is the lamp at the back. The distance between L1 and L2 is l. l = l0 * SQRT(1-v*v/c*c)
3. When the back of the train is at position FD1, FD1 turns Lamp 1 ON. The light of Lamp 1 reaches the Observer A at t1.
4. When the front of the train is at position FD2, FD2 turns Lamp 2 ON. This is at t5. The light of Lamp 2 reaches the Observer A at t2.
5. When the back of the train is at position FD1, FD1 turns Lamp 1 ON. The light of Lamp 1 reaches the Observer C at t3.
6. When the front of the train is at position FD2, FD2 turns Lamp 2 ON. This is at t5. The light of Lamp 2 reaches the Observer C at t4.
7. The point FD1,L1 is considered the origin.
8. In order to calculate t1 we proceed as follows:
The line going from A to t1 is : 0.5*l0
The line going from L1,FD1 to t1 is: c*t
As such we get c*t1 = 0.5*l0
or t1 = 0.5*l0/c
9. In order to calculate t5 we proceed as follows.:
The line going from FD2 to t5 is: l0
The line going from L2 to t5 is: l+v*t
As such we get l+v*t = l0
or t5 = (l0-l)/v
10. In order to calculate t2 we proceed as follows.:
The general equation for the dotted line through t5 is a - c*t
For t5 we get: a - c*t5 = l0 or a - c*(l0-l)/v = l0
This gives: a = l0 + c*(l0-l)/v For line going from t5 to t2 is: l0 + c*(l0-l)/v - c*t
The line going from A to t2 is: 0.5*l0
As such we get l0 + c*(l0-l)/v - c*t = 0.5*l0
or t2 = 0.5*l0/c + (l0-l)/v
11. In order to calculate t3 we proceed as follows.:
The line going from C to t3 is: 0.5*l + v*t
The line going from L1 to t3 is: c*t
As such we get 0.5*l + v*t = c*t
or t3 = 0.5*l / (c-v)
12. In order to calculate t4 we proceed as follows.:
The line going from C to t4 is: 0.5*l + v*t
The line going from t5 to t4 is: l0 + c*(l0-l)/v - c*t
As such we get 0.5*l + v*t = l0 + c*(l0-l)/v - c*t
or t4 = {(l0-0.5*l) + c/v*(l0-l)}/(c+v)

In order to perform the mathematics for a particular value of v/c you can use the following calculator:
v/c v c gamma
length contr l0 l=l0/gamma t5
t1 t2 t3 t4

• The first line shows the value v/c in red box.
This value can be modified:
Enter a value and select any other point on this diplay in order to excute the calculations.
Enter 0.1, 0.2, 0.3, 0.4 and 0.6
Observe that t2=t1+t5
• The first paramater of the next lines indicates if "Length Contraction" is used.
This value can be modified:
Enter a ZERO and select any other point on this diplay in order to excute the calculations.
Repeat the previous test values for v/c.
Observe that t1=t2 and that t3<>t4.
The following table shows the values for t1, t2, t3, t4 and t6 for "Length Contraction"=1.
The results shows that both observers never see the two events simultaneous. (Except for v=0)
v/c t1 t2 t3 t4
00.50.50.50.5
0.10.50.5500.5520.502
0.20.50.6010.6120.509
0.30.50.6530.6810.520
0.40.50.7080.7630.536
0.60.50.833310.5833

### Moving Train Hoax Experiment ?

One more Moving Train Experiment. This is called: Experiment 4
Consider a train with has a Firing Device and a lamp at the centre. There is also an Observer C at the centre. There are Two mirrors at the front and the back of the train.
There is one contact at the track. (The point X in the following sketch). When the train goes over the contact the Firing Device activates the lamp. The light from the lamp shines in the direction of the mirrors. The moment that the light reflects a mirror is considered one event. As such there are two events (t1 and t2) The moment that the light reflects a mirror also leaves a mark on the track (Identical as when lightning hits the front or back of the train). As such there are two marks on the track. (M1 and M2)
```                    /        .t3      /
/       ./  .     /
/      . /     .  /
/     .  /        .t2
/    .   /       ./
/   .    /      . /
/  .     /     .  /
/ .      /    .   /
/.       /   .    /
.t1      /  .     /
/  .     / .      /
/     .  /.       /     ----> v
<--------C-------->
-----------M1----X-----A----------M2---track ----
|   .   .   |           |
| .       . |           |
.           .           |
| .         | .         |
|   .       |   .       |
|     .     |     .     |
|       .   |       .   |
|         . |         . |
|           .t4         .
|           |         . |
|           |       .   |
|           |     .     |
|           |   .       |
|           | .         |
|           .t5         |

figure 8
```
The top part shows the situation for the moving observer C.
The bottom part shows the situation for the Observer A at rest, at the center of the two marks M1 and M2.
There are a couple of questions and answers.
1. Does the Observer C at the Centre of the Moving train see the two reflected lights simultaneous ?
2. IMO the answer is Yes. This experiment is identical as clock synchronization on a moving frame. The moving observer sees the reflected sinals at t3.
3. Does the Observer A at the Centre of the two marks see the two reflected lights simultaneous ?
4. IMO the answer is No. Observer A sees the reflected signals at t4 and t5.
5. What distinquish experiment #4 from the experiment #1 by T&W ?
Experiment #1 is written by T&W as: "Lightning strikes the front and back ends of a rapidly moving train leaving char marks on the train and on the track etc. An observer standing halfway between the two char marks on the track receives the receives the two light flashes"
This piece of text is identical for the two experiments.
Next the text by T&W continues: "at the same time.", while for experiment #4 this is not true.
6. The problem with experiment #1 is that the moving Observer C agrees that if Observer A sees the two flashes simultaneous than Observer C will not see them simultaneous. However there is one problem, it is also can be other way around i.e. that Observer C will claim that he or she will see the two flashes simultaneous (Figure 3.1 in the book by T&W does not depict the full story) and not Observer A.
The reason why Observer C can make this claim is because experiment #1 by T&W is symmetrical; both Observers have the same right to claim that they see the lights simultaneous. Experiment #4 is not symmetrical. In fact the most common outcome of Experiment #1 is, that both Observers don't see the two flashes simultaneous.
7. To solve this problem in experiment #1 you need clocks all along the track and all those clocks have to be synchronized in the same frame.
If the clocks are all synchronized in the track frame and if each clock nearest to each track mark both have the same time at the moment when lightning hits than observer A will see the two flashes simultaneous and not the moving Observer C.
8. In experiment #4 you do not need those clocks because the moving Observer C will always see the two flashes simultaneous because the total path that each light signal follows has the same length.
9. IMO experiment #4 shows that this experiment has "nothing" to do (compared with experiment #1) with Special Relativity i.e. Length Contraction and Time Dilation.
10. IMO experiment #4 can not be used to explain the Michelson and Morley experiment.
Experiment #4 is also called: "The Moving Train Hoax Experiment ?"
It is the reader to judge how to decide if this Experiment is the best one.

### Reflection part 2.

Experiment #3 and experiment #4 are (almost) the same.
Experiment #4 is a more accurate description because the starting event is a contact on the track, which allows you to perform the experiment easier.
In fact each time at a certain speed v you have to perform the experiment twice
• The first time without Observer A, in order to establish the position of the two markers M1 and M2.
• The second time with Observer A, to establish that Observer A does not see the two flashes simultaneous.
In the book by T&W at page 62 is written:
Did the two lightning bolts strike the front and the back of the train simultaneously? Or did they strike at different times? Decide!
... there is no unique answer to this question. For the situation described above, the two events are simultaneous as measured in the Earth frame; are not simultaneous as measured in the train frame.

Now consider the following question to the moving Observer C in Experiment #4:
Did the two events (when the signals were reflected or what is equivalent when lightning hit the mirrors) happened at the same time ?
The answer will be: (1) Yes. Each time at each speed of the train the two events happened at the same time.
Observer C also could have given two slightly different answers:
(2) Yes, the two events happened each time simultaneous
(3) Yes, the two events happened each time simultaneous in the frame of the moving train.
So how important is it? Is it really true that each time (with different v) you can get the same reply: "The two events happened at the same time" or what does reply (3) really mean.
The interesting aspect is that I. Newton agrees that the observer C will see the two events simultaneous but not that they happened simultaneous.

IMO we can learn the most if Observer A measures the difference in arriving times of the two signals t5 and t4 (See figure 8) which is identical as the difference between t2 and t1
i.e. equal to 0.5*l/(c-v)-0.5*l/(c+v) = l*v/(c*c-v*v)
See :Example for more details. The difference is the same as between t4 and t3.

• I. Newton will claim that the results should show that the length l=l0 and is fixed.
• Accordingly to SR the results should show that l = l0 * sqrt(1-v*v/c*c) and is subject to Lorentz Contraction.
The "sad" part is that you can not perform such an experiment accurately in practice.

E-mail:nicvroom@pandora.be.

Created: 4 October 2002
Modified: 19 November 2002