Train FeedBack Form

Moving Train Experiment

Train Feedback Form

"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

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Moving train question 1:

The description of the moving train experiment by T&W starts with a moving train which moves over a track. This is called: Experiment 1

  \                                /
   \                              /
    \                            /
     B--------------------------F    -->
-----M2-------------------------M1------- Track
                   A            

               figure 1

This moving train is hit by two lightning flashes. One lightning flash hits the front(F) of the train. One lightning flash hits the back(B) of the train.
Each of those lightning flashes also leaves a mark (M1 and M2)on the track.
There is an observer A which stands on (near) the track, at equal distances from those two marks. Observer A sees those two lightning flashes simultaneous. As such for observer A, (in the rest frame or track frame) those two flashes happened simultaneous.

The question is: When the train stops, is the length of the train equal as the distance between the two marks?

Answer Moving train question 1

Moving train question 2:

    L2--------------------------L1    -->
----ED2-------------------------ED1------ Track
                   A             

              figure 2

The moving train experiment as described by d'Inverno is slightly different. (Assuming my interpretation is correct).
This is called: Experiment 2
First we discuss when the train stops, is at rest.
Starting point of the train experiment are two Electrical Devices (ED1 and ED2) which are a distance l0 apart. When the train stops above those EDs the front of the train makes contact which ED1 and turn on light L1 on the front of the train. The same for the back of the train with ED2 and with the light L2 on the back of the train. i.e. when the train stops above those EDs both lights L1 and L2 are on.
There is an observer A which stands on (near) the track, at equal distance between those two ED's

Secondly we discuss when the train moves
The train moves from left to right.
When the back of the train makes contact with ED2, light L2 produces a short flash.
When the front of the train makes contact with ED1, light L1 produces a short flash.

The question is: Will observer A see the two flashes simultaneous?

Answer Moving train question 2
For a mathematical evaluation of this question See: Mathematics of Train Experiment 2 (d'Inverno)

Moving Train question 3:

Starting point is the Experiment as described by T&W, but now there is also as Observer C at the centre of the moving train.

  \                                /
   \                              /
    \              C             /
     B--------------------------F    -->
-----M2-------------------------M1------- Track
                   A            

                figure 3

The above sketch shows the position of the train, the position of the Observers A and C, the two marks M1 and M2 at the moment that lightning hits the front(F) and back(B) of the train.

Observer A sees the flashes simultaneous. What will Observer C see? IMO that is simple. The above sketch shows the situation at impact in the rest frame. Because C moves towards F, C will see the lightning flash from front(F) first and from back(B) later.

The question is: The fact that Observer C does not see the two flashes simultaneous, has this anything to do with SR i.e. length contraction or time dilation?

Answer Moving train question 3

Moving Train question 4a and 4b:

As part of this question we perform an Experiment rather similar as the one described by T&W but different.
This is called: Experiment 3
Starting point is an Observer C at the centre of the moving train. Observer C sends out a light signal to the front and back end of the train. At the front end there is a mirror M1, which reflects this signal. At the back end there is a Mirror M2, which also reflects this signal. At the same time when the signals reach the mirrors they also leave a mark at the track.
Again there is an Observer A, near the track, at the centre of those two marks.

                   C
     M2-------------------------M1    
-----M2-------------------------M1------- Track
      <---         A            

              figure 4

The above sketch shows the position of the train, the position of the Observers A and C, the position of the two mirrors M1 and M2 and the two marks M1 and M2 at the moment that the light flashes hit the two mirrors in the frame of the moving train.

Observer C sees the flashes simultaneous. What will Observer A see? IMO again that is simple. The above sketch shows the situation at impact. Because A moves (relative) towards M2, A will see the light flash from back(M2) first and from the front(M1) later.

The important part of this experiment is that Observer C always sees the two signals simultaneous at any speed in any direction and Observer A never, except when the train stops i.e. at v=0.

The first question is: If Observer A measures the arrival time of the two signals each, (using rods and clocks in the rest frame) has this anything to do with SR i.e. length contraction or time dilation?

The second question is: If Observer C measures the arrival time of the two signals each, (using rods and clocks in the moving frame) has this anything to do with SR i.e. length contraction or time dilation?

Answer Moving train questions 4a and 4b

Moving Train question 5a and 5b:

The questions are based on the previous Experiment.
Starting point is an Observer C at the centre of the moving train, but now the train becomes more a platform. Observer C sends out a light signal to the front and back end of the train. At the front end there is not a mirror but a separate light source L1, which "reflects" this signal. At the back end there is a separate light source L2, which also "reflects" this incoming signal.
Each of the light signals L1 and L2 send light in the direction of observer D which position is on a line perpendicular to the line L1,L2 going through observer C.

                  
      L2..........C...........L1    
      | .                   . |   --->
      |   .               .   |     
------|     .           .     |------- Track
      |       .       .       |
      |         .   .         |
       ---------- D ----------            

              figure 5

The above sketch shows the position of the train from above, the position of the Observers C and D, the position of the two light sources L1 and L2.
The dotted lines shows the the two light signals starting from C. One going via L1 towards D and one going via L2 going towards Observer D

The issue is what will observer D see. Will Observer D always see the two light simultaneous with any speed v of the platform?

The first question is: Does Observer D always see the two flashes simultaneous using Newton's Law ?

The second question is: Does Observer D always see the two flashes simultaneous using SR ?

Answer Moving train questions 5a and 5b

What is your suggestion to find out which of the two questions 5a or 5b is correct:

Enter some comments about the questions in general, specific if you do not agree with the sugested answers:

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

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.
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)
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.
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.
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.
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.
The point FD1,L1 is considered the origin.
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

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

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

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)

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:

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
0	0.5	0.5	0.5	0.5
0.1	0.5	0.550	0.552	0.502
0.2	0.5	0.601	0.612	0.509
0.3	0.5	0.653	0.681	0.520
0.4	0.5	0.708	0.763	0.536
0.6	0.5	0.8333	1	0.5833

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.

Does the Observer C at the Centre of the Moving train see the two reflected lights simultaneous ?

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.

Does the Observer A at the Centre of the two marks see the two reflected lights simultaneous ?

IMO the answer is No. Observer A sees the reflected signals at t4 and t5.

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.
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.
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.
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.
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.
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

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v/c	v	c	gamma

length contr	l0	l=l0/gamma	t5

t1	t2	t3	t4

Moving Train Experiment