Comments about "Relativity of simultaneity" in Wikipedia

This document contains comments about "Relativity of simultaneity" in Wikipedia In the last paragraph Reflection I explain my own opinion.



The article starts with the text:
In physics, the relativity of simultaneity is the concept that distant simultaneity – whether two spatially separated events occur at the same time – is not absolute, but depends on the observer's reference frame.
The first question to answer, without thinking about clocks, is: Does it make sense to call, the events which all happen at the same moment (now) somewhere in the Universe, simultaneous?
The property of such simultaneous events is that one can never be the cause of the other and vice versa. The cause of both can be the same, but previous, event.
This definition of simultaneity has nothing to do with any observer. The question remains how do humans decide that events are simultaneous.
Next we read:
According to the special theory of relativity, it is impossible to say in an absolute sense that two distinct events occur at the same time if those events are separated in space.
For example, a car crash in London and another in New York, which appear to happen at the same time to an observer on the earth, will appear to have occurred at slightly different times to an observer on an airplane flying between London and New York.
This example is too complex, partly because the earth is not flat.
There is a small chance that the observer in the airplane also observes these two crashes simultaneous. However because this observer is high in the sky he always will observe (in this specific case) both crashes later.
The question of whether the events are simultaneous is relative:
This is not the issue. There are two issues:
  1. There is a high chance that when you observe two simultaneous events not simultaneous.
  2. There is a high chance that when you observe two events simultaneous that they are not simultaneous.
immediate next
in the stationary earth reference frame the two accidents may happen at the same time but in other frames (in a different state of motion relative to the events) the crash in London may occur first, and in still other frames the New York crash may occur first.
First of all it is a question if the earth is a stationary reference frame. Secondly within this same frame dependent about the position of the observer, both events can be observed simultaneous, the Londeon crash first or the New York crash.

1. The train-and-platform thought experiment

A popular picture for understanding this idea is provided by Einstein's thought experiment consisting of a moving train with one observer midway in the train, and another observer midway on the platform as the train moves past.
Thought experiments in science are always tricky.
You can discuss experiments in your mind before you actual build and perform them.
What is dangerous to discus the actual outcome of an experiment without performing the experiment.
Next we read:
(1) A flash of light is given off at the center of the train just when the two observers pass each other.
(2) The observer on the train sees the front and back of the train at fixed distances away from the source of the light
(3) and as such according to this observer, the light flashes reach the front and back of the traincar at the same time.
This scenario is wrong and it demonstrates clearly the danger of a thought experiment!
What you need are mirrors at both ends. What the observer at the center of the train will see are the two reflections from the light flash.
see 1.1 Spacetime diagrams for a better explanation.

The observer standing on the platform, on the other hand, sees the rear of the traincar moving (catching up) toward the point at which the flash was given off and the front of the traincar moving away from it.
Clearly also this text is very misleading.
What you need are mirrors at both ends of the train. What the observer at the platform will see are the two reflections from the light flash. However not simultaneous.
see 1.1 Spacetime diagrams for a better explanation.
As the speed of light is finite and the same in all directions for all observers, the light headed for the back of the train will have less distance to cover than the light headed for the front.
The movement of photons is physical the same in all directions only for one reference frame.
The calculated speed of light in that reference frame is c and the same in all directions
In all other reference frames, based on moving observers the speed of light is physical not the same all directions, because the speed of the reference frame has to be taken into account.

1.1 Space Diagrams

This paragraph starts with the following sentence:
It is sometimes helpful to visualize this situation with spacetime diagrams.
The following sketch shows the two possibilities.
The left picture is describes the situation for the train at rest
The right picture is describes the situation for a moving train with a speed v to the right
In both cases the speed of light is the same.
   |                   | 
   |                   | 
   |                   |  
   |                   |  
   |                   | 
   |                   |  
   |                   |  
   |                   |  
   |      t2 .         |  
   |       .   .       |  
   |     .       .     | 
   |   .           .   |  
   | .               . |  
 t1.                   .t3
   | .               . |  
   |   .           .   | 
   |     .       .     |  
   |       .   .       |  
 t0|         Y         | 
    Figure 1A  v=0        
         t5 .       |             
              .    |          
                . |            
                 |.                  | 
                |   .               | 
               |      .            | 
              |         .t4       | 
             |        .   .      | 
            |       .       .   | 
           |      .           .|t3
          |     .           . |
         |    .           .  |
        |   .t2         .   |
       |  .           .    |
      | .           .     |
   t1|.           .      |  
    |   .       .       |   
   |      .   .        |   
t0|         Y         |
   Figure 1B v > 0
      .               |             | 
        .            |             | 
          .         |             | 
            .t5    |             | 
              .   |             | 
                .|             | 
                | .           | 
               |    .        | 
              |       .t4   | 
             |      .   .  |
            |     .       .t3
           |    .       .|
          |   .       . |
         |  .t2     .  |
        | .       .   |
     t1|.       .    |  
      |   .   .     |   
   t0|      Y      |
   Figure 1C v > 0
What is important that the two events t1 and t3 (in Figure 1B and 1C) are not simultaneous and that t4 is larger than t2
This means when you consider each meeting point of the two flashes as a tick of a clock that the moving clock runs slower. To take care that both the clock at rest and the moving clock show the same time you have to introduce length contraction. This is depicted at Figure 1C.
In the first diagram, we see the two ends of the train drawn as grey lines. Because the ends of the train are stationary with respect to the observer on the train, these lines are just vertical lines, showing their motion through time but not space. The flash of light is shown as the 45° red lines. We see that the points at which the two light flashes hit the ends of the train are at the same level in the diagram. This means that the events are simultaneous.
The first diagram shows the bottom part of the left picture. This is situation for a train at rest. It is obvious that the first diagram is not complete.
In the second diagram, we see the two ends of the train moving to the right, shown by parallel lines. The flash of light is given off at a point exactly halfway between the two ends of the train, and again form two 45° lines, expressing the constancy of the speed of light. In this picture, however, the points at which the light flashes hit the ends of the train are not at the same level; they are not simultaneous.
The second diagram shows the situation for a moving train. Also here the picture is not complete because it does not show what any observer actual observes.

2. Lorentz transformations

The relativity of simultaneity can be calculated using Lorentz transformations, which relate the coordinates used by one observer to coordinates used by another in uniform relative motion with respect to the first.
The problem with this paragraph is that the actual derivations are not shown. For a simple derivation see: Reflection 3

3. Accelerated observers

The Lorentz-transform calculation above uses a definition of extended-simultaneity (i.e. of when & where events occur at which you were not present) that might be referred to as the co-moving or "tangent free-float-frame" definition.
That may be true. However it is far to complex. What is it purpose?

4. History

This was done by Henri Poincaré who already in 1898 emphasized the conventional nature of simultaneity and who argued that it is convenient to postulate the constancy of the speed of light in all directions.
When you are at rest and when you assume that the speed is constant in all directions the concept of simultaneity becomes easy. That means which events are simultaneous and which events are not.
However, this paper does not contain any discussion of Lorentz's theory or the possible difference in defining simultaneity for observers in different states of motion
The issue is if motions of observers have any thing to do with the question if two events are actual simultaneous or not. IMO it does not.
This was done in 1900, when he derived local time by assuming that within the aether the speed of light is invariant.
When you assume that the speed of light is constant (locally) relative to eather this is easy, but that does not mean it is correct.
Due to the "Principle of relative motion" also moving observers within the aether assume that they are at rest and that the speed of light is constant in all directions (only to first order in v/c).
Again here the word assume is used.
If you want to compare a situation with an observer at rest (See Figure 1A) with the same situation assuming an eather than you have to give the observer a speed opposite the eather drift in order to compare the same.
A much simpler situation is when the eather drift is zero but that does not mean that the observer is at rest.

4.1 Einstein's train thought experiment

Einstein's version of the experiment presumed slightly different conditions, where a train moving past the standing observer is struck by two bolts of lightning simultaneously, but at different positions along the axis of train movement (back and front of the traincar).
   |          |        |Y         |
   |         |         Yt3       | 
   |        |        .Y|        |
   |       |       . Y |       |
   |      |      .  Y  |      |
   |     |     .   Y   |     |
   |    | t2 .    Y    |    |
   |   |   .   . Y     |   |
   |  |  .      Y.t1   |  |     
   | | .       Y   .   | |
   ||.        Y      . ||
 t0.         Y         .t0
   | .               . |
   |   .           .   |
   |     .       .     |
   |       .   .       |
   |         Y         |
   Figure 2  v --->           
The events are simulataneous assuming an observer at rest if the distance between the observer and the two markers (at rest) is the same.

In figure 2 the two bolts of lightning are the two events t0. The observer on the platform observes them simultaneous at t2.
The observer Y on the moving train observes these two events at t1 and t3 not simultaneous.

This whole effect is independent of the length of the train. As such this issue is not special for SR or GR because no Time dilation and Length contraction in this example is involved.

Events which occurred at space coordinates in the direction of train movement (in the stationary frame), happen earlier than events at coordinates opposite to the direction of train movement. In the moving train's inertial frame, this means that lightning will strike the front of the traincar before two observers align (face each other).
The issue is that an observer at the center of the moving train will observe the ligtning in the direction first at t1 in the forward direction of the moving train and secondly at t3.

6. 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


When you study the concept of simultaneous it is very important to indicate what we mean.

Reflection part 1

There are two other documents which explain the same:
  1. The original version by Albert Einstein: Albert Einstein (1879–1955). IX. The Relativity of Simultaneity (1920). It is simple.
    In that document we read:
    (1) Are two events (e.g. the two strokes of lightning A and B) which are simultaneous with reference to the railway embankment also are simultaneous relatively to the train? (2) We shall show directly that the answer must be in the negative.
    The second sentence is easy. Both observers will never both claim, that each sees the two events simultaneous.
    The first sentence is much more difficult to evaluate. How do you know that the events are simultaneous with reference to the embankment and not to the train ? Why not the reverse ? Or why not neither one ?
  2. A different version is from the book "Introducing Einstein's Relativity" by Ray d'Inverno. See for more detail: Introducing Einstein's Relativity The most serious problem here is that length contraction is involved.

Reflection part2

The central issue of the discussion is the following:
Suppose two events happen along a straight line, and I'am standing at the center of those two events. Suppose I see those two events simultaneous. The question is now: Are those two events simultaneous ?
SR takes length contraction into account. The issue is how much.

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Created: 7 January 2008
Modified 22 August 2008
Modified 29 January 2015
Modified 11 Februari 2015

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