Experiment to establish the fastest running clock

The set up of the experiment is that the platform that has the slowest speed at least should have at least two clocks. The startegy is that the platform which has the fastest speed (slower clock rate) will pass the slower clocks and by comparing the counts of the first with the counts of two slower clocks you can conclude, which platform (spaceship) has the slowest speed.

8 a4 b4 c4 | a a | b b | c 7 a b c | a a | b b | c 6 | a3 b3 c3 | a a | b b | c 5 z z z z | a a | b b | c 4 | a2 | b2 | c2 | a a | b b | c 3 y y y y | a a | b b | c 2 | a1 | b1 | c1 | a a | b b | c c 1 x x x x | a a | b b | c c 0 | a0 | b0 | c0 ----0-------1-------2-------3 v=0 Picture 1

8 k k . l . k3 . l 7 . k z . k k. l2 6 .k k . l y z k . l l. 5 . k2 .l l . m . k y l . m 4 . k k. l1 .m .k k . l x m 3 y k . l l. m0 . k1 .l l . 2 . k x l . . k k. l0 . 1 .k k . l l x k . l l. 0 . k0 .l l . ----0-------1-------2-------3 v<>0 Picture 2

The two most important points on the left picture versus the right picture are the points c4 and k3.
One the left picture (v=0) we have a platform (or train) with 3 observers A, B and C. On the right picture (v<>0) we also have a platform with 3 observers K, L and M.
At each platform the observers are on one line, separated by mirrors in between.

Observer A emits at a0 a flash. This flash is reflected at the two points x.
Observer A see the flashes at a1. This pattern repeats itself.
Observer A sees the flashes again at a1,a2,a3 and a4.
For Observer B a similar situation exists. He emits at b0. Observer B sees the flashes at b1,b2,b3 and b4
What the left sketch also show are simultaneous events from the perspective of the platform or train.
The events a0,b0 and c0 are simultaneous. The three events a1,b1 and c1 etc The three x events are simultaneous. Also the three y events etc.

The picture at the right shows the situation for a platform which moves towards the right.
The mirrors are identified by the dots.
The most important events are k0,k1,k2 and k3. The events a0 and k0 are the same.
K0 is the moment when observer K emits his flash. k1, k2 and k3 when K sees the reflections. The right picture also shows simultaneous. Also here simultaneous means relative to the moving platform.
As such the events: k0,l0 and m0 are simultaneous. And so are k1 and l1. And k2 and l2.
The same for the three "x" events and for the three "y" events.

It is important when you study the picture at the right that observer K emits his flash at k0. Towards the left the flash is reflected almost immediate at point x, but towards the right this happens much "later" also at point x. Next the flashes are observed simultaneous at point k1. Now the same repeats it self. Towards the left the flash is reflected almost immediate at point y, but towards the right this happens much "later" also at point y. Next the flashes are observed simultaneous at point k2. For the third time at point k3 which coincides almost with point c4.

As already mentioned the two events k3 and c4 are the most important.

• The event c4 is the fourth time that observed by C sees the reflected light signal.
• The event k3 is the third time that observed by K sees the reflected light signal.

Now it is important to realize that all the events: a0, c0 and k0 are simultaneous.
The two events a0 and c0 are simultaneous because they are synchronised at the same platform. The (horizontal) events x or for that reason y demonstrate that.
The events a0 and k0 are synchronised at the start of the experiment. This is the moment when observer A meets obsever K.

From the experiment we see that observer K passes by observer A and C.
The experiment is finished when observer K meets observer C. In the two pictures is this close at the points c4 and k3.

• At the start at the events a0 and k0 the number of counts both clocks A and K is zero.
• At the end at the events c4 and k3 the number of counts of the clock of C is 4 and of K is three.

This means that all the clocks in the left picture run faster (4 counts versus 3 counts) than in the right picture. This inturn means that the left picture has a slower speed than the right picture.
That is what we want to demonstrate.

Experimental results with two clocks moving in opposite directions.

              .       .    b   .
8          q .  a    b    b  .  c   
    q    q  . a    a.   b3  . c    
7      q4  .a    a .  b    z    
     q    a    a  . b    b.   c2    
6       q.   a3  .b    b .  c    y
        .  a    z    b  . c    c.
5      . a    a.   b2  .c    c .  d  
      .     a .  b    y    c  . d
4    .    a  . b    b.   c1  .d
    .   a2  .b    b .  c    x    d
3  .  a    y    b  . c    c.   d0
  . a     .   b1  .c    c .
2.a      .  b    x    c  .
a       . b    b.   c0  .
1  a1  .b    b .       .         
      x    b  .       .
0   a.   b0  .       .
 0----1----2----3----4----5----6

                                         
  .       . m     .       .   
8  .l    l .  m    m       .
    . l    l.   m3  .       .  
7    .  l    z    m  .          o4  
     k.   l2  .m    m .       n
6      y    l  . m    m.   n3  .
    k1  .l    l .  m    z       . 
5x    k  . l    l.   m2  .n      .
  .k    k .  l    y    m  . n     . 
4  . k    k.   l1  .m    m .  n 
    .  k    x    l  . m    m.   n2
3    .   k0  .l    l .  m    y        
      .       . l    l.   m1  .
2      .       .  l    x    m  .
                .   l0  .m    m .
1                .       . m    m.   
                  .       .  m    x   
0                  .       .   m0   .  
 0----1----2----3----4----5----6----

The two central points or calibration points are the events c0 in picture 3 and l0 in picture 4.

• c0 is the event that observer C emits a light flash in two directions. These flashes are reflected at the events x and observer sees the reflections at event c1 and for the second time at event c2.
• l0 is the event that observer L emits a light flash in two directions. These flashes are also reflected at two events x and observer sees the reflections at event l1 and for the second time at event l2.

In picture 3 b0 is the event that observer B emits a light flash. These flashes are also reflected at the event x. All the three events x in picture 3 are simultaneous.
The same for the 3 events a1,b1 and c1. The same for the 3 events a2,b2 and c2.

In Picture 3 when observer C travels from c0, via c1 to c2 he or she will also observe some of the flashes of the observers in Picture 4.
To be more specific when observer C is at c2 observer O is (almost simultaneous) at o4. That means when the clock of observer C counts 2, the clock of observer O counts 4.

In picture 4 the same is observed. When observer L travels from l0, via l1 to l2 he or she will also observe some of the flashes of the observers in Picture 3.
To be more specific when observer L is at L2 observer Q is (almost simultaneous) at q4. That means when the clock of observer L counts 2, the clock of observer Q counts 4.

This means that observer C will claim that his clocks runs the slowest and his speed is the fastest. But so will observer L. The numbers used will be the same.
The solution is to agree upon that both speeds are identical but in opposite directions.

Reflection 1

As indicated above in both platforms there are simultaneous events. There exists no physical meaning in the simultaneous events at each platform, because it is based on what observers see.
There is only one exception and that are the events a0 and k0 because they are used to establish one reference event between the two platforms or frames.

What is of physical importance is to establish the frame or platform with the lowest speed.

Reflection 2 - Relativity of simultaneity

This concept is called: "Relativity of simultaneity", which means that in each reference frame observers can establish simultaneous events (relative to the frame) but these events are not simultaneous in a different frame.
The question is what is the purpose when there is no general agreement, when there is no common rule to establish which events are happening simultaneous and which not. This is important to establish what is the cause (which is first, earlier) and what are the effects (which are later).

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