Appendix 2 is part of 1905 Article Review section: "Reflection 4  Conclusion" . To read select: Reflection 4  Conclusion.
The 1905 Article Review also contains an Appendix 1. In order to read "Reflection 4  Conclusion  Appendix 1" select: Article_Review_Moving Bodies_Appendix.htm
clock  v0  n0  v1  v^2  c^2  gamma  n1  time 0  time 1 
2  0  0  0  100  100/100  
3  0  1000  1  1  100  99/100  990  1000  990 
4  0  500  2  4  100  96/100  480  1500  1470 
5  0  333  3  9  100  91/100  303  1833  1773 
6  0  250  4  16  100  84/100  210  2083  1983 
7  0  200  5  25  100  75/100  150  2283  2133 
8  0  166  6  36  100  64/100  106  2449  2239 
9  0  166  6  36  100  64/100  106  2615  2345 

clock  n0  v0  v1  v^2  c^2  gamma  n1  time 0  time 1 
2  0  0  0  100  100/100  
1  1000  0  1  1  100  99/100  990  1000  990 
0  500  0  2  4  100  96/100  480  1500  1470 
1  333  0  3  9  100  91/100  303  1833  1773 
2  250  0  4  16  100  84/100  210  2083  1983 

clock  n0  v0  v1  v^2  c^2  gamma  n1  time 0  time 1 
19  166  0  6  36  100  64/100  106  4275  3405 
20  166  0  6  36  100  64/100  106  4441  3511 
21  200  0  5  25  100  75/100  150  4641  3661 
22  250  0  4  16  100  84/100  210  4891  3871 
23  333  0  3  9  100  91/100  303  5224  4174 
24  500  0  2  4  100  96/100  480  5724  4650 
25  1000  0  1  1  100  99/100  990  6724  5640 
25  1000  0  0  0  100  100/100  1000  7724  6640 

clock  v0  v0  v1  v^2  c^2  gamma  n1  time 0  time 1 
20  6  6  0  100  100/100  
21  6  1000  5  1  100  99/100  1010  1000  1010 
22  6  500  4  4  100  96/100  520  1500  1530 
23  6  333  3  9  100  91/100  365  1833  1895 
24  6  250  2  16  100  84/100  297  2083  2192 
25  6  166  1  25  100  75/100  221  2249  2413 
26  6  0  36  100  64/100  2249  2413 





What this experiment demonstrates is that a moving clock ticks slower.
Table 5a can also be used in the opposite direction i.e. in both directions.
After reaching clock #11 the engine should be stopped and set in reverse. When the engine has stopped the speed of the moving clock stays the same i.e. at v=4. When the engine is started at clock #12 the next clock readings should be #15 (v=3), #17 (v=2), #18 (v=1) and engine off (v=0)
Also, this experiment demonstrates that a moving clock ticks slower.
This same signal can also be used to reset the two clocks at the front end and back end of a rod, which has the distance l and which position coincides with two clocks at rest.
In order to observe the behaviour of moving clocks, perform the following experiment:
The following picture indicates what this means:

Picture 3 on the left shows the position of a moving rod: A blue one, a red one, and a brown one. Each of these lines shows an observation point (at the back), along the rod, which can move along the xaxis. At that observation position, there is a clock and an observer. Normally there are two observation points along the rod: one in front and one in the back. Along the xaxis are there are 6 clocks. These 6 clocks are synchronized and considered at rest.

Using the equation v/c = sqrt((nAnB)/nA) with nA being the number of counts of the clock at rest and nB the number of counts of the moving clock:
We get with nA=20 and nB= 19: that v/c= sqrt(1/20) = 0,2236 or v = 0,2236 * c
We get with nA=18 and nB= 16: that v/c= sqrt(2/18) = 0,3333 or v = 0,3333 * c
We get with nA=16 and nB= 13: that v/c= sqrt(3/16) = 0,4430 or v = 0,4430 * c
see: Reflection 3  Worldline Perpendicular Mirrors  Twin Paradox
In the above, the moving object is a rod with length l the same as the distance between the clocks at rest.
What you can also do is to make the moving rod much longer and add extra clocks a distance l apart.
What that means is that now all observers near the clocks at rest can observe the behaviour of the moving clocks.
Summary
But now consider that the clocks along the red line are at rest.

What this means, if the reasoning is correct, it is possible to decide, by means of an experiment if a single clock is moving or at rest.
The only way to do that is to assume that the clock is moving and to demonstrate that there can be clocks which move with a lesser speed. See for more detail 2. Experiment 1
It also should be mentioned that all clocks attached to a rod move in a straight line. Any form of rotation introduces different forces on the moving clocks and jeopardize the synchronization. As such it should be clear that different clocks, attached to each other, in orbit around the earth, never can stay synchronized.
Picture 4 
Picture 5 
Picture 6 
Picture 7 
The next 3 tables give a physical indication of the physical length change involved.



Table 6B is the easiest to understand. In this case v=0.
In line 6 there are two numbers 499 in the Blue section. They indicate the standard number of counts (500) between two clocks readings, for an observers which moves at a speed of v=0.1 along a standard distance of 50 in a frame considered at rest. Because there are 8 clocks the total distance is 7*50=350.
In line 7 the speed is v=0.2, this is twice as fast. The number of counts changes to 500/2 = 250.
In line 8 the speed is v=0.3, this is three times as fast. The number of counts changes to 500/3 = 166.
The Red part considers the situation for the moving clock.
In line 6 in the red section there are two numbers 499 and 494. The first number in the column c0 indicates the number of counts compared with a clock at rest. The second number, in the column c1, indicates the number of counts with a moving clock.
For example: consider the situation that all the clocks are at rest and receive a reset signal, including the clock #1 for observer A at position #1. At the same moment when observer A receives his reset signal he starts to move with a fixed speed. At the moment when observer A reaches position #2, his moving clock will read 494 and clock #2 at rest 499.
In line 7 in the red section there are the two numbers 250 and 240. The first number in the column c0 indicates the number of counts compared with a clocks at rest, which should be 500/2 because the clock travels twice as fast. The second number, in the column c1, indicates the number of counts with a moving clock, which indicates that the moving clock starts to run slower and slower.
Table 6A shows information belonging to Picture 7.
Table 6C shows information belonging to Picture 6.


#  colour  v  x1  y1  x2  y2  x  y  n0  nv  
1  blue  0  205  175  205  375  205  341,66  166  166  
2  green  0.3  155  175  187,96  284,89  205  341,66  166  158  
3  blue  0  105  175  105  375  105  341,66  166  166  
4  red  0.3  155  175  122,03  284,89  105  341,66  166  158 
#  colour  v  x1  y1  x2  y2  x  y  n0  nv  
1  blue  0.3  155,27  167,58  221,2  387,36  210,21  350,73  183  174  
2  green  0  210,21  184,06  210,21  284,06  210,21  350,73  166  166  
3  blue  0.3  265,16  200,54  331,09  420,32  310,21  350,73  150  143  
4  red  0.6  210,21  184,06  303,96  340,31  310,21  350,73  166  133 

Table 8 is divided in two parts: A top part and a bottom part.

Because the Blue clock is not moving (v=0) the number of counts in both the columns n0 and nv, in each line, are the same.


It is not possible by studying the behaviour of these clocks, which of these set of clocks is actual at rest.
Under the assumption that we start from one set and we divide them in two sets:
In all the cases after, changing the speeds of the synchronized clocks belonging to one set, all these clocks will seem to run lower.
Only by studying the distances between the clocks within one set, and the distance does not change such a set of clocks can be called at rest. The same is true when the clocks in someway are internally connected. When there are internally no physical tensions the clocks clocks can be called at rest.
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