On the Electrodynamics of moving Bodies - by A. Einstein 1905 - Article review - Appendix 1

Appendix 1 is part of the Article Review "On the Electrodynamics of moving Bodies - by A. Einstein 1905 - Article review".
To read the article review select: Article_Review_On The Electrodynamics Of Moving Bodies.htm

Appendix 1 belongs to "Reflection 4 Conclusion".
To read select: Reflection 4 - Conclusion.

Appendix 2 is also part of the Article Review "On the Electrodynamics of moving Bodies - by A. Einstein 1905 - Article review".
To read "Reflection 4 - Conclusion - Appendix 2" select: Article_Review_Moving Bodies_Appendix2.htm

Contents

• 1. Introduction
• 2. Detailed explanation of frame 1 to 6.
• 3. Conclusion

1. Introduction

In Reflection 4 two experiments are discussed, called Experiment 1 and Experiment 2. Picture 1 shows the details of these experiments.
When you move the mouse over picture 1 there is a small change in Frame 4.

Picture 1

Picture 1 is divided into two parts.

• The left part shows the results of experiment 1
• The right part shows the results of experiment 2.

In each experiment, from a principle point of view, two objects are involved: A clock at rest and a moving clock.
In fact, in each experiment, many clocks at rest and many moving clocks can be involved, but if that is the case all the clocks (considered) at rest have the same speed and all the moving clocks have the same speed and are connected to a moving rod or grid.
What is also important that all the clocks at rest are synchronized as discussed in the article in Paragraph 1. The easiest way is to connect all clocks to a grid with all the nearest clocks at the same distance.
For the moving clocks, the same strategy should be followed i.e start with synchronization at rest and then move the grid with the speed and in the direction as planned. Because all the clocks have the same speed and direction and all the clocks experience the same physical forces and conditions, all the clocks stay synchronized within the moving grid. It is important to understand that the behaviour of the clocks between different grids is not the same. That is the situation studied in the two experiments in which one clock of each grid is studied.

Going back to picture 1 both parts are divided into three sections:

• The top parts shows speeds of one clock at rest and one moving clock in one direction. The clock at rest is shown in green and the moving clock in red.
• The middle part shows the ticking rate of both clocks
• The bottom part shows the time of both clocks.
  When you compare the difference between frame 3 at the left side versus frame 6 at the right side, it is rather easy to observe that in frame 3 the moving clock (the red clock) runs slower and in frame 6 faster. This will be explained in the second half of this document

2. Detailed explanation of frame 1 to 6.

1. Frame 1 shows the speed of a clock at rest versus the speed of a moving rod. The clock at rest is the green line. The moving clock the red line.
   Because the speed of the clock at rest is constant, the green line is straight.
   For the moving clock, the situation is different. When you consider frame 3 you can see that the speed is changed at 8 different events, which are paired. The events 1,2 are a pair. The events 3,4 are a pair etc.
   Because each clock can be considered a space ship (or the rod or the grid to which all the clocks are attached) event 1 indicates that an engine is started and event 2 that the engine is stopped. The physical meaning is that the clock or rod or grid moves in a straight line through space.
   Events 3 and 4 are used to stop the movement of the clock (etc). To do that the direction of engines which control the movement is set in reverse. At event 3 the engine is started and at event 4 the engine is stopped.
   Starting from event 4 the green line and the red line coincide.
   Events 5 and 6 are used to bring the clock back to base. Event 5 is used to start the engine and event 6 to stop the engine because the engine is still in reverse the clock (etc) will move back to base. Events 7 and 8 are used to stop the clock. To do that first the engines are set back in the original direction (like in event 1). The engine is started at event 7 and stopped at event 8. This will bring the clock back to base. (in picture 1)

   Frame 1 shows what is commonly named the twin paradox. One twin stays at home (clock 1) and another twin is sent to another star and travels back to base. (clock 2)

2. Frame 2 shows the rate of the clock at rest versus the rate of the moving rod.
   Because the rate of the clock at rest is constant the green light is straight
   Initially, the moving clock is also at rest, that means initially the red line and the green line coincide.
   At events 1 and 2, the clock starts to move and starting after event 2 the moving clock has a lower rate.
   The events 3 and 4 have a different effect. The speed of the clock decreases and the rate of the clock increases and is the same as the clock at rest when the speed of the clock is zero.
   The events 5 and 6 are used to move the clock in the opposite direction, but this has no extra consequences for the behaviour of the clock. In between the events 5 and 6, the speed of the clock increases and the rate of the clock decreases and becomes constant thereafter.
   The events 7 and 8 are similar to the events 3 and 4. The speed of the clock decreases and the rate increases and at the end is the same as the clock at rest.
3. Frame 3 shows the time of the clock at rest and the moving clock.
   Because the rate of the clock at rest is always the same the time of the clock increases linear.
   For the moving clock, the situation is different. Specific after event 2 and after event 3 the rate is lower, the time of the moving clocks either ticks at the same rate as the clock at rest or lower. The conclusion is that the moving clock runs slower as the clock at rest.
   This coincides with experiments which are used to demonstrate the twin paradox.
4. Frame 4 shows more or less the same situation as Frame 1 but from a slightly different angle.
   When you observe frame 1 there is a vertical line in between the events 2 and 3. That situation is the starting condition for experiment 2. From a physical point of view, the engine of the moving clock is turned off and the clock moves in a straight line through space. Experiment 2 starts with a whole new set of clocks which are all synchronized with the moving clock from experiment 1. (somewhere in between event 2 and 3). The observer now can consider himself at rest and as such experiment 1 and 2 are the same.
   What we are discussing is the initial state of each experiment i.e. the period before event 1. In all the frames 1-6 the green line and red line coincide.
   That means the initial physical condition for both clocks in experiment 1 are the same. For experiment 2 both clocks are also the same.
   But if you compare a clock in experiment 1 with a clock in experiment 2 they are physical different.
   In frame 1 and frame 4 each, the green line coincides with the red line, but in frame 4 (experiment 2) the green line does not coincide with the green line of frame 1. The starting condition for experiment 2 is the moving clock after event 2 in experiment 1. The moving clock (or observer) is considered at rest in experiment 2. This is also realised by synchronizing all the clocks in experiment 2 with the moving clock of experiment 1. Physical all the clocks in experiment 2 are not at rest but moving.
   This is important, to understand what happens next.
5. Event 3 in experiment 1 involves that the direction is set in reverse and that the engine is started.
   Event 1 in experiment 2 involves the same: the direction is set in reverse and the engine is started.
   In both, this is done to stop the clock.
   If you compare the red line in frame 1 at event 3 and 4 with the red line in frame 4 in the events 1 and 2: they are the same. In both cases the speed goes to zero.
   When you compare the red line in frame 2 at the events 3 and 4 with the red line in frame 5 in the events 1 and 2: they are also the same. The difference is here that the clock rate is increasing.

   An important difference exists if you compare event 1 and 2 in frame 2 with event 1 and 2 in frame 5.
   In frame 2 starting from an initial state with all the clocks at rest synchronized, the moving clock runs slower.
   In frame 5 starting from an initial state with all the clocks, considered at rest, synchronized, the moving clock runs faster.
   When you compare frame 3 with frame 6 this becomes visible after event 2.

6. When the mouse is not above picture 1 you will see that the shape of the red curve is identical when you compare the event pairs (3,4) with (1,2), the pairs (5,6) with (3,4) and the pairs (7,8) with (5,6): they are physical the same. That means the experiments 1 and 2 are physical almost the same, except after event 2 in experiment 1 a different clock at rest is selected, at the start of experiment 2. The clock at rest in experiment 2 is the moving clock in experiment 1.

When you put the mouse above picture 1 (or picture 2) the speed of the clock involved in the events 4,5 and 6 in frame 4 changes from negative to positive. This does not influence the outcome of the experiment. The reason is to amplify the importance of speed versus at rest and not so much the direction i.e. either positive or negative.

Picture 2

3. Conclusion

In experiment 1 we started with 2 clocks we physical considered at rest.
In experiment 2 we started with 2 clocks which are physical moving, but which we considered at rest.
The result is that in experiment 1 a moving clock is running slow and in experiment 2 a clock, we considered moving, is running fast. This smells to a contradiction.
The importance of the two experiments is based on the assumptions which clock is at rest because the outcome of the experiment is different. Is this the clock at rest in experiment 1 or the clock at rest in experiment 2? It can not be both, because the two experiments are physical, different.
The only thing we now that:

1. If experiment 1 is performed 100 times, based on a clock we have selected, which we call our standard clock at rest, each time with the same speed v and a different direction and in all cases the moving clock run faster than we know that our standard clock is a very bad selection. Our next step is to select a better standard clock and repeat the same procedure.
2. If experiment 1 is performed 100 times, based on a clock we have selected, which we call our standard clock at rest, each time with the same speed v and a different direction and in 50% of the cases the moving clock run slower and in 50% faster than we know that our standard clock is a mediocre selection. The next step is to decrease the speed v and see if we can increase the accuracy the experiment 1.
3. If experiment 1 is performed 100 times, based on a clock we have selected, which we call our standard clock at rest, each time with the same speed v and a different direction and in all cases the moving clock run slower, than we know that our standard clock is a very good selection. The next step is to decrease the speed v and see if we can increase the accuracy the experiment 1.

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