Comments about "Einstein synchronisation" in Wikipedia

This document contains comments about the document "Einstein synchronisation" in Wikipedia

• The text in italics is copied from that url
  
• Immediate followed by some comments
  

In the last paragraph I explain my own opinion.

Contents

• 1. Einstein
• 2. History: Poincaré
• 3. See Also

Reflection

• Reflection 1 - Definition synchonization
• Reflection 2 - How to synchronise clocks
• Reflection 3 - One way light speed.
• Reflection 4 - Michelson-Morley Experiment.
• Reflection 5 - Thought experiment.

Introduction

The article starts with the following sentence.

Einstein synchronisation (or Poincaré–Einstein synchronisation) is a convention for synchronising clocks at different places by means of signal exchanges. etc Its principal value is for clocks within a single inertial frame.

Nothing is mentioned what synchronisation physical means.
IMO synchronised clocks should all show, what you should call universal time. Synchronised clocks in principle should all indicate the age of the universe.
See also: Reflection 1 - Definition synchonization

1. Einstein

The document starts with a convention:

According to Albert Einstein's prescription from 1905, a light signal is sent at time T1 from clock 1 to clock 2 and immediately back, e.g. by means of a mirror. Its arrival time back at clock 1 is T2. This synchronisation convention sets clock 2 so that the time T3 of signal reflection is defined to be T3 = T1 + 0.5 * (T2 - T1) = 0.5 * (T1 + T2).

The first question to answer is:

If you position two identical clocks at whatever position on the surface of the earth does the time difference between these two clocks always stays the same?

If the anser is No than you can never synchronise these two clocks, implying that you cannot use this prescription to synchronise clocks at the surface of the earth.
The second question is:

Where or in what type of system can you use this prescription?

IMO only in an artificial 3D frame consisting of a 3D grid of rods with the same fixed length.
When you place identical rods at the grid points then by using this prescription all the clocks run "synchroneous"

The literature discusses many other thought experiments for clock synchronisation giving the same result.

Why is this called a thought experiment?
Thought experiments can not be used to perform science.

The problem is whether this synchronisation does really succeed in assigning a time label to any event in a consistent way.

Why this doubt ?
To answer that question you should place at each position two clocks and perform the convention twice.
If after the second synchronisation experiment the difference between all the pairs of clocks is not identical than your clocks are not correctly synchronised.

To that end one should find conditions under which
(a) clocks once synchronised remain synchronised,

This seems to me a rather ad hoc sentence.
IMO the only (?) way to have synchronised clocks is to take care that the distance between the clocks stays the same, that means to place them in some sort of grid,
The only way to test this is to perform Einstein Synchronization twice.

If point (a) holds then it makes sense to say that clocks are synchronised.

See also Reflection 1 - Definition synchonization

For this reason, and since more recent developments are not so well known, some physical papers still present the assumption of consistency of Einstein synchronisation among the postulates of relativity theory.

Einstein synchronisation is also important to apply Newton's Law. With out a frame and synchronised clock's you cannot measure positions and velocities.

Once clocks are synchronised one can measure the one-way light speed.

Only when all clocks are synchronised. See Reflection 1 - Definition synchonization How do you do that in practice ?
In theory when a signal is transmitted at 0 seconds and received 1 msec later and the distance is 300 km and constant than the speed of light is 300000 km/second. In practice this is more difficult.

However, the previous conditions that guarantee the applicability of Einstein's synchronisation do not imply that the one-way light speed turns out to be the same all over the frame

What does this mean? Does this imply that the speed of light is not constant?
IMO light i.e. the movement of photons or the movement of energy, most probably is not a process that will continue at infinitum in "space".

Consider Von Laue and Weyl's round-trip condition: The time needed by a light beam to traverse a closed path of length L is L/c, where L is the length of the path and c is a constant independent of the path.

Einstein synchronisation convention describes also a closed path. This is the simplest version of a closed path. In fact the Michelson Morley uses that same approach in two perpendicular directions. The whole problem is that both clock1 and clock2 rotated versus the center of the earth. This means that when the lightsignals moves from clock1(T1) to clock2(T2) and back to clock1 (T3) that clock1 has moved making it not a closed path.
Next we read:

Since it is meaningless to measure a one-way velocity prior to the synchronisation of distant clocks, experiments claiming a measure of the one-way speed of light can often be reinterpreted as verifying the Von Laue and Weyl's round-trip condition.

Before measuring one-way velocity ofcourse it is important to synchronise the clocks involved.
In order to synchronise you have to perform the Einstein Synchronisation Convention which is the simplest form of a round trip.

The Einstein synchronisation looks this natural only in inertial frames

Consider that I perform clock synchronisation as discussed in Reflection 2 - How to synchronise clocks not once but twice in different inertial frames.

One can easily forget that it is only a convention. In rotating frames, even in special relativity, the non-transitivity of Einstein synchronisation diminishes its usefulness.

This raises the question what is a convention? Is that a thought experiment?
what is even more "painfull" is that almost all reference frames are rotating
either around the earth, around the sun or around our galaxy.

Synchronisation around the circumference of a rotating disk gives a non vanishing time difference that depends on the direction used.

That is why a previous comment claimed that if you perform the same chronisation procedure twice and the results are not the same none of the clocks are synchronised.

2 History: Poincaré

In 1898 (in a philosophical paper) he argued that the postulate of light speed constancy in all directions is useful to formulate physical laws in a simple way.

Did he mean this constancy strictly local or global for the entire universe?
The problem is, based because light is a physical proces, is it true?
For example what about black holes?

3. See Also

Following is a list with "Comments in Wikipedia" about related subjects

• One-way speed of light Comments
• Relativity of Simultaneity Comments.
• Time_dilation Comments

Reflection - synchonization

A4. - - - /D4 |B4 /C4 | . / | / A3. D3 . | / | . / . | / | / . . / A2| - / - - . - | - .C2 A1| - / - - - - - .B1 / | / . | / | / . | / |/ . |/ A0-------D0---------B0 C0

The sketch on the left shows a light source at A0 and two mirrors. There are two clocks at A0 and B0. mirror's at rest at the line A0 - A4 and B0 - B4. mirror's with a speed v at the line A0 - D4 and B0 - C4 c = 1, v = 0.2 c * t1 = A0B0 , A0B0 = 100: t1 = 100: B0 - B1 = 100 = A0 - A1 A0C0 = A0B0 + v * t2 = c * t2 : t2 = A0B0/(c-v) : t2 = 125 : C2 - C0 = 125 v * t3 + c* t3 = 2 * A0C0 : t3 = 2 * A0C0 / (v + c) : t3 = 208,33 D0 - D3 = 208,33 A0 - A1 = 100 , A0 - A2 = 125, A0 - A3 = 200, A0 - A4 = 250

What this sketch shows:

• is that the mirror at rest can be used to synchronise clocks at rest.
  The arrival times are resp 100 and 200 counts which can be used to synchronise the two clock's using Einstein synchronisation.
• is that the moving mirror can not be used to synchronise a clock at rest.
  The arrival times are resp 125 and 208,33 counts which cannot be used to synchronise the clock's using Einstein synchronisation.

Reflection 1 - Definition synchonization

What does it mean that two clocks are synchronised?
It should mean that the two clocks show the same time. Always. In fact the time on the clocks should run "synchroneous" with the age of the Universe.
To be more specific if you have two clocks anywhere in the Universe if they are synchronised they both should indicate the same age of the Universe.

Consider one sets of identical clocks, all clocks moving with the same speed, all clocks are at a fixed distance of each other, all clocks are synchronized and show the same time. This is set 1 and each clock is called clock 1.
Consider a second set of identical clocks. This is set 2 and each clock is called clock 2.
The difference beteen set 1 and set 2 that the clocks of set 2 have a speed v relative to set 1.
When you consider both sets as a total than the whole group is not synchronised implying that not all clocks can show universal time.

• Suppose the first time that any clock 1 meets a clock 2 the time on clock 1 is 100 and clock 2 is 100 counts.
• Suppose the second time that any clock 1 meets a clock 2 the time on clock 1 is 200 and clock 2 is 180 counts.
• Suppose the second time that any clock 1 meets a clock 2 the time on clock 1 is 300 and clock 2 is 260 counts.

That means the set of clock 2's are not synchronised with the clock 1's, they run the slowest and do not show the Universal time. There are two ways to make this visible with depends how the clocks are synchronised,

1. In the first scenario we start from a situation that the distance between the clock's in frame 2 is shorter than the distance between the clocks in frame 1 that the clocks are not connected with fixed rods and that the speed of each clock is controlled individually. See also "Bell's spaceship paradox" in Wikipedia.
   In this scenario there is no length contraction involved.

   100 100 100 100 100 A1 B1 C1 D1 E1 A2 B2 C2 D2 E2 100 100 100 100 100 Figure 1A

   200 200 200 200 200 A1 B1 C1 D1 E1 A2 B2 C2 D2 E2 180 180 180 180 180 Figure 1B

   300 300 300 300 300 A1 B1 C1 D1 E1 A2 B2 C2 D2 E2 260 260 260 260 260 Figure 1C

   • The Clocks A1,B1,C1 and D1 belong to set 1 and are synchronised in reference frame 1.
     
   • The Clocks A2,B2,C2 and D2 belong to set 2 and are synchronised in reference frame 2.
     
   In Figure 1A Clock C1 and C2 are at the same position.
   In Figure 1B Clock D1 and D2 are at the same position.
   In Figure 1C Clock E1 and E2 are at the same position, but also B1 and A2
   Clock 1 runs the fastest and because the two sets will always show different values it are only the clocks of set 1 that are truelly called synchronised and show the Universal time.
   This continues untill a different set is observed which shows even more faster running clocks.

   Figure 1A is based on the concept that the clocks of C1 and C2 are initialized when they meet with a count of 100 and that all the clocks are synchronised with this same count using Einstein synchronisation. In Figure 1A the difference between C1 and C2 = 0. In Figure 1B the difference between D1 and D2 = 20 and in Figure 1 C the difference is 40. That means there is a linear increase.
   

2. In the second scenario we start from a situation that the distance between the clock's in frame 1 and frame 2 is the same and that the clocks in frame 2 are not connected with fixed rods and that the speed of frame 2 is controlled from 1 point. The result is length contraction.
   
   • Figure 2A, 2B and 2C are based on reference frame 1.
   • Figure 3A, 3B and 3C are based on reference frame 2.

   100 100 100 100 100 A1 B1 C1 D1 E1 A2 B2 C2 D2 E2 120 110 100 90 80 Figure 2A

   200 200 200 200 200 A1 B1 C1 D1 E1 A2 B2 C2 D2 E2 200 190 180 170 160 Figure 2B

   300 300 300 300 300 A1 B1 C1 D1 E1 A2 B2 C2 D2 E2 280 270 260 250 240 Figure 2C

   80 90 100 110 120 A1 B1 C1 D1 E1 A2 B2 C2 D2 E2 100 100 100 100 100 Figure 3A

   180 190 200 210 220 A1 B1 C1 D1 E1 A2 B2 C2 D2 E2 180 180 180 180 180 Figure 3B

   280 290 300 310 320 A1 B1 C1 D1 E1 A2 B2 C2 D2 E2 260 260 260 260 260 Figure 3C

For more information about this experiment see also: "Relativity of Simultaneity" Comments wik_relofsim.htmReflection

Reflection 2 - How to synchronise clocks

In order to discus "How to synchronise clocks" and to make things simple we do not use time-of-the-day notation but counts.

1. First (as an example) with "Einstein synchronisation" when T1 (the start time of clock 1) = 0 counts and T2 (the arrival time of clock 1) = 10 counts then T3 (signal reflection time) is 5 counts.
   
2. Next in order to synchronise clock 2 with clock 1 (as an example) when clock 1 is 1000 counts we send to clock 2 a synchronisation signal of 1005 counts. When this signal reaches clock 2 the time of clock 1 will be also 1005 counts.
   This terminates clock synchronisation.

   This seems simple but is it correct? The problem starts when you consider clocks in a moving frame.

   | | / Q | / . . / | / . x | / . . / | x . / | / . . / |/ S / --------------

   In the picture at the left we have one source which transmits two light signals. They will both reach the point Q (Clock 2) simultaneous. When we issue a synchronisation signal of 1005, this signal will not reach the two points x simultaneous in the frame at rest.

Reflection 3 - One way light speed.

In order to calculate "One way light speed"

1. First you have to perform clock synchronisation as explained in Reflection 2 - How to synchronise clocks
2. Next in order to calculate "One way light speed" you need an observer at clock 2. When the observer receives the test signal he should monitor his clock. For example when the test signal is transmitted at 2000 counts the observer should receive this test signal at 2005 counts.

When this is the case everything is fine.
When this is not the case the time to forward and backward is different. The next thing to investigate is if this difference is direction dependent.
IMO there is a great chance that the arriving times are a function of the x direction of the grid. There will be a maximum and a minimum.

x 2005 2004 x x 2006 2003 x o x 2007 2004 x x 2006 x 2005 Figure 3

Figure 3 shows the different arriving times in arbitrary direction. Clock 1 is at the origin O and clock 2 is at the position marked 2. In all the cases the signal is transmitted when T1 of clock 1 is 2000 and T2 of clock 1 is 2010.

If the above is true or even worse that you measure different values but they are not on circle but more or less random, than it becomes clear that it is impossible to measure the speed of light only in one direction.
The "solution" of this problem is to introduce length contraction which takes care that the time of all the clocks are 2005

Reflection 4 - Michelson-Morley Experiment.

Consider an apartus i.e. a light source which produces laser light in 4 different directions with 4 detectors.

N ^ | W <- o -> E | V S v ---> Figure 4

Figure 4 shows the source at O and 4 four detectors marked N,E,S, and W The idea behind is to study this process from two perspectives. From a frame that moves with the aparatus. In that frame the source is at rest. From a frame centered about the center of the earth. In that frame the apparatus (source and detectors) moves in the direction of the arrow towards the East. The question is what are the differences in those two situations and how can they be detected.

• When you consider this problem from a frame at rest with the apparatus the behaviour of the process will be identical in all directions. IMO this is not very realistic because we know that the apparatus is placed on the surface of the earth which is rotating around its axis and in space around the sun.
  
• There are two ways in the case when you consider the movement from the center of the earth:
  1. The first way to consider is that as a result of the movement there is no physical change in the process at O.
     • When you consider O - E the distance will stay constant. This implies that the same frequency of transmitter and detector will be measured. The number of waves inbetween O - E will increase but this increase will not be detected.
     • When you consider W - O the same reasoning applies. The number of waves will decrease but will not be detected.
     • The directions O - N and O - S are physical identical. In this case the length of the light path will be longer and the number of waves will slightly increase.
     What the Michelson-Morley experiment does is to combine East West signals with the North South signal.
     It does that by placing at N and E a mirror which reflects each signal such that they combine at O. The result will be an interference pattern.
     When you do the math this interference pattern should change as a function of the speed v. The result of the experiment is that not such a change is detected. The solution is Length contraction which means that the physical length of the apparatus is shortened in the W/E direction.
  2. The second way is consider that the process itself changes as a result of the movement. The idea behind is that the process which generates the laser light (which is a process which generates light of one frequency) by itself is also a clock. The rate (freqeuncy) can be a function in which direction the clock moves (time dilation)

Reflection 5 - Thought experiment.

Remark: Thought experiments are not the same as physical experiments. They can easily be wrong.

• Consider a string of 9 clocks (counters) which are all synchronised using Einstein synchronisation. The distance between all the clocks is the same. When clock 1 performs Einstein synchronisation the results are T1=0 and T2=20 and T3=10 (clock 2)

  1 2 3 4 5 6 7 8 9 t0 1' 2' 3' 4' 5' 6' 7' 8' 9' --> t1 1' 2' 3' 4' 5' 6' 7' 8' 9' --> Figure 5

• Next consider a second string of 9 clocks (clocks) at the same position as string 1 with the same count. That means all the 18 clocks are synchronised. This are identified with an apostrophe (').
• At the same count all the clocks of the second string will start to move with a speed v.
  What will happen next. With each clock there is also an observer with a logbook.
  Two different scenarios are possible:
  1. In this case only time dilution is taken into account, implying that moving clocks run slower.
     • The results of this experiment shows that when clock 2 and clock 1' meets their counts are respectivily 100 and 90 (Example) That means the moving clocks tick slower.
     • For clock 9 and 8' when they meet their counts are also 100 and 90. That means the distance between all the clocks of both strings stay the same and all the clocks of the second string are all synchronised. This can be explained because all the process involved in the second string are identical.
     • Next clock 1' of string 2 will perform Einstein synchronisation. The results are monitored by the clocks (observers) of string 1. That means the observers of string 1 can observe the events T1, T2 and T3 using their synchronised clocks. The mathematics used is the same as the horizontal arm of the Michelson-Morley Experiment.
       The results will be that T1=0 T2=100/9 + 100/11 and T3=100/9 (Assuming distance = 1000, c=100 and v= 10)
       Their conclusion will be: You cannot use Einstein Synchronisation to synchronise your clocks because T3 <>(T1+T2)/2
  2. A whole different scenario is when both time dilution and length contraction a of string 2 are taken into account.
     • In that case the following results are possible:

       1 2 3 4 5 6 7 8 9 t1 1' 2' 3' 4' 5' 6' 7' 8' 9' --> t2 1' 2' 3' 4' 5' 6' 7' 8' 9' --> t7 1' 2' 3' 4' 5' 6' 7' 8' 9' --> t14 1' 2' 3' 4' 5' 6' 7' 8' 9' --> Figure 6

     • The line marked t7 shows the situation when clock 1' meets clock 2. In this situation clock 7'just starts to move and clock 8'and 9'did not move at all. What this indicates that all the clocks have a different time (count)
       In this case the counts of clock 2 and clock 1' are respectivily 100 and 90. The counts of clock 7 and 7' are each 100. The counts of clocks 2' to clock 6' are roughly 91.7, 93.3, 95, 96.7 and 98.3
     • The line marked t14 shows the situation when clock 1' meets clock 3. The distances between all the clocks is smaller and the total length is smaller.
       In this case also clock 7'meets clock 8 and clock 13' meets clock 13.
       Clock 3, clock 8 and clock 13 each will be 200.
       Clock 1' will be 180 and clock 7' will be 190 and clock 13' will be 200 (which just starts to move).
     • The problem is how do you do this thought experiment in practice.
  The second scenario raises a subtle problem related to Length Contraction : How does Length Contraction work in practice ?
  When you take a rod with a fixed length and you push the rod at the end with a speed v there are two options:
  1. The rod behaves as a fixed length rod. That means a change in speed at the end is instantaneous propagated throughout the rod untill the beginning including length contraction. That means the speed at the beginning is lower during a certain period than at the end. The fact that the speeds are different implies that the counts of a clock at the end could be 90 while the count at the beginning is still 100 (which is a clock at rest)

  In Figure 5 the clocks in string 2 are synchronised in the rest frame. In that case the speed of light is measured as c-v. In Figure 6 the clocks in string 2 are synchronised in the moving frame because length contraction is included. In that case the speed of light is measured as c. But physical the photons involved and the speeds are the same. The clocks in the moving frame do not show the time (age) of the universe.

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