Special relativity & Synchronization of clocks

[noxurxo]

Lets consider the following experiment:
A-------CD-------B
where C and D are synchronized clocks (same position), while A and B are two points at the "same distance" from CD.
We move the clock C to A and take a photo Pa when it reaches A.
We move the clock D to B and take a photo Pb when it reaches B.
I see a problem: how we know the distances AC and DB are the same?
Lets repeat this experiment where the clocks are in the center of a sphere and the positions A and B are at opposite points on the surface of the sphere.
Will be all the photos taken at the different Ai and Bi points show the same time?

 

[Ibix]

You mean, you zero the clocks before they start moving and record the times they show when they reach A and B? No, they will not record the same time in general. You need to specify the velocity profile of the clocks on their trips so that they vome out equal. Having exactly the same profile for both clocks (except in opposite directions) in the rest frame of the sphere is the easiest way to do it.

 

[noxurxo]

You mean, you zero the clocks before they start moving and record the times they show when they reach A and B? No, they will not record the same time in general. You need to specify the velocity profile of the clocks on their trips so that they vome out equal. Having exactly the same profile for both clocks (except in opposite directions) in the rest frame of the sphere is the easiest way to do it.

Sorry, my fault. They start at zero and move at the same speed (theoretically).

 

[Ibix]

Same speed in which frame?

 

[noxurxo]

Same speed in which frame?

Lets say you push each of the clocks with the same force.

 

[PeroK]

Lets say you push each of the clocks with the same force.

Generally, if you have a symmetrical experiment, then the results will be symmetrical.

I'm not sure where your thought experiment is leading?

 

[noxurxo]

Generally, if you have a symmetrical experiment, then the results will be symmetrical.

I'm not sure where your thought experiment is leading?

If the clocks at A and B show the same time, and we only take a photo when reaching A and B but we do not stop the clocks, this would mean that we could emit a beam of light from A to B and measure the speed of light in one direction (obviously not but I do not see the error).

 

[FactChecker]

To get the same distances, A->CD and CD ->B:
Flash a light from A to a mirror at CD and record the elapsed time for the reflection to return to A.
Similarly, flash a light from CD to a mirror at B and record the elapsed time for the reflection to return to CD.
If the elapsed times are identical, the distances are identical.
This allows the clocks to be stationary and each elapsed time is measured by one stationary clock. It also allows the light paths to be identical up to a translation.

 

[Ibix]

Lets say you push each of the clocks with the same force.

That doesn't help unless you specify the frame - forces are not invariant in relativity.

I guess you want the clocks to have equal and opposite velocities in the frame where the sphere is at rest. In this case they will record equal times, but if you pick sny other frame they will not.

A big challenge for people starting with relativity seems to be how clear you have to be about which frame you are using to measure things. So many more things depend on it than in Newtonian physics.

 

[noxurxo]

That doesn't help unless you specify the frame - C

I guess you want the clocks to have equal and opposite velocities in the frame where the sphere is at rest. In this case they will record equal times, but if you pick sny other frame they will not.

A big challenge for people starting with relativity seems to be how clear you have to be about which frame you are using to measure things. So many more things depend on it than in Newtonian physics.

 

[Dale]

A and B are two points at the "same distance" from CD ... how we know the distances AC and DB are the same?

Since we are given that A and B are two points at the same distnace from CD then the distances AC and DB are the same.

This is simply something that you specified in the setup. No mystery whatsoever.

 

[noxurxo]

I do not understand this, sorry. The force is applied at the same position CD. I do not see clearly why this matters, may I have to study more. Thanks for your answers.

 

[noxurxo]

That doesn't help unless you specify the frame - C

I guess you want the clocks to have equal and opposite velocities in the frame where the sphere is at rest. In this case they will record equal times, but if you pick sny other frame they will not.

A big challenge for people starting with relativity seems to be how clear you have to be about which frame you are using to measure things. So many more things depend on it than in Newtonian physics.

To get the same distances, A->CD and CD ->B:
Flash a light from A to a mirror at CD and record the elapsed time for the reflection to return to A.
Similarly, flash a light from CD to a mirror at B and record the elapsed time for the reflection to return to CD.
If the elapsed times are identical, the distances are identical.

I try to understand why this experiment is wrong trying to measure the speed of light in one direction. I know that it has to be wrong but I do not see where.

 

[Dale]

In a synchronization convention where the one way speed of light is not isotropic, force is also not isotropic. Pushing with a mass with a given force in one direction gives a different velocity than pushing the same mass with the same force in the opposite direction.

 

[noxurxo]

In a synchronization convention where the one way speed of light is not isotropic, force is also not isotropic. Pushing with a mass with a given force in one direction gives a different velocity than pushing the same mass with the same force in the opposite direction.

Ok, thanks, I think I understand that. So, we could have the same value for the clock at positions A and B because the force differs in the same proportion as the speed changes. Thank you for your explanation.

 

[Ibix]

I try to understand why this experiment is wrong trying to measure the speed of light in one direction.

You aren't measuring the speed of anything, as far as I can see.

You can use this approach as a clock synchronisation methodology, and it's usually called "slow clock transport". However, it's equivalent to Einstein clock synchronisation. The problem is that if you assume anything other than an isotropic speed of light then you get an anisotropic clock drift as the clocks move - time dilation is stronger in one direction than the other. So the fact that the clocks show the same time tells you that they're out of sync.

 

[FactChecker]

I try to understand why this experiment is wrong trying to measure the speed of light in one direction. I know that it has to be wrong but I do not see where.

Measuring in one direction will always raise the question of how the clocks at both ends are synchronized. No matter how you hard you try, you can not get around that problem.

 

[PeroK]

I try to understand why this experiment is wrong trying to measure the speed of light in one direction. I know that it has to be wrong but I do not see where.

You can measure the speed of light in one direction. However, the answer you get depends on the simultaneity convention. There is no single convention. Your convention- using symmetric clock transport- is equivalent to the Einstein simultaneity convention. This is, however, not the only option.