How are watches syncronized

[Gerenuk]

How, in theory, would you syncronize watches provided all you can do is sending a signal to another spot in space?

What if you cannot make any assumptions about the travel time of the signal? I mean what if it's possible that that signal travels at unknown speeds and the speeds in different directions might be different (speed in and out are different)?

What if you cannot even assume that your watch will run at the same frequency as somewhere else?

 

[Jonathan Scott]

How, in theory, would you syncronize watches provided all you can do is sending a signal to another spot in space?

The way we synchronize watches in physics assumes the time a signal takes to go in one direction is the same as it takes to come back again.

 

[Bob S]

I once had to synchronize 8 "clocks" to a few nanoseconds over a period of days. I used a master "clock" (oscillator) at about 1 MHz and 8 slave clocks on VCXOs (voltage controlled crystal oscillators).
Bob S

 

[Gerenuk]

I rather mean the case where you sit at one train station and all you have to syncronize with a guy at another distant train station, is a slowly traveling train. There might even be the difficulty that you cannot be sure that the train travels the same speed in both direction. Is there anything you can do from here?

In case that you are actually forced to assume that the travel speeds are equal and this assumption will never bring up any contradiction (even if it isn't true), could this be the explanation why the speed of light is supposed to be equal in all frames?

 

[Jonathan Scott]

I rather mean the case where you sit at one train station and all you have to syncronize with a guy at another distant train station, is a slowly traveling train. There might even be the difficulty that you cannot be sure that the train travels the same speed in both direction. Is there anything you can do from here?

In case that you are actually forced to assume that the travel speeds are equal and this assumption will never bring up any contradiction (even if it isn't true), could this be the explanation why the speed of light is supposed to be equal in all frames?

For non-relativistic speeds, you can carry watches around and they are nearly correct everywhere. If you know relativity and you keep track of your own acceleration (as in an inertial guidance system) and the internal mechanism of the "watch" is not affected directly by the motion, then you can use relativity to calculate the time that has elapsed in the original frame and adjust the "watch" (which would need to be an atomic clock to be accurate enough) accordingly, to allow it to be used to synchronize other clocks relative to the original frame.

We normally assume that distances are the same in both directions and that light travels at the same speed in both directions. When we get into relativity, we find that relative to someone else who is moving, neither of these holds, but the Lorentz transformation can be used to transform one person's viewpoint into another.

 

[Dale]

In the absence of any reliable way of signalling you need to use slow clock transport. In other words, bring all of the clocks together, synchronize them, then move them slowly to their destination. You can use SR to determine how slowly you must go based on your precision requirements.

 

[DrGreg]

How, in theory, would you syncronize watches provided all you can do is sending a signal to another spot in space?

What if you cannot make any assumptions about the travel time of the signal? I mean what if it's possible that that signal travels at unknown speeds and the speeds in different directions might be different (speed in and out are different)?

What if you cannot even assume that your watch will run at the same frequency as somewhere else?

This is a perceptive question. Clock synchronisation is a convention rather than an experimentally verifiable fact.

We need to make a distinction between

• the "one-way" speed of light from A to B
• the "two-way" speed of light sent from A to a mirror at B and reflected back to A again

The 2-way speed can be measured by experiment: you measure the distance A to B, double it, and divide by the time taken measured by a single clock at A. All experiments show the 2-way speed of light is constant (when A and B are both inertial and relatively stationary).

But for the 1-way speed you need two clocks at A and B which need to be synchronised. The truth is, we could choose to synchronise the clocks in lots of different ways and we'd get lots of different answers for the 1-way speed of light. It is a convention that we choose to sync clocks in such a way to make the 1-way speed equal to the 2-way speed. That convention works and gives rise to a self-consistent theory we call special relativity.

Another way to sync clocks would be to use a slow train as you suggest. It has to be a slow train. A fast train would give rise to the twins paradox: you could take a train from A to B to sync B to A, but if the train returned to A, the train clock would be out of sync with A's clock, showing the procedure is inconsistent. But we can use a slow train and consider the calculus limit as the train speed approaches zero. It can be shown that this "ultra slow clock transport" method syncs clocks in exactly the same way as the standard "Einstein synchronisation convention".

Postscript: since 1983 the 2-way speed of light has been constant by definition, as the metre is now defined in terms of light. Before then, the 2-way speed of light was determined by experiment.

 

[pervect]

Note that if you use "unconventional" clock synchronizations, you cannot, in general, apply standard physics. Specifically, the relation between velocity and momentum gets seriously messed up if you measure velocities using non-synchronized clocks.