Clock Synchronization and the Effects of Gravity in a Two-Story Building

[actionintegral]

My friend and I are in a two story building. I am on the lower floor, he is on the upper. We are in a constant gravitational field.

Is it true that our watches cannot be synchronized? If so, what is the proof of this claim?

 

[nakurusil]

My friend and I are in a two story building. I am on the lower floor, he is on the upper. We are in a constant gravitational field.

Is it true that our watches cannot be synchronized? If so, what is the proof of this claim?

They can be synchronized (as proven by the http://relativity.livingreviews.org/open?pubNo=lrr-2003-1&page=node5.html

 

[actionintegral]

Are you referring to the phenomenon known as "gravitational time dilation"?

 

[lalbatros]

I think that the clocks cannot really be synchronised.
However, an observer can use one clock (signal) from the other frame as time coordinate. And in this sense the two observers could be "synchronised" or better "coordinated". This would be more a coordinate choice than a clock synchronisation.

I wonder now what the definition is for "synchronisation". Help please!

In special relativity too, as I understood it, clocks from observers in relative motion cannot be synchronised. Synchronisation works only in one inertial frame, in SR.

If two observers at different heights are using two clocks working on the same physical principle (an atomic clock for example), these clocks will always disagree after some time even if they had been "synchronized at one earlier time". This is due to the red or blue shift produced by the gravitational field. This reminds me how the Mossbauer effect was used in this context, a wonderful experiment.

Michel

 

[actionintegral]

Thanks, guys. I will read up on this gravitational time dilation and pursue this after that.

 

[lalbatros]

Just one more short comment.

Within some given precision, the clocks can be synchronised for a certain lapse of time, but they cannot be totally synchronised over all times. That's why the GPS system is always re-synchronising all the atomic clocks in the system, the main correction is then for relative velocity but gravity play a non-negligible role too.

Michel

 

[Chris Hillman]

Hi, all,

I sense some confusion here between an "initial synchronization" and keeping clocks at different locations (perhaps in a curved spacetime, and/or undergoing acceleration), which are exchaning time signals, running at carefully adjusted rates so that they continue to remain "in synch" over a substantial period of time.

Just one more short comment.
the GPS system is always re-synchronising all the atomic clocks in the system

This isn't quite right. The GPS satellite clocks are set to run slow by "the basic GPS correction factor" (the frequency shift for "Hagihara observers" exchanging time signals with observers on the surface of an isolated nonrotating spherically symmetric massive object, which works out to 38 microseconds per day) precisely to avoid the procedure lalbatros imagines. On top of this, from time to time small corrections are made from the control center to deal with stuff which is impossible to predict far in advance, like solar wind buffeting of the satellites, but the point is that if the satellite clocks were not set to run slow as just described, the corrections needed to keep everything in synch would not be small. That would be a serious problem, so they are set to run slow by the precise factor obtained from the above mentioned gtr model.

See http://www.arxiv.org/abs/gr-qc/0507121 and http://relativity.livingreviews.org/Articles/lrr-2003-1/index.html for two readable expositions of "relativistic corrections" to the GPS.

Note that the GPS is basically designed using Newtonian theory (for the astrodynamics) plus Maxwell's theory of EM (i.e. in flat spacetime, for the signals) overlaid with somewhat cumbersome corrections, which is obviously not a very pretty way of thinking about this. But there is nothing to prevent one from designing a spacetime charting/navigation satellite beaconing system which is inherently relativistic. There has been considerable interest of this lately, because it leads to a little-noticed revolution in the history of ideas, the first self-consistent timekeeping/locating schemes. That is, in traditional coordinatizations of the Earth, topological considerations ensure awkward and ugly coordinate singularites like the International Date Line, the Earth (not to mention the solar system) is plenty large enough that the finite speed of light and other relativistic effects becomes very noticeable, and calendars based on quasiperiodic astronometric phenomena are notoriously difficult to maintain over long periods. All of these problems are obviated by the relativistic satellite beaconing scheme of Bartolome Coll; see for example http://www.arxiv.org/abs/gr-qc/0606044

 

[russ_watters]

My friend and I are in a two story building. I am on the lower floor, he is on the upper. We are in a constant gravitational field.

Is it true that our watches cannot be synchronized? If so, what is the proof of this claim?

This experiment has been performed many, many times: http://www.upscale.utoronto.ca/GeneralInterest/Key/relgen.htm

A) In 1959 Pound and Rebka placed an atomic clock at the top of a seven storey office building at Harvard University and compared its frequency with that of a similar clock placed in the basement. Using an effect named after the German physicist, Mossbauer, they confirmed the prediction of General Relativity to within 1%. More recent experiments along these lines have improved the precision to 0.02%.

 

[lalbatros]

Chris,

It is very nice that you provide us with good references.
Till now I was never able to undestand how my pocket GPS gets its position. Would you have a clear text on this topic? My problem was with how the receiver becomes able to detect the time delays needed for the positioning.

Concerning the discussion here, I think it could be useful if the word "synchronisation" was defined. Could you provide some reference for that too? In the classical books this is never explained in much detail. (and for special relativity it is very clear anyway)

Now, for the GPS system, it is clear that the clocks are drifting rather regularly under the effect of gravity. Therefore a regular correction is enough, as long as other perturbations are negligible. That's why I guessed that one clock in the GPS system (and in general) can be used to define a coordinate, but this does not mean that clocks are synchronised, as far as I understand now, before I know the definition for "synchronisation".

This leads me to a further question: how much is "synchronisation" a useful concept in general relativity? The two guys introduced by actionintegral can observe each other's laboratories without synchronizing their clocks. Synchonising clocks does not seem important to me in this context. It was only necessary for Special Relativity where this synchronisation is always possible in an inertial frame and where it leads to the relativity between inertial frames.

I am very interrested by your comments on this.

Michel

 

[nakurusil]

Hi, all,

I sense some confusion here between an "initial synchronization" and keeping clocks at different locations (perhaps in a curved spacetime, and/or undergoing acceleration), which are exchaning time signals, running at carefully adjusted rates so that they continue to remain "in synch" over a substantial period of time.

The links I gave refer to the latter, i.e. the basis of GPS way of working.

 

[russ_watters]

It is very nice that you provide us with good references.
Till now I was never able to undestand how my pocket GPS gets its position. Would you have a clear text on this topic? My problem was with how the receiver becomes able to detect the time delays needed for the positioning.

The signals are time signals. So all the GPS receiver has to do is compare them to each other.

Now, for the GPS system, it is clear that the clocks are drifting rather regularly under the effect of gravity. Therefore a regular correction is enough, as long as other perturbations are negligible.

Might be a nitpick, but they aren't so much a regular correction as simply making the clocks tick at a different rate.

This leads me to a further question: how much is "synchronisation" a useful concept in general relativity?

It is critical. And to answer your various questions on the definition, it can be defined pretty much however you want, as long as you define it clearly. You pick a frame of reference and a method that arrives at a useful synchronization scheme.

The two guys introduced by actionintegral can observe each other's laboratories without synchronizing their clocks. Synchonising clocks does not seem important to me in this context. It was only necessary for Special Relativity where this synchronisation is always possible in an inertial frame and where it leads to the relativity between inertial frames.

True - all they really need to do is compare them several times to see how they are changing relative to each other.