Atomic clocks & general relativity

[AlfaEcosse]

Hi all,
I have recently been listening to one of Professor Richard Wolfson's physics lectures, and a question has occurred about an aspect of general relativity; that time 'slows down' in strongly curved spacetime.
In this particular lecture, he mentions an experiment done some years ago in a University stairwell, where one atomic clock was placed at the top (some 70-80' above ground level) of the stairwell and another at the bottom. After some time, the experiment showed a (fairly trivial) discrepancy between the two previously synchronised clocks. The clock at ground level had run 'more slowly' than the other due gravity being stronger.

My question is this; If I bought two of those relatively inexpensive clocks which take their time signal from the atomic clock at NPL in Cumbria, would this effect still occur if I tried to repeat that experiment. (I realize that the clocks would probably not ever show the difference as they only display, say 10ths of one second, and we're talking about differences of nanoseconds here) but in principle would this work?

Thanks
Ed.
p.s. apologies if I've used the wrong terminology or whatever, I don't have any formal grounding in physics but just have an interest in it as a sort of hobby.

 

[Janus]

No, it would not. The clocks wouldn't be ticking by local time but by the signal they both get from a single atomic clock.

 

[Dale]

In that situation there would not be two clocks. There is only the one atomic clock at NPL with two displays.

 

[AlfaEcosse]

Thanks for that, I suspected that might be the case. But then I thought, would the electromagnetic radio wave carrying the same timing signal to both clocks be affected by the height difference between the two; i.e. the signal ariving at the lower one be slowed?

Or am I confusing that with special relativity?

Thanks again
Ed

 

[AlfaEcosse]

Dalespam, thanks for your reply. I maybe wasn't clear in my first post. The atomic clock at the NPL sends the timing signal out across the U.K. and beyond. The two displays I was meaning was on two entirely separate little domestic clocks which you can buy for the home.

I suspect the atomic clock at the NPL will have *many* displays

Thanks
Ed

 

[Dale]

No, you were perfectly clear.

The point is that those two little domestic clocks are not "entirely separate" clocks, they both get their primary time signal from the same NPL clock and only use their local quartz oscillators for interpolation. For all practical purposes they are one clock with two displays.

 

[AlfaEcosse]

I see what you mean now Dalespam, that makes sense. Do you think there would be any slowing of the timing signal at the lower clock due to SR? Or would there need to be a greater differential in height/gravity to produce such an effect?

 

[UrchinStar47]

You would need at least two proper atomic clocks (preferably 3 clocks per location, just to be on the safe side, to guard against malfunction). Then you can do the experiment.

It's been done privately already, and in the configuration I mention (though the guy used a mountain for a week to gain 27 nanoseconds or so).

 

[russ_watters]

But then I thought, would the electromagnetic radio wave carrying the same timing signal to both clocks be affected by the height difference between the two; i.e. the signal ariving at the lower one be slowed?

Assuming the signal came from directly above, there would be a delay between when the top clock got the signal and when the bottom clock got it, but that delay would be constant, so the difference between the times displayed on the clocks would never change. With GR effects, it is the rate that is different, so you get an difference that builds over time.

 

[ZapperZ]

Actually, until now, the accuracy of atomic clock isn't sufficient enough for GR to come into play, at least not when we are using it on the Earth's surface (it needs to be compensated for when we compare to the Earth and an orbiting satellite).

I wrote about this in another place, but I'll copy it here since it is peripherally relevant:

Time-Keeping Milestone

There are a couple of interesting reports in the latest issue of Science this week (Science 28 March 2008). Two papers have made the most accurate measurement of time-keeping to date. One uses the optical transition from ions[1], while the other uses neutral atoms[2]. They produced a time accuracy of up to 10^-17 and 10^-16 second, respectively, which is significantly more accurate than the Cs atomic clock.

However, as pointed out in the Perspective by Daniel Kleppner in the same issue, with an error budget that includes perturbation of the order of 10^-18 s, such precision now has to consider the effects of General Relativity.

When precision is pushed to new levels, ever more subtle effects must be taken into account. For instance, the error budget includes a small contribution, 1 mult 10-18, due to an uncertainty in the gravitational potential of the two clocks. This corresponds to a difference in their altitudes of 1 cm. This heralds one of the most interesting aspects of time keeping with optical clocks: The effects of general relativity that mix time with gravity are starting to approach a point that will require rethinking the basic concept of "keeping time."

The "two clocks" referred here are the two ion clocks used in the T. Rosenband et al. experiments - Al+ ion and Hg+ ion clocks. Having clocks that are now sensitive enough to detect effects of GR would certainly open up a whole possibility of testing GR even more.

Zz.

[1] T. Rosenband et al., Science v.319, p.1808 (2008).
[2] A. D. Ludlow et al., Science v.319, p.1805 (2008).

 

[tiny-tim]

Welcome to PF!

In this particular lecture, he mentions an experiment done some years ago in a University stairwell, where one atomic clock was placed at the top (some 70-80' above ground level) of the stairwell and another at the bottom. After some time, the experiment showed a (fairly trivial) discrepancy between the two previously synchronised clocks. The clock at ground level had run 'more slowly' than the other due gravity being stronger.

Hi AlfaEcosse! Welcome to PF!

I don't think these were clocks … they were just two lumps of iron, and the bottom one absorbed gamma rays (ultra-high-frequency light) at a particular frequency emitted by the top one which was attached to a vibrating speaker-cone … so the top clock was changing speed extremely fast, and was only in synch with the bottom one for (I'm guessing) a few nanoseconds at a time. i don't think there was any question of counting the "ticks" of the top lump.

See http://en.wikipedia.org/wiki/Pound-Rebka_experiment:

… This allowed Pound and Rebka to set up their experiment as a variation of Mößbauer spectroscopy. The test was carried out at Harvard University's Jefferson laboratory. A solid sample containing iron (57Fe) emitting gamma rays was placed in the center of a loudspeaker cone which was placed near the roof of the building. Another sample containing 57Fe was placed in the basement. The distance between this source and absorber was 22.5 meter (73.8 ft). … … …