Is There an Atomic Clock Experiment on the Moon Testing Relativity?

[DanMP]

TL;DR

Do we have an atomic clock on the Moon or orbiting the Moon? If the answer is yes, it was used in a Hafele-Keating type experiment, in which the other clock is on Earth?

I learned recently that there are plans to create a dedicated global satellite navigation system (GNSS) for the Moon, so we will have atomic clocks on and around the Moon, but we have at least one there now, in order to compare it with a clock on Earth? You know about such an experiment and its results?

 

[Nugatory]

Whether there is an atomic clock on the moon or not, it could not be part of a Hafele-Keating type experiment as these practical realizations of the twin paradox thought experiment require comparing two clocks that are in the same place at the beginning and end of the experiment. That is, we'd need to synchronize the clock with one on the earth, send it to the moon, bring it back, then compare with the earth clock - flying a clock around on commercial airliners is way more practical.

This has little or nothing to do with the Nature article you cited, which (according to the summary - the rest is behind a paywall) is going to be about choosing a coordinate time standard that is useful in the same way that the GPS time standard is useful.

 

[Vanadium 50]

There are about 75 atomic clocks in space. The article behind the paywall might explain what phenomena a lunar atomic clock would be sensitive to that the others are not, but if it's just "But we never tried it on the moon!" that line of argument gets old fast: "But we never tried it on Pluto in a month with an R in it!"

 

[Ibix]

Also worth noting that there are mirrors on the Moon, and laser range finding is sufficiently precise that you need GR to predict the results. So we can chalk that up as a test that EM and gravity both obey relativity and both do on the moon.

 

[Vanadium 50]

The lunar ranging measurements are incredibly good - better than a millimeter. That's so good there is a real question about exactly what is being measured: it;'s not the center to center measurement, and at this level the surface-to-surface distance is poorly defined.

A few years back I reviewed a proposal to do even better - right now this is not the best test (by about a factor of 2) of GR: that comes from a binary system with a pulsar and a white dwarf. But a better laser would improve on this. It's all very impressive.

However, I would not say this shows that GR correctly predicts the behavior of the moon and the behavior of light. I think the more accurate statement is that if GT is wrong, it gets both of them wrong by the exact same amount.

However, there is an esnemble of measurements that look at slightly different combinations of possibilities: we know that the Apollo radios were still tuned to the correct frequency, for example. That's 30 kHz over 2 GHz, or 15 ppm right there. (One second per day)

 

[Ibix]

However, I would not say this shows that GR correctly predicts the behavior of the moon and the behavior of light. I think the more accurate statement is that if GT is wrong, it gets both of them wrong by the exact same amount.

Fair enough. Laser ranging is insensitive to gravitational redshift, for example, because it's zero over a closed path, and the failure of this path to be closed is quite small (although I note that at millimeter scale errors over half light second distances I may be being naive by mentioning gravitational time dilation at all). So it's a test, but not a perfect one.

But your mention of a binary system helps to close that hole. You can look at the frequency shifts of spectral lines in the stars and also predict the observed period of the stars. Those seem to me to be "one way" measures through the gravitational field while laser ranging is two way, so would seem to be a separate test similar to your Apollo radios.

That's 30 kHz over 2 GHz, or 15 ppm right there. (One second per day)

The gamma factor for something travelling at escape velocity is about $1+\frac 12\left(\frac{11}{300000}\right)^2$ which is a drift of about 0.7ppb, though. So if that's the kind of scale, 15ppm isn't a particularly tight bound.

 

[vanhees71]

There are about 75 atomic clocks in space. The article behind the paywall might explain what phenomena a lunar atomic clock would be sensitive to that the others are not, but if it's just "But we never tried it on the moon!" that line of argument gets old fast: "But we never tried it on Pluto in a month with an R in it!"

The article is about the idea to establish a local atomic time on the moon as we have it on Earth, and that's because it's not easy to use the established Earthly time at high accuracy on the moon.

All this has nothing to do with once more testing (general-) relativistic kinematic effects concerning clocks and time. It's rather used as an established fact that this spacetime model is correct, and indeed the Earthly GPS is an everyday practical confirmation that this is indeed the case.

 

[Vanadium 50]

15ppm isn't a particularly tight bound.

No, it's not. That's because the Apollo astronauts used a crystal oscillator and not an atomic clock for their radios.

It is, however, the data we have.

 

[DanMP]

Whether there is an atomic clock on the moon or not, it could not be part of a Hafele-Keating type experiment as these practical realizations of the twin paradox thought experiment require comparing two clocks that are in the same place at the beginning and end of the experiment. That is, we'd need to synchronize the clock with one on the earth, send it to the moon, bring it back, then compare with the earth clock

Ok, but I also wrote:

we have at least one there now, in order to compare it with a clock on Earth?

so it's ok (for me) to just compare the 2 clocks, using signals and subtracting the time needed for the signal to travel from one clock to the other, something I think they would use to synchronize the clocks.

From the same article, see here:

Although the definition of the second is the same everywhere, the general theory of relativity dictates that clocks tick slower in stronger gravitational fields. The Moon’s gravitational pull is weaker than Earth’s, meaning that, to an observer on Earth, a lunar clock would run faster than an Earth one. Gramling estimates that a lunar clock would gain about 56 microseconds over 24 hours. Compared with one on Earth, a clock’s speed would also subtly change depending on its position on the lunar surface, because of the Moon’s rotation, says Tavella. “This is a paradise for experts in relativity, because you have to take into account so many things,” she adds.

I'm interested to see if the predicted difference (56 microseconds?) was correct, an even more interested if it was confirmed by actual experiments.

I hope that the time difference can be estimated and measured with greater accuracy, at least 2 digits more. For an atomic clock it would be an easy job. How about the accuracy of the predicted value?

This has little or nothing to do with the Nature article you cited

Sorry, try the improved link: plans to create a dedicated global satellite navigation system (GNSS) for the Moon. The message in blue is/was there. I cited the article only as a source for my statements/quotes.

From the same article: space agencies plan to install this lunar GNSS from around 2030

Also worth noting that there are mirrors on the Moon, and laser range finding is sufficiently precise

However, there is an esnemble of measurements that look at slightly different combinations of possibilities: we know that the Apollo radios were still tuned to the correct frequency, for example. That's 30 kHz over 2 GHz, or 15 ppm right there. (One second per day)

the Apollo astronauts used a crystal oscillator and not an atomic clock for their radios.

Can we use the Apollo radios on the Moon or the mirrors on the Moon + lasers in order to measure time differences per day with an accuracy of 0.1 microseconds or better? It was done? Can you offer a link? On the other hand, regarding the radios: "crystals undergo slow gradual change of frequency with time, known as aging ...", so their reliability decreases.

How about the Chinese missions/probes? They have or had an atomic clock on the Moon or orbiting the Moon? If so, they performed GR tests? How about their radios? Again, there are studies about using them in testing GR with an accuracy of 0.1 microsecond per day or better?

 

[Motore]

As google told me, there is no atomic clock on the moon.
But there is a deep space atomic clock: https://www.nasa.gov/feature/jpl/five-things-to-know-about-nasas-deep-space-atomic-clock

 

[Ibix]

so it's ok (for me) to just compare the 2 clocks, using signals and subtracting the time needed for the signal to travel from one clock to the other, something I think they would use to synchronize the clocks.

The "time needed for the signal to travel from one clock to the other" would depend on your choice of synchronisation convention, and there's probably significant room for choice in that definition. So it's nowhere near as simple as you seem to be making out.

Can we use the Apollo radios on the Moon or the mirrors on the Moon + lasers in order to measure time differences per day with an accuracy of 0.1 microseconds or better? It was done? Can you offer a link?

Laser ranging experiments put some bounds on possible disagreement with GR in the behaviour of lasers near the moon. That puts some bounds on the behaviour of light clocks on the moon, and hence on other clocks unless you're willing to jettison the principle of relativity (but only on the moon, since it's well tested here). How tight are the bounds? No idea. I suspect you'd have to play around with the PPN model and find out how much you can get away with turning off GR without breaking the lunar laser ranging measurements. Then you can see what variability that introduces into a light clock.

 

[Vanadium 50]

unless you're willing to jettison the principle of relativity (but only on the moon, since it's well tested here)

Magnetism is a relativistic effect. If relativity didn't work on the moon, neither would all the solenoids and pumps and any circuit with an inductor. It's a non-starter.

 

[Nugatory]

so it's ok (for me) to just compare the 2 clocks, using signals and subtracting the time needed for the signal to travel from one clock to the other, something I think they would use to synchronize the clocks.

That’s not a way of comparing clocks, it’s choosing a synchronization convention that makes the comparison come out in a particular way. But this is a bit of a red herring (as are mentioning the Hafele-Keating experiment and the Nature article in the original post) when your question is

I'm interested to see if the predicted difference (56 microseconds?) was correct, an even more interested if it was confirmed by actual experiments

about experimental tests of relativity in the vicinity of the moon, as opposed to everywhere else.

This thread is going the same way as your recent one about tests of relativity that do not involve electromagnetism. That discussion was not productive, this one isn’t any better, and it is now closed.

As with all thread closures, we can reopen the thread for additional informative comments, but “not good enough to satisfy me” isn’t that.