It's an amazing time to be alive. While not this precise, you can have atomic cesium beam clocks of your own for a few thousand dollars each, and some elbow grease.
If not, it'd make for a pretty cool plot device if done well.
https://apps.dtic.mil/sti/pdfs/AD1012150.pdf
Though, that 1989 paper concludes that because gravimeters would need a sensitivity of at least one part in 10^13 for practical usage, far beyond what was capable at the time, "[t]he concept of detecting submarines by means of detecting gravitational anomalies they produce, should be abandoned."
No.
Assuming my math is correct, it's already affected by nearby human scale masses, for certain values of "near".
However, according to that logic, an object located in a cavity in the center of earth should experience no more dilation than an object outside the earth's potential well, because the gravitational forces / curvature gradient cancels out, and should be zero. But that isn't the case according to the same sources, for example, Wikipedia says' "Relative to Earth's age in billions of years, Earth's core is in effect 2.5 years younger than its surface."
Something's not right about how we verbalize this story about gravity
To an observer at the infinity, a clock at the core of the Earth will tick slower than a clock on the surface of the Earth because the "core clock" is sitting in a more curved space, and that's it.
The difference between the clock on the surface of the Earth and the clock at the core is that the surface clock can't follow the "straight lines" (geodesics) in that curved space. So it experiences acceleration due to the force of inertia. And the thing preventing that movement is the repulsive force between atoms that make up the bulk of the Earth.
If this repulsive force magically disappears, then the Earth's atoms will immediately start moving at the straight lines, in trajectories that will lead them all into a point at the center of the Earth.
To add: the force of inertia due to moving in curved lines instead of geodesics depends on the "steepness" of the curved space. Which decreases as you reach the center of the Earth. So you get essentially the same result as with the classic Newtonian gravity, but through an entirely different path.
no net force, but net potential energy - thus gravitational dilation
How hard or expensive would it be for a reasonably equipped lab to build their own optical clock though? I see there are optical clocks the size of few rack units on the market for a rather hefty price, are the materials needed that expensive or is it just the expertise?
Once optical comb sources are commoditized to the extent that solid-state lasers are now, a lot of fun stuff will become possible.
Re the commoditization: Part of the problem is that customers, especially the scientific ones, don't want "commodity" frequency combs. Nearly every comb we sell is tailored to the specific customer in one way or another.
Industrial customers start to be interested in frequency combs more and more. I guess this will be the clientele that values off-the-shelf products more, eventually paving the way for commoditization.
Oh and to know if it's any good you have to either build two (ideally more) of them to compare against each other (ideally using different approaches so their errors are less correlated), or have access to a clock better than the one you're building to compare to. So you can rarely get away with building just one if you want to know if you've succeeded.
Source: I work on the software for these portable optical clocks: https://phys.org/news/2025-07-quantum-clocks-accuracy-curren...
Satellite, ACES, was launched recently that uses atomic clocks to accurately measure Earth's gravity field.
On second thought, you need a base station on the ground to tell you its time for comparison anyway, so if that base station is nearby the density thing should mostly work itself out
In what amount of time? Not instantly, right?
Let's imagine that there is a huge amount of time dilation (we live on the surface of a neuron star or something). By climbing a bit, we experience 1.1 seconds instead of 1.0 seconds experienced by someone who left down.
We have a clock that can measure milliseconds as the smallest tick. But climbing up, back down, and comparing the amount of ticks won't let us conclude anything after a single millisecond. If anything, we must spend at least 11 milliseconds up to have a noticeable 11 to 10 millisecond difference.
Now, if the dilation was 1.01 seconds vs 1.00, we would need to spend at least 101 milliseconds up, to get a minimal comparison between 101 and 100 milliseconds.
That idea is the premise of https://en.wikipedia.org/wiki/Incandescence_(novel)
Nevertheless, in order to measure a frequency difference between two optical clocks you do not need to count their signals. The optical signals can be mixed in a non-linear optical medium, which will provide a signal whose frequency is equal to the difference between the input frequencies.
That signal might have a frequency no greater than 1 GHz, so it might be easy to count with a digital counter.
Of course, the smaller the frequency difference is, the longer must be the time used for counting, to get enough significant digits.
The laser used in this clock has a frequency around 200 THz (like for optical fiber lasers), i.e. about 2E14 Hz. This choice of frequency allows the use of standard optical fibers to compare the frequencies of different optical clocks, even when they are located at great distances.
Mixing the light beams of 2 such lasers, in the case of a 1E-17 frequency difference would give a difference signal with a period of many minutes, which might need to be counted for several days to give an acceptable precision. The time can be reduced by a small factor selecting some harmonic, but it would still be of some days.
So then the question has to be asked, does the effect really happen instantly? Or do the same mechanisms that impose an inverse relationship between bandwidth and SNR mean that, in fact, it doesn't happen instantly at all?
But you would need a more precise characterization of the clock to answer this.
There might be significant noise on individual measurements, meaning that you need to take multiples to get precise enough (see https://en.wikipedia.org/wiki/Allan_variance).
Edit: If you just have clock output in ticks, you also need enought time to elapse to get a deviation of at least one tick between both bot clocks you are comparing. This is a big limitation, because at a clock rate of 1GHz you are still waiting for like 30 years (!!). (In practice you could probably cheat a bit to get around this limit)
In practice with this level of precision you are usually measuring the relative phase of the two clocks, which allows substantially greater resolution than just looking at whole cycles, which is 'cheating' to some degree, I guess. (The limit is usually how noisy your phase measurement is)
(To give some intuition, imaging comparing two pendulum clocks. I think you can probably see how if you take a series of pictures of the pendulums next to each other you could gauge whether one of them is running fast relative to the other, and by how much, without one completing one full swing more than the other)
It takes a longer measurement to be more confident.
[0] https://sci-hub.se/https://doi.org/10.1126/science.1192720 ("Optical Clocks and Relativity" (2010))
This improves the clock’s stability, reducing the time required to measure down to the 19th decimal place from three weeks to a day and a half.
I'm not above buying a toy to look at logs and geek out over it, but I can't justifying spending several grand for it.
Just something very cool about the idea of a hyper-accurate clock living in my house. I don’t know what I would do with it, just that it would be neat.
If I ever become a billionaire or something, I will absolutely buy one. Sadly I don’t think that’s likely to happen any time soon.
How can anything … you know what? Never mind. No matter what answer anyone provides, I won’t understand.
I think this new clock is simply able to generate more precisely spaced ticks than those of a traditional Cs clock. Less jitter and variation in the timing of those ticks. Similar to how a one-hour water clock or sand timer's runtime will vary between "transitions", but a one-hour quartz stopwatch timer is much more regular. I could keep going, but I'm already out on a limb so I'll stop before my own uncertainty rises too much.
(Edit: I read the article. I don't think my words above are correct.)
Yes
> How can anything …
So your cesium counting device will fauthfully provide such a count and depending on their altitude it will be at different rates.
Both clocks are each experiencing time at the usual one second per second but gravity dilates spacetime.
Locally, a second is always a second, but from everywhere there is no such asbsolute, just as there is no universal "now".
I propose calling it TIGO(Time Interferometer Gravitational-Wave Observatory) ;-)
I think.