New atomic clock loses only one second every 300B years

As a general rule, sampling a normal distribution N times decreases the uncertainty by a multiple of 1/sqrt(N). For instance, to know the mean of an unknown distribution to within N digits, the number of observations must be on the order of 2N digits long. I learned this the hard way when attempting some statistical experiments; it may answer your question here.

TAI is a weighted average of the clocks. The lower the estimated uncertainty of a clock, the more it contributes to the average. This is given in the second to last column in the first table of Circular T [1]. For example, in the last reporting period, Germany's PTB reported the lowest uncertainty, and therefore contributed most. Probably both their cesium fountains were running well. So a single much better clock would immediately improve the quality of TAI.

[1] https://webtai.bipm.org/ftp/pub/tai/Circular-T/cirt/cirt.409

I don’t think the sample rate is high enough to detect individual waves.

Of course it's some four-page Avi Loeb homework problem, er, I mean, "paper".

"One second per 300 billion years" is really a statement about the bandwidth of the signal that the clock generates, translated for lay readers. We don't know what the actual bandwidth of the signal is, since it's not stated in the article. Bandwidth is measured in Hz.

In order to measure the bandwidth of the signal (and how accurate the clock is), you have to measure the clock over a period of time. The shorter that period of time, the worse your measurement will be. The smaller the bandwidth, the more time you need to measure it.

Note that a signal with 5 Hz bandwidth and 5 Hz center frequency would make a very terrible clock, while a signal with 5 Hz bandwidth and 5 GHz center frequency would make a very nice clock. The bandwidth is the same in both cases, and the amount of time required to measure bandwidth is the same, but they make very different clocks.

The "over 300 billion years" kind of headlines always bother the crap out of me. The clock won't run for 300 billion years. It'll probably run for ten or twenty.

But during that time there will be several copies of it built, and they'll run in several locations around the world, and the outputs of those copies will deviate less than some tinysecond per longtime. Attoseconds per month or whatever.

And the useful timescale is more like, how much do they deviate over five seconds?

Because they'll be used for something like astronomical ranging. Say you have two radio telescopes at distant points on the earth, both observing a distant stellar source simultaneously. The long baseline forms one side of a triangle, and the distances from the two observatories to the star form the other two sides. The more precisely you can determine those distances, the better you can resolve the position of the source. So you've got coherent receivers that can measure individual wavefronts in the signal, but how coherent are they, anyway? That depends on the clock they share. But they're on opposite sides of the planet, they don't actually share a clock...

And the measurement period over which you can compensate for other confounding factors (probe and measure the atmospheric distortions in the way, for instance) might be very brief, so the clocks' stability over brief periods is salient.

This is my lay understanding, so if someone more versed in the art wants to chime in, I'm all ears!

If you think of the Fourier transform as letting you express a function as a sum of sine waves, then in quantum mechanics, you could also choose to express a wavefunction as a sum of energy levels—or as a sum of momentums, or a sum of positions.

https://en.wikipedia.org/wiki/Conjugate_variables

Lower bounds on the product of the variances of a function and of its Fourier transform are pretty standard in physics texts. See e.g. the discussion leading to Eq. 16.34 in Feynman's lectures of physics https://www.feynmanlectures.caltech.edu/III_16.html

The weird thing is not that there is a relationship between a function and its Fourier transform. That's pretty "elementary" math, as you observe. The weird thing is that physically meaningful quantities such as position and momentum should be related via Fourier transform in the first place. No amount of math can prove this fact---you need experiments.

By the way, in Heisenberg-type lower bounds, you allow both the function and its Fourier transform to be nonzero everywhere, yielding the result that the Gaussian distribution minimizes the product of the variances. But you can also ask a different question: assuming that I want the function to be band-limited, i.e., I want the Fourier transform to be strictly 0 outside an interval [-B, B], which function minimizes the dispersion in the time domain? This question yields the beautiful theory of the "prolate spheroidal functions", which are far from elementary. This kind of question is useful e.g. in signal processing: if you are allowed to look at N samples of an audio signal, what is the best low-pass filter that you can design?

One semi-famous example from MIT would be Jerrold Zacharias's attempt to build a cesium fountain clock ( https://en.wikipedia.org/wiki/Atomic_fountain ). It took decades of additional research before anyone managed to make fountain clocks work.

Norman Ramsey's biography of Zacharias at http://www.nasonline.org/publications/biographical-memoirs/m... (.pdf link) talks a little about it:

Zacharias at this time became interested in developing atomic clocks and pursued two versions concurrently. One was a cesium atomic beam clock using my (Ramsey's) separated oscillatory field method, well engineered for reliability and commercial applications, including a source and vacuum system that could be operated for years rather than hours. He cooperated with the National Company in developing a commercial clock known as the Atomichron. The availability of this highly successful cesium atomic beam clock contributed greatly to the adoption of atomic time and to the international definition of the second as 9,192,631,770 oscillations of the cesium atom.

His other version had the potential for much greater accuracy but the risk of total failure. A very slow beam of atomic cesium was directed upward and allowed to fall as a fountain, with separated oscillatory field excitation on the way up and down. The half second required for the roundtrip in the fountain was approximately fifty times greater than that for an atom to traverse the oscillatory field region of a conventional atomic beam apparatus, so the resonance width, by the Heisenberg uncertainty principle, would be fifty times narrower with correspondingly increased clock accuracy. Despite valiant efforts by Zacharias and his associates, the fountain experiment failed because the numbers of ultraslow atoms in the beam were far below theoretical predictions, probably due to scattering in the nonequilibrium region between the slits. It is of interest to note that thirty years later, in 1989, Steven Chu succeeded in making an atomic fountain by using the new laser cooling techniques to produce ultra-slow atoms. The atomic fountain with laser cooling is now one of the most promising prospects for increasing the accuracy of clocks and frequency standards.

What the MIT group achieved was implementing spin-squeezing to clock operation, but their results are not QPN-limited (in fact, they made it above the SQL, so they actually make things worse instead of making it better) [1].

They attributed their major obstacle as their laser phase noise, and they claimed if they subtract the estimated laser noise from the result they would get sub-SQL. But hey, that's not how things work. If you think you can make it, you just make it.

[1] : https://www.nature.com/articles/s41586-020-3006-1

Yes, LIGO has already implemented squeezed states in their measurements. What I'm referring to is making a spin-squeezed atomic clock with enhanced metrological gain compared to QPN limit. There're several groups working on it and so far no one has succeed.

There're problems with increasing atom number. It is true that more atoms will allow one to resolve QPN easier, more atoms make clock rotations (along the Bloch sphere) much harder, as for a spin-squeezed clock doing Ramsey sequence, you need at least two pi/2 rotations to rotate the squeezed state.

I think the point is that it provides very precise measurements for each independent experiment.

I don't think anyone is trying to track the absolute time elapsed over long periods with this clock since it started.

It doesn't have to have the accuracy, if both computers had their own atomic clocks they would end up out of sync every couple of years, just like GPS satellites do.

Another atomic clock.

For that matter, what is being compared to when they said “Current atomic clocks are 1 second every few hundred million years”?

"NOVA: A white dwarf star pulls matter off of a companion red giant star until a powerful nuclear fusion explosion occurs on the dwarf’s surface"

A supernova, no. But a nova to me, a layperson sounds possible but highly unlikely. sun-> white dwarf->random red giant intersecting our solar system

https://www.space.com/31608-supernovas-star-explosions-infog...

After strontium atoms coming from an oven (usually at 400-ish degrees) reaches the main chamber, they're trapped via both optically (via lasers) and magnetically (there's coils surrounding the chamber), which we called magneto-optical trap, or MOT. For strontium, there're two stages of MOT, one is a blue (461nm) MOT which cools and traps hotter atoms into temperature of ~mK, and the second stage is the red (689nm) MOT that further cools the atoms into ~uK range. A MOT typically consists of 3 laser beams at different directions, and retroreflected on the other side after hitting the atoms (so 6 beams effectively). Some MOT can be done with less lasers. All 3 pairs of lasers (and 2 MOT, so 6 pairs) have to align perfectly so that they all hit the same point of intersection within the chamber.

To align these lasers, one method is to shine another 461nm pulse to the chamber and check for fluorescence signal via a photodiode or camera located on the other side of the chamber. Since the beams are generally much larger than the atomic cloud itself, as long as you hit something, it is easy to optimize the signal. For a blue MOT with very high atom number, you can even see a small blue bulb suspending in the mid-air inside the chamber, which could serve as a rough reference to start with.

So now atoms are trapped into the red MOT, you then turn off the red lasers while having the lattice laser (at 813nm) on, so the atoms are loaded into the optical lattice. Using the same method, you take a fluorescence image at the end of the experimental sequence to check if there's any signal. Note that the position of the red MOT depends on both the laser alignment and magnetic fields, so one can either (1) align the lattice beam, in this case, a vertical beam from top to bottom and retroreflected or (2) adjust the magnetic fields to fine-tune the red MOT position. It's an iteration of fine adjustments and looking at images.

Another way to align the lattice to the atoms is instead of shining lattice beams to the atoms, you first send red light through the same fiber. When they hit the atoms in the red MOT, the red light will excite the atoms so you won't see anything now with the fluorescence imaging (as they no longer in the ground state that responds to the blue transition). We call this "the killing beam" as the name suggest. Once you know the rough alignment, switch it back to lattice laser and do the optimizations until you see atoms loaded into the lattice (the distribution and spread of the atom ensemble are different when viewed with camera for atoms that are still in red MOT vs loaded into lattice).

With GPS you can measure time with <100ns person.

Hundreds of milliseconds? A receiver like [0] is specced for single-digit nanoseconds. Even the standard-precision modules [1] are double-digit.

My understanding is that GPS wouldn't function if the timing was inaccurate to several hundred milliseconds.

[0]: https://www.u-blox.com/en/product/lea-f9t-module

[1]: https://www.u-blox.com/en/product/neo-m9n-module

Giving your GPS the ability to calculate gravitational time dilation would be cool.

According to Wikipedia [1] gravitational redshift is about 1e-16 per meter. Someone else posted a clock costing around $2k with a precision of around 1e-11 [2], so, the current commercial clock is giving us the elevation with a precision of around 100km.

To get per-meter resolution we'd need 1e-16 precision, which is on par with the more "standard" clocks in research laboratories and better than the clocks we put on GPS satellites by a few orders of magnitude. Unfortunately that just puts us on par with an existing GPS.

On the other hand, the bleeding-edge optical-lattice based atomic clocks described in this article give us altimeters with mm resolution. So we might actually be reaching the point where atomic clocks would be useful in "everyday devices". All it takes is for someone to shrink a tabletop experiment down to the size of a bar of soap, and to make it work without all the climate control, electromagnetic shielding, and vibration damping that come standard in a state-of-the-art atomic physics lab.

[1]: https://en.wikipedia.org/wiki/Gravitational_redshift

[2]: https://www.sparkfun.com/products/14830

In the specific case of timekeeping though what is the point?

For everything that probably 99.9999% of people do that just involves their at-home devices with no outside communications they don't need time more accurate and stable than a quartz resonator. Heck, most people could get by fine at home if all their clocks dropped the seconds display only showing hours and minutes, provided that they also had a stopwatch for when they need to time intervals smaller than a minute.

You generally only need something better when you are coordinating things that do involve communicating with the outside world in which case you can sync with outside clocks.

GPS satellites broadcast time signals; you don’t need Internet access to receive them.

But if you don’t want to be dependent even on GPS, you can apparently buy a small atomic clock for $1500, well within reach of many tech enthusiasts: https://physicsworld.com/a/atomic-clock-is-smallest-on-the-m...

You can buy SDR based GPS receiver (using atomic clocks on satellites) for very cheap. For ~1500 you can buy a 1x PCIe atomic clock and then run a sNTP server to update everything.

A car can measure its speed in kilometers per hour without having to travel for an hour. The choice of units is completely arbitrary and is ultimately a matter of taste.

Most people know what a second is, and that a billion years is a really long time. They probably have no idea what a picosecond is. Clock experts generally use fractional frequency errors which have no unit at all.

There's two parts to the original question:

- What kind of high precision clocks are there

- How do I synchronize them (implying NTP is not for serious use)

Since any "smart" device including your "simple" smartphone, smart watch or even your laptop will synchronize itself via NTP, their time keeping abilities are likely already better or at least equal than that of any high tech mechanical watch, because the first question ties into the other: there is no point in perfect accuracy if you can have constant error-correction.

While my inability to understand why anyone would care about a 10 second per year loss for personal use -- especially since the time and effort required to recalibrate even a manual clock is tiny if it does matter -- is completely subjective, I don't think the comparison between NTP-enabled devices and "ultra-correct" time keeping devices is. I just don't see a convincing argument for buying something like an atomic watch, or a high-end wristwatch, unless in the first case you yourself plan on hosting an NTP service for example (and you would, of course, even then at least verify it via: NTP!) -- or in the second case if you knew you would for an extended time be without access to any other trustworthy time-keeping device, via the Internet or otherwise.

Everyone obviously has their own interests and anyone is free to spend any amount they want on expensive time keeping devices, I just think one should be aware of what the level of normality already is these days for many devices we use, which in my mind is pretty high.