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.
I'm speculating here, but I think the idea is to ascribe accuracy to processes, not to specific clocks.
So you make two clocks on the same principle, say pendulum oscillations, and measure how quickly they start to disagree. Then you make two clocks based on a new principle, say quartz oscillations, and measure their rate of disagreement. You'll notice that the two quartz clocks agree with each other better than the two pendulum clocks do. So quartz clocks keep time better than pendulum clocks.
Then you build a new type of clock, say of the atomic kind, and compare two atomic clocks to each other and to quartz clocks. As you repeat this process, I suppose the clock frequencies have to get progressively higher (Cesium clocks are measuring radiation at about 9 GHz), but this allows you to measure finer and finer discrepancies between them.
> You'll notice that the two quartz clocks agree with each other better than the two pendulum clocks do. So quartz clocks keep time better than pendulum clocks.
What? That doesn't make any sense. Keeping good time isn't about agreeing with another copy of yourself. It's about agreeing with an objective reference time, like "sunrise in Singapore" or "astronomical noon".
Yes exactly. But how would you measure astronomical noon? You might build some instruments that look at the sky and produce some readings.
Now you might build multiple copies of your instrument and compare their readings. But they disagree by some amount.
So you build a better instrument. Or choose some other thing to measure instead. Rinse repeat until you have a more precise instrument.
Atomic clocks are instruments that are measuring something in the universe. They are not generating some time stamp out of nothing. The thing that you say as an objective reference still very much applies.
Such 'objective reference time' doesn't really exist at the precisions we are talking about (both in terms of the precision to which you can define them and effects like relativity). And the difference between 'objective time' and 'keeping time with another copy of yourself' is basically just a scaling factor, which is irrelevant a lot of the time, when the far more relevant parameters for high-precision clocks in actual applications are stability, noise, and bandwidth.
> And the difference between 'objective time' and 'keeping time with another copy of yourself' is basically just a scaling factor, which is irrelevant a lot of the time
This assumes that your own divergence from objective time is linear in the amount of time that passes.
He drove three Cesium clocks up Mount Rainier and returned after a week. He compared them to a clock he left at home for the journey. The graph that he shows on the page and his associated commentary is interesting.
Ultimately, a clock is simply an abstract device that goes tick-tick-tick at some regular rate. Once one starts measuring the phenomenon itself---mechanics of the human heart, tidal forces on the Earth, friction in a pendulum, or the uncertainty principle in atoms---it is no longer feasible to treat it as objective time.
International Atomic Time (TAI) itself consists of an ensemble of 400 atomic clocks, with the collective being more accurate (the proper word is "stable", I think?) than any of its constituents.
I love claims like this headline that rely entirely on our inability to observe the clock after the stated interval. We can be pretty sure that the clock will not be working at all, let alone accurate, but we can't be certain. At least until we get claims in the trillion year range, at which point the heat death effect will make the claim even more unlikely.
It's just a matter of poor wording. I would hope that everyone's pedantry would be at bay should the title be "New atomic clock loses only one 300 billionth of a second every year".
I think it is more than pedantry. The clock will not last even a billionth of "300B years", and losing a whole second would be disastrous to its purpose. The kind of people who are interested in atomic clocks can surely understand "loses only 3 picoseconds per year".
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.
At this level of accuracy, I wonder if there are effects even the researchers aren't aware of that could cause drift. Or maybe it's best to say they're that accurate under certain assumptions. I would expect a cosmic ray or a lightning strike or an earthquake to violate the umpteenth nines of accuracy they're claiming.
Previous optical clocks were able to measure gravitational time dilation from under a meter of altitude. I'll bet that this one measures it to the order of a centimeter.
And it isn't just height that is going to have an impact. Any major mass shift affects it. For example in Scandinavia, melting ice in Greenland and rising land will combine to make ultra-precise clocks there run measurably faster over time relative to where they started.
So this accuracy claim is not saying that they engineered a clock that will only lose 1 second in several trillion years. For one thing that clock would have to survive the sun going nova.
Rather it's a statement about the width of the frequency they are measuring and their ability to divide that down to a second. They are saying that they have two clocks measuring the same frequency and have analyzed their dispersion against each other over a period of time and gotten this result.
Long-term aging effects aren't going to change the frequency of the atoms (except new physics, but we can rule that out via observations of the Lamb shift in distant hydrogen), but things like gas infiltration, lamp aging, changes in laser characteristics can all cause atomic clocks to drift.
This is pretty significant for rubidium which is why the lamps need recalibration periodically.
I think this is poor design. If he clock had used ZFS, I don’t think it would lose any seconds. I blame it on poor error correction or possibly non-ECC memory.
> which separated strontium atoms into a line in a single vacuum chamber
I’ve always wondered how stuff like this works in practice. Even with particular accelerators, how did they figure out how to control the particles to line them up and synchronized it to be blasted at high speeds? I always assumed it was something less sophisticated like bombarding it and just letting whatever gets sent across get measured. But this is taking about lining them up in a vacuum.
This type of physics is like black magic to an outsider.
A simple way of thinking it is consider laser as waves, they act like harmonic potentials (like sine curves) with crests and troughs. Atoms that are inside the potentials are trapped, like a ball in a deep well. Atoms trapped in optical lattices have a lifetime with a time constant which the population of trapped atoms keeps decreasing, but the timescale is like tens of seconds, so the atom loss is not significant when the clock interrogation is in milliseconds.
In this paper the lattice is a 1D vertical lattice, so you can think of atoms being trapped in a huge stack of pancakes.
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).
Honest noob question: when we get to this level of precision with time, do we have to start worrying about Heisenburgian effects? As in, having such precision in our timing measurements influences the outcome of our results?
I know nothing about physics but I find this fascinating.
The Heisenberg uncertainty principle applies here… you cannot make a measurement which is both precise in frequency and compact in time.
This should be, in some sense, natural to people who understand how a Fourier transform works… basically, when you apply a “window” function to measure a signal over a limited period of time, you end up with the signal smeared in the frequency domain.
"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.
Yes, since that corresponds to a sine wave with fixed frequency extending forwards and backwards in time infinitely. (NB: it does depend on how you measure it. To truely get this you would also need to measure the clock output for all time).
My understanding of this from the domain of GPS time, has always been; you can have a good clock (GPS is slow, accurate over a long time) or a good ocillator (fast, inaccurate over along time). But together you can have both.
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!
THANKS!!! I keep trying to get a good understanding of at least the beginnings, i.e., foundations, of quantum mechanics and of the Heiserberg uncertainty principle, but I get frustrated at everything I can find on the Internet including the lectures of courses at MIT. So, for me, the physics is an obscure disaster.
But Fourier theory!!!! That's FINE!!! I went carefully through the very careful treatment of Fourier series in the third edition of the W. Rudin Principles of Mathematical Analysis and also his very careful treatment of the Fourier transform in his Real and Complex Analysis, also distributions in his Functional Analysis. Also read and used the Blackman and Tukey The Measurement of Power Spectra, wrote some corresponding software that pleased some people in the US Navy, etc. Then I took a course at the level of the second Rudin book, and in the class when the prof got to the Fourier transform one of the students, with a physics background blurted out "That's the Heisenberg uncertainty principle!"
So, now as I look at the MIT lectures, etc., I expect to see a good, solid, clear connection with the Fourier transform -- but so far I've found NOTHING.
Yup, so, thanks for confirming that, yup, the Heisenberg uncertainty principle is not some weird and obscure feature of nature but, really, just an elementary result of any elementary but precise math derivation of the Fourier transform!!!!
But, looks like I will have to make the connections with the basics of quantum mechanics myself.
Yup, multiply in the time domain is the same as doing a convolution in the frequency domain -- that is, if take the Fourier transform of a function zero outside of a finite interval, then in effect have multiplied the function by a box, 1 in the interval and 0 otherwise, and then for the transform are doing a convolution, that is, a weighted sum, of the transform of the box which is just a version of sin(x)/x, that is, with a peak at the origin and falling off rapidly away from the origin. That is, the weighted sum of the convolution is a "smearing out". So, on to the connection with the physics ..., hopefully.
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.
is both an eigenvector of simple versions of Schrödinger's equation and also, essentially via Fourier theory, one axis of an orthogonal basis of a linear algebra (or Hilbert space if prefer that since it permits infinitely many orthogonal basis vectors) representation of quite general wave function solutions to the equation. And just by including more basis vectors, can get whatever level of accuracy we might want.
That is, the terns in the Fourier transform act like the coefficients in the linear combination of basis vectors, the linear combination that approximates the wave function solution of Schrödinger's equation.
So, essentially we are into harmonic motion, e.g., swinging pendulums, whether we wanted to be or not.
Then we are ready to guess that for treatment of the electron in a hydrogen atom we will be into something like Sturm-Liouville theory of two point boundary value problems and standing waves, vibrating violin strings, etc. That is, an electron in what it does with a hydrogen nucleus will be like a vibrating violin string.
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?
And thanks for the URL to Feynman's lectures -- I lost my paper copy in a move.
Yup, I understand that early on in quantum mechanics, we will get to both energy and momentum of these particles that have wave functions that evolve as in Schrõdinger's equation. Then I was wondering what math was going to take a wave function and pop out energy and momentum. I began to suspect something that smelled like it popped out of someone's back side. Good to hear that the theory was guessing and experiment confirmed, likely not the first time.
You are farther into digital filtering than I ever got: For a while I was doing such things for the US Navy with data they collected in sea trials. At the time the fast Fourier transform (FFT) was a hot topic. Actually it was later that I studied Fourier theory with some care.
I'm going after quantum mechanics just out of curiosity and with the basic assumption that it's not quite right and I want to check carefully. Maybe it's not really the final theory.
Occasionally I get torqued: E.g., okay, sure, there is a Hilbert space (as I recall, Rudin shows that, really, there is only one) and each wave function is a point in that space, but no way will I easily accept that all the wave function FORM a Hilbert space: That is, via Rudin and more, a Hilbert space is a complete inner product space where here complete means that every Cauchy convergent sequence converges. Then I recall the common, old examples that nice, smooth, likely even infinitely differentiable, functions can converge to a square wave with its jump discontinuities. But the physics people assure me that each wave function is differentiable and also continuous. And that's a point of small irritation -- of course they are continuous; it's an elementary exercise to show that every differentiable function is continuous.
And I got torqued at Feynman where in his Lectures he has that a particle of unknown position has position probability density uniform everywhere -- no it doesn't; it can't; there can be no such density since its integral would not be 1, actually either 0 or infinity.
I don't even like the common integration from minus infinity to infinity: Rudin develops the Riemann integral very carefully but only on closed intervals of finite length, that is, on compact sets. Sure the integral from minus infinity to infinity can be defined as a limit, an improper integral, but then we have a problem: Start with some standard Rudin material that there can be an infinite series that does converge but is conditionally convergent and then with rearrangements can have the series converge to anything might want. Well, the same could hold for integrating from minus infinity to infinity -- the result get can depend on just how the limiting operation is done. E.g., integrate on Monday, Tuesday, and Wednesday, then on Saturday, Friday, Thursday, then Sunday, and continue this pattern for each week. So, without more assumptions, that improper integral is not so good. So, sure, measure theory and the Lebesgue integral clean up this mess, have some assumptions and derivations that do permit integrating from minus infinity to infinity. Right, I can be picky. Uh, who's to say that God is not?
The relevant version of the uncertainty principle here is the energy time one. \Delta E \Delta T <= \hbar. As time uncertainty tends to 0, energy uncertainty tends to infinity. What does that mean? It means the clock system has to get an increasingly heavier pendulum, or increasingly tighter spring, or some analog thereof. When you make the pendulum Bob twice as heavy, it is half as sensitive to random stray influence, but whatever uncertainty you had about the bobs kinetic energy is multiplied by two. Infinite precision is only possible with an infinitely heavy pendulum.
Yes, in fact, the current state-of-the-art atomic clocks are hitting a limit called the standard quantum limit (SQL) of the quantum projection noise (QPN). Basically, atomic clocks operate by probing atoms with an accurate local oscillator, in this case, the laser, to drive the clock transition (here, 698.446nm or 429.228 THz). In this two-level system (a ground state, g and excited state, e), you can think of the measurement yields a "pointer" that points the state of the system (which is a superposition of g and e, which is related the the fraction of atoms in the ensemble being excited, i.e. the excitation fraction), however, such measurement is not certain, hence QPN.
However, there're workarounds to beat this SQL. One approach people are working on is called the "spin squeezing", which, one can think of the uncertainties of a measurement mapped onto a 2D plane, for simplicity, a circle. Spin squeezing is used to improve the uncertainty in one axis while sacrificing the other, like squeezing the circle into an eclipse. There's a group in MIT which attempted to show metrological gain from spin squeezing in 2020, which they failed.
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.
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.
IIRC LIGO/VIRGO use squeezed light to lower the uncertainty in the ~~frequency~~ phase[1] of the laser they're using to improve the sensitivity of their measurements.
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.
Stupid question: what you're describing looks very similar to NMR (using RF to shape ensembles of magnetic spins, often shifting them around the bloch sphere).
These "clocks" are used more like stopwatches. They're useful for doing incredibly precise science experiments.
The added timing precision translates into better precision of other measurements like distance if you're doing time-of-flight experiments like OPERA did[1].
For the most part we do. For instance, communications protocols -- both wired and wireless -- allow for a certain amount of error, typically defined in the specs for the protocol. If there's a small amount of frequency drift in the sending device, the receiver can detect the actual timing of bit transitions and adjust.
Prior to the computer age, radios and TV's had oscillators that locked themselves to the timings of the transmitting signal. That way, the receiver didn't need to have a precise timer at all.
Timing requirements tend to get more precise when you're trying to cram more data into a particular channel.
On a more gross scale, bus and train systems can afford timing errors of seconds or even minutes.
But precision science needs precision instruments, when the interesting effects are very small.
Since it is obvious it wouldn't last 300B years, how do they plan to synchronise time on a replacement clock? And if they can't do that with equal precision, what good is having it at all?
These experimental clocks are generally not used for time keeping. They are room-filling atomic physics experiments, which are not reliable enough for permanent operation. It is better to think of them as frequency standards. This means that the clock laser will have the same frequency in a month as it does today (to a very high level of precision).
If you have multiple such frequency standards, you can put them in different locations and compare their frequencies via optical fiber links. The frequencies are affected by gravitational time dilation, so this can be used for mapping the earth's gravitational potential. In the future, it might also allow detecting gravitational waves.
There are time and frequency standards that people rely on for all sorts of things. This sort of equipment can be used to calibrate the current time and frequency standards. Also for high precision physics measurements etc.
I, for one, hope that more research would be put into lowering the cost of atomic clocks, not into precision, so it is possible to put atomic clock into everyday devices.
They are not mutually exclusive. There're groups that are developing portable atomic clocks, and then we have this group that are pushing the frontiers. While not in everyday devices, cesium/ rubidium clocks which are less accurate but there're already commercial products that are used in observatories around the world. The standard time of your country might already be referenced to one of these.
Actually, I think spending research time on lowering cost is much more beneficial to accuracy in the long run. It is possible to spend much more on research in case when there are tens of millions of devices produced each year, than in the case when these things cost a couple of grand per PCIe card, which is reasonable cost for servers, but not for consumer devices.
It is usually much simpler to put a GPS receiver in the device and to make use of the dozens of atomic clocks flying over our heads. Or to use NTP over the internet.
You should tell that to meta, since they are putting atomic clocks into each one of their servers, which is, according to you, unnecessary, because same or better result can be achieved by just constantly syncing with GPS.
I think that's a fallacious argument. On the face of it, that they're not using GPS doesn't necessarily mean that it's because of a lack of precision. There could be other factors than precision that influence their choice.
You're assuming that Meta developed the Time Card [0] because GNSS or NTP aren't accurate enough. That's not the case, Meta tells us exactly why they developed it, in the "Why do we need a new time device" section of [0]. TL;DR: openness and software support.
And they're not putting one in every server, they're using it as a reference for their new NTP-based timing protocol [1], with which they showed an uncertainty of only a few hundred microseconds.
The atomic clock on their card performs much worse than the built-in GPS receiver. In normal operation, it serves no real purpose. I guess some bored engineers wanted to have something fun to play with.
Usually the reason for including the atomic clock is reliability: the atomic clock can keep good enough time for a short period if the GPS signal is lost. Their time cards still primarily run off of GPS (in fact there are 3 nested clocks in the standard design of these systems: an oven-controlled crystal oscillator which is already quite stable by itself, but more importantly gives a very clean sine wave output, then an atomic clock (usually rubidium) which is more stable but higher noise which is used to tune the crystal oscillator, then the GPS signal which is even more stable with even higher noise used to tune the atomic clock. You can often just skip the atomic clock in the arrangement and you'll get the same performance while you have a GPS signal.)
Most everyday devices use quartz resonators, which, with some temperature stabilization, will gain or loose around 25 seconds a year [1]. As others have mentioned the clocks can be synced to other time sources (easily multiple times a day) such that this drift is always far less than a second. This is good enough for most everyday purposes.
You mention in another reply that some companies are installing atomic clocks on servers. As I understand it this is mainly to deal with synchronization across distributed databases. Since most everyday devices aren't actually maintaining these databases they probably make due fine with quartz resonators.
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.
There is certainly no need to have an atomic clock in each everyday device.
However, when you own one atomic clock, which you can use to calibrate all quartz resonators and many other kinds of devices used for measurement, then that is one less dependency of the outside world.
Some people like to be as independent as possible.
As long as you don't have your own atomic clock, you are dependent of Internet or other communication means and of access to institutions that do have atomic clocks, to synchronize and calibrate your devices.
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.
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.
The state of the art is the chip-scale atomic clock https://en.wikipedia.org/wiki/Chip-scale_atomic_clock which came out of a research project at NIST. It is useful for devices that need good accuracy for long holdover times without radio reception. A Microsemi SA.45 CASC retails for around $1500.
What’s the most precise clock I can buy, as an overpaid computer programmer?
I suppose anything that shows a human time representation is out of the question. It wouldn’t be able to incorporate legal changes to time such as let’s insert a leap second! or days are now divided into 32 hourlets!.
I would settle for an output that shows elapsed seconds from an agreed upon datum. I guess having a human readable time would be fine but the science part is more interesting.
With a clock of such precision, how could I synchronise it? Or rather: is there something better than NTP that Serious Clock Owners(tm) use?
Perhaps what I want is a clock with reasonable-ish accuracy but incredible longevity. Having a long running independent mechanical source
of time is appealing, and kind of orthogonal to having an ultra accurate but electrical one.
There’s nothing wrong with NTP and anything beyond the accuracy of a normal Casio watch is a fools errand in my mind: unless you get a watch that actually NTP syncs itself (like a smart watch), but the battle for an “on-wrist” super accurate watch was won by the digital wrist watch decades ago, there are no serious mechanical competitors.
There are differences even among quartz watches, due to the quality of the crystal and the circuitry surrounding it. A normal sub-$50 Casio watch will gain or lose a few seconds every month, accumulating to more than 1 minute of error per year. A particularly bad one I've had gained a minute a month, worse than some of my mechanical watches!
Meanwhile, Seiko sells quartz movements that are accurate to within 10 seconds per year. Citizen's top line is accurate to within 1 second per year, uses GPS signals to correct even that little error, and charges itself from any available light source. It's going to be accurate to within a few milliseconds for the next 20 years with no maintenance, all at a price that a typical overpaid programmer can easily afford.
- 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.
Precise is not a term that's often used when considering clocks in the unqualified sense.
The two usual dimensions you consider are accuracy and stability.
Accuracy is about how well your clock tracks the target timebase over a long period, like a month. If your clock is free-running then this is important to you. Many kinds of clocks have aging effects, meaning that they become less accurate over time.
Stability is about whether the individual "ticks" of the clocks have the same duration. Phase noise and clock stability are the same thing, so if you're using your clock to generate radio frequencies, this might actually be more important to you than accuracy.
A clock can be accurate but unstable, or stable but inaccurate and so on.
The most accurate clock technology is the atomic clock. The high-end of that market is represented by cesium standards, with rubidium standards at the lower-end.
The most stable clocks outside the laboratory setting are ovenized crystal oscillators (OCXO). This is fundamentally a quartz crystal inside a metal box with a heater to keep a constant temperature.
The next aspect is clock disciplining. Unless you intend to run your clock free and rely on its fundamental accuracy, you're probably going to synchronize it vs a superior standard. A common option for clock discipline is GPS, i.e. you're synchronizing your clock to the atomic clocks of the GPS satellites.
NTP is simply a network-based mechanism for disciplining a clock. If you want "better NTP", that's called "PTP" but it's really only a local-area network thing.
Afaik its not currently available for purchase, so it is more of a diy route. If you want a standalone unit, it probably wouldn't be too big of hassle to ducktape that Time Card to e.g. Raspberry Pi CM4 or similar module with pcie and drive a display (or whatev) that way. Or that FPGA on the Time Card probably has enough spare capacity to do it directly too, for a simplified architecture (and maybe better hard realtime control).
Thank you for posting this! A fun (if not slightly sad towards the end) list to go through. Just trying to wrap your brain around some of the timescales in there (not that you really can but it is fun to ponder it) is crazy
I've read somewhere someone having a clock so precise that it was affected by the relativistic effects of small changes in Earth's gravity caused by the natural movements of tectonic plates. Don't these sorts of things also limit the practical accuracy of clocks -- if they can only accurately measure the time passing at their specific spot in the ever changing curvature of space-time which is different from every other spot?
Thanks, I did not know this. But then comes the follow up question. For every increase in accuracy of an individual clock, how many extra of these improved clocks scattered around the world do you need to improve the overall accuracy of the system time?
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.
It works the same way. Nine times the clocks, three times smaller standard deviation for both the mean and the median of their readings. In a normal (and any symmetric) distribution these two are the same anyway, so their difference will tend to zero as you increase the number of clocks and the measurements from a single reading of all the clocks look more and more like a bell curve. This is asymptotic behavior so the "rejects the outliers better" aspect does not come into play, and I do not know whether it is useful in this situation or not.
In large samples the error bars for the median are sqrt(pi/2) times the error bars for the mean if the underlying distribution is normal (the link gives more general results, but that helps give some intuitions about being directly comparable)
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.
but how do you estimate the uncertainty without another clock to compare against? It seems like a circular problem.... how do you prove you built a better clock without already having a better clock?
Estimating the uncertainty is indeed quite difficult.
Stability can be measured by comparing two uncorrelated clocks. This is why standard institutes tend to build them in pairs.
Measuring absolute accuracy is a different beast, since two similar clocks will also have similar systematic errors. Of course, one can estimate the magnitude of these errors, but there can always be unknown contributions. It is therefore useful to compare different implementations, for example cesium fountain clocks built at different institutes. Still, there can always be some conceptual problem that affects all clocks in a similar way.
At that point the clocks become interesting not as "time keeping devices", but rather as "the only sensor capable of detecting such small space-time curvatures.
These clocks depend dilute gasses of atoms. Usually the process for preparing and probing the atoms takes at least a few hundred milliseconds, and usually in the seconds range. There's a bunch of reasons for this, probably two main reasons IMO:
1. Generally for precision clocks you need "cold" or "ultracold" atoms (essentially random doppler shifts of hot atoms kill your accuracy). This means something like microkelvins - this is hard to prepare quickly. And atoms are constantly lost/heated due to collisions with stray gas molecules, even though the pressure is usually something like a quadrillion times lower than atmosphere. There's research into continuous ultracold atom sources, and you could prepare way more than you need and siphon a few off at a time, but both are technically challenging.
2. The way these clocks work is essentially you have some laser, and an atom that only reacts to laser light of a very specific frequency. If the laser frequency is off from the exact frequency you can tell. A variety of effects means that the measurement process takes some time. It's like trying to accurately measure your heart rate in 1s vs 10s - a lot easier to do in the latter case.
Nothing fundamental, just technically quite painful.
The International Atomic Time (TAI) is defined on earth's geoid. The participating institutions correct their clocks for the offset due to the local gravitational redshift. The geoid is fairly stable, but with future optical clocks time variation will probably have to be taken into account.
This is my understanding but the term "loses" implies to laypeople like me that it is slow. Maybe better phrasing could avoid implying if it gained or lost time in the long term.
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[ 240 ms ] story [ 3414 ms ] thread(No, really: with three uncorrelated clocks you can separate their variances.)
So you make two clocks on the same principle, say pendulum oscillations, and measure how quickly they start to disagree. Then you make two clocks based on a new principle, say quartz oscillations, and measure their rate of disagreement. You'll notice that the two quartz clocks agree with each other better than the two pendulum clocks do. So quartz clocks keep time better than pendulum clocks.
Then you build a new type of clock, say of the atomic kind, and compare two atomic clocks to each other and to quartz clocks. As you repeat this process, I suppose the clock frequencies have to get progressively higher (Cesium clocks are measuring radiation at about 9 GHz), but this allows you to measure finer and finer discrepancies between them.
What? That doesn't make any sense. Keeping good time isn't about agreeing with another copy of yourself. It's about agreeing with an objective reference time, like "sunrise in Singapore" or "astronomical noon".
Yes exactly. But how would you measure astronomical noon? You might build some instruments that look at the sky and produce some readings.
Now you might build multiple copies of your instrument and compare their readings. But they disagree by some amount.
So you build a better instrument. Or choose some other thing to measure instead. Rinse repeat until you have a more precise instrument.
Atomic clocks are instruments that are measuring something in the universe. They are not generating some time stamp out of nothing. The thing that you say as an objective reference still very much applies.
This assumes that your own divergence from objective time is linear in the amount of time that passes.
He drove three Cesium clocks up Mount Rainier and returned after a week. He compared them to a clock he left at home for the journey. The graph that he shows on the page and his associated commentary is interesting.
Ultimately, a clock is simply an abstract device that goes tick-tick-tick at some regular rate. Once one starts measuring the phenomenon itself---mechanics of the human heart, tidal forces on the Earth, friction in a pendulum, or the uncertainty principle in atoms---it is no longer feasible to treat it as objective time.
International Atomic Time (TAI) itself consists of an ensemble of 400 atomic clocks, with the collective being more accurate (the proper word is "stable", I think?) than any of its constituents.
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.
And it isn't just height that is going to have an impact. Any major mass shift affects it. For example in Scandinavia, melting ice in Greenland and rising land will combine to make ultra-precise clocks there run measurably faster over time relative to where they started.
Rather it's a statement about the width of the frequency they are measuring and their ability to divide that down to a second. They are saying that they have two clocks measuring the same frequency and have analyzed their dispersion against each other over a period of time and gotten this result.
Long-term aging effects aren't going to change the frequency of the atoms (except new physics, but we can rule that out via observations of the Lamb shift in distant hydrogen), but things like gas infiltration, lamp aging, changes in laser characteristics can all cause atomic clocks to drift.
This is pretty significant for rubidium which is why the lamps need recalibration periodically.
Off-topic, but our sun won’t go nova.
https://www.space.com/14732-sun-burns-star-death.html
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...
/j
I’ve always wondered how stuff like this works in practice. Even with particular accelerators, how did they figure out how to control the particles to line them up and synchronized it to be blasted at high speeds? I always assumed it was something less sophisticated like bombarding it and just letting whatever gets sent across get measured. But this is taking about lining them up in a vacuum.
This type of physics is like black magic to an outsider.
A lot of clever people have worked very hard for a long time.
At the end of the day, though, colliders get two beams as focused as they can in space and time, point them at each other, and hope for the best.
Then they look at the results, make an adjustment, and try again.
In this paper the lattice is a 1D vertical lattice, so you can think of atoms being trapped in a huge stack of pancakes.
Do you know how they get the strontium atoms in place to be hit by the lasers? That’s the part that throws me given the scale.
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).
I know nothing about physics but I find this fascinating.
This should be, in some sense, natural to people who understand how a Fourier transform works… basically, when you apply a “window” function to measure a signal over a limited period of time, you end up with the signal smeared in the frequency domain.
So can it be precise in frequency?
Am I misunderstanding?
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.
My understanding of this from the domain of GPS time, has always been; you can have a good clock (GPS is slow, accurate over a long time) or a good ocillator (fast, inaccurate over along time). But together you can have both.
A signal that goes from 9 Hz to 11 Hz has a center frequency of 10 Hz and a bandwidth of 2 Hz.
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!
But Fourier theory!!!! That's FINE!!! I went carefully through the very careful treatment of Fourier series in the third edition of the W. Rudin Principles of Mathematical Analysis and also his very careful treatment of the Fourier transform in his Real and Complex Analysis, also distributions in his Functional Analysis. Also read and used the Blackman and Tukey The Measurement of Power Spectra, wrote some corresponding software that pleased some people in the US Navy, etc. Then I took a course at the level of the second Rudin book, and in the class when the prof got to the Fourier transform one of the students, with a physics background blurted out "That's the Heisenberg uncertainty principle!"
So, now as I look at the MIT lectures, etc., I expect to see a good, solid, clear connection with the Fourier transform -- but so far I've found NOTHING.
Yup, so, thanks for confirming that, yup, the Heisenberg uncertainty principle is not some weird and obscure feature of nature but, really, just an elementary result of any elementary but precise math derivation of the Fourier transform!!!!
But, looks like I will have to make the connections with the basics of quantum mechanics myself.
Yup, multiply in the time domain is the same as doing a convolution in the frequency domain -- that is, if take the Fourier transform of a function zero outside of a finite interval, then in effect have multiplied the function by a box, 1 in the interval and 0 otherwise, and then for the transform are doing a convolution, that is, a weighted sum, of the transform of the box which is just a version of sin(x)/x, that is, with a peak at the origin and falling off rapidly away from the origin. That is, the weighted sum of the convolution is a "smearing out". So, on to the connection with the physics ..., hopefully.
https://en.wikipedia.org/wiki/Conjugate_variables
Yes, it has begun to dawn on me that since
d/dt e^(iwt) = iwe^(iwt)
(frequency w, time t) that
e^(iwt)
is both an eigenvector of simple versions of Schrödinger's equation and also, essentially via Fourier theory, one axis of an orthogonal basis of a linear algebra (or Hilbert space if prefer that since it permits infinitely many orthogonal basis vectors) representation of quite general wave function solutions to the equation. And just by including more basis vectors, can get whatever level of accuracy we might want.
That is, the terns in the Fourier transform act like the coefficients in the linear combination of basis vectors, the linear combination that approximates the wave function solution of Schrödinger's equation.
So, essentially we are into harmonic motion, e.g., swinging pendulums, whether we wanted to be or not.
Then we are ready to guess that for treatment of the electron in a hydrogen atom we will be into something like Sturm-Liouville theory of two point boundary value problems and standing waves, vibrating violin strings, etc. That is, an electron in what it does with a hydrogen nucleus will be like a vibrating violin string.
Thanks.
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?
And thanks for the URL to Feynman's lectures -- I lost my paper copy in a move.
Yup, I understand that early on in quantum mechanics, we will get to both energy and momentum of these particles that have wave functions that evolve as in Schrõdinger's equation. Then I was wondering what math was going to take a wave function and pop out energy and momentum. I began to suspect something that smelled like it popped out of someone's back side. Good to hear that the theory was guessing and experiment confirmed, likely not the first time.
You are farther into digital filtering than I ever got: For a while I was doing such things for the US Navy with data they collected in sea trials. At the time the fast Fourier transform (FFT) was a hot topic. Actually it was later that I studied Fourier theory with some care.
I'm going after quantum mechanics just out of curiosity and with the basic assumption that it's not quite right and I want to check carefully. Maybe it's not really the final theory.
Occasionally I get torqued: E.g., okay, sure, there is a Hilbert space (as I recall, Rudin shows that, really, there is only one) and each wave function is a point in that space, but no way will I easily accept that all the wave function FORM a Hilbert space: That is, via Rudin and more, a Hilbert space is a complete inner product space where here complete means that every Cauchy convergent sequence converges. Then I recall the common, old examples that nice, smooth, likely even infinitely differentiable, functions can converge to a square wave with its jump discontinuities. But the physics people assure me that each wave function is differentiable and also continuous. And that's a point of small irritation -- of course they are continuous; it's an elementary exercise to show that every differentiable function is continuous.
And I got torqued at Feynman where in his Lectures he has that a particle of unknown position has position probability density uniform everywhere -- no it doesn't; it can't; there can be no such density since its integral would not be 1, actually either 0 or infinity.
I don't even like the common integration from minus infinity to infinity: Rudin develops the Riemann integral very carefully but only on closed intervals of finite length, that is, on compact sets. Sure the integral from minus infinity to infinity can be defined as a limit, an improper integral, but then we have a problem: Start with some standard Rudin material that there can be an infinite series that does converge but is conditionally convergent and then with rearrangements can have the series converge to anything might want. Well, the same could hold for integrating from minus infinity to infinity -- the result get can depend on just how the limiting operation is done. E.g., integrate on Monday, Tuesday, and Wednesday, then on Saturday, Friday, Thursday, then Sunday, and continue this pattern for each week. So, without more assumptions, that improper integral is not so good. So, sure, measure theory and the Lebesgue integral clean up this mess, have some assumptions and derivations that do permit integrating from minus infinity to infinity. Right, I can be picky. Uh, who's to say that God is not?
The way this would probably he mediated physically is that sampling the clock changes its energy level, which changes its oscillation frequency.
However, there're workarounds to beat this SQL. One approach people are working on is called the "spin squeezing", which, one can think of the uncertainties of a measurement mapped onto a 2D plane, for simplicity, a circle. Spin squeezing is used to improve the uncertainty in one axis while sacrificing the other, like squeezing the circle into an eclipse. There's a group in MIT which attempted to show metrological gain from spin squeezing in 2020, which they failed.
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.
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
[1] https://www.optica-opn.org/home/newsroom/2019/december/squee...
Usually other systematic errors are the problem though.
Wly_cdgr: Why don't we just make things bigger?
The added timing precision translates into better precision of other measurements like distance if you're doing time-of-flight experiments like OPERA did[1].
[1]: https://en.wikipedia.org/wiki/OPERA_experiment
Prior to the computer age, radios and TV's had oscillators that locked themselves to the timings of the transmitting signal. That way, the receiver didn't need to have a precise timer at all.
Timing requirements tend to get more precise when you're trying to cram more data into a particular channel.
On a more gross scale, bus and train systems can afford timing errors of seconds or even minutes.
But precision science needs precision instruments, when the interesting effects are very small.
If you use it for 10 years to study gravitation waves, it'd be fit for that purpose since you'd be comparing intervals from the same clock.
So you lose a second over a vast timescale but the micro incremental losses still count right?
I don't think anyone is trying to track the absolute time elapsed over long periods with this clock since it started.
If you have multiple such frequency standards, you can put them in different locations and compare their frequencies via optical fiber links. The frequencies are affected by gravitational time dilation, so this can be used for mapping the earth's gravitational potential. In the future, it might also allow detecting gravitational waves.
Clocks aren’t really that important with 10ms resolution at best, although it can be fun playing with old time standard kit http://www.leapsecond.com/pages/atomic-bill/
And they're not putting one in every server, they're using it as a reference for their new NTP-based timing protocol [1], with which they showed an uncertainty of only a few hundred microseconds.
[0]: https://engineering.fb.com/2021/08/11/open-source/time-appli...
[1]: https://engineering.fb.com/2020/03/18/production-engineering...
The big weaknesses of GPS are when you're accelerating and way up north or way down south where satellite coverage is poor
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
Most everyday devices use quartz resonators, which, with some temperature stabilization, will gain or loose around 25 seconds a year [1]. As others have mentioned the clocks can be synced to other time sources (easily multiple times a day) such that this drift is always far less than a second. This is good enough for most everyday purposes.
You mention in another reply that some companies are installing atomic clocks on servers. As I understand it this is mainly to deal with synchronization across distributed databases. Since most everyday devices aren't actually maintaining these databases they probably make due fine with quartz resonators.
[1]: https://en.wikipedia.org/wiki/Quartz_clock#Accuracy
You could have a GPS that is far more precise. Or a altimeter that detects height changes based on gravitational time-dilation.
There are tons of things you can build on top of precision timing.
The use cases may have nothing to do with time, like in the altimeter case.
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
However, when you own one atomic clock, which you can use to calibrate all quartz resonators and many other kinds of devices used for measurement, then that is one less dependency of the outside world.
Some people like to be as independent as possible.
As long as you don't have your own atomic clock, you are dependent of Internet or other communication means and of access to institutions that do have atomic clocks, to synchronize and calibrate your devices.
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.
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...
I suppose anything that shows a human time representation is out of the question. It wouldn’t be able to incorporate legal changes to time such as let’s insert a leap second! or days are now divided into 32 hourlets!.
I would settle for an output that shows elapsed seconds from an agreed upon datum. I guess having a human readable time would be fine but the science part is more interesting.
With a clock of such precision, how could I synchronise it? Or rather: is there something better than NTP that Serious Clock Owners(tm) use?
Perhaps what I want is a clock with reasonable-ish accuracy but incredible longevity. Having a long running independent mechanical source of time is appealing, and kind of orthogonal to having an ultra accurate but electrical one.
Meanwhile, Seiko sells quartz movements that are accurate to within 10 seconds per year. Citizen's top line is accurate to within 1 second per year, uses GPS signals to correct even that little error, and charges itself from any available light source. It's going to be accurate to within a few milliseconds for the next 20 years with no maintenance, all at a price that a typical overpaid programmer can easily afford.
- 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.
"loses a second every 4,000 years or so"
The two usual dimensions you consider are accuracy and stability.
Accuracy is about how well your clock tracks the target timebase over a long period, like a month. If your clock is free-running then this is important to you. Many kinds of clocks have aging effects, meaning that they become less accurate over time.
Stability is about whether the individual "ticks" of the clocks have the same duration. Phase noise and clock stability are the same thing, so if you're using your clock to generate radio frequencies, this might actually be more important to you than accuracy.
A clock can be accurate but unstable, or stable but inaccurate and so on.
The most accurate clock technology is the atomic clock. The high-end of that market is represented by cesium standards, with rubidium standards at the lower-end.
The most stable clocks outside the laboratory setting are ovenized crystal oscillators (OCXO). This is fundamentally a quartz crystal inside a metal box with a heater to keep a constant temperature.
The next aspect is clock disciplining. Unless you intend to run your clock free and rely on its fundamental accuracy, you're probably going to synchronize it vs a superior standard. A common option for clock discipline is GPS, i.e. you're synchronizing your clock to the atomic clocks of the GPS satellites.
NTP is simply a network-based mechanism for disciplining a clock. If you want "better NTP", that's called "PTP" but it's really only a local-area network thing.
Afaik its not currently available for purchase, so it is more of a diy route. If you want a standalone unit, it probably wouldn't be too big of hassle to ducktape that Time Card to e.g. Raspberry Pi CM4 or similar module with pcie and drive a display (or whatev) that way. Or that FPGA on the Time Card probably has enough spare capacity to do it directly too, for a simplified architecture (and maybe better hard realtime control).
https://en.m.wikipedia.org/wiki/Timeline_of_the_far_future
https://iag.dgfi.tum.de/fileadmin/IAG-docs/Travaux2013/08_BI...
https://en.wikipedia.org/wiki/Median#Sampling_distribution
[1] https://webtai.bipm.org/ftp/pub/tai/Circular-T/cirt/cirt.409
Stability can be measured by comparing two uncorrelated clocks. This is why standard institutes tend to build them in pairs.
Measuring absolute accuracy is a different beast, since two similar clocks will also have similar systematic errors. Of course, one can estimate the magnitude of these errors, but there can always be unknown contributions. It is therefore useful to compare different implementations, for example cesium fountain clocks built at different institutes. Still, there can always be some conceptual problem that affects all clocks in a similar way.
Maybe.
https://www.arxiv-vanity.com/papers/1501.00996/
https://ui.adsabs.harvard.edu/abs/2021nova.pres.8631W/abstra...
1. Generally for precision clocks you need "cold" or "ultracold" atoms (essentially random doppler shifts of hot atoms kill your accuracy). This means something like microkelvins - this is hard to prepare quickly. And atoms are constantly lost/heated due to collisions with stray gas molecules, even though the pressure is usually something like a quadrillion times lower than atmosphere. There's research into continuous ultracold atom sources, and you could prepare way more than you need and siphon a few off at a time, but both are technically challenging.
2. The way these clocks work is essentially you have some laser, and an atom that only reacts to laser light of a very specific frequency. If the laser frequency is off from the exact frequency you can tell. A variety of effects means that the measurement process takes some time. It's like trying to accurately measure your heart rate in 1s vs 10s - a lot easier to do in the latter case.
Nothing fundamental, just technically quite painful.
You only know that your error is between -1s and +1s.