[HN Gopher] NIST ion clock sets new record for most accurate clock
___________________________________________________________________
NIST ion clock sets new record for most accurate clock
Author : voxadam
Score : 229 points
Date : 2025-07-15 15:56 UTC (7 hours ago)
(HTM) web link (www.nist.gov)
(TXT) w3m dump (www.nist.gov)
| mikewarot wrote:
| To keep things in perspective, a vertical shift of a few
| centimeters could be measured if two of these clocks were placed
| next to each other, just by the lesser gravity/time dilation at
| the increased "altitude".
|
| It's an amazing time to be alive. While not this precise, you can
| have atomic cesium beam clocks of your own for a few thousand
| dollars each, and some elbow grease.
| ortusdux wrote:
| This is compared to the ~1 mile vertical shift resolution of
| cesium clocks. The fun part of cesium clocks is that you throw
| three in the back of a minivan and take them camping!
|
| http://leapsecond.com/great2005/
| jahnu wrote:
| Could we realistically get so accurate that we can measure
| time changes due to (human scale) mass movements near a
| clock?
| accrual wrote:
| That would be an amazing proximity sensor. "Looks like time
| slowed down again, there must be someone close by."
| gooseus wrote:
| I'm curious if any sci-fi authors were knowledgable and
| prescient enough to write this into their world building?
|
| If not, it'd make for a pretty cool plot device if done
| well.
| ghkbrew wrote:
| My calculations says that moving 1cm up or down earths
| gravity well (at the surface) changes the acceleration of
| gravity about 5x more than the acceleration you'd feel from
| a 100kg mass 1m away.
|
| Assuming my math is correct, it's already affected by
| nearby human scale masses, for certain values of "near".
| bravoetch wrote:
| There's an article, I think on wired.com, years ago about
| exactly this. It talked about using a vast array of
| accurate clocks as a kind of radar. Seems plausible only
| with a few more orders of magnitude accuracy and
| miniaturization.
| bryced wrote:
| Asked this and related questions to o3. I do not vouch for
| the answers at all but you may find it interesting. https:/
| /chatgpt.com/share/6876cdd1-dfbc-8011-a55f-6915a90275...
| lemonberry wrote:
| I'd love to hear what the kids remember about this trip. It's
| been awhile!
| nuker wrote:
| > ... vertical shift of a few centimeters could be measured
|
| In what amount of time? Not instantly, right?
| hcknwscommenter wrote:
| Instantly more or less. Time instantly moves differently at
| altitude because you are in a weaker gravitational field. The
| time dilation effect would be noticeable after 1 (or at most
| a few) ticks of the clocks.
| mitthrowaway2 wrote:
| I'm _very_ skeptical of this claim. While the physical
| effect of time dilation acts immediately, I expect it would
| take many many ticks of both clocks before the rate
| difference between them became resolvable.
| Plutoberth wrote:
| I don't understand. Wouldn't it only be possible to find
| out by comparing two identical clocks that were at
| different altitudes for some larger number of ticks,
| allowing you to then compare the elapsed ticks? How would
| you conduct such an experiment? My mental model is that I
| have a black box that outputs an electrical signal every
| tick, and then maybe we could just figure out which clock
| ticked first with a simple circuit. But that seems like we
| would need to sync them, and that it's fundamentally wrong
| due to the fact that the information of the tick is also
| subject to the speed of light. I don't know much beyond
| high school physics, fwiw.
| GolDDranks wrote:
| According to ChatGPT, the speedup factor for getting 10 cm
| higher is 1 + 1.09e-17. (With DT = gh /(c^2) The math seems
| to check out, but not sure if the formula itself is
| correct.) Surely, if the clock ticks at rate 1e-19 in a
| second, i.e. one tick is hundred times smaller than the
| dilation difference in a second, the clock would still need
| at least a hundreth of a second to accumulate enough ticks
| for the count of ticks to differ even by one tick because
| of the dilation.
| GolDDranks wrote:
| To make this even clearer:
|
| Let's imagine that there is a huge amount of time
| dilation (we live on the surface of a neuron star or
| something). By climbing a bit, we experience 1.1 seconds
| instead of 1.0 seconds experienced by someone who left
| down.
|
| We have a clock that can measure milliseconds as the
| smallest tick. But climbing up, back down, and comparing
| the amount of ticks won't let us conclude anything after
| a single millisecond. If anything, we must spend at least
| 11 milliseconds up to have a noticeable 11 to 10
| millisecond difference.
|
| Now, if the dilation was 1.01 seconds vs 1.00, we would
| need to spend at least 101 milliseconds up, to get a
| minimal comparison between 101 and 100 milliseconds.
| josephcsible wrote:
| > Let's imagine that there is a huge amount of time
| dilation (we live on the surface of a neuron star or
| something).
|
| That idea is the premise of
| https://en.wikipedia.org/wiki/Incandescence_(novel)
| adrian_b wrote:
| The frequency that is actually counted with a digital
| counter in this clock is only 500 MHz (i.e. after a
| frequency divider, because no counter can be used at the
| hundreds of THz of an optical signal).
|
| Nevertheless, in order to measure a frequency difference
| between two optical clocks you do not need to count their
| signals. The optical signals can be mixed in a non-linear
| optical medium, which will provide a signal whose
| frequency is equal to the difference between the input
| frequencies.
|
| That signal might have a frequency no greater than 1 GHz,
| so it might be easy to count with a digital counter.
|
| Of course, the smaller the frequency difference is, the
| longer must be the time used for counting, to get enough
| significant digits.
|
| The laser used in this clock has a frequency around 200
| THz (like for optical fiber lasers), i.e. about 2E14 Hz.
| This choice of frequency allows the use of standard
| optical fibers to compare the frequencies of different
| optical clocks, even when they are located at great
| distances.
|
| Mixing the light beams of 2 such lasers, in the case of a
| 1E-17 frequency difference would give a difference signal
| with a period of many minutes, which might need to be
| counted for several days to give an acceptable precision.
| The time can be reduced by a small factor selecting some
| harmonic, but it would still be of some days.
| CamperBob2 wrote:
| Yes, and no. The time-dilation effect will happen
| instantly, but the more quickly you want to observe it, the
| better your measurement's S/N ratio will have to be... and
| that, in turn, requires narrow measurement bandwidths that
| imply longer observation times.
|
| So then the question has to be asked, does the effect
| _really_ happen instantly? Or do the same mechanisms that
| impose an inverse relationship between bandwidth and SNR
| mean that, in fact, it doesn 't happen instantly at all?
| myrmidon wrote:
| Time dilation from general relativity is approximately gh/c^2
| (1e-18 -ish), which is an order of magnitude bigger than the
| uncertainty on your clock frequency (1e-19 -ish).
|
| But you would need a more precise characterization of the
| clock to answer this.
|
| There might be significant noise on individual measurements,
| meaning that you need to take multiples to get precise enough
| (see https://en.wikipedia.org/wiki/Allan_variance).
|
| Edit: If you _just_ have clock output in ticks, you also need
| enought time to elapse to get a deviation of at least one
| tick between both bot clocks you are comparing. This is a big
| limitation, because at a clock rate of 1GHz you are still
| waiting for like 30 years (!!). (In practice you could
| probably cheat a bit to get around this limit)
| rcxdude wrote:
| >Edit: If you just have clock output in ticks, you also
| need enought time to elapse to get a deviation of at least
| one tick between both bot clocks you are comparing. This is
| a big limitation, because at a clock rate of 1GHz you are
| still waiting for like 30 years (!!). (In practice you
| could probably cheat a bit to get around this limit)
|
| In practice with this level of precision you are usually
| measuring the relative phase of the two clocks, which
| allows substantially greater resolution than just looking
| at whole cycles, which is 'cheating' to some degree, I
| guess. (The limit is usually how noisy your phase
| measurement is)
| MengerSponge wrote:
| https://en.wikipedia.org/wiki/Allan_variance
|
| It takes a longer measurement to be more confident.
| perihelions wrote:
| In a 2010 experiment based on an older version of this
| clock[0], NIST succeeding in measuring the gravitational time
| dilation across a 33 cm vertical separation--a frequency
| difference of 4.1x10^{-17}--with 140,000 seconds of
| integration time (<2 days). I don't really understand how
| that worked.
|
| [0] https://sci-
| hub.se/https://doi.org/10.1126/science.1192720 ( _" Optical
| Clocks and Relativity"_ (2010))
| dlcarrier wrote:
| From the article: This improves the clock's
| stability, reducing the time required to measure down to the
| 19th decimal place from three weeks to a day and a half.
|
| So no, not instantly.
| Avamander wrote:
| > It's an amazing time to be alive. While not this precise, you
| can have atomic cesium beam clocks of your own for a few
| thousand dollars each, and some elbow grease.
|
| How hard or expensive would it be for a reasonably equipped lab
| to build their own optical clock though? I see there are
| optical clocks the size of few rack units on the market for a
| rather hefty price, are the materials needed that expensive or
| is it _just_ the expertise?
| wbl wrote:
| Expertise
| CamperBob2 wrote:
| What keeps your average home experimenter from building an
| optical clock is the fact that femtosecond combs are still
| way too expensive and exotic. Some progress has been made --
| you can get them from ThorLabs, for instance ( https://www.th
| orlabs.com/newgrouppage9.cfm?objectgroup_id=11... ) -- but
| they are still in the "Call for pricing and lead time"
| category.
|
| Once optical comb sources are commoditized to the extent that
| solid-state lasers are now, a lot of fun stuff will become
| possible.
| pumphaus wrote:
| Heh, I would not ever have expected to see my company
| mentioned on HN. I'm the software tech lead at Menlo
| Systems, we're building those frequency combs that Thorlabs
| sells.
|
| Re the commoditization: Part of the problem is that
| customers, especially the scientific ones, don't want
| "commodity" frequency combs. Nearly every comb we sell is
| tailored to the specific customer in one way or another.
|
| Industrial customers start to be interested in frequency
| combs more and more. I guess this will be the clientele
| that values off-the-shelf products more, eventually paving
| the way for commoditization.
| nativeit wrote:
| The presence of individuals such as yourself is what
| makes the HN comments such a frequently meaningful place
| to find insightful discussions. Thanks for the context!!
| FredPret wrote:
| This is a great way to compare ultra-precise clocks! Also, I'm
| looking forward to Einsteinian altimeters everywhere.
| jl6 wrote:
| I fear this altimeter idea may be scuppered by local
| variations in the Earth's density (it's not an exactly
| uniform sphere of rock). Or maybe that just means the clocks
| could be great density-mappers!
| bravoetch wrote:
| Are you saying they would be relatively inaccurate?
| ianburrell wrote:
| It is easier to measure density with gravimeter than
| measure gravitational force directly.
|
| Satellite, ACES, was launched recently that uses atomic
| clocks to accurately measure Earth's gravity field.
| FredPret wrote:
| I had the same thought, but I still want one!
|
| On second thought, you need a base station on the ground to
| tell you its time for comparison anyway, so if that base
| station is nearby the density thing should mostly work
| itself out
| naikrovek wrote:
| Isn't the second defined as a specific number of cesium
| transitions?
|
| How can anything ... you know what? Never mind. No matter what
| answer anyone provides, I won't understand.
| nhecker wrote:
| I don't think this changes the way the second is defined.
| Rather, that definition describes some theoretical ideal
| where the cesium transitions are all perfectly equally spaced
| over the course of the second.
|
| I think this new clock is simply able to generate more
| precisely spaced ticks than those of a traditional Cs clock.
| Less jitter and variation in the timing of those ticks.
| Similar to how a one-hour water clock or sand timer's runtime
| will vary between "transitions", but a one-hour quartz
| stopwatch timer is much more regular. I could keep going, but
| I'm already out on a limb so I'll stop before my own
| uncertainty rises too much.
|
| (Edit: I read the article. I don't think my words above are
| correct.)
| shric wrote:
| > Isn't the second defined as a specific number of cesium
| transitions?
|
| Yes
|
| > How can anything ...
|
| So your cesium counting device will fauthfully provide such a
| count and depending on their altitude it will be at different
| rates.
|
| Both clocks are each experiencing time at the usual one
| second per second but gravity dilates spacetime.
|
| Locally, a second is always a second, but from everywhere
| there is no such asbsolute, just as there is no universal
| "now".
| bilsbie wrote:
| Could you detect gravity waves with accurate enough clocks?
| dtgriscom wrote:
| They would have to be extremely low-frequency. Plus, you'd
| need something to compare them to that wasn't affected by the
| wave, which is hard. (You'd need as accurate a clock, placed
| at a distance greater than the gravitational wavelength.)
|
| I think.
| kridsdale3 wrote:
| Someone call Hodinkee to write about this.
| net01 wrote:
| Jeff Geerling
| Jeremy1026 wrote:
| I honestly just Ctrl+F'd for him to see if he commented yet.
| _joel wrote:
| I'm not a fan, I'm a human being.
| perihelions wrote:
| Preprint,
|
| https://arxiv.org/abs/2504.13071 ( _" High-Stability Single-Ion
| Clock with $5.5\times10^{-19}$ Systematic Uncertainty"_)
| jasonthorsness wrote:
| The article is very good and has some cool pictures of the
| device. Aluminum is apparently just better than cesium but harder
| to use and now they have solved the problems preventing it from
| being the standard.
| tguvot wrote:
| Somewhat topical: in case you want authenticated access to NIST
| NTP servers, you need to send a letter to NIST using the US mail
| or FAX machine (e-mail is not acceptable).
|
| NIST will reply with a key number and a key value. The reply will
| be by US mail only, e-mail will never be used.
|
| The office that normally receives US mail and FAX messages
| currently has limited access, which may result in significant
| delays in processing requests
|
| https://www.nist.gov/pml/time-and-frequency-division/time-se...
|
| (things you discover when you implement fedramp)
| doublerabbit wrote:
| Seems pretty tight for those outside of the USA. Is FAX allowed
| for those who live outside?
| GuB-42 wrote:
| I was thinking that it may be the point. This is a service
| paid by Americans, for Americans, and I suspect they don't
| want to make it too convenient, especially for non-Americans.
|
| From the link:
|
| > The service will be provided at no charge, and user keys
| may be used to connect to any of the servers whose addresses
| are listed below. Additional hardware will be added in the
| future if the demand for the service is sufficiently great to
| warrant it.
|
| Making it clear that they are going to shoulder the extra
| costs.
| tguvot wrote:
| better question is will be they willing to mail you reply
| outside of usa.
|
| if you really want it, there are plenty of services that
| provide you with virtual mailbox in usa
| mccoyc wrote:
| I wonder if they'd consider implementing NTS.
|
| https://github.com/jauderho/nts-servers/tree/main
| tguvot wrote:
| NTS uses AES-SIV and looks like it's not NIST approved and
| doesn't have FIPS validated implementation.
|
| in other words - no
| Babkock wrote:
| How do you measure the accuracy of a clock? What if every clock
| is wrong, just a little bit?
| theultdev wrote:
| it doesn't matter? it's the average of multiple atomic clocks
| and that's the time we distribute.
|
| it's a human construct so whatever is agreed upon is correct.
| monktastic1 wrote:
| If this were true, then why even bother to make atomic
| clocks? Why would an article about the "most accurate clock"
| be interesting to smart people like HN readers if there's no
| objective measure of accuracy (or if it didn't matter)? The
| correct answer is in a sibling comment to yours: we base it
| on other things we know (or believe, anyway) to be constant.
| theultdev wrote:
| I'm fully aware, but you seem to have misinterpreted what I
| was saying.
|
| If "all the clocks are wrong" it doesn't matter as long as
| they are consistent. (in the case of atomic clocks,
| frequency of energy transitions within atoms)
|
| All ntp servers get the average of atomic clocks, which is
| then distributed to all phones and computers.
|
| If the constants from these atomic clocks "are a little bit
| wrong" it does not matter (for most human activities)
|
| That's why we average them and distribute the average.
|
| For physics related research, this new clock being more
| precise does have use, but for pretty much everything else,
| whatever constant we have is good enough as long as it's
| consistently used.
|
| Back in the day it was someone just running around with a
| pocket watch giving everyone the time from the clock tower
| which was calibrated from a sundial and that was good
| enough.
|
| Replace the sun's shadow with electron transitions and the
| timekeepers with ntp servers and that's what you have
| today.
| xorcist wrote:
| Since 1967 the second has a physical defintion:
|
| https://en.wikipedia.org/wiki/Second#Atomic_definition
| dguest wrote:
| This new clock is way more accurate than that baseline
| definition though. The SI definition is a practical one for
| almost everything, the new clock is useful if you are e.g.
| looking for shifts in physical constants over time.
| colechristensen wrote:
| You define time based on a physical phenomenon which does not
| vary.
|
| For example, every electron is exactly the same as every other
| electron, they do not vary in the slightest. You utilize
| properties like that to make exact references to time.
| ars wrote:
| You are not actually measuring the accuracy of the clock,
| rather you are measuring the magnitude of the noise. The clock
| source itself is something physically fundamental and
| unchanging, but it gets mixed with noise.
|
| For example even very small magnetic fields will change the
| clock speed, thermal changes will as well (so will lots of
| other things). So you try to shield from that, and keep the
| temperature stable (and of course you need to figure out every
| other things that could add noise).
|
| Then you measure all those influences that you just are unable
| to control, and calculate what affect they have on the clock,
| and that's your accuracy number.
|
| One way to directly measure that, instead of calculate it, is
| to have two identical clocks, synchronize them, and let them
| run. Then compare them, and see if they differ. (Watch out for
| relativity messing with time.)
| dguest wrote:
| You define it to be accurate, and then measure the precision.
|
| You can build two and see how much they shift relative to each
| other. That gives you precision.
|
| So what's the point of a clock if you just define it to be
| correct? Again, having two clocks is what makes it interesting.
| Some people have commented that according to general relatively
| there will be measuralbe time dilation, but there are other fun
| experiments, e.g.
|
| - Measure shift of fundamental "constants": If you have two
| clocks that use different elements, the frequency ratio can be
| related to some things we thought were constants in the
| universe. If they shift, they aren't constant.
|
| - Look for preferred directions in space: does one clock give a
| different reading if you turn it on its side?
|
| - Some theories predict that dark matter might induce a
| frequency shift in these clocks. Put the clocks far apart and
| look for spacial modulations in the dark matter density.
|
| - Measure anything else that had to be tweaked to make the
| clock stable. This includes the magnetic field, for example, so
| the clock is also a really sensitive magnetometer.
| mlhpdx wrote:
| Is it a "clock" or a "clock signal", in a similar sense that
| position encoders can be relative or "absolute" (but only within
| a specific range)?
| s0rce wrote:
| Is there really an absolute reference point to measure time
| other than the big bang or something?
| colechristensen wrote:
| Relativity. Every path starting at the big bang to the
| present has its own unique clock.
|
| These clocks can measure the difference in the flow of time
| between your head and your feet (and quite a lot more
| accurate than that)
| aeve890 wrote:
| We can both agree that the Big Bang happened 13.8 billion
| years ago but that's all, we'll still disagree about the
| timing of everything else. Not even the CMB can be used as an
| universal rest frame. I'm not a cosmologist though.
| colechristensen wrote:
| The clock signals can be counted and are accurate over long
| periods, it is not just a rate that drifts.
|
| Being able to count trillions of ticks is entirely possible in
| clocks or rotary encoders, just nobody bothers to do so on
| rotary encoders very often.
| adrian_b wrote:
| Optical atomic clocks based on trapped single ions like this,
| and also those based on lattices of neutral atoms do not
| provide a continuous clock signal.
|
| They are used together with a laser (which is a component
| included in a so-called frequency comb, which acts as a
| frequency divider between the hundreds of THz of the optical
| signal and some hundreds of MHz or a few GHz of a clock signal
| that can be counted with a digital counter; that digital
| counter could be used as a date and time clock, except that you
| would need more such optical clocks, to guard against downtime;
| the present optical clocks do not succeed to operate for very
| long times before needing a reset because the trapped ion has
| been lost from the trap or the neutral atoms have been lost
| from the optical lattice; therefore you need many of them to
| implement a continuous time scale).
|
| The laser is the one that provides a continuous signal. In this
| case the laser produces infrared light in the same band as the
| lasers used for optical fiber communications, and it is based
| on glass doped with erbium and ytterbium. The frequency of the
| laser is adjusted to match some resonance frequency of the
| trapped ion (in this case a submultiple of the frequency,
| because the frequency of the transition used in the aluminum
| ion is very high, in ultraviolet). For very short time
| intervals, when it cannot follow the reference frequency,
| because that must be filtered of noise, the stability of the
| laser frequency is determined by a resonant cavity made of
| silicon (which is transparent for the infrared light of the
| laser), which is cooled at a very low temperature, in order to
| improve its quality factor.
|
| So this is similar to the behavior of the clock of a computer,
| which for long time intervals has the stability of the clocks
| used by the NTP servers used by it for synchronization, but for
| short time intervals it has the stability of its internal
| quartz oscillator.
|
| This new optical atomic clock has the lowest ever uncertainty
| for the value of its reference frequency, but being a trapped
| single ion clock it has a higher noise than the clocks based on
| lattices of neutral atoms (because those can use thousands of
| atoms instead of one ion), so its output signal must be
| averaged over long times (e.g. many days) in order to reach the
| advertised accuracy.
|
| For short averaging times, e.g. of one second, its accuracy is
| about a thousand times worse than the best attainable (however,
| its best accuracy is so high that even when averaged for a few
| seconds it is about as good as the best microwave clocks based
| on cesium or hydrogen).
| mlhpdx wrote:
| Thank you for that very excellent reply.
| infogulch wrote:
| Some recent discussions about atomic clocks:
|
| New atomic fountain clock joins group that keeps the world on
| time (nist.gov) | 118 points | 76 days ago | 33 comments |
| https://news.ycombinator.com/item?id=43831792
|
| Major leap for nuclear clock paves way for ultraprecise
| timekeeping (nist.gov) | 12 points | 7 months ago | 10 comments |
| https://news.ycombinator.com/item?id=42362215
|
| I left a comment on the first that summarizes the second one,
| which describes how they're working on a new type of atomic
| "nuclear" clock based on the atomic _nucleus_ instead of electron
| orbitals. It doesn 't mention the accuracy, I wonder how it would
| compare to this "ion" clock.
| throw0101c wrote:
| That's great and all, but stepping back a bit: the US (and the
| West?) seems to be falling behind in distribution and resiliency.
| For high-accuracy timing stuff, China has space (BeiDou),
| terrestrial broadcast (eLoran), and fiber in production:
|
| * https://rntfnd.org/2024/10/03/china-completes-national-elora...
|
| As we've seen regularly, GPS/GNSS has major risks with it, and it
| seems to have become a single point of failure:
|
| * https://gpsjam.org
|
| * https://www.marineinsight.com/shipping-news/msc-container-sh...
|
| * https://gcaptain.com/gps-jamming-in-strait-of-hormuz-raises-...
| searine wrote:
| Yet another advance brought to you by US tax dollars funding
| basic science for the public good.
|
| Please don't let them embezzle the future of scientific
| innovation.
| duncangh wrote:
| Imagine trying to set your oven and microwave clock to line up
| with it precisely after they reset from a power outage
| gwerbret wrote:
| Pedant here!
|
| > NIST researchers have made the most accurate atomic clock to
| date -- one that can measure time down to the 19th decimal place.
|
| That's precision, not accuracy.
| _se wrote:
| Nope, it is not.
|
| A single measurement cannot be precise. Precision is a measure
| of how close multiple measurements are to one another. Accuracy
| is how close a single measurement is to its true value.
|
| A clock that can measure a point in time to 19 decimal places
| with respect to its true value is accurate.
| johnnyballgame wrote:
| What is that true value? And was it accurate?
| _se wrote:
| Unfortunately, I am not a time lord, so I don't know. But I
| do know the definitions of these words, and that is what
| they are. You are free to argue with someone else about the
| true meaning of time.
|
| A single measurement can _never_ be precise, it is simply
| not possible.
| riwsky wrote:
| It's about time.
| frankfrank13 wrote:
| SKO BUFFS
|
| I briefly worked at NOAA, on this same campus, and I loved
| walking around NIST. Such a cool building. The entire campus is
| at risk -> https://www.cpr.org/2025/07/01/proposed-noaa-budget-
| would-cl...
| kaapipo wrote:
| So fun even NIST can't get right the difference between precise
| and accurate
| johnnyballgame wrote:
| Does it come with a snooze button?
| user3939382 wrote:
| If I'm not mistaken this improves a critical bottleneck on GPS
| precision, solutions to which will open up amazing applications.
| Driving lane boundaries just being one example.
| AlotOfReading wrote:
| It could improve accuracy and does help a significant error
| factor, but the biggest error sources in GNSS aren't clock
| errors. Even a perfect clock could still have several meters of
| error.
| rcxdude wrote:
| The main errors in GPS are usually due to variation in the
| propagation of the signals through the atmosphere, and
| uncertainty in the exact position of the satellites. (Solutions
| for these exist, but are generally too expensive and/or
| impractical for a lot of applications. But e.g. realtime GPS on
| the order of cm is something you can get now, if you pay for a
| subscription to the right service or operate your own reference
| base station)
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(page generated 2025-07-15 23:00 UTC)