4 ms·

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

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?

weberer 5y ago
Yes, which is why the International Atomic Time standard is based on the averaged value of readings from over 400 clocks around the world. https://iag.dgfi.tum.de/fileadmin/IAG-docs/Travaux2013/08_BIPM.pdf https://iag.dgfi.tum.de/fileadmin/IAG-docs/Travaux2013/08_BI...
- Eddy_Viscosity2 5y ago
  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?
  - LegionMammal978 5y ago
    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.
    - amelius 5y ago
      How does that work for the median (as opposed to the mean)? Asking because median rejects outliers better than the mean.
      - d_tr 5y ago
        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.
      - jmalicki 5y ago
        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) https://en.wikipedia.org/wiki/Median#Sampling_distribution https://en.wikipedia.org/wiki/Median#Sampling_distribution
  - fsh 5y ago
    TAI is a weighted average of the clocks. The lower the estimated uncertainty of a clock, the more it contributes to the average. This is given in the second to last column in the first table of Circular T [1]. For example, in the last reporting period, Germany's PTB reported the lowest uncertainty, and therefore contributed most. Probably both their cesium fountains were running well. So a single much better clock would immediately improve the quality of TAI. [1] https://webtai.bipm.org/ftp/pub/tai/Circular-T/cirt/cirt.409 https://webtai.bipm.org/ftp/pub/tai/Circular-T/cirt/cirt.409
    - dataangel 5y ago
      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?
      - fsh 5y ago
        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.
krastanov 5y ago
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.
- willis936 5y ago
  Could we not use these timebases as a planet-sized gravitational wave antenna array? Maybe. https://www.arxiv-vanity.com/papers/1501.00996/ https://www.arxiv-vanity.com/papers/1501.00996/ https://ui.adsabs.harvard.edu/abs/2021nova.pres.8631W/abstract https://ui.adsabs.harvard.edu/abs/2021nova.pres.8631W/abstra...
  - fennecfoxen 5y ago
    I don’t think the sample rate is high enough to detect individual waves.
    - willis936 5y ago
      Why would the sample rate be below 10 kHz?
      - gji 5y ago
        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.
fsh 5y ago
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.

weberer 5y ago

Yes, which is why the International Atomic Time standard is based on the averaged value of readings from over 400 clocks around the world. https://iag.dgfi.tum.de/fileadmin/IAG-docs/Travaux2013/08_BIPM.pdf https://iag.dgfi.tum.de/fileadmin/IAG-docs/Travaux2013/08_BI...

Eddy_Viscosity2 5y ago
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?
- LegionMammal978 5y ago
  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.
  - amelius 5y ago
    How does that work for the median (as opposed to the mean)? Asking because median rejects outliers better than the mean.
    - d_tr 5y ago
      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.
    - jmalicki 5y ago
      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) https://en.wikipedia.org/wiki/Median#Sampling_distribution https://en.wikipedia.org/wiki/Median#Sampling_distribution
- fsh 5y ago
  TAI is a weighted average of the clocks. The lower the estimated uncertainty of a clock, the more it contributes to the average. This is given in the second to last column in the first table of Circular T [1]. For example, in the last reporting period, Germany's PTB reported the lowest uncertainty, and therefore contributed most. Probably both their cesium fountains were running well. So a single much better clock would immediately improve the quality of TAI. [1] https://webtai.bipm.org/ftp/pub/tai/Circular-T/cirt/cirt.409 https://webtai.bipm.org/ftp/pub/tai/Circular-T/cirt/cirt.409
  - dataangel 5y ago
    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?
    - fsh 5y ago
      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.

krastanov 5y ago

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.

willis936 5y ago
Could we not use these timebases as a planet-sized gravitational wave antenna array? Maybe. https://www.arxiv-vanity.com/papers/1501.00996/ https://www.arxiv-vanity.com/papers/1501.00996/ https://ui.adsabs.harvard.edu/abs/2021nova.pres.8631W/abstract https://ui.adsabs.harvard.edu/abs/2021nova.pres.8631W/abstra...
- fennecfoxen 5y ago
  I don’t think the sample rate is high enough to detect individual waves.
  - willis936 5y ago
    Why would the sample rate be below 10 kHz?
    - gji 5y ago
      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.

fsh 5y ago

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.