# [time-nuts] NPR Story I heard this morning

Tom Van Baak tvb at LeapSecond.com
Mon Nov 3 16:50:15 EST 2014

```> I have a question about that.  If I understand correctly, recent IAU
> resolutions have decoupled the definition of the SI second from the
> terrestrial geoid, which is too fuzzy to be used for a definition.  Instead
> the geoid potential is held fixed by (or defined by) a constant.  Potential
> with respect to what exactly?  "At infinity" is all very well, but there
> are local gravity sources (solar, even galactic) that would seem to
> complicate any operational realization of this definition.
>
> Sorry if this is a bit off-topic.  I'd like a simple, clear explanation for
> the layman that drills down on exactly how the current definitional scheme
> can be realized to arbitrary precision.  For example, assume that we must
> go off-earth at some point to get a better timescale.  How fuzzy is the
> solar potential ("soloid")?
>
> Cheers,
> Peter

Hi Peter,

Based on mass and radius, a clock here on Earth ticks about 6.969e-10 slower than it would at infinity. The correction drops roughly as 1/R below sea level and 1/R² above sea level. For practical and historical reasons we define the SI second at sea level.

The non-local gravity perturbations you speak of are 2nd or 3rd order and so you probably don't need to worry about them. Then again, if you want to get picky, it's easy to compute how much the earth recoils when you stand up vs. sit down. So it's best to avoid the notion of "arbitrary" precision; that's for mathematicians. For normal people, including scientists, we know that precision and accuracy have practical limits.

The most obvious gravitational perturbation is that of the Moon. You can predict, and even measure, that g changes in the 7th decimal place as the moon orbits the earth. This is so minor it cannot as yet be measured by the best atomic clocks, but it has been measured by the best pendulum clocks (because pendulum clock make better gravimeters than atomic clocks). For details, see:
http://leapsecond.com/hsn2006/

Your "fuzzy" question is good. When error or noise is constant one can simply use standard deviation or rms to quantify the amount of fuzz. But when the perturbations are not simple and fixed in time you want a statistic that incorporates not just accuracy, but stability. For this you need something like ADEV and its log-log plots of stability as a function of tau. As an example, here is the ADEV of Earth:
http://leapsecond.com/museum/earth/

/tvb
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